apm - User contributions [en]

Ethyne

2026-10-12T18:34:53Z

Apm: /* External links */ Added Wikipedia pages: Acetylene Polyyne Cumulene

{{stub}}
[[File:Acetylene-3D-vdW.png|thumb|320px|right|Ethyne H-C≡C-H or C2H2 (more commonly known as the welding gas acetylene)]]
[[File:Acetylen-welding-setup.jpg|320px|thumb|right|Acetylene (Ethyne, C2H2) as distributed today for welding purposes. – – Interesting trivia: These bottles are filled with some acetone (or dimethylformamide) soaked ultra fine solid powder (like e.g. diatomaceous earth) to keep the pressure low by dissolution of the ethyne. When pressurizing ethyne too much (>2.07 atmospheres) at room temperature is starts to react with itself so much that it can lead to a runaway chain reaction (explosion of the whole bottle at once!!). This can also be induced by flashback => flashback arrestors are essential.]]

Ethyne (also known as acetylene) with formula C2H2 is a potential [[resource molecule]] for future [[gemstone metamaterial on chip factories]]. It received especially much attention in theoretical analysis due to a few advantageous properties.

* low hydrogen content
* reactive highly unsaturated carbon-carbon triple bond
* high energy compound

Another interesting (energy devoid) [[resource molecule]] for carbon would be carbon dioxide CO2. 
But it wasn't investigated in detail in the context of [[piezochemical mechanosynthesis]] as of yet (2021).

== Alternate carbon [[resource molecule]]s ==

[[Carbon dioxide]] tapped directly from the air. Given renewable or nuclear energy this would be "carbon negative".

[[Methane]]: 
There will be quite a bit of ultra pure water as a side product though due to methanes high hydrogen content. 
Maybe methane is not a good carbon resource for for deep space operations where you either need to bring the oxygen or store pure hydrogen. 
More processing steps may influence the internal efficiency negatively. But efficiency gains o external conventional chemical preprocessing must be considered too.

Possibly Carbohydrates like e.g. sugars? 
Handling floppy chain molecules are resource molecules may pose additional design challenges. 
Also sugars like to from rings and self polymerize.

== Notes on interesting properties of Ethyne ==

Today Ethyne (also known as acetylene) is mainly used for gas welding (oxyacetylene welding).
* It can create an especially hot flame
* It can create a reducing environment good for welding

Storing etyne in large quantities in pure form can be dangerous since (given enough pressure and temperature)
it likes to self polymerize in a runaway exothermic reaction.
Etyne gas tanks are thus filled with a compound that counteracts this self polymerization tendency.
Lowering pressure by adsorption and slowing reaction kinetics (to check).

== Related ==

* [[Methane]] – another possible carbon carrying [[resource molecule]] – more stable, less reactive, carries for times more hydrogen atoms per carbon atom
* [[Resource molecule]] – [[Moiety]]
* '''[[Acetylene sorting pump]]s''' are supposed to sort/purifies these molecules.
* [[Piezochemical mechanosynthesis]]
* [[Carbon dioxide]]
* [[Polyyne rods]]

== External links ==

* Calcium_carbide CaC2 {{WikipediaLink|https://en.wikipedia.org/wiki/Trimethylphosphine}} – released [[acetylene]] on contact with water
* Carbide_lamp {{WikipediaLink|https://en.wikipedia.org/wiki/Carbide_lamp}}
----
* [https://en.wikipedia.org/wiki/Acetylene Acetylene]
* [https://en.wikipedia.org/wiki/Polyyne Polyyne]
* [https://en.wikipedia.org/wiki/Cumulene Cumulene]

Gem-gum waste dissolution

2026-10-12T07:54:28Z

Apm: /* Related */ == External links ==

Gemstone based metamaterials ([[gem-gum]]) will often contain a lot of incombustible slag froming elements making conventional incineration like it is possible with plasics not possible. Like silicones burn badly but worse. Silicones still have all side chains plugged by carbon. Gen-gum will often be no carbon at all.

So long possible [[recycling]] should be attempted at the [[component]] level.
If things are no longer needed anywhere anytime soon but still quite intact then [[atomically precise disassembly]] could be attempted.
More challenging than constructive [[mechanosynthesis]].

If damaged too much for capabilities of [[atomically precise disassembly]] only [[Diamondoid waste incineration]] or [[Gem-gum waste dissolution]] remain the last options to get the lelements back from damaged [[mechanosphere]] to [[biosphere]] and other natural "spheres".

== Method ==

Just like in a [[Rock digestion chamber]] hot acids and lyes will do the job. Liquid metals are an option too.
Specific gemstones may known to be in the waste and may need specific treatment as … 
– some are especially resilient and 
– some may be amenable to solvents 

Sodium or potassium ion beams may help with especially stubborn compounds as 
they penetrate deeply and make everything and anything dissolvable.

== Energy (in)efficiency ==

Operating in a [[gem-gum-tec]] camber with heat pumps 
thermal energy can be recuperated to a good degree 
but entropic losses are fundamental.

== Related ==

* '''[[Gem-gum waste crisis]]'''
* '''[[Diamondoid waste incineration]]'''
* '''[[Recycling]]'''
* [[Rock digestion chamber]] (& [[Soil processing]])
* [[Unknown matter claimer]]
* [[Mechanosphere]]
* [[Atomically precise disassembly]]

== External links ==

* [https://en.wikipedia.org/wiki/Sodium_hydroxide Sodium hydroxide (NaOH)] (lab classic), ([[Na]] is highly abundant and highly accessible via salt in sea water)
* [https://en.wikipedia.org/wiki/Potassium_hydroxide Potassium hydroxide (KOH)] (lab classic),([[K]] is highly abundant)
* [https://en.wikipedia.org/wiki/Rubidium_hydroxide Rubidium hydroxide (RbOH)] ([[Rb]] is not too abundant)
* [https://en.wikipedia.org/wiki/Caesium_hydroxide Caesium hydroxide (CsOH)] ([[Cs]] is not too abundant)
----
* [https://en.wikipedia.org/wiki/Hydrogen_fluoride Hydrogen fluoride (HF)] ([[F]] is nasty to handle)
* [https://en.wikipedia.org/wiki/Hydrogen_chloride Hydrogen chloride (HCl)] (lab classic)
* [https://en.wikipedia.org/wiki/Hydrogen_bromide Hydrogen bromide (HBr)] (weaker)
* [https://en.wikipedia.org/wiki/Hydrogen_iodide Hydrogen iodide (HI)] (weaker)
----
chalkogen oxoacids
* [https://en.wikipedia.org/wiki/Sulfuric_acid Sulfuric acid (H2SO4)] (lab classic)
* [https://en.wikipedia.org/wiki/Selenic_acid Selenic acid (H2SeO4)]
* [https://en.wikipedia.org/wiki/Telluric_acid Telluric acid (Te(OH)6)] (weak, [[Te]] is extremely rare)
----
pnictogen oxoacids
* [https://en.wikipedia.org/wiki/Nitric_acid Nitric acid (HNO3)] (lab clasic)
* [https://en.wikipedia.org/wiki/Phosphoric_acid Phosphoric acid (H3PO4)] (weaker)
* [https://en.wikipedia.org/wiki/Arsenic_acid Arsenic acid (H3AsO4)] (weaker)
* Sb antimonic acid? Bi bismuth acid? (borderline acids?)
* Side-note: [[Salts of oxoacids]]
----
* [https://en.wikipedia.org/wiki/Chemical_garden Chemical garden]
----
* [https://en.wikipedia.org/wiki/Superbase Superbase]
* [https://en.wikipedia.org/wiki/Superacid Superacid]

[[Category:Far term target]]

Useful math

2026-10-10T07:48:37Z

Apm: /* Useful algorithms in computer graphics */

This page is about useful math in the wide context of [[atomically precise manufacturing]].

Specific application areas include:
----
* friction and dissipation
* thermally driven self assembly
----
* quantum chemistry
* molecular modelling
----
* 3d modelling
* differential geometry for larger scale gears
* ...

== Thermodynamics and statistical physics ==

Summing up over all the possible microstate configurations of a system. 
Thereby deriving a partitioning function – (some [[exotic math]] involved in there) 
From this partitioning function then [[thermodynamic laws]] can be re-derived and explained. 
These [[thermodynamic laws]] can be (and historically have been) formerly phemomenologically derived. 
Meaning derived from their effects not their causes.

Related:
* '''Thermodynamic potentials''' and associated '''statistical ensembles'''
* Transformation between the potentials – Legendre Transformation
* Conjugated pairs of valuables (extrinsic and intrinsic) – a pairs product always gives the physical unit of energy

=== General note on solid state physics ===

Prevalent are long chains of simplifications by approximations that pile up and up and up. 
Changing the application area of the models hugely may requires reevaluation of all these approximation steps. 
Given that the chains of approximation are not formalized on computers (state 2021) this is difficult error prone and tedious.

Also: Following all the derivations from the lowermost assumptions 
it becomes very evident that energy is a relative concept. (Not talking about relativity theory here).

== Math for modelling with atomistic detail ==

=== From first principles – e.g. for quantum chemistry ===

The exact solutions of the Schrödinger equation for the hydrogen problem. 
Using the property of it being a "separable partial differential equation"
* Laguerre polynomials for the radial part
* Spherical harmonics for the angular parts

The major reason '''why exact solutions are way off''' for other elements than hydrogen 
(and the less relevant highly charged one electron ions) is '''the shielding effect of the inner electrons'''. 
To get good approximations for orbitals it is necessary to do iterative self-consistent-field methods. 
The exact hydrogen solutions can serve as a good initial guess starting point. 

Also Useful in getting good starting points:
* the '''Grahm Schmidt orthogonalization method'''
* composing Gaussian distributions as base functions for orbitals
* the '''Hartree-Fock method''' – helps filling up states consistent with pauli exclusion rules – antideterminant for fermionic states
Related: Density functional theory.

=== Phenomenological models – e.g. for molecular modelling ===

* Lennard Jones potential – and similar ones – good for molecular dynamics simulations
* Hund's rule of maximum multiplicity – not particularly useful in the context of chemically bond atoms

== Misc ==

Derivation of [[London dispersion forces]] from first principles by 
integrating over virtual electron states (related: virtual particles, feynman graphs) ... 
Related: Born–Oppenheimer approximation – and its deceiving pseudo convergence (to check)

== Generally useful math tools ==

Hamiltonian mechanics finds heavy use in in quantummechaincs. 
Interestingly in [[gem-gum]] systems at slightly larger scales things behave very classically. 
Lagrangian mechanics might be useful there.

* [https://en.wikipedia.org/wiki/Hamiltonian_mechanics Hamiltonian mechanics]
* [https://en.wikipedia.org/wiki/Lagrangian_mechanics Lagrangian mechanics]
Related: [https://en.wikipedia.org/wiki/Stationary_Action_Principle principle of least action] and [https://en.wikipedia.org/wiki/Variational_principle variational principle (and calculus)]

=== Basic math for physics ===

* Finding zeros: – [https://en.wikipedia.org/wiki/Newton%27s_method Newton's method] – [https://en.wikipedia.org/wiki/Regula_falsi Regula falsi]
* Integrating differential equations: – [https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods Runge Kutta methods] – [https://en.wikipedia.org/wiki/Leapfrog_integration Leapfrog integration] – [https://en.wikipedia.org/wiki/Verlet_integration Verlet Integration]
----
* [https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors Eigenvalues and eigenvectors] – (linear algebra)
* Vector spaces with functions as base vectors – ([https://en.wikipedia.org/wiki/Hilbert_space Hilbert spaces])
* "Integral kernels" – [https://en.wikipedia.org/wiki/Integral_transform Integral transform]
* [https://en.wikipedia.org/wiki/Fourier_transform Fourier transformations] – (convolution becomes multiplication)
* ([https://en.wikipedia.org/wiki/Laplace_transform Laplace transformations] – more used in electrical system engineering)
* [https://en.wikipedia.org/wiki/Convolution Convolution (aka folding)]
* [https://en.wikipedia.org/wiki/Linear_form Linear functional] – [https://en.wikipedia.org/wiki/Adjoint_functors Adjoint_functors]
* https://en.wikipedia.org/wiki/Self-adjoint_operator Self-adjoint operator]
* [https://en.wikipedia.org/wiki/Orbital_overlap Orbital overlap / Overlap integral]
----
* All sorts of tricks an hackery with matrix math – selfadjunctness & co – [https://en.wikipedia.org/wiki/Category:Matrix_theory (Category:Matrix_theory)]
----
* '''[https://en.wikipedia.org/wiki/List_of_equations_in_quantum_mechanics List of equations in quantum mechanics]'''
* ([https://en.wikipedia.org/wiki/Heisenberg_picture Heisenberg picture] and [https://en.wikipedia.org/wiki/Matrix_mechanics Matrix mechanics])
----
[https://en.wikipedia.org/wiki/Category:Perturbation_theory Category:Perturbation_theory] – particularly:
* [https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics) Perturbation_theory_(quantum_mechanics)] which employs the
* [https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process Gram–Schmidt_process] in Hilbert space (? IIRC)
'''[https://en.wikipedia.org/wiki/Category:Condensed_matter_physics Category:Condensed_matter_physics]'''

=== Useful for 3D modelling and robotics ===

* screws (math object), wrenches (math objects), dual numbers – useful for robotics (forwards & backwards kinematic) and differential geometry for gear flanks
* math tools for surface based commuter graphics (manly dealing with triangulations)
* math tools for volume based computer graphics:
* functional-representation (F-Rep), implicit surfaces, algebraic varieties, distance fields (magnitude of gradient is 1 for these)
* ray-marching algorithms

=== Some multi-purpouse misc math ===

* [https://en.wikipedia.org/wiki/Gradient_descent Gradient descent]
* (Reversely calculated) gradient descent in multi-dimensional scalar fields: [https://en.wikipedia.org/wiki/Conjugate_gradient_method Conjugate gradient method]
* [https://en.wikipedia.org/wiki/Lagrange_multiplier Lagrange multipliers] – finding extrema under geometric side constraints
* [https://en.wikipedia.org/wiki/Implicit_function#Implicit_differentiation Implicit differentiation]

'''Generalized functions (1D):'''
* [https://en.wikipedia.org/wiki/Dirac_delta_function Dirac delta function] … derivative of Heaviside function
* [https://en.wikipedia.org/wiki/Heaviside_step_function Heaviside step function] … antiderivative of Dirac delta function

=== Basic higher dimensional higher order derivatives ===

* [https://en.wikipedia.org/wiki/Gradient Gradient] … First order derivative of a scalar field
* [https://en.wikipedia.org/wiki/Directional_derivative Directional derivative] … gradient projected into direction vector at specific point
* [https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant Jacobian matrix and determinant]
* [https://en.wikipedia.org/wiki/Hessian_matrix Hessian matrix]

'''For a taylor series of a scalar field:'''
* First derivative: Gadient
* Second derivative: Hessian Matrix
* Third derivative: unnamed three index tensor

'''For a taylor series of a vector field:'''
* First derivative of a scalar field: Jacobian matrix
* Second derivative: unnamed three index tensor

'''For a taylor series of a tensor fields of arbitrary rank (all derivatives):'''
* See: [[Beautiful differentiation (Conal Elliott)]]

'''Other uses of the Jacobian matrix:'''
* For a transformation of a coordinate system into an other coordinate system. For locally linear transformations – unless generalized derivatives are allowed (like multidimensional analogs to Dirac-deltas)
* For [https://en.wikipedia.org/wiki/Propagation_of_uncertainty propagation of uncertainty] in scientific measurements near sigma limit

=== Useful for analysis of selfassembly and dissipation ===

* [https://en.wikipedia.org/wiki/Arrhenius_equation Arrhenius equation] – "a formula for the temperature dependence of reaction rates"
* [https://en.wikipedia.org/wiki/Onsager_reciprocal_relations Onsager reciprocal relations] – modelling transport phenomena – [[statistical physics]]
* '''[https://en.wikipedia.org/wiki/Fluctuation-dissipation_theorem Fluctuation-dissipation theorem]''' – links drag to Brownian motion – [[friction]] – The paper "[[Evaluating the Friction of Rotary Joints in Molecular Machines (paper)]]" uses a simplified result from this.
* [https://en.wikipedia.org/wiki/Langevin_equation Langevin equation] – for modelling brownian motion – [[statistical physics]] – [https://en.wikipedia.org/wiki/Einstein_relation_(kinetic_theory) Einstein relation (kinetic theory)] – diffusion coefficient from microscopic mobility

=== Important for non-qunatum mechanical molecular dynamics simulations ===

* [https://en.wikipedia.org/wiki/Molecular_dynamics Molecular dynamics]
* [https://en.wikipedia.org/wiki/Lennard-Jones_potential Lennard-Jones potential]
Tools to set up the right initial distribution of particle motions:
* '''[https://en.wikipedia.org/wiki/Equipartition_theorem Equipartition theorem]'''
* [https://en.wikipedia.org/wiki/Thermodynamic_beta Thermodynamic beta (kBT)] in the Boltzmann factor in the [https://en.wikipedia.org/wiki/Boltzmann_distribution Boltzmann distribution]
* For fermions like electrons: [https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics Fermi–Dirac statistics]
* For bosons like phonons (and photons): [https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics Bose–Einstein statistics]
* [https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_statistics Maxwell–Boltzmann statistics] & [https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution Maxwell–Boltzmann distribution]

=== Thermodynamics ===

[https://en.wikipedia.org/wiki/Statistical_ensemble_(mathematical_physics) Statistical ensemble (mathematical physics)]
[https://en.wikipedia.org/wiki/Statistical_ensemble_(mathematical_physics)#Correcting_overcounting_in_phase_space (overcounting)]
[https://en.wikipedia.org/wiki/Category:Statistical_ensembles (list of ensembles)]:
* [https://en.wikipedia.org/wiki/Canonical_ensemble Canonical ensemble] – NVE – heat bath
* [https://en.wikipedia.org/wiki/Microcanonical_ensemble Microcanonical ensemble] – NVT – isolated
----
Changes in the rate of a chemical reaction against temperature. (chemical kinetics)
* [https://en.wikipedia.org/wiki/Eyring_equation Eyring equation] – from first principles – ([https://en.wikipedia.org/wiki/Transition_state_theory Transition state theory])
* [https://en.wikipedia.org/wiki/Arrhenius_equation Arrhenius equation] – empirical / phenomenological

=== For more precise quantum mechanical calculations ===

* [https://en.wikipedia.org/wiki/Square_(algebra)#Absolute_square Absolute square] – to the the density from the wave function
* [https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation Bra-ket notation] – abstracting math from positional 3D space – treating positional space and impulse equally
----
* [https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation] – and exact exact solutions – and iterative methods
* ([https://en.wikipedia.org/wiki/Helium_atom Helium atom] as the simplemost three body case and first case where there is electron shielding)
* Approximations: [https://en.wikipedia.org/wiki/Slater-type_orbital Slater type orbital] and [https://en.wikipedia.org/wiki/Gaussian_orbital Gaussian_orbital]
* "overlap integrals" – e.g. [https://en.wikipedia.org/wiki/Orbital_overlap Orbital overlap] – projections in vector spaces with functions as base vectors
* (The crazy math symbol of an integral with a sum drawn over for quantum systems that contain both continuous band and discrete energy states)
* [https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process Gram–Schmidt process] – for getting a reasonable orthonormal basis as a starting point
----
* '''[https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method Hartree–Fock method]'''
* '''[https://en.wikipedia.org/wiki/Density_functional_theory Density functional theory]'''
----
* [https://en.wikipedia.org/wiki/Complete_set_of_commuting_observables Complete set of commuting observables] – "the measurement of one observable has no effect on the result of measuring another observable in the set"
* commutators and anti-commutators – [https://en.wikipedia.org/wiki/Commutator#Ring_theory Commutator ~> Ring theory]
----
* [https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients Clebsch–Gordan coefficients] – for coupling angular momenta – [https://pdg.lbl.gov/2019/reviews/rpp2019-rev-clebsch-gordan-coefs.pdf a good table] and [https://youtu.be/UPyf9ntr-B8 a good video explanation how to use it]
----
* [https://en.wikipedia.org/wiki/Density_matrix Density matrix]

=== Maybe more relevant for high energy free particle physics ===

* [https://en.wikipedia.org/wiki/Green%27s_function Green's function] – needed for scattering problems
* [https://en.wikipedia.org/wiki/Liouville%27s_theorem_(Hamiltonian) Liouville's theorem (Hamiltonian)] – on incompessibility of phase space – Liouville's theorem puts limits on focusing particle beams after they left solid state – To cheat and reduce the phase space of a free floating particle beam at least some indirect interaction with solid state matter (for removal of excess phase space) is necessary [http://www.iap.tuwien.ac.at/www/atomic/surface/capillaries (Capillary guiding)]
* Canonical transformations
* [https://en.wikipedia.org/wiki/Canonical_coordinates Canonical coordinates] – (in [https://en.wikipedia.org/wiki/Hamiltonian_mechanics Hamiltonian mechanics])
* [https://en.wikipedia.org/wiki/Generalized_coordinates Generalized coordinates] – (in [https://en.wikipedia.org/wiki/Lagrangian_mechanics Lagrangian mechanics])
----
* [https://en.wikipedia.org/wiki/Distribution_(mathematics) Distributions] (one class of [https://en.wikipedia.org/wiki/Generalized_function generalized functions]) – including [https://en.wikipedia.org/wiki/Dirac_delta_function Dirac deltas] and [https://en.wikipedia.org/wiki/Heaviside_step_function Heaviside steps] – quite a bit of math rules to memorize there
* [https://en.wikipedia.org/wiki/Support_(mathematics)#Compact_support support function] [https://de.wikipedia.org/wiki/Stetige_Funktion_mit_kompaktem_Tr%C3%A4ger (de)]
* Support functions => Test functions => [https://en.wikipedia.org/wiki/Bump_function Bump_function] – (in the limit a Dirac delta) ~ [[unusual math]]
----
* [https://en.wikipedia.org/wiki/Liouville%27s_theorem_(complex_analysis) Liouville's theorem (complex analysis)]
* [https://en.wikipedia.org/wiki/Cauchy%E2%80%93Riemann_equations Cauchy–Riemann equations] – complex differentiability; holomorphic; analytic; ...
* Cauchy's integral theorem
----
* [https://en.wikipedia.org/wiki/Ladder operator Ladder_operator]
* [https://en.wikipedia.org/wiki/Creation_and_annihilation_operators Creation and annihilation operators] – ([https://en.wikipedia.org/wiki/Coherent_state Coherent state])
----
* [https://en.wikipedia.org/wiki/Einstein_notation Einstein notation]
----
* '''[https://en.wikipedia.org/wiki/Noether%27s_theorem Nöther's theorem]''' – linking conserved quantities to invariance under transformations (aka symmetries) – related: generating functions => [[unusual math]]

== Most fundamental concepts ==

* causation vs correlation
* necessity vs sufficiency (if and only if aka iff)
* convergence ... ''(one or two closely associated topics are missing here ... which ones? ...)''

== Useful algorithms in computer graphics ==

* GJK algorithm (collision detection) [https://en.wikipedia.org/wiki/Gilbert%E2%80%93Johnson%E2%80%93Keerthi_distance_algorithm (leave to wikipedia)]
* Raymarching and more general
* Walk on Spheres [https://en.wikipedia.org/wiki/Walk-on-spheres_method (leave to wikipedia)] (also useful for physical simulations)
* Octree and more advanced subdivision algorithms
* Marching cubes (for ugly triangulations – somehow this is everyone's favorite though)

== Useful math for larger scale gear-train design ==

Differential geometry for generation of conjugate profiles in generalized gear-sets 
(only solved for general axial alignments cycloid gear profiles as of yet 2021) 
Associated math includes:
* [https://en.wikipedia.org/wiki/Pl%C3%BCcker_coordinates Plücker coordinates]
* [https://en.wikipedia.org/wiki/Screw_theory screw theory] – [https://en.wikipedia.org/wiki/Screw_axis screw axis]
* [https://en.wikipedia.org/wiki/Dual_number dual numbers]

== Potentially extremely useful computer science ==

'''Automatic differentiation ...'''
* generalized to arbitrary dimensionality (Jaconian matrix is first deerivative of vector field, Hessian matrix is second derivative of a scalar field, following are higher tensors)
* generalized to arbitrary degree (Basically a taylor series)
See: "Beautiful differentiation" by Conal Elliott (March 2009) Appeared in ICFP 2009 [http://conal.net/papers/beautiful-differentiation/ (link)]

'''Generalized code interpretation for vastly more resuability ...'''
* generalizing lambda calculus to a category theoretic interpretation that allows for reuse of exactly the same code in vastly different compilation targets
See: "Compiling to categories" by Conal Elliott (February 2017) Appeared at ICFP 2017 [http://conal.net/papers/compiling-to-categories/ (link)]

----

The revolution to "'''[[content addressed]]'''" systems. 
Maybe the most powerful weapon against '''dependency hell''' and all its various workaround hacks.

== Notes / Misc ==

* Not to confuse "Holomorphic function" and "Holonomic constraints"

* Wikipedia [[https://en.wikipedia.org//wiki/Functional_derivative Functional derivative]]

== Related ==

* [[Useful algorithms]]
* [[Atomic orbitals]]
* [[Hartree-Fock method]]
----
* [[Pages with math]]
----
* [[Exotic math]]
----
* [[Triangle of power]]

[[Category:Pages with math]]
[[category:Information]]

Useful math

2026-10-10T07:41:43Z

Apm: /* Related */ link to yet unwritten page useful algorithms

This page is about useful math in the wide context of [[atomically precise manufacturing]].

Specific application areas include:
----
* friction and dissipation
* thermally driven self assembly
----
* quantum chemistry
* molecular modelling
----
* 3d modelling
* differential geometry for larger scale gears
* ...

== Thermodynamics and statistical physics ==

Summing up over all the possible microstate configurations of a system. 
Thereby deriving a partitioning function – (some [[exotic math]] involved in there) 
From this partitioning function then [[thermodynamic laws]] can be re-derived and explained. 
These [[thermodynamic laws]] can be (and historically have been) formerly phemomenologically derived. 
Meaning derived from their effects not their causes.

Related:
* '''Thermodynamic potentials''' and associated '''statistical ensembles'''
* Transformation between the potentials – Legendre Transformation
* Conjugated pairs of valuables (extrinsic and intrinsic) – a pairs product always gives the physical unit of energy

=== General note on solid state physics ===

Prevalent are long chains of simplifications by approximations that pile up and up and up. 
Changing the application area of the models hugely may requires reevaluation of all these approximation steps. 
Given that the chains of approximation are not formalized on computers (state 2021) this is difficult error prone and tedious.

Also: Following all the derivations from the lowermost assumptions 
it becomes very evident that energy is a relative concept. (Not talking about relativity theory here).

== Math for modelling with atomistic detail ==

=== From first principles – e.g. for quantum chemistry ===

The exact solutions of the Schrödinger equation for the hydrogen problem. 
Using the property of it being a "separable partial differential equation"
* Laguerre polynomials for the radial part
* Spherical harmonics for the angular parts

The major reason '''why exact solutions are way off''' for other elements than hydrogen 
(and the less relevant highly charged one electron ions) is '''the shielding effect of the inner electrons'''. 
To get good approximations for orbitals it is necessary to do iterative self-consistent-field methods. 
The exact hydrogen solutions can serve as a good initial guess starting point. 

Also Useful in getting good starting points:
* the '''Grahm Schmidt orthogonalization method'''
* composing Gaussian distributions as base functions for orbitals
* the '''Hartree-Fock method''' – helps filling up states consistent with pauli exclusion rules – antideterminant for fermionic states
Related: Density functional theory.

=== Phenomenological models – e.g. for molecular modelling ===

* Lennard Jones potential – and similar ones – good for molecular dynamics simulations
* Hund's rule of maximum multiplicity – not particularly useful in the context of chemically bond atoms

== Misc ==

Derivation of [[London dispersion forces]] from first principles by 
integrating over virtual electron states (related: virtual particles, feynman graphs) ... 
Related: Born–Oppenheimer approximation – and its deceiving pseudo convergence (to check)

== Generally useful math tools ==

Hamiltonian mechanics finds heavy use in in quantummechaincs. 
Interestingly in [[gem-gum]] systems at slightly larger scales things behave very classically. 
Lagrangian mechanics might be useful there.

* [https://en.wikipedia.org/wiki/Hamiltonian_mechanics Hamiltonian mechanics]
* [https://en.wikipedia.org/wiki/Lagrangian_mechanics Lagrangian mechanics]
Related: [https://en.wikipedia.org/wiki/Stationary_Action_Principle principle of least action] and [https://en.wikipedia.org/wiki/Variational_principle variational principle (and calculus)]

=== Basic math for physics ===

* Finding zeros: – [https://en.wikipedia.org/wiki/Newton%27s_method Newton's method] – [https://en.wikipedia.org/wiki/Regula_falsi Regula falsi]
* Integrating differential equations: – [https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods Runge Kutta methods] – [https://en.wikipedia.org/wiki/Leapfrog_integration Leapfrog integration] – [https://en.wikipedia.org/wiki/Verlet_integration Verlet Integration]
----
* [https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors Eigenvalues and eigenvectors] – (linear algebra)
* Vector spaces with functions as base vectors – ([https://en.wikipedia.org/wiki/Hilbert_space Hilbert spaces])
* "Integral kernels" – [https://en.wikipedia.org/wiki/Integral_transform Integral transform]
* [https://en.wikipedia.org/wiki/Fourier_transform Fourier transformations] – (convolution becomes multiplication)
* ([https://en.wikipedia.org/wiki/Laplace_transform Laplace transformations] – more used in electrical system engineering)
* [https://en.wikipedia.org/wiki/Convolution Convolution (aka folding)]
* [https://en.wikipedia.org/wiki/Linear_form Linear functional] – [https://en.wikipedia.org/wiki/Adjoint_functors Adjoint_functors]
* https://en.wikipedia.org/wiki/Self-adjoint_operator Self-adjoint operator]
* [https://en.wikipedia.org/wiki/Orbital_overlap Orbital overlap / Overlap integral]
----
* All sorts of tricks an hackery with matrix math – selfadjunctness & co – [https://en.wikipedia.org/wiki/Category:Matrix_theory (Category:Matrix_theory)]
----
* '''[https://en.wikipedia.org/wiki/List_of_equations_in_quantum_mechanics List of equations in quantum mechanics]'''
* ([https://en.wikipedia.org/wiki/Heisenberg_picture Heisenberg picture] and [https://en.wikipedia.org/wiki/Matrix_mechanics Matrix mechanics])
----
[https://en.wikipedia.org/wiki/Category:Perturbation_theory Category:Perturbation_theory] – particularly:
* [https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics) Perturbation_theory_(quantum_mechanics)] which employs the
* [https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process Gram–Schmidt_process] in Hilbert space (? IIRC)
'''[https://en.wikipedia.org/wiki/Category:Condensed_matter_physics Category:Condensed_matter_physics]'''

=== Useful for 3D modelling and robotics ===

* screws (math object), wrenches (math objects), dual numbers – useful for robotics (forwards & backwards kinematic) and differential geometry for gear flanks
* math tools for surface based commuter graphics (manly dealing with triangulations)
* math tools for volume based computer graphics:
* functional-representation (F-Rep), implicit surfaces, algebraic varieties, distance fields (magnitude of gradient is 1 for these)
* ray-marching algorithms

=== Some multi-purpouse misc math ===

* [https://en.wikipedia.org/wiki/Gradient_descent Gradient descent]
* (Reversely calculated) gradient descent in multi-dimensional scalar fields: [https://en.wikipedia.org/wiki/Conjugate_gradient_method Conjugate gradient method]
* [https://en.wikipedia.org/wiki/Lagrange_multiplier Lagrange multipliers] – finding extrema under geometric side constraints
* [https://en.wikipedia.org/wiki/Implicit_function#Implicit_differentiation Implicit differentiation]

'''Generalized functions (1D):'''
* [https://en.wikipedia.org/wiki/Dirac_delta_function Dirac delta function] … derivative of Heaviside function
* [https://en.wikipedia.org/wiki/Heaviside_step_function Heaviside step function] … antiderivative of Dirac delta function

=== Basic higher dimensional higher order derivatives ===

* [https://en.wikipedia.org/wiki/Gradient Gradient] … First order derivative of a scalar field
* [https://en.wikipedia.org/wiki/Directional_derivative Directional derivative] … gradient projected into direction vector at specific point
* [https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant Jacobian matrix and determinant]
* [https://en.wikipedia.org/wiki/Hessian_matrix Hessian matrix]

'''For a taylor series of a scalar field:'''
* First derivative: Gadient
* Second derivative: Hessian Matrix
* Third derivative: unnamed three index tensor

'''For a taylor series of a vector field:'''
* First derivative of a scalar field: Jacobian matrix
* Second derivative: unnamed three index tensor

'''For a taylor series of a tensor fields of arbitrary rank (all derivatives):'''
* See: [[Beautiful differentiation (Conal Elliott)]]

'''Other uses of the Jacobian matrix:'''
* For a transformation of a coordinate system into an other coordinate system. For locally linear transformations – unless generalized derivatives are allowed (like multidimensional analogs to Dirac-deltas)
* For [https://en.wikipedia.org/wiki/Propagation_of_uncertainty propagation of uncertainty] in scientific measurements near sigma limit

=== Useful for analysis of selfassembly and dissipation ===

* [https://en.wikipedia.org/wiki/Arrhenius_equation Arrhenius equation] – "a formula for the temperature dependence of reaction rates"
* [https://en.wikipedia.org/wiki/Onsager_reciprocal_relations Onsager reciprocal relations] – modelling transport phenomena – [[statistical physics]]
* '''[https://en.wikipedia.org/wiki/Fluctuation-dissipation_theorem Fluctuation-dissipation theorem]''' – links drag to Brownian motion – [[friction]] – The paper "[[Evaluating the Friction of Rotary Joints in Molecular Machines (paper)]]" uses a simplified result from this.
* [https://en.wikipedia.org/wiki/Langevin_equation Langevin equation] – for modelling brownian motion – [[statistical physics]] – [https://en.wikipedia.org/wiki/Einstein_relation_(kinetic_theory) Einstein relation (kinetic theory)] – diffusion coefficient from microscopic mobility

=== Important for non-qunatum mechanical molecular dynamics simulations ===

* [https://en.wikipedia.org/wiki/Molecular_dynamics Molecular dynamics]
* [https://en.wikipedia.org/wiki/Lennard-Jones_potential Lennard-Jones potential]
Tools to set up the right initial distribution of particle motions:
* '''[https://en.wikipedia.org/wiki/Equipartition_theorem Equipartition theorem]'''
* [https://en.wikipedia.org/wiki/Thermodynamic_beta Thermodynamic beta (kBT)] in the Boltzmann factor in the [https://en.wikipedia.org/wiki/Boltzmann_distribution Boltzmann distribution]
* For fermions like electrons: [https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics Fermi–Dirac statistics]
* For bosons like phonons (and photons): [https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics Bose–Einstein statistics]
* [https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_statistics Maxwell–Boltzmann statistics] & [https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution Maxwell–Boltzmann distribution]

=== Thermodynamics ===

[https://en.wikipedia.org/wiki/Statistical_ensemble_(mathematical_physics) Statistical ensemble (mathematical physics)]
[https://en.wikipedia.org/wiki/Statistical_ensemble_(mathematical_physics)#Correcting_overcounting_in_phase_space (overcounting)]
[https://en.wikipedia.org/wiki/Category:Statistical_ensembles (list of ensembles)]:
* [https://en.wikipedia.org/wiki/Canonical_ensemble Canonical ensemble] – NVE – heat bath
* [https://en.wikipedia.org/wiki/Microcanonical_ensemble Microcanonical ensemble] – NVT – isolated
----
Changes in the rate of a chemical reaction against temperature. (chemical kinetics)
* [https://en.wikipedia.org/wiki/Eyring_equation Eyring equation] – from first principles – ([https://en.wikipedia.org/wiki/Transition_state_theory Transition state theory])
* [https://en.wikipedia.org/wiki/Arrhenius_equation Arrhenius equation] – empirical / phenomenological

=== For more precise quantum mechanical calculations ===

* [https://en.wikipedia.org/wiki/Square_(algebra)#Absolute_square Absolute square] – to the the density from the wave function
* [https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation Bra-ket notation] – abstracting math from positional 3D space – treating positional space and impulse equally
----
* [https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation] – and exact exact solutions – and iterative methods
* ([https://en.wikipedia.org/wiki/Helium_atom Helium atom] as the simplemost three body case and first case where there is electron shielding)
* Approximations: [https://en.wikipedia.org/wiki/Slater-type_orbital Slater type orbital] and [https://en.wikipedia.org/wiki/Gaussian_orbital Gaussian_orbital]
* "overlap integrals" – e.g. [https://en.wikipedia.org/wiki/Orbital_overlap Orbital overlap] – projections in vector spaces with functions as base vectors
* (The crazy math symbol of an integral with a sum drawn over for quantum systems that contain both continuous band and discrete energy states)
* [https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process Gram–Schmidt process] – for getting a reasonable orthonormal basis as a starting point
----
* '''[https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method Hartree–Fock method]'''
* '''[https://en.wikipedia.org/wiki/Density_functional_theory Density functional theory]'''
----
* [https://en.wikipedia.org/wiki/Complete_set_of_commuting_observables Complete set of commuting observables] – "the measurement of one observable has no effect on the result of measuring another observable in the set"
* commutators and anti-commutators – [https://en.wikipedia.org/wiki/Commutator#Ring_theory Commutator ~> Ring theory]
----
* [https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients Clebsch–Gordan coefficients] – for coupling angular momenta – [https://pdg.lbl.gov/2019/reviews/rpp2019-rev-clebsch-gordan-coefs.pdf a good table] and [https://youtu.be/UPyf9ntr-B8 a good video explanation how to use it]
----
* [https://en.wikipedia.org/wiki/Density_matrix Density matrix]

=== Maybe more relevant for high energy free particle physics ===

* [https://en.wikipedia.org/wiki/Green%27s_function Green's function] – needed for scattering problems
* [https://en.wikipedia.org/wiki/Liouville%27s_theorem_(Hamiltonian) Liouville's theorem (Hamiltonian)] – on incompessibility of phase space – Liouville's theorem puts limits on focusing particle beams after they left solid state – To cheat and reduce the phase space of a free floating particle beam at least some indirect interaction with solid state matter (for removal of excess phase space) is necessary [http://www.iap.tuwien.ac.at/www/atomic/surface/capillaries (Capillary guiding)]
* Canonical transformations
* [https://en.wikipedia.org/wiki/Canonical_coordinates Canonical coordinates] – (in [https://en.wikipedia.org/wiki/Hamiltonian_mechanics Hamiltonian mechanics])
* [https://en.wikipedia.org/wiki/Generalized_coordinates Generalized coordinates] – (in [https://en.wikipedia.org/wiki/Lagrangian_mechanics Lagrangian mechanics])
----
* [https://en.wikipedia.org/wiki/Distribution_(mathematics) Distributions] (one class of [https://en.wikipedia.org/wiki/Generalized_function generalized functions]) – including [https://en.wikipedia.org/wiki/Dirac_delta_function Dirac deltas] and [https://en.wikipedia.org/wiki/Heaviside_step_function Heaviside steps] – quite a bit of math rules to memorize there
* [https://en.wikipedia.org/wiki/Support_(mathematics)#Compact_support support function] [https://de.wikipedia.org/wiki/Stetige_Funktion_mit_kompaktem_Tr%C3%A4ger (de)]
* Support functions => Test functions => [https://en.wikipedia.org/wiki/Bump_function Bump_function] – (in the limit a Dirac delta) ~ [[unusual math]]
----
* [https://en.wikipedia.org/wiki/Liouville%27s_theorem_(complex_analysis) Liouville's theorem (complex analysis)]
* [https://en.wikipedia.org/wiki/Cauchy%E2%80%93Riemann_equations Cauchy–Riemann equations] – complex differentiability; holomorphic; analytic; ...
* Cauchy's integral theorem
----
* [https://en.wikipedia.org/wiki/Ladder operator Ladder_operator]
* [https://en.wikipedia.org/wiki/Creation_and_annihilation_operators Creation and annihilation operators] – ([https://en.wikipedia.org/wiki/Coherent_state Coherent state])
----
* [https://en.wikipedia.org/wiki/Einstein_notation Einstein notation]
----
* '''[https://en.wikipedia.org/wiki/Noether%27s_theorem Nöther's theorem]''' – linking conserved quantities to invariance under transformations (aka symmetries) – related: generating functions => [[unusual math]]

== Most fundamental concepts ==

* causation vs correlation
* necessity vs sufficiency (if and only if aka iff)
* convergence ... ''(one or two closely associated topics are missing here ... which ones? ...)''

== Useful algorithms in computer graphics ==

* GJK algorithm (collision detection)
* Raymarching and more general "Walk on Spheres" (also useful.for physical simulations)
* Octree and more advanced subdivision algorithms
* Marching cubes (for ugly triangulations – somehow this is everyone's favorite though)

== Useful math for larger scale gear-train design ==

Differential geometry for generation of conjugate profiles in generalized gear-sets 
(only solved for general axial alignments cycloid gear profiles as of yet 2021) 
Associated math includes:
* [https://en.wikipedia.org/wiki/Pl%C3%BCcker_coordinates Plücker coordinates]
* [https://en.wikipedia.org/wiki/Screw_theory screw theory] – [https://en.wikipedia.org/wiki/Screw_axis screw axis]
* [https://en.wikipedia.org/wiki/Dual_number dual numbers]

== Potentially extremely useful computer science ==

'''Automatic differentiation ...'''
* generalized to arbitrary dimensionality (Jaconian matrix is first deerivative of vector field, Hessian matrix is second derivative of a scalar field, following are higher tensors)
* generalized to arbitrary degree (Basically a taylor series)
See: "Beautiful differentiation" by Conal Elliott (March 2009) Appeared in ICFP 2009 [http://conal.net/papers/beautiful-differentiation/ (link)]

'''Generalized code interpretation for vastly more resuability ...'''
* generalizing lambda calculus to a category theoretic interpretation that allows for reuse of exactly the same code in vastly different compilation targets
See: "Compiling to categories" by Conal Elliott (February 2017) Appeared at ICFP 2017 [http://conal.net/papers/compiling-to-categories/ (link)]

----

The revolution to "'''[[content addressed]]'''" systems. 
Maybe the most powerful weapon against '''dependency hell''' and all its various workaround hacks.

== Notes / Misc ==

* Not to confuse "Holomorphic function" and "Holonomic constraints"

* Wikipedia [[https://en.wikipedia.org//wiki/Functional_derivative Functional derivative]]

== Related ==

* [[Useful algorithms]]
* [[Atomic orbitals]]
* [[Hartree-Fock method]]
----
* [[Pages with math]]
----
* [[Exotic math]]
----
* [[Triangle of power]]

[[Category:Pages with math]]
[[category:Information]]

Useful math

2026-10-10T07:39:56Z

Apm: /* Basic math for physics */ added link to WP page on Verlet integration

This page is about useful math in the wide context of [[atomically precise manufacturing]].

Specific application areas include:
----
* friction and dissipation
* thermally driven self assembly
----
* quantum chemistry
* molecular modelling
----
* 3d modelling
* differential geometry for larger scale gears
* ...

== Thermodynamics and statistical physics ==

Summing up over all the possible microstate configurations of a system. 
Thereby deriving a partitioning function – (some [[exotic math]] involved in there) 
From this partitioning function then [[thermodynamic laws]] can be re-derived and explained. 
These [[thermodynamic laws]] can be (and historically have been) formerly phemomenologically derived. 
Meaning derived from their effects not their causes.

Related:
* '''Thermodynamic potentials''' and associated '''statistical ensembles'''
* Transformation between the potentials – Legendre Transformation
* Conjugated pairs of valuables (extrinsic and intrinsic) – a pairs product always gives the physical unit of energy

=== General note on solid state physics ===

Prevalent are long chains of simplifications by approximations that pile up and up and up. 
Changing the application area of the models hugely may requires reevaluation of all these approximation steps. 
Given that the chains of approximation are not formalized on computers (state 2021) this is difficult error prone and tedious.

Also: Following all the derivations from the lowermost assumptions 
it becomes very evident that energy is a relative concept. (Not talking about relativity theory here).

== Math for modelling with atomistic detail ==

=== From first principles – e.g. for quantum chemistry ===

The exact solutions of the Schrödinger equation for the hydrogen problem. 
Using the property of it being a "separable partial differential equation"
* Laguerre polynomials for the radial part
* Spherical harmonics for the angular parts

The major reason '''why exact solutions are way off''' for other elements than hydrogen 
(and the less relevant highly charged one electron ions) is '''the shielding effect of the inner electrons'''. 
To get good approximations for orbitals it is necessary to do iterative self-consistent-field methods. 
The exact hydrogen solutions can serve as a good initial guess starting point. 

Also Useful in getting good starting points:
* the '''Grahm Schmidt orthogonalization method'''
* composing Gaussian distributions as base functions for orbitals
* the '''Hartree-Fock method''' – helps filling up states consistent with pauli exclusion rules – antideterminant for fermionic states
Related: Density functional theory.

=== Phenomenological models – e.g. for molecular modelling ===

* Lennard Jones potential – and similar ones – good for molecular dynamics simulations
* Hund's rule of maximum multiplicity – not particularly useful in the context of chemically bond atoms

== Misc ==

Derivation of [[London dispersion forces]] from first principles by 
integrating over virtual electron states (related: virtual particles, feynman graphs) ... 
Related: Born–Oppenheimer approximation – and its deceiving pseudo convergence (to check)

== Generally useful math tools ==

Hamiltonian mechanics finds heavy use in in quantummechaincs. 
Interestingly in [[gem-gum]] systems at slightly larger scales things behave very classically. 
Lagrangian mechanics might be useful there.

* [https://en.wikipedia.org/wiki/Hamiltonian_mechanics Hamiltonian mechanics]
* [https://en.wikipedia.org/wiki/Lagrangian_mechanics Lagrangian mechanics]
Related: [https://en.wikipedia.org/wiki/Stationary_Action_Principle principle of least action] and [https://en.wikipedia.org/wiki/Variational_principle variational principle (and calculus)]

=== Basic math for physics ===

* Finding zeros: – [https://en.wikipedia.org/wiki/Newton%27s_method Newton's method] – [https://en.wikipedia.org/wiki/Regula_falsi Regula falsi]
* Integrating differential equations: – [https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods Runge Kutta methods] – [https://en.wikipedia.org/wiki/Leapfrog_integration Leapfrog integration] – [https://en.wikipedia.org/wiki/Verlet_integration Verlet Integration]
----
* [https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors Eigenvalues and eigenvectors] – (linear algebra)
* Vector spaces with functions as base vectors – ([https://en.wikipedia.org/wiki/Hilbert_space Hilbert spaces])
* "Integral kernels" – [https://en.wikipedia.org/wiki/Integral_transform Integral transform]
* [https://en.wikipedia.org/wiki/Fourier_transform Fourier transformations] – (convolution becomes multiplication)
* ([https://en.wikipedia.org/wiki/Laplace_transform Laplace transformations] – more used in electrical system engineering)
* [https://en.wikipedia.org/wiki/Convolution Convolution (aka folding)]
* [https://en.wikipedia.org/wiki/Linear_form Linear functional] – [https://en.wikipedia.org/wiki/Adjoint_functors Adjoint_functors]
* https://en.wikipedia.org/wiki/Self-adjoint_operator Self-adjoint operator]
* [https://en.wikipedia.org/wiki/Orbital_overlap Orbital overlap / Overlap integral]
----
* All sorts of tricks an hackery with matrix math – selfadjunctness & co – [https://en.wikipedia.org/wiki/Category:Matrix_theory (Category:Matrix_theory)]
----
* '''[https://en.wikipedia.org/wiki/List_of_equations_in_quantum_mechanics List of equations in quantum mechanics]'''
* ([https://en.wikipedia.org/wiki/Heisenberg_picture Heisenberg picture] and [https://en.wikipedia.org/wiki/Matrix_mechanics Matrix mechanics])
----
[https://en.wikipedia.org/wiki/Category:Perturbation_theory Category:Perturbation_theory] – particularly:
* [https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics) Perturbation_theory_(quantum_mechanics)] which employs the
* [https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process Gram–Schmidt_process] in Hilbert space (? IIRC)
'''[https://en.wikipedia.org/wiki/Category:Condensed_matter_physics Category:Condensed_matter_physics]'''

=== Useful for 3D modelling and robotics ===

* screws (math object), wrenches (math objects), dual numbers – useful for robotics (forwards & backwards kinematic) and differential geometry for gear flanks
* math tools for surface based commuter graphics (manly dealing with triangulations)
* math tools for volume based computer graphics:
* functional-representation (F-Rep), implicit surfaces, algebraic varieties, distance fields (magnitude of gradient is 1 for these)
* ray-marching algorithms

=== Some multi-purpouse misc math ===

* [https://en.wikipedia.org/wiki/Gradient_descent Gradient descent]
* (Reversely calculated) gradient descent in multi-dimensional scalar fields: [https://en.wikipedia.org/wiki/Conjugate_gradient_method Conjugate gradient method]
* [https://en.wikipedia.org/wiki/Lagrange_multiplier Lagrange multipliers] – finding extrema under geometric side constraints
* [https://en.wikipedia.org/wiki/Implicit_function#Implicit_differentiation Implicit differentiation]

'''Generalized functions (1D):'''
* [https://en.wikipedia.org/wiki/Dirac_delta_function Dirac delta function] … derivative of Heaviside function
* [https://en.wikipedia.org/wiki/Heaviside_step_function Heaviside step function] … antiderivative of Dirac delta function

=== Basic higher dimensional higher order derivatives ===

* [https://en.wikipedia.org/wiki/Gradient Gradient] … First order derivative of a scalar field
* [https://en.wikipedia.org/wiki/Directional_derivative Directional derivative] … gradient projected into direction vector at specific point
* [https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant Jacobian matrix and determinant]
* [https://en.wikipedia.org/wiki/Hessian_matrix Hessian matrix]

'''For a taylor series of a scalar field:'''
* First derivative: Gadient
* Second derivative: Hessian Matrix
* Third derivative: unnamed three index tensor

'''For a taylor series of a vector field:'''
* First derivative of a scalar field: Jacobian matrix
* Second derivative: unnamed three index tensor

'''For a taylor series of a tensor fields of arbitrary rank (all derivatives):'''
* See: [[Beautiful differentiation (Conal Elliott)]]

'''Other uses of the Jacobian matrix:'''
* For a transformation of a coordinate system into an other coordinate system. For locally linear transformations – unless generalized derivatives are allowed (like multidimensional analogs to Dirac-deltas)
* For [https://en.wikipedia.org/wiki/Propagation_of_uncertainty propagation of uncertainty] in scientific measurements near sigma limit

=== Useful for analysis of selfassembly and dissipation ===

* [https://en.wikipedia.org/wiki/Arrhenius_equation Arrhenius equation] – "a formula for the temperature dependence of reaction rates"
* [https://en.wikipedia.org/wiki/Onsager_reciprocal_relations Onsager reciprocal relations] – modelling transport phenomena – [[statistical physics]]
* '''[https://en.wikipedia.org/wiki/Fluctuation-dissipation_theorem Fluctuation-dissipation theorem]''' – links drag to Brownian motion – [[friction]] – The paper "[[Evaluating the Friction of Rotary Joints in Molecular Machines (paper)]]" uses a simplified result from this.
* [https://en.wikipedia.org/wiki/Langevin_equation Langevin equation] – for modelling brownian motion – [[statistical physics]] – [https://en.wikipedia.org/wiki/Einstein_relation_(kinetic_theory) Einstein relation (kinetic theory)] – diffusion coefficient from microscopic mobility

=== Important for non-qunatum mechanical molecular dynamics simulations ===

* [https://en.wikipedia.org/wiki/Molecular_dynamics Molecular dynamics]
* [https://en.wikipedia.org/wiki/Lennard-Jones_potential Lennard-Jones potential]
Tools to set up the right initial distribution of particle motions:
* '''[https://en.wikipedia.org/wiki/Equipartition_theorem Equipartition theorem]'''
* [https://en.wikipedia.org/wiki/Thermodynamic_beta Thermodynamic beta (kBT)] in the Boltzmann factor in the [https://en.wikipedia.org/wiki/Boltzmann_distribution Boltzmann distribution]
* For fermions like electrons: [https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics Fermi–Dirac statistics]
* For bosons like phonons (and photons): [https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics Bose–Einstein statistics]
* [https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_statistics Maxwell–Boltzmann statistics] & [https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution Maxwell–Boltzmann distribution]

=== Thermodynamics ===

[https://en.wikipedia.org/wiki/Statistical_ensemble_(mathematical_physics) Statistical ensemble (mathematical physics)]
[https://en.wikipedia.org/wiki/Statistical_ensemble_(mathematical_physics)#Correcting_overcounting_in_phase_space (overcounting)]
[https://en.wikipedia.org/wiki/Category:Statistical_ensembles (list of ensembles)]:
* [https://en.wikipedia.org/wiki/Canonical_ensemble Canonical ensemble] – NVE – heat bath
* [https://en.wikipedia.org/wiki/Microcanonical_ensemble Microcanonical ensemble] – NVT – isolated
----
Changes in the rate of a chemical reaction against temperature. (chemical kinetics)
* [https://en.wikipedia.org/wiki/Eyring_equation Eyring equation] – from first principles – ([https://en.wikipedia.org/wiki/Transition_state_theory Transition state theory])
* [https://en.wikipedia.org/wiki/Arrhenius_equation Arrhenius equation] – empirical / phenomenological

=== For more precise quantum mechanical calculations ===

* [https://en.wikipedia.org/wiki/Square_(algebra)#Absolute_square Absolute square] – to the the density from the wave function
* [https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation Bra-ket notation] – abstracting math from positional 3D space – treating positional space and impulse equally
----
* [https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation Schrödinger equation] – and exact exact solutions – and iterative methods
* ([https://en.wikipedia.org/wiki/Helium_atom Helium atom] as the simplemost three body case and first case where there is electron shielding)
* Approximations: [https://en.wikipedia.org/wiki/Slater-type_orbital Slater type orbital] and [https://en.wikipedia.org/wiki/Gaussian_orbital Gaussian_orbital]
* "overlap integrals" – e.g. [https://en.wikipedia.org/wiki/Orbital_overlap Orbital overlap] – projections in vector spaces with functions as base vectors
* (The crazy math symbol of an integral with a sum drawn over for quantum systems that contain both continuous band and discrete energy states)
* [https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process Gram–Schmidt process] – for getting a reasonable orthonormal basis as a starting point
----
* '''[https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method Hartree–Fock method]'''
* '''[https://en.wikipedia.org/wiki/Density_functional_theory Density functional theory]'''
----
* [https://en.wikipedia.org/wiki/Complete_set_of_commuting_observables Complete set of commuting observables] – "the measurement of one observable has no effect on the result of measuring another observable in the set"
* commutators and anti-commutators – [https://en.wikipedia.org/wiki/Commutator#Ring_theory Commutator ~> Ring theory]
----
* [https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients Clebsch–Gordan coefficients] – for coupling angular momenta – [https://pdg.lbl.gov/2019/reviews/rpp2019-rev-clebsch-gordan-coefs.pdf a good table] and [https://youtu.be/UPyf9ntr-B8 a good video explanation how to use it]
----
* [https://en.wikipedia.org/wiki/Density_matrix Density matrix]

=== Maybe more relevant for high energy free particle physics ===

* [https://en.wikipedia.org/wiki/Green%27s_function Green's function] – needed for scattering problems
* [https://en.wikipedia.org/wiki/Liouville%27s_theorem_(Hamiltonian) Liouville's theorem (Hamiltonian)] – on incompessibility of phase space – Liouville's theorem puts limits on focusing particle beams after they left solid state – To cheat and reduce the phase space of a free floating particle beam at least some indirect interaction with solid state matter (for removal of excess phase space) is necessary [http://www.iap.tuwien.ac.at/www/atomic/surface/capillaries (Capillary guiding)]
* Canonical transformations
* [https://en.wikipedia.org/wiki/Canonical_coordinates Canonical coordinates] – (in [https://en.wikipedia.org/wiki/Hamiltonian_mechanics Hamiltonian mechanics])
* [https://en.wikipedia.org/wiki/Generalized_coordinates Generalized coordinates] – (in [https://en.wikipedia.org/wiki/Lagrangian_mechanics Lagrangian mechanics])
----
* [https://en.wikipedia.org/wiki/Distribution_(mathematics) Distributions] (one class of [https://en.wikipedia.org/wiki/Generalized_function generalized functions]) – including [https://en.wikipedia.org/wiki/Dirac_delta_function Dirac deltas] and [https://en.wikipedia.org/wiki/Heaviside_step_function Heaviside steps] – quite a bit of math rules to memorize there
* [https://en.wikipedia.org/wiki/Support_(mathematics)#Compact_support support function] [https://de.wikipedia.org/wiki/Stetige_Funktion_mit_kompaktem_Tr%C3%A4ger (de)]
* Support functions => Test functions => [https://en.wikipedia.org/wiki/Bump_function Bump_function] – (in the limit a Dirac delta) ~ [[unusual math]]
----
* [https://en.wikipedia.org/wiki/Liouville%27s_theorem_(complex_analysis) Liouville's theorem (complex analysis)]
* [https://en.wikipedia.org/wiki/Cauchy%E2%80%93Riemann_equations Cauchy–Riemann equations] – complex differentiability; holomorphic; analytic; ...
* Cauchy's integral theorem
----
* [https://en.wikipedia.org/wiki/Ladder operator Ladder_operator]
* [https://en.wikipedia.org/wiki/Creation_and_annihilation_operators Creation and annihilation operators] – ([https://en.wikipedia.org/wiki/Coherent_state Coherent state])
----
* [https://en.wikipedia.org/wiki/Einstein_notation Einstein notation]
----
* '''[https://en.wikipedia.org/wiki/Noether%27s_theorem Nöther's theorem]''' – linking conserved quantities to invariance under transformations (aka symmetries) – related: generating functions => [[unusual math]]

== Most fundamental concepts ==

* causation vs correlation
* necessity vs sufficiency (if and only if aka iff)
* convergence ... ''(one or two closely associated topics are missing here ... which ones? ...)''

== Useful algorithms in computer graphics ==

* GJK algorithm (collision detection)
* Raymarching and more general "Walk on Spheres" (also useful.for physical simulations)
* Octree and more advanced subdivision algorithms
* Marching cubes (for ugly triangulations – somehow this is everyone's favorite though)

== Useful math for larger scale gear-train design ==

Differential geometry for generation of conjugate profiles in generalized gear-sets 
(only solved for general axial alignments cycloid gear profiles as of yet 2021) 
Associated math includes:
* [https://en.wikipedia.org/wiki/Pl%C3%BCcker_coordinates Plücker coordinates]
* [https://en.wikipedia.org/wiki/Screw_theory screw theory] – [https://en.wikipedia.org/wiki/Screw_axis screw axis]
* [https://en.wikipedia.org/wiki/Dual_number dual numbers]

== Potentially extremely useful computer science ==

'''Automatic differentiation ...'''
* generalized to arbitrary dimensionality (Jaconian matrix is first deerivative of vector field, Hessian matrix is second derivative of a scalar field, following are higher tensors)
* generalized to arbitrary degree (Basically a taylor series)
See: "Beautiful differentiation" by Conal Elliott (March 2009) Appeared in ICFP 2009 [http://conal.net/papers/beautiful-differentiation/ (link)]

'''Generalized code interpretation for vastly more resuability ...'''
* generalizing lambda calculus to a category theoretic interpretation that allows for reuse of exactly the same code in vastly different compilation targets
See: "Compiling to categories" by Conal Elliott (February 2017) Appeared at ICFP 2017 [http://conal.net/papers/compiling-to-categories/ (link)]

----

The revolution to "'''[[content addressed]]'''" systems. 
Maybe the most powerful weapon against '''dependency hell''' and all its various workaround hacks.

== Notes / Misc ==

* Not to confuse "Holomorphic function" and "Holonomic constraints"

* Wikipedia [[https://en.wikipedia.org//wiki/Functional_derivative Functional derivative]]

== Related ==

* [[Atomic orbitals]]
* [[Hartree-Fock method]]
----
* [[Pages with math]]
----
* [[Exotic math]]
----
* [[Triangle of power]]

[[Category:Pages with math]]
[[category:Information]]

Incremental path

2026-10-09T07:49:25Z

Apm: /* Why necessarily early – fist climbing hierarchical self-assembly – then climbing technology levels */

{| class="wikitable" style="float:right; margin-left: 10px; text-align: center"
! colspan = "2"|Technology levels and steps of the incremental path
|-
| [[Technology level 0|Level 0]]
| [[side products of technology level 0|side products]]
|-
| [[Introduction of total positional control]]
| xxx
|-
| [[Technology level I|Level I]]
| [[side products of technology level I|side products]]
|-
| [[switch-over to stiffer materials]]
| xxx
|-
| [[Technology level II|Level II]]
| [[side products of technology level II|side products]]
|-
| [[introduction of practically perfect vacuum]]
| xxx
|-
| [[Technology level III|Level III]]
| [[diamondoid metamaterials|basis for products]] [[further improvement at technology level III|advanced products]] [[most speculative potential applications| maybe-products]]
|}
[[File:Incremental path - MMCS Modular Molecular Composite Nanosystems.svg|500px|thumb|right|'''Very crude conceptual example of part of an MMCN.''' Red may represent proteins, Blue dots may represent binding sites/active sites. Dark grey blocks and grid of black may represent bigger structures (maybe [[structural DNA nanotechnology]]). Yellow way represent a gold contact on a chip for electrostatic interaction. White outline: A hinge. ... Moe details on page: [[Modular molecular composite nanosystem]].]]
Up: [[Pathways to advanced APM systems]] 
{{Wikitodo|Collage and add image of sequence of material classes. DNA/RNA, peptide/protein, artificial foldamer, spiroligomer, solvent gem (CeO2), vacuum gem (diamond)}}

The '''incremental path''' towards advanced APM systems describes a desired process of slowly increasing technological capabilities (tools making better tools) with avoidance of loss of a strong orientation towards the far term goal of the [[stiffness|stiff nanomachinery]] in [[In-vacuum gem-gum technology|gem-gum technology]].
This translates into starting off by using [[soft nanomachines]] to the fullest to get away from soft nanomachines ASAP.

The '''incremental path''' towards advanced APM systems is complementary to the [[direct path]].
The direct path to advanced APM systems in comparison describes a desired process of jumping to the advanced far term goal ASAP without significant detours. It is specifically focused on early usage of scanning probe microscopy for [[mechanosynthesis]] of diamond (or silicon) with throughput levels that are significant enough for the bootstrapping of a [[gem-gum factory]]. Following the [[direct path]] alone may be problematic.

* Sometimes a direction that on first inspection looks like it would lead fast to the goal actually does lead to it very slowly (or even not at all).
* Sometimes a direction that on first inspection looks as if it would lead only very slowly to the goal actually would lead to the goal fastest (which might still be slow).

This was the reason for the introduction of the distinction between direct path and incremental path. 
Details on the critics towards the direct path will be located on the "[[direct path]]"-page.

As historical note there is also the '''[[Feynman path]]''' but as-is in its unmodified version 
it is clearly not practical for several reasons 
elucidated on the dedicated page linked above.

== Dodge the trapdoors ==

'''Do not be fooled by the symmetry and scale of artificial self assembled molecule crystals!''' 
'''What matters most is [[termination control]].''' Especially on surfaces. 
This is a way better (but less visually conspicuous and stunning) measure for technological progress.

This is in analogy to metallic or mineral nanoparticles. 
Despite them having an atomically precise interior crystal structure they 
are not being considered atomically precise because their surface geometry is usually a combination of ...
* a statistical distribution and
* a predetermined shape (usually simple convex polyhedra, sometimes constrained to 2D sheets or even 1D rods).

Also note: Self assembly of an arc into a full circle 
can be considered as absence of termination control in angular direction 
as angles are constrained to 360° by nature already. 
When averting hitting the start when going around by 360° and thus going helical 
a lack of termination control becomes trivially obvious if present.

== High level map for the incremental path ==

[[File:APM-EarlyDevelopmentPaths.jpg|500px|thumb|right|Possible map for the incremental path. Left axis: [[technology levels]] Right axis see: [[convergent assembly comparison]] and [[hierarchical self-assembly]].]]

This map here plots:
* '''technology levels''' by use/control of material and means of assembly against ...
* '''assembly levels''' as in the degree to which [[hierarchical selfassembly]] has been achieved.

The starting-point of technological development/progression is the bottom-most asterisk-star. 
Green asterisks mark ares where some results have already been achieved.

=== The window of escape ===

The argument this map-diagram here is trying to justify is that there might be kind of a 
'''[[window of escape]]''' between the blockades in pathways of development (red, orange, and yellow) .

'''Blockades:'''
* The red, orange, and yellow stars tagged with "redundant" mean: Everything that positional assembly can do here selfassembly can do equally well (yellow) or better (red).
* The red, orange, and yellow stars tagged with "too big to diffuse" means: [[Thermally driven selfassembly]] faces increasing problems due larger parts moving slower.

Starting out to the left right away is both
* technically hardly possible (noncomposable primitive selfassemblies hardly can introduce positional assembly) and
* economically not at all motivatable (due to the [[positional assembly redundancy blockade]] mentioned above)

=== Degree of directness of the indirect path ===

Note that there is kind of a degree of directness in the indirect path. 
Directness in the sense of:
* How early/aggressively one attempts to take a hard tun left in the map-diagram.
* How early/aggressively one attempts to get to a [[positional assembly kinematic loop]] with proper [[separation of concerns]]
* How tightly one attempts to circumnavigate the '''[[positional assembly redundancy blockade]]'''.
* How far to run up against the '''[[diffusion slowdown blockade]]''' before taking the left-turn

Depending on the directness of the indirect path further sub approaches of the indirect path can be identified:
* Early-most leftward-turn: [[Catalysis construction kit approach]]
* Later leftward-turn: [[Printer approach]] (See: [[Foldamer printer]])
* Very late leftward-turn: [[Robo approach]] (See: [[Modular molecular composite nanosystem]] MMCN)

== System complexity – Climbing [[hierarchical self-assembly]] levels ==

Or more generally: Increasing essential system complexity by expanding on [[noncyclic termination contol]] capabilities.

=== Why necessarily early – fist climbing [[hierarchical self-assembly]] – then climbing [[technology levels]] ===

Scaling of essential system complexity before starting climbing the technology level ladder of increasingly better materials. 
is critically needed to gain sufficient [[separation of concerns]] to get engineerability of systems capable to do the climbing. 

Specifically scaling of essential system complexity is needed for [[expanding the kinematic loop]]. 

Trying to climb the technology level ladder to better materials early 
gives insufficient [[separation of concerns]] and sends one straight into [[fat finger problem]]. 

As a more concrete example (based on some personal startup company participation experience of this wikis author) 
Trying to gain side functions like small molecule binding (or catalysis) for for-profit sellable products too early. 
Is much like trying to climb the technology level ladder to better materials too early. 

This is the [[Functional block construction kit approach]] for binding 
or the even more challenging [[Catalysis construction kit approach]] for catalysis. 
This is not to confuse with conventional protein engineering for binding and/or catalysis, 
which is more like singe protein holistic systems that need AI or better even quantum computers for one off solutions. 

This is about trying to beat that with systematic engineerable cominatorics at a (too) early point 
still (too) low in the capabilities of 
– [[noncyclic termination control]] 
– [[essential system complexity]] 
– [[hierarchical self-assembly]] 

From the technology perspective (but not from the funding perspective) the best path seems 
– [[Robo approach (incremental path)]] … just a focus on scaling [[hierarchical self-assembly]] 
– [[Modular molecular composite nanosystem]] (MMCNs) … proteins joining in on [[noncyclic termination control]] 
– [[Foldamer printer approach (incremental path)]] as [[MMCN]] subsystems … finally getting to [[technology level climbig capability]] 

----
Side-note: The [[direct path]] has the opposite order. 
There the fist blocker/challenge is to get [[vacuum gemstone]] [[force applying mechanosynthesis]] 
of (eventually surface separable) 3D structures to work at all before any kind of scaling can begin. 
There the analog to [[hierarchical self assembly]] is called [[convergent positional assembly]]. 
Different names as the names emerged from different contexts. 

=== Quantification ===

A main early blocker/challenge along the incremental path is increasing the essential useful system complexity. 
This must not be confused with system size. 

It is easier but much less useful to 
(A) have really large periodic structures than to 
(B) have small ones with precisely controlled termination of self assembly. 
See page "[[Noncyclic termination control]]" which describes the principle of core importance. 
There is no essential system complexity beyond the base period. 

(A) has been done with both structural DNA and proteins {{wikitodo|reference examples}} 
(B) is still mostly reserved to structural DNA alone (as of 2026) 
(protein capsid like structures are merely cyclically terminating which in limited useful) 

Out of this reason in the critical regard of scaling of system complexity structural DNA seems ahead of proteins as of 2026. 
And that despite the big downside of DNA severely lacking stiffness compared to protein assemblies. 

There are at least two variants of proper [[noncyclic termination control]]: 
– Full voxel canvas adressability (like in [[structural DNA nanotechnology]]) 
– [[Algorithmic selv assembly]] 
These can serve as a basis for quantization of [[essential system complexity]] 
via entropy i.e. log of number of possible encodable states. 

{{wikitodo|Below are older subsection to better integrate.}}

=== State of progress of [[self assembly]] ===

A good place to look at is [[foldamer R&D]] specifically [[structural DNA nanotechnology]]. 
Several [[reached milestones in foldamer R&D|noteworthy milestones]] have already been reached.

=== Metrics for progress ===

'''Bad metrics for progress (superficially impressive):'''
* symmetry of self-assembles
* size of self-assemblies

'''Good metrics for progress (more subtle):'''
* degree of [[termination control]]
* stiffness originating from geometry of formed structures '''persistence length''' but in relative terms: [https://en.wikipedia.org/wiki/Persistence_length (wikipedia)]

=== Pushing against the limits of artificial self-assembly ===

'''What are the limitations to scaling up selfassembly?'''
* (A) more blocks taking more time to find each other
* (B) bigger blocks diffusing more slowly – The [[diffusion slowdown blockade]]
* (C) limits in implementability of sets of complementary interfaces where correct pair bind well but wrong pairs do not
* (D) wrong assembles not coming apart again – [[kinetic traps]]
* ... and certainly more

'''Counterstrategies:'''
* (1) using longer chain molecules to increase local [[effective concentration]] – so done in some forms of [[SDN]] and always present in single chain [[self folding]].
* (2) [[Squigglesembly]] – using [[iterative self-assembly]] to getaway with small sets of complementary interfaces
* (3) [[Circumsembly]] – using parallel selfassembly pathways to circumvent selfassembly errors (that may be tolerable)
* (4) algorithmic selfassembly ...
* (5) going for [[nonthermal self-assembly]] at larger scales
* ... and certainly more

== Base material – Climbing '''technology levels''' ==

The recently developed self assembling [[structural DNA nanotechnology]] and similar reliably designable foldamer structures might be a good starting point from [[technology level 0]]. 
* By [[Method of assembly#Loose stereotactic control with self assisted assembly|introducing robotic (more precisely stereotactic) control]] one could reach something like a "''block level precision robotic technology''" [[technology level I]] from there in a first step. 
* In a second step one could change to e.g. Pyrite or Silica [[technology level II]] as building material to increase structural stiffness, reduce vibration amplitudes and get thus more placing accuracy. 
* And finally in a third step one could switch from fluid phase to vacuum so that carbon and silicon can be assembled [[technology level III]].

This very crude temporal outline is by no means the only possible way to go to eventually arrive at [[positional atomic precision]]. 
There may be shortcuts or other paths. (See: [[Direct path]]) 

=== Literature ===

In Appendix II of the book "[[Radical Abundance]]" <ref name="RA">Radical Abundance: How a Revolution in Nanotechnology Will Change Civilization - by K. Eric Drexler</ref> it is proposed to go through several levels of APM technology to reach advanced ([[positional atomic precision]] & diamondoid) APM.
These levels will serve as a rough guideline for the structuring of this Wiki.
In "Nanosystems" <ref name="nasy">[[Nanoystems|Nanosystems: Molecular Machinery, Manufacturing, and Computation - by K. Eric Drexler]]</ref> technology stages are mentioned beginning with section 16.5.2. (written before the emergence of structural DNA nanotechnology). 

== Combining the best of different selfassembly technologies ==

[[File:Foldeamer-printer-stiffness-adapters.jpg|thumb|right|350px|'''Left:''' Adding small inserts that can be made stiffer in a lower stiffness background framework that can be made bigger. '''Right:''' Application of such a combining of self-assembly technologies technology demonstrated in the context of the [[foldamer printer]] concept.]]

Combining self assembly technologies could perhaps boost progress. 
See main page: '''[[Combining advantages of different selfassembly technologies]]'''

== Why positional control must be introduced before switchover to stiffest materials ==

For water synthesizable gemstone materials every crystal site looks exactly the same. Sites are featureless. 
So to add atoms (or [[AP]] groups thereof) to such a crystal at desired locations (and there only), 
the one single option available is [[positional assembly]]. 
The same holds for materials made out of many identical small organic molecules.

'''Details:'''
* [[switch-over to stiffer materials]] at some point is critically dependent on
* [[introduction of total positional control]] ...
... this is because stiffer materials cannot afford to '''encode the position of their constitute parts within the shape of their constitute parts''' which is what [[selfassembly]] mandates as fundamental prerequisite. 
Such '''position in shape encoding''' forces a minimum size of constitute parts and bonds weak enough to be suitable for thermal annealing averting [[kinetic traps]].

'''But what about Biomineralization?''' 
Does it not work without positional assembly? 

In biology biomineralization is likely not atomically precise. Bones & teeth (apatite or calcium-phosphate), shells (calcite or calcium-carbonate), diatoms (silica) all have no need to be atomically precise. Variously sized batches of phosphate, carbonate, silicate, sulfate, ions are probably just dumped in the general location to push the concentration locally to levels of where percipitation starts happening. 
{{todo|verify lack of [[AP]] in biomineralization}}

Yes, there is biomineral with atomic precision in the active center of some proteins, but this is usually just a few unit-cells. 
The protein provides a one-off specialized solution for this exact nano-crystal.

== Atomically precise positional control requires positional atomic precision ==

Attaining [[positional control]] mandates going from mere [[topological atomic precision]] (no errors in what links to what) to actual proper [[positional atomic precision]] (sub building block sized resolution – possibly subatomic resolution).

Weaker: Placing super-atomar blocks (small molecules, stiff compact de-novo-proteins) only requites block level precision. 
See: [[Lattice scaled stiffness]]

== Terminology ==

Since a [[nanofactory]] at the endpoint of an incremental path will inherit the capability of handling at least the materials of one generation before it, it may be better to call the products '''gemoid''' instead of '''diamondoid''' this terminology would make it more clear that gemstone like bio-minerals like quartz are included.

== Paths that are treated separately because its harder to find a concrete goal for them ==

Note that the behavior of mobile electrons at the nanoscale is not as easily predictable as the behavior of mechanics at the same scale thus there's less [[exploratory engineering]] for nanoelectronics than nanomechanics.
See:

* [[non mechanical technology path]] (including nanoelectronics)
* [[brownian technology path]]. (including things like synthetic biology)

['''Todo:''' improve article quality]

== Terminology for early systems ==

In [[Erics blog]] (2018-11-10) early foldamer based systems were referred to as: 
'''"modular molecular composite nanosystems (MMCNs)"''' 
One could also perhaps call them: 
'''"coarse-block atomically precise systems"''' 

== Related ==

* '''[[Technology levels]]''' (axis to the left in diagram)
* '''[[Hierarchical self-assembly]] levels''' (axis to the right in diagram)
* [[Pathways to advanced APM systems]]
* [[Pathway controversy]]
* [[Bridging the gaps]]
----
* [[Bootstrapping methods for productive nanosystems]]
* [[Bootstrapping atomic precision]]
----
* [[Automated research]]
----
* '''[[Thermally driven self assembly]]'''
* [[Termination control]]
----
* '''[[Foldamer technology stiffness nesting]]'''
* '''[[Stiffness focusing]]'''
----
* [[Microfluidics]] & [[Transflooder]] & [[Automated research]]

== External links ==

* Slides: "Toward Modular Molecular Composite Nanosystems" -- K. Eric Drexler, PhD -- U.C. Berkeley -- 26 April 2009 -- [http://metamodern.com/b/wp-content/uploads/2009/05/Molecular_Nanosystems_Berkeley.pdf]

== References ==

<references />

[[Category:General]]
[[Category:Disquisition]]

[[category:Incremental path]]

Incremental path

2026-10-09T07:48:59Z

Apm: /* Why necessarily early – fist climbing hierarchical self-assembly – then climbing technology levels */

{| class="wikitable" style="float:right; margin-left: 10px; text-align: center"
! colspan = "2"|Technology levels and steps of the incremental path
|-
| [[Technology level 0|Level 0]]
| [[side products of technology level 0|side products]]
|-
| [[Introduction of total positional control]]
| xxx
|-
| [[Technology level I|Level I]]
| [[side products of technology level I|side products]]
|-
| [[switch-over to stiffer materials]]
| xxx
|-
| [[Technology level II|Level II]]
| [[side products of technology level II|side products]]
|-
| [[introduction of practically perfect vacuum]]
| xxx
|-
| [[Technology level III|Level III]]
| [[diamondoid metamaterials|basis for products]] [[further improvement at technology level III|advanced products]] [[most speculative potential applications| maybe-products]]
|}
[[File:Incremental path - MMCS Modular Molecular Composite Nanosystems.svg|500px|thumb|right|'''Very crude conceptual example of part of an MMCN.''' Red may represent proteins, Blue dots may represent binding sites/active sites. Dark grey blocks and grid of black may represent bigger structures (maybe [[structural DNA nanotechnology]]). Yellow way represent a gold contact on a chip for electrostatic interaction. White outline: A hinge. ... Moe details on page: [[Modular molecular composite nanosystem]].]]
Up: [[Pathways to advanced APM systems]] 
{{Wikitodo|Collage and add image of sequence of material classes. DNA/RNA, peptide/protein, artificial foldamer, spiroligomer, solvent gem (CeO2), vacuum gem (diamond)}}

The '''incremental path''' towards advanced APM systems describes a desired process of slowly increasing technological capabilities (tools making better tools) with avoidance of loss of a strong orientation towards the far term goal of the [[stiffness|stiff nanomachinery]] in [[In-vacuum gem-gum technology|gem-gum technology]].
This translates into starting off by using [[soft nanomachines]] to the fullest to get away from soft nanomachines ASAP.

The '''incremental path''' towards advanced APM systems is complementary to the [[direct path]].
The direct path to advanced APM systems in comparison describes a desired process of jumping to the advanced far term goal ASAP without significant detours. It is specifically focused on early usage of scanning probe microscopy for [[mechanosynthesis]] of diamond (or silicon) with throughput levels that are significant enough for the bootstrapping of a [[gem-gum factory]]. Following the [[direct path]] alone may be problematic.

* Sometimes a direction that on first inspection looks like it would lead fast to the goal actually does lead to it very slowly (or even not at all).
* Sometimes a direction that on first inspection looks as if it would lead only very slowly to the goal actually would lead to the goal fastest (which might still be slow).

This was the reason for the introduction of the distinction between direct path and incremental path. 
Details on the critics towards the direct path will be located on the "[[direct path]]"-page.

As historical note there is also the '''[[Feynman path]]''' but as-is in its unmodified version 
it is clearly not practical for several reasons 
elucidated on the dedicated page linked above.

== Dodge the trapdoors ==

'''Do not be fooled by the symmetry and scale of artificial self assembled molecule crystals!''' 
'''What matters most is [[termination control]].''' Especially on surfaces. 
This is a way better (but less visually conspicuous and stunning) measure for technological progress.

This is in analogy to metallic or mineral nanoparticles. 
Despite them having an atomically precise interior crystal structure they 
are not being considered atomically precise because their surface geometry is usually a combination of ...
* a statistical distribution and
* a predetermined shape (usually simple convex polyhedra, sometimes constrained to 2D sheets or even 1D rods).

Also note: Self assembly of an arc into a full circle 
can be considered as absence of termination control in angular direction 
as angles are constrained to 360° by nature already. 
When averting hitting the start when going around by 360° and thus going helical 
a lack of termination control becomes trivially obvious if present.

== High level map for the incremental path ==

[[File:APM-EarlyDevelopmentPaths.jpg|500px|thumb|right|Possible map for the incremental path. Left axis: [[technology levels]] Right axis see: [[convergent assembly comparison]] and [[hierarchical self-assembly]].]]

This map here plots:
* '''technology levels''' by use/control of material and means of assembly against ...
* '''assembly levels''' as in the degree to which [[hierarchical selfassembly]] has been achieved.

The starting-point of technological development/progression is the bottom-most asterisk-star. 
Green asterisks mark ares where some results have already been achieved.

=== The window of escape ===

The argument this map-diagram here is trying to justify is that there might be kind of a 
'''[[window of escape]]''' between the blockades in pathways of development (red, orange, and yellow) .

'''Blockades:'''
* The red, orange, and yellow stars tagged with "redundant" mean: Everything that positional assembly can do here selfassembly can do equally well (yellow) or better (red).
* The red, orange, and yellow stars tagged with "too big to diffuse" means: [[Thermally driven selfassembly]] faces increasing problems due larger parts moving slower.

Starting out to the left right away is both
* technically hardly possible (noncomposable primitive selfassemblies hardly can introduce positional assembly) and
* economically not at all motivatable (due to the [[positional assembly redundancy blockade]] mentioned above)

=== Degree of directness of the indirect path ===

Note that there is kind of a degree of directness in the indirect path. 
Directness in the sense of:
* How early/aggressively one attempts to take a hard tun left in the map-diagram.
* How early/aggressively one attempts to get to a [[positional assembly kinematic loop]] with proper [[separation of concerns]]
* How tightly one attempts to circumnavigate the '''[[positional assembly redundancy blockade]]'''.
* How far to run up against the '''[[diffusion slowdown blockade]]''' before taking the left-turn

Depending on the directness of the indirect path further sub approaches of the indirect path can be identified:
* Early-most leftward-turn: [[Catalysis construction kit approach]]
* Later leftward-turn: [[Printer approach]] (See: [[Foldamer printer]])
* Very late leftward-turn: [[Robo approach]] (See: [[Modular molecular composite nanosystem]] MMCN)

== System complexity – Climbing [[hierarchical self-assembly]] levels ==

Or more generally: Increasing essential system complexity by expanding on [[noncyclic termination contol]] capabilities.

=== Why necessarily early – fist climbing [[hierarchical self-assembly]] – then climbing [[technology levels]] ===

Scaling of essential system complexity before starting climbing the technology level ladder of increasingly better materials. 
is critically needed to gain sufficient [[separation of concerns]] to get engineerability of systems capable to do the climbing. 

Specifically scaling of essential system complexity is needed for [[expanding the kinematic loop]]. 

Trying to climb the technology level ladder to better materials early 
gives insufficient [[separation of concerns]] and sends one straight into [[fat finger problem]]. 

As a more concrete example (based on some personal startup company participation experience of this wikis author) 
Trying to gain side functions like small molecule binding (or catalysis) for for-profit sellable products too early. 
Is much like trying to climb the technology level ladder to better materials too early. 

This is the [[Functional block construction kit approach]] for binding 
or the even more challenging [[Catalysis construction kit approach]] for catalysis. 
This is not to confuse with conventional protein engineering for binding and/or catalysis, 
which is more like singe protein holistic systems that need AI or better even quantum computers for one off solutions. 

This is about trying to beat that with systematic engineerable cominatorics at a (too) early point 
still (too) low in the capabilities of 
– [[noncyclic termination control]] 
– [[essential system complexity]] 
– [[hierarchical self-assembly]] 

From the technology perspective (but not from the funding perspective) the best path seems 
– [[Robo approach (incremental path)]] … just a focus on scaling [[hierarchical assembly]] 
– [[Modular molecular composite nanosystem]] (MMCNs) … proteins joining in on [[noncyclic termination control]] 
– [[Foldamer printer approach (incremental path)]] as [[MMCN]] subsystems … finally getting to [[technology level climbig capability]] 

----
Side-note: The [[direct path]] has the opposite order. 
There the fist blocker/challenge is to get [[vacuum gemstone]] [[force applying mechanosynthesis]] 
of (eventually surface separable) 3D structures to work at all before any kind of scaling can begin. 
There the analog to [[hierarchical self assembly]] is called [[convergent positional assembly]]. 
Different names as the names emerged from different contexts. 

=== Quantification ===

A main early blocker/challenge along the incremental path is increasing the essential useful system complexity. 
This must not be confused with system size. 

It is easier but much less useful to 
(A) have really large periodic structures than to 
(B) have small ones with precisely controlled termination of self assembly. 
See page "[[Noncyclic termination control]]" which describes the principle of core importance. 
There is no essential system complexity beyond the base period. 

(A) has been done with both structural DNA and proteins {{wikitodo|reference examples}} 
(B) is still mostly reserved to structural DNA alone (as of 2026) 
(protein capsid like structures are merely cyclically terminating which in limited useful) 

Out of this reason in the critical regard of scaling of system complexity structural DNA seems ahead of proteins as of 2026. 
And that despite the big downside of DNA severely lacking stiffness compared to protein assemblies. 

There are at least two variants of proper [[noncyclic termination control]]: 
– Full voxel canvas adressability (like in [[structural DNA nanotechnology]]) 
– [[Algorithmic selv assembly]] 
These can serve as a basis for quantization of [[essential system complexity]] 
via entropy i.e. log of number of possible encodable states. 

{{wikitodo|Below are older subsection to better integrate.}}

=== State of progress of [[self assembly]] ===

A good place to look at is [[foldamer R&D]] specifically [[structural DNA nanotechnology]]. 
Several [[reached milestones in foldamer R&D|noteworthy milestones]] have already been reached.

=== Metrics for progress ===

'''Bad metrics for progress (superficially impressive):'''
* symmetry of self-assembles
* size of self-assemblies

'''Good metrics for progress (more subtle):'''
* degree of [[termination control]]
* stiffness originating from geometry of formed structures '''persistence length''' but in relative terms: [https://en.wikipedia.org/wiki/Persistence_length (wikipedia)]

=== Pushing against the limits of artificial self-assembly ===

'''What are the limitations to scaling up selfassembly?'''
* (A) more blocks taking more time to find each other
* (B) bigger blocks diffusing more slowly – The [[diffusion slowdown blockade]]
* (C) limits in implementability of sets of complementary interfaces where correct pair bind well but wrong pairs do not
* (D) wrong assembles not coming apart again – [[kinetic traps]]
* ... and certainly more

'''Counterstrategies:'''
* (1) using longer chain molecules to increase local [[effective concentration]] – so done in some forms of [[SDN]] and always present in single chain [[self folding]].
* (2) [[Squigglesembly]] – using [[iterative self-assembly]] to getaway with small sets of complementary interfaces
* (3) [[Circumsembly]] – using parallel selfassembly pathways to circumvent selfassembly errors (that may be tolerable)
* (4) algorithmic selfassembly ...
* (5) going for [[nonthermal self-assembly]] at larger scales
* ... and certainly more

== Base material – Climbing '''technology levels''' ==

The recently developed self assembling [[structural DNA nanotechnology]] and similar reliably designable foldamer structures might be a good starting point from [[technology level 0]]. 
* By [[Method of assembly#Loose stereotactic control with self assisted assembly|introducing robotic (more precisely stereotactic) control]] one could reach something like a "''block level precision robotic technology''" [[technology level I]] from there in a first step. 
* In a second step one could change to e.g. Pyrite or Silica [[technology level II]] as building material to increase structural stiffness, reduce vibration amplitudes and get thus more placing accuracy. 
* And finally in a third step one could switch from fluid phase to vacuum so that carbon and silicon can be assembled [[technology level III]].

This very crude temporal outline is by no means the only possible way to go to eventually arrive at [[positional atomic precision]]. 
There may be shortcuts or other paths. (See: [[Direct path]]) 

=== Literature ===

In Appendix II of the book "[[Radical Abundance]]" <ref name="RA">Radical Abundance: How a Revolution in Nanotechnology Will Change Civilization - by K. Eric Drexler</ref> it is proposed to go through several levels of APM technology to reach advanced ([[positional atomic precision]] & diamondoid) APM.
These levels will serve as a rough guideline for the structuring of this Wiki.
In "Nanosystems" <ref name="nasy">[[Nanoystems|Nanosystems: Molecular Machinery, Manufacturing, and Computation - by K. Eric Drexler]]</ref> technology stages are mentioned beginning with section 16.5.2. (written before the emergence of structural DNA nanotechnology). 

== Combining the best of different selfassembly technologies ==

[[File:Foldeamer-printer-stiffness-adapters.jpg|thumb|right|350px|'''Left:''' Adding small inserts that can be made stiffer in a lower stiffness background framework that can be made bigger. '''Right:''' Application of such a combining of self-assembly technologies technology demonstrated in the context of the [[foldamer printer]] concept.]]

Combining self assembly technologies could perhaps boost progress. 
See main page: '''[[Combining advantages of different selfassembly technologies]]'''

== Why positional control must be introduced before switchover to stiffest materials ==

For water synthesizable gemstone materials every crystal site looks exactly the same. Sites are featureless. 
So to add atoms (or [[AP]] groups thereof) to such a crystal at desired locations (and there only), 
the one single option available is [[positional assembly]]. 
The same holds for materials made out of many identical small organic molecules.

'''Details:'''
* [[switch-over to stiffer materials]] at some point is critically dependent on
* [[introduction of total positional control]] ...
... this is because stiffer materials cannot afford to '''encode the position of their constitute parts within the shape of their constitute parts''' which is what [[selfassembly]] mandates as fundamental prerequisite. 
Such '''position in shape encoding''' forces a minimum size of constitute parts and bonds weak enough to be suitable for thermal annealing averting [[kinetic traps]].

'''But what about Biomineralization?''' 
Does it not work without positional assembly? 

In biology biomineralization is likely not atomically precise. Bones & teeth (apatite or calcium-phosphate), shells (calcite or calcium-carbonate), diatoms (silica) all have no need to be atomically precise. Variously sized batches of phosphate, carbonate, silicate, sulfate, ions are probably just dumped in the general location to push the concentration locally to levels of where percipitation starts happening. 
{{todo|verify lack of [[AP]] in biomineralization}}

Yes, there is biomineral with atomic precision in the active center of some proteins, but this is usually just a few unit-cells. 
The protein provides a one-off specialized solution for this exact nano-crystal.

== Atomically precise positional control requires positional atomic precision ==

Attaining [[positional control]] mandates going from mere [[topological atomic precision]] (no errors in what links to what) to actual proper [[positional atomic precision]] (sub building block sized resolution – possibly subatomic resolution).

Weaker: Placing super-atomar blocks (small molecules, stiff compact de-novo-proteins) only requites block level precision. 
See: [[Lattice scaled stiffness]]

== Terminology ==

Since a [[nanofactory]] at the endpoint of an incremental path will inherit the capability of handling at least the materials of one generation before it, it may be better to call the products '''gemoid''' instead of '''diamondoid''' this terminology would make it more clear that gemstone like bio-minerals like quartz are included.

== Paths that are treated separately because its harder to find a concrete goal for them ==

Note that the behavior of mobile electrons at the nanoscale is not as easily predictable as the behavior of mechanics at the same scale thus there's less [[exploratory engineering]] for nanoelectronics than nanomechanics.
See:

* [[non mechanical technology path]] (including nanoelectronics)
* [[brownian technology path]]. (including things like synthetic biology)

['''Todo:''' improve article quality]

== Terminology for early systems ==

In [[Erics blog]] (2018-11-10) early foldamer based systems were referred to as: 
'''"modular molecular composite nanosystems (MMCNs)"''' 
One could also perhaps call them: 
'''"coarse-block atomically precise systems"''' 

== Related ==

* '''[[Technology levels]]''' (axis to the left in diagram)
* '''[[Hierarchical self-assembly]] levels''' (axis to the right in diagram)
* [[Pathways to advanced APM systems]]
* [[Pathway controversy]]
* [[Bridging the gaps]]
----
* [[Bootstrapping methods for productive nanosystems]]
* [[Bootstrapping atomic precision]]
----
* [[Automated research]]
----
* '''[[Thermally driven self assembly]]'''
* [[Termination control]]
----
* '''[[Foldamer technology stiffness nesting]]'''
* '''[[Stiffness focusing]]'''
----
* [[Microfluidics]] & [[Transflooder]] & [[Automated research]]

== External links ==

* Slides: "Toward Modular Molecular Composite Nanosystems" -- K. Eric Drexler, PhD -- U.C. Berkeley -- 26 April 2009 -- [http://metamodern.com/b/wp-content/uploads/2009/05/Molecular_Nanosystems_Berkeley.pdf]

== References ==

<references />

[[Category:General]]
[[Category:Disquisition]]

[[category:Incremental path]]

Incremental path

2026-10-09T07:48:39Z

Apm: /* Why necessarily early – fist climbing hierarchical self-assembly – then climbing technology levels */

{| class="wikitable" style="float:right; margin-left: 10px; text-align: center"
! colspan = "2"|Technology levels and steps of the incremental path
|-
| [[Technology level 0|Level 0]]
| [[side products of technology level 0|side products]]
|-
| [[Introduction of total positional control]]
| xxx
|-
| [[Technology level I|Level I]]
| [[side products of technology level I|side products]]
|-
| [[switch-over to stiffer materials]]
| xxx
|-
| [[Technology level II|Level II]]
| [[side products of technology level II|side products]]
|-
| [[introduction of practically perfect vacuum]]
| xxx
|-
| [[Technology level III|Level III]]
| [[diamondoid metamaterials|basis for products]] [[further improvement at technology level III|advanced products]] [[most speculative potential applications| maybe-products]]
|}
[[File:Incremental path - MMCS Modular Molecular Composite Nanosystems.svg|500px|thumb|right|'''Very crude conceptual example of part of an MMCN.''' Red may represent proteins, Blue dots may represent binding sites/active sites. Dark grey blocks and grid of black may represent bigger structures (maybe [[structural DNA nanotechnology]]). Yellow way represent a gold contact on a chip for electrostatic interaction. White outline: A hinge. ... Moe details on page: [[Modular molecular composite nanosystem]].]]
Up: [[Pathways to advanced APM systems]] 
{{Wikitodo|Collage and add image of sequence of material classes. DNA/RNA, peptide/protein, artificial foldamer, spiroligomer, solvent gem (CeO2), vacuum gem (diamond)}}

The '''incremental path''' towards advanced APM systems describes a desired process of slowly increasing technological capabilities (tools making better tools) with avoidance of loss of a strong orientation towards the far term goal of the [[stiffness|stiff nanomachinery]] in [[In-vacuum gem-gum technology|gem-gum technology]].
This translates into starting off by using [[soft nanomachines]] to the fullest to get away from soft nanomachines ASAP.

The '''incremental path''' towards advanced APM systems is complementary to the [[direct path]].
The direct path to advanced APM systems in comparison describes a desired process of jumping to the advanced far term goal ASAP without significant detours. It is specifically focused on early usage of scanning probe microscopy for [[mechanosynthesis]] of diamond (or silicon) with throughput levels that are significant enough for the bootstrapping of a [[gem-gum factory]]. Following the [[direct path]] alone may be problematic.

* Sometimes a direction that on first inspection looks like it would lead fast to the goal actually does lead to it very slowly (or even not at all).
* Sometimes a direction that on first inspection looks as if it would lead only very slowly to the goal actually would lead to the goal fastest (which might still be slow).

This was the reason for the introduction of the distinction between direct path and incremental path. 
Details on the critics towards the direct path will be located on the "[[direct path]]"-page.

As historical note there is also the '''[[Feynman path]]''' but as-is in its unmodified version 
it is clearly not practical for several reasons 
elucidated on the dedicated page linked above.

== Dodge the trapdoors ==

'''Do not be fooled by the symmetry and scale of artificial self assembled molecule crystals!''' 
'''What matters most is [[termination control]].''' Especially on surfaces. 
This is a way better (but less visually conspicuous and stunning) measure for technological progress.

This is in analogy to metallic or mineral nanoparticles. 
Despite them having an atomically precise interior crystal structure they 
are not being considered atomically precise because their surface geometry is usually a combination of ...
* a statistical distribution and
* a predetermined shape (usually simple convex polyhedra, sometimes constrained to 2D sheets or even 1D rods).

Also note: Self assembly of an arc into a full circle 
can be considered as absence of termination control in angular direction 
as angles are constrained to 360° by nature already. 
When averting hitting the start when going around by 360° and thus going helical 
a lack of termination control becomes trivially obvious if present.

== High level map for the incremental path ==

[[File:APM-EarlyDevelopmentPaths.jpg|500px|thumb|right|Possible map for the incremental path. Left axis: [[technology levels]] Right axis see: [[convergent assembly comparison]] and [[hierarchical self-assembly]].]]

This map here plots:
* '''technology levels''' by use/control of material and means of assembly against ...
* '''assembly levels''' as in the degree to which [[hierarchical selfassembly]] has been achieved.

The starting-point of technological development/progression is the bottom-most asterisk-star. 
Green asterisks mark ares where some results have already been achieved.

=== The window of escape ===

The argument this map-diagram here is trying to justify is that there might be kind of a 
'''[[window of escape]]''' between the blockades in pathways of development (red, orange, and yellow) .

'''Blockades:'''
* The red, orange, and yellow stars tagged with "redundant" mean: Everything that positional assembly can do here selfassembly can do equally well (yellow) or better (red).
* The red, orange, and yellow stars tagged with "too big to diffuse" means: [[Thermally driven selfassembly]] faces increasing problems due larger parts moving slower.

Starting out to the left right away is both
* technically hardly possible (noncomposable primitive selfassemblies hardly can introduce positional assembly) and
* economically not at all motivatable (due to the [[positional assembly redundancy blockade]] mentioned above)

=== Degree of directness of the indirect path ===

Note that there is kind of a degree of directness in the indirect path. 
Directness in the sense of:
* How early/aggressively one attempts to take a hard tun left in the map-diagram.
* How early/aggressively one attempts to get to a [[positional assembly kinematic loop]] with proper [[separation of concerns]]
* How tightly one attempts to circumnavigate the '''[[positional assembly redundancy blockade]]'''.
* How far to run up against the '''[[diffusion slowdown blockade]]''' before taking the left-turn

Depending on the directness of the indirect path further sub approaches of the indirect path can be identified:
* Early-most leftward-turn: [[Catalysis construction kit approach]]
* Later leftward-turn: [[Printer approach]] (See: [[Foldamer printer]])
* Very late leftward-turn: [[Robo approach]] (See: [[Modular molecular composite nanosystem]] MMCN)

== System complexity – Climbing [[hierarchical self-assembly]] levels ==

Or more generally: Increasing essential system complexity by expanding on [[noncyclic termination contol]] capabilities.

=== Why necessarily early – fist climbing [[hierarchical self-assembly]] – then climbing [[technology levels]] ===

Scaling of essential system complexity before starting climbing the technology level ladder of increasingly better materials. 
is critically needed to gain sufficient [[separation of concerns]] to get engineerability of systems capable to do the climbing. 

Specifically scaling of essential system complexity is needed for [[expanding the kinematic loop]]. 

Trying to climb the technology level ladder to better materials early 
gives insufficient [[separation of concerns]] and sends one straight into [[fat finger problem]]. 

As a more concrete example (based on some personal startup company participation experience of this wikis author) 
Trying to gain side functions like small molecule binding (or catalysis) for for-profit sellable products too early. 
Is much like trying to climb the technology level ladder to better materials too early. 

This is the [[Functional block construction kit approach]] for binding 
or the even more challenging [[Catalysis construction kit approach]] for catalysis. 
This is not to confuse with conventional protein engineering for binding and/or catalysis, 
which is more like singe protein holistic systems that need AI or better even quantum computers for one off solutions. 

This is about trying to beat that with systematic engineerable cominatorics at a (too) early point 
still (too) low in the capabilities of 
– [[noncyclic termination control]] 
– [[essential system complexity]] 
– [[hierarchical assembly]] 

From the technology perspective (but not from the funding perspective) the best path seems 
– [[Robo approach (incremental path)]] … just a focus on scaling [[hierarchical assembly]] 
– [[Modular molecular composite nanosystem]] (MMCNs) … proteins joining in on [[noncyclic termination control]] 
– [[Foldamer printer approach (incremental path)]] as [[MMCN]] subsystems … finally getting to [[technology level climbig capability]] 

----
Side-note: The [[direct path]] has the opposite order. 
There the fist blocker/challenge is to get [[vacuum gemstone]] [[force applying mechanosynthesis]] 
of (eventually surface separable) 3D structures to work at all before any kind of scaling can begin. 
There the analog to [[hierarchical self assembly]] is called [[convergent positional assembly]]. 
Different names as the names emerged from different contexts. 

=== Quantification ===

A main early blocker/challenge along the incremental path is increasing the essential useful system complexity. 
This must not be confused with system size. 

It is easier but much less useful to 
(A) have really large periodic structures than to 
(B) have small ones with precisely controlled termination of self assembly. 
See page "[[Noncyclic termination control]]" which describes the principle of core importance. 
There is no essential system complexity beyond the base period. 

(A) has been done with both structural DNA and proteins {{wikitodo|reference examples}} 
(B) is still mostly reserved to structural DNA alone (as of 2026) 
(protein capsid like structures are merely cyclically terminating which in limited useful) 

Out of this reason in the critical regard of scaling of system complexity structural DNA seems ahead of proteins as of 2026. 
And that despite the big downside of DNA severely lacking stiffness compared to protein assemblies. 

There are at least two variants of proper [[noncyclic termination control]]: 
– Full voxel canvas adressability (like in [[structural DNA nanotechnology]]) 
– [[Algorithmic selv assembly]] 
These can serve as a basis for quantization of [[essential system complexity]] 
via entropy i.e. log of number of possible encodable states. 

{{wikitodo|Below are older subsection to better integrate.}}

=== State of progress of [[self assembly]] ===

A good place to look at is [[foldamer R&D]] specifically [[structural DNA nanotechnology]]. 
Several [[reached milestones in foldamer R&D|noteworthy milestones]] have already been reached.

=== Metrics for progress ===

'''Bad metrics for progress (superficially impressive):'''
* symmetry of self-assembles
* size of self-assemblies

'''Good metrics for progress (more subtle):'''
* degree of [[termination control]]
* stiffness originating from geometry of formed structures '''persistence length''' but in relative terms: [https://en.wikipedia.org/wiki/Persistence_length (wikipedia)]

=== Pushing against the limits of artificial self-assembly ===

'''What are the limitations to scaling up selfassembly?'''
* (A) more blocks taking more time to find each other
* (B) bigger blocks diffusing more slowly – The [[diffusion slowdown blockade]]
* (C) limits in implementability of sets of complementary interfaces where correct pair bind well but wrong pairs do not
* (D) wrong assembles not coming apart again – [[kinetic traps]]
* ... and certainly more

'''Counterstrategies:'''
* (1) using longer chain molecules to increase local [[effective concentration]] – so done in some forms of [[SDN]] and always present in single chain [[self folding]].
* (2) [[Squigglesembly]] – using [[iterative self-assembly]] to getaway with small sets of complementary interfaces
* (3) [[Circumsembly]] – using parallel selfassembly pathways to circumvent selfassembly errors (that may be tolerable)
* (4) algorithmic selfassembly ...
* (5) going for [[nonthermal self-assembly]] at larger scales
* ... and certainly more

== Base material – Climbing '''technology levels''' ==

The recently developed self assembling [[structural DNA nanotechnology]] and similar reliably designable foldamer structures might be a good starting point from [[technology level 0]]. 
* By [[Method of assembly#Loose stereotactic control with self assisted assembly|introducing robotic (more precisely stereotactic) control]] one could reach something like a "''block level precision robotic technology''" [[technology level I]] from there in a first step. 
* In a second step one could change to e.g. Pyrite or Silica [[technology level II]] as building material to increase structural stiffness, reduce vibration amplitudes and get thus more placing accuracy. 
* And finally in a third step one could switch from fluid phase to vacuum so that carbon and silicon can be assembled [[technology level III]].

This very crude temporal outline is by no means the only possible way to go to eventually arrive at [[positional atomic precision]]. 
There may be shortcuts or other paths. (See: [[Direct path]]) 

=== Literature ===

In Appendix II of the book "[[Radical Abundance]]" <ref name="RA">Radical Abundance: How a Revolution in Nanotechnology Will Change Civilization - by K. Eric Drexler</ref> it is proposed to go through several levels of APM technology to reach advanced ([[positional atomic precision]] & diamondoid) APM.
These levels will serve as a rough guideline for the structuring of this Wiki.
In "Nanosystems" <ref name="nasy">[[Nanoystems|Nanosystems: Molecular Machinery, Manufacturing, and Computation - by K. Eric Drexler]]</ref> technology stages are mentioned beginning with section 16.5.2. (written before the emergence of structural DNA nanotechnology). 

== Combining the best of different selfassembly technologies ==

[[File:Foldeamer-printer-stiffness-adapters.jpg|thumb|right|350px|'''Left:''' Adding small inserts that can be made stiffer in a lower stiffness background framework that can be made bigger. '''Right:''' Application of such a combining of self-assembly technologies technology demonstrated in the context of the [[foldamer printer]] concept.]]

Combining self assembly technologies could perhaps boost progress. 
See main page: '''[[Combining advantages of different selfassembly technologies]]'''

== Why positional control must be introduced before switchover to stiffest materials ==

For water synthesizable gemstone materials every crystal site looks exactly the same. Sites are featureless. 
So to add atoms (or [[AP]] groups thereof) to such a crystal at desired locations (and there only), 
the one single option available is [[positional assembly]]. 
The same holds for materials made out of many identical small organic molecules.

'''Details:'''
* [[switch-over to stiffer materials]] at some point is critically dependent on
* [[introduction of total positional control]] ...
... this is because stiffer materials cannot afford to '''encode the position of their constitute parts within the shape of their constitute parts''' which is what [[selfassembly]] mandates as fundamental prerequisite. 
Such '''position in shape encoding''' forces a minimum size of constitute parts and bonds weak enough to be suitable for thermal annealing averting [[kinetic traps]].

'''But what about Biomineralization?''' 
Does it not work without positional assembly? 

In biology biomineralization is likely not atomically precise. Bones & teeth (apatite or calcium-phosphate), shells (calcite or calcium-carbonate), diatoms (silica) all have no need to be atomically precise. Variously sized batches of phosphate, carbonate, silicate, sulfate, ions are probably just dumped in the general location to push the concentration locally to levels of where percipitation starts happening. 
{{todo|verify lack of [[AP]] in biomineralization}}

Yes, there is biomineral with atomic precision in the active center of some proteins, but this is usually just a few unit-cells. 
The protein provides a one-off specialized solution for this exact nano-crystal.

== Atomically precise positional control requires positional atomic precision ==

Attaining [[positional control]] mandates going from mere [[topological atomic precision]] (no errors in what links to what) to actual proper [[positional atomic precision]] (sub building block sized resolution – possibly subatomic resolution).

Weaker: Placing super-atomar blocks (small molecules, stiff compact de-novo-proteins) only requites block level precision. 
See: [[Lattice scaled stiffness]]

== Terminology ==

Since a [[nanofactory]] at the endpoint of an incremental path will inherit the capability of handling at least the materials of one generation before it, it may be better to call the products '''gemoid''' instead of '''diamondoid''' this terminology would make it more clear that gemstone like bio-minerals like quartz are included.

== Paths that are treated separately because its harder to find a concrete goal for them ==

Note that the behavior of mobile electrons at the nanoscale is not as easily predictable as the behavior of mechanics at the same scale thus there's less [[exploratory engineering]] for nanoelectronics than nanomechanics.
See:

* [[non mechanical technology path]] (including nanoelectronics)
* [[brownian technology path]]. (including things like synthetic biology)

['''Todo:''' improve article quality]

== Terminology for early systems ==

In [[Erics blog]] (2018-11-10) early foldamer based systems were referred to as: 
'''"modular molecular composite nanosystems (MMCNs)"''' 
One could also perhaps call them: 
'''"coarse-block atomically precise systems"''' 

== Related ==

* '''[[Technology levels]]''' (axis to the left in diagram)
* '''[[Hierarchical self-assembly]] levels''' (axis to the right in diagram)
* [[Pathways to advanced APM systems]]
* [[Pathway controversy]]
* [[Bridging the gaps]]
----
* [[Bootstrapping methods for productive nanosystems]]
* [[Bootstrapping atomic precision]]
----
* [[Automated research]]
----
* '''[[Thermally driven self assembly]]'''
* [[Termination control]]
----
* '''[[Foldamer technology stiffness nesting]]'''
* '''[[Stiffness focusing]]'''
----
* [[Microfluidics]] & [[Transflooder]] & [[Automated research]]

== External links ==

* Slides: "Toward Modular Molecular Composite Nanosystems" -- K. Eric Drexler, PhD -- U.C. Berkeley -- 26 April 2009 -- [http://metamodern.com/b/wp-content/uploads/2009/05/Molecular_Nanosystems_Berkeley.pdf]

== References ==

<references />

[[Category:General]]
[[Category:Disquisition]]

[[category:Incremental path]]

Incremental path

2026-10-09T07:48:06Z

Apm: /* System complexity – Climbing hierarchical self-assembly levels */

{| class="wikitable" style="float:right; margin-left: 10px; text-align: center"
! colspan = "2"|Technology levels and steps of the incremental path
|-
| [[Technology level 0|Level 0]]
| [[side products of technology level 0|side products]]
|-
| [[Introduction of total positional control]]
| xxx
|-
| [[Technology level I|Level I]]
| [[side products of technology level I|side products]]
|-
| [[switch-over to stiffer materials]]
| xxx
|-
| [[Technology level II|Level II]]
| [[side products of technology level II|side products]]
|-
| [[introduction of practically perfect vacuum]]
| xxx
|-
| [[Technology level III|Level III]]
| [[diamondoid metamaterials|basis for products]] [[further improvement at technology level III|advanced products]] [[most speculative potential applications| maybe-products]]
|}
[[File:Incremental path - MMCS Modular Molecular Composite Nanosystems.svg|500px|thumb|right|'''Very crude conceptual example of part of an MMCN.''' Red may represent proteins, Blue dots may represent binding sites/active sites. Dark grey blocks and grid of black may represent bigger structures (maybe [[structural DNA nanotechnology]]). Yellow way represent a gold contact on a chip for electrostatic interaction. White outline: A hinge. ... Moe details on page: [[Modular molecular composite nanosystem]].]]
Up: [[Pathways to advanced APM systems]] 
{{Wikitodo|Collage and add image of sequence of material classes. DNA/RNA, peptide/protein, artificial foldamer, spiroligomer, solvent gem (CeO2), vacuum gem (diamond)}}

The '''incremental path''' towards advanced APM systems describes a desired process of slowly increasing technological capabilities (tools making better tools) with avoidance of loss of a strong orientation towards the far term goal of the [[stiffness|stiff nanomachinery]] in [[In-vacuum gem-gum technology|gem-gum technology]].
This translates into starting off by using [[soft nanomachines]] to the fullest to get away from soft nanomachines ASAP.

The '''incremental path''' towards advanced APM systems is complementary to the [[direct path]].
The direct path to advanced APM systems in comparison describes a desired process of jumping to the advanced far term goal ASAP without significant detours. It is specifically focused on early usage of scanning probe microscopy for [[mechanosynthesis]] of diamond (or silicon) with throughput levels that are significant enough for the bootstrapping of a [[gem-gum factory]]. Following the [[direct path]] alone may be problematic.

* Sometimes a direction that on first inspection looks like it would lead fast to the goal actually does lead to it very slowly (or even not at all).
* Sometimes a direction that on first inspection looks as if it would lead only very slowly to the goal actually would lead to the goal fastest (which might still be slow).

This was the reason for the introduction of the distinction between direct path and incremental path. 
Details on the critics towards the direct path will be located on the "[[direct path]]"-page.

As historical note there is also the '''[[Feynman path]]''' but as-is in its unmodified version 
it is clearly not practical for several reasons 
elucidated on the dedicated page linked above.

== Dodge the trapdoors ==

'''Do not be fooled by the symmetry and scale of artificial self assembled molecule crystals!''' 
'''What matters most is [[termination control]].''' Especially on surfaces. 
This is a way better (but less visually conspicuous and stunning) measure for technological progress.

This is in analogy to metallic or mineral nanoparticles. 
Despite them having an atomically precise interior crystal structure they 
are not being considered atomically precise because their surface geometry is usually a combination of ...
* a statistical distribution and
* a predetermined shape (usually simple convex polyhedra, sometimes constrained to 2D sheets or even 1D rods).

Also note: Self assembly of an arc into a full circle 
can be considered as absence of termination control in angular direction 
as angles are constrained to 360° by nature already. 
When averting hitting the start when going around by 360° and thus going helical 
a lack of termination control becomes trivially obvious if present.

== High level map for the incremental path ==

[[File:APM-EarlyDevelopmentPaths.jpg|500px|thumb|right|Possible map for the incremental path. Left axis: [[technology levels]] Right axis see: [[convergent assembly comparison]] and [[hierarchical self-assembly]].]]

This map here plots:
* '''technology levels''' by use/control of material and means of assembly against ...
* '''assembly levels''' as in the degree to which [[hierarchical selfassembly]] has been achieved.

The starting-point of technological development/progression is the bottom-most asterisk-star. 
Green asterisks mark ares where some results have already been achieved.

=== The window of escape ===

The argument this map-diagram here is trying to justify is that there might be kind of a 
'''[[window of escape]]''' between the blockades in pathways of development (red, orange, and yellow) .

'''Blockades:'''
* The red, orange, and yellow stars tagged with "redundant" mean: Everything that positional assembly can do here selfassembly can do equally well (yellow) or better (red).
* The red, orange, and yellow stars tagged with "too big to diffuse" means: [[Thermally driven selfassembly]] faces increasing problems due larger parts moving slower.

Starting out to the left right away is both
* technically hardly possible (noncomposable primitive selfassemblies hardly can introduce positional assembly) and
* economically not at all motivatable (due to the [[positional assembly redundancy blockade]] mentioned above)

=== Degree of directness of the indirect path ===

Note that there is kind of a degree of directness in the indirect path. 
Directness in the sense of:
* How early/aggressively one attempts to take a hard tun left in the map-diagram.
* How early/aggressively one attempts to get to a [[positional assembly kinematic loop]] with proper [[separation of concerns]]
* How tightly one attempts to circumnavigate the '''[[positional assembly redundancy blockade]]'''.
* How far to run up against the '''[[diffusion slowdown blockade]]''' before taking the left-turn

Depending on the directness of the indirect path further sub approaches of the indirect path can be identified:
* Early-most leftward-turn: [[Catalysis construction kit approach]]
* Later leftward-turn: [[Printer approach]] (See: [[Foldamer printer]])
* Very late leftward-turn: [[Robo approach]] (See: [[Modular molecular composite nanosystem]] MMCN)

== System complexity – Climbing [[hierarchical self-assembly]] levels ==

Or more generally: Increasing essential system complexity by expanding on [[noncyclic termination contol]] capabilities.

=== Why necessarily early – fist climbing [[hierarchical self-assembly]] – then climbing [[technology levels]] ===

Scaling of essential system complexity before starting climbing the technology level ladder of increasingly better materials. 
is critically needed to gain sufficient [[separation of concerns]] to get engineerability of systems capable to do the climbing. 

Specifically scaling of essential system complexity is needed for [[expanding the kinematic loop]]. 

Trying to climb the technology level ladder to better materials early 
gives insufficient [[separation of concerns]] and sends one straight into [[fat finger problem]]. 

As a more concrete example (based on some personal startup company participation experience of this wikis author) 
Trying to gain side functions like small molecule binding (or catalysis) for for-profit sellable products too early. 
Is much like trying to climb the technology level ladder to better materials too early. 

This is the [[Functional block construction kit approach]] for binding 
or the even more challenging [[Catalysis construction kit approach]] for catalysis. 
This is not to confuse with conventional protein engineering for binding and/or catalysis, 
which is more like singe protein holistic systems that need AI or better even quantum computers for one off solutions. 

This is about trying to beat that with systematic engineerable cominatorics at a (too) early point 
still (too) low in the capabilities of 
– [[noncyclic termination control]] 
– [[essential system complexity]] 
– [[hierarchical assembly]] 

From the technology perspective (but not from the funding perspective) the best path seems 
– [[Robo approach (incremental path)]] … just a focus on scaling [[hierarchical assembly]] 
– [[MMCN]]s … proteins joining in on [[noncyclic termination control]] 
– [[Foldamer printer approach (incremental path)]] as [[MMCN]] subsystems … finally getting to [[technology level climbig capability]] 

----
Side-note: The [[direct path]] has the opposite order. 
There the fist blocker/challenge is to get [[vacuum gemstone]] [[force applying mechanosynthesis]] 
of (eventually surface separable) 3D structures to work at all before any kind of scaling can begin. 
There the analog to [[hierarchical self assembly]] is called [[convergent positional assembly]]. 
Different names as the names emerged from different contexts. 

=== Quantification ===

A main early blocker/challenge along the incremental path is increasing the essential useful system complexity. 
This must not be confused with system size. 

It is easier but much less useful to 
(A) have really large periodic structures than to 
(B) have small ones with precisely controlled termination of self assembly. 
See page "[[Noncyclic termination control]]" which describes the principle of core importance. 
There is no essential system complexity beyond the base period. 

(A) has been done with both structural DNA and proteins {{wikitodo|reference examples}} 
(B) is still mostly reserved to structural DNA alone (as of 2026) 
(protein capsid like structures are merely cyclically terminating which in limited useful) 

Out of this reason in the critical regard of scaling of system complexity structural DNA seems ahead of proteins as of 2026. 
And that despite the big downside of DNA severely lacking stiffness compared to protein assemblies. 

There are at least two variants of proper [[noncyclic termination control]]: 
– Full voxel canvas adressability (like in [[structural DNA nanotechnology]]) 
– [[Algorithmic selv assembly]] 
These can serve as a basis for quantization of [[essential system complexity]] 
via entropy i.e. log of number of possible encodable states. 

{{wikitodo|Below are older subsection to better integrate.}}

=== State of progress of [[self assembly]] ===

A good place to look at is [[foldamer R&D]] specifically [[structural DNA nanotechnology]]. 
Several [[reached milestones in foldamer R&D|noteworthy milestones]] have already been reached.

=== Metrics for progress ===

'''Bad metrics for progress (superficially impressive):'''
* symmetry of self-assembles
* size of self-assemblies

'''Good metrics for progress (more subtle):'''
* degree of [[termination control]]
* stiffness originating from geometry of formed structures '''persistence length''' but in relative terms: [https://en.wikipedia.org/wiki/Persistence_length (wikipedia)]

=== Pushing against the limits of artificial self-assembly ===

'''What are the limitations to scaling up selfassembly?'''
* (A) more blocks taking more time to find each other
* (B) bigger blocks diffusing more slowly – The [[diffusion slowdown blockade]]
* (C) limits in implementability of sets of complementary interfaces where correct pair bind well but wrong pairs do not
* (D) wrong assembles not coming apart again – [[kinetic traps]]
* ... and certainly more

'''Counterstrategies:'''
* (1) using longer chain molecules to increase local [[effective concentration]] – so done in some forms of [[SDN]] and always present in single chain [[self folding]].
* (2) [[Squigglesembly]] – using [[iterative self-assembly]] to getaway with small sets of complementary interfaces
* (3) [[Circumsembly]] – using parallel selfassembly pathways to circumvent selfassembly errors (that may be tolerable)
* (4) algorithmic selfassembly ...
* (5) going for [[nonthermal self-assembly]] at larger scales
* ... and certainly more

== Base material – Climbing '''technology levels''' ==

The recently developed self assembling [[structural DNA nanotechnology]] and similar reliably designable foldamer structures might be a good starting point from [[technology level 0]]. 
* By [[Method of assembly#Loose stereotactic control with self assisted assembly|introducing robotic (more precisely stereotactic) control]] one could reach something like a "''block level precision robotic technology''" [[technology level I]] from there in a first step. 
* In a second step one could change to e.g. Pyrite or Silica [[technology level II]] as building material to increase structural stiffness, reduce vibration amplitudes and get thus more placing accuracy. 
* And finally in a third step one could switch from fluid phase to vacuum so that carbon and silicon can be assembled [[technology level III]].

This very crude temporal outline is by no means the only possible way to go to eventually arrive at [[positional atomic precision]]. 
There may be shortcuts or other paths. (See: [[Direct path]]) 

=== Literature ===

In Appendix II of the book "[[Radical Abundance]]" <ref name="RA">Radical Abundance: How a Revolution in Nanotechnology Will Change Civilization - by K. Eric Drexler</ref> it is proposed to go through several levels of APM technology to reach advanced ([[positional atomic precision]] & diamondoid) APM.
These levels will serve as a rough guideline for the structuring of this Wiki.
In "Nanosystems" <ref name="nasy">[[Nanoystems|Nanosystems: Molecular Machinery, Manufacturing, and Computation - by K. Eric Drexler]]</ref> technology stages are mentioned beginning with section 16.5.2. (written before the emergence of structural DNA nanotechnology). 

== Combining the best of different selfassembly technologies ==

[[File:Foldeamer-printer-stiffness-adapters.jpg|thumb|right|350px|'''Left:''' Adding small inserts that can be made stiffer in a lower stiffness background framework that can be made bigger. '''Right:''' Application of such a combining of self-assembly technologies technology demonstrated in the context of the [[foldamer printer]] concept.]]

Combining self assembly technologies could perhaps boost progress. 
See main page: '''[[Combining advantages of different selfassembly technologies]]'''

== Why positional control must be introduced before switchover to stiffest materials ==

For water synthesizable gemstone materials every crystal site looks exactly the same. Sites are featureless. 
So to add atoms (or [[AP]] groups thereof) to such a crystal at desired locations (and there only), 
the one single option available is [[positional assembly]]. 
The same holds for materials made out of many identical small organic molecules.

'''Details:'''
* [[switch-over to stiffer materials]] at some point is critically dependent on
* [[introduction of total positional control]] ...
... this is because stiffer materials cannot afford to '''encode the position of their constitute parts within the shape of their constitute parts''' which is what [[selfassembly]] mandates as fundamental prerequisite. 
Such '''position in shape encoding''' forces a minimum size of constitute parts and bonds weak enough to be suitable for thermal annealing averting [[kinetic traps]].

'''But what about Biomineralization?''' 
Does it not work without positional assembly? 

In biology biomineralization is likely not atomically precise. Bones & teeth (apatite or calcium-phosphate), shells (calcite or calcium-carbonate), diatoms (silica) all have no need to be atomically precise. Variously sized batches of phosphate, carbonate, silicate, sulfate, ions are probably just dumped in the general location to push the concentration locally to levels of where percipitation starts happening. 
{{todo|verify lack of [[AP]] in biomineralization}}

Yes, there is biomineral with atomic precision in the active center of some proteins, but this is usually just a few unit-cells. 
The protein provides a one-off specialized solution for this exact nano-crystal.

== Atomically precise positional control requires positional atomic precision ==

Attaining [[positional control]] mandates going from mere [[topological atomic precision]] (no errors in what links to what) to actual proper [[positional atomic precision]] (sub building block sized resolution – possibly subatomic resolution).

Weaker: Placing super-atomar blocks (small molecules, stiff compact de-novo-proteins) only requites block level precision. 
See: [[Lattice scaled stiffness]]

== Terminology ==

Since a [[nanofactory]] at the endpoint of an incremental path will inherit the capability of handling at least the materials of one generation before it, it may be better to call the products '''gemoid''' instead of '''diamondoid''' this terminology would make it more clear that gemstone like bio-minerals like quartz are included.

== Paths that are treated separately because its harder to find a concrete goal for them ==

Note that the behavior of mobile electrons at the nanoscale is not as easily predictable as the behavior of mechanics at the same scale thus there's less [[exploratory engineering]] for nanoelectronics than nanomechanics.
See:

* [[non mechanical technology path]] (including nanoelectronics)
* [[brownian technology path]]. (including things like synthetic biology)

['''Todo:''' improve article quality]

== Terminology for early systems ==

In [[Erics blog]] (2018-11-10) early foldamer based systems were referred to as: 
'''"modular molecular composite nanosystems (MMCNs)"''' 
One could also perhaps call them: 
'''"coarse-block atomically precise systems"''' 

== Related ==

* '''[[Technology levels]]''' (axis to the left in diagram)
* '''[[Hierarchical self-assembly]] levels''' (axis to the right in diagram)
* [[Pathways to advanced APM systems]]
* [[Pathway controversy]]
* [[Bridging the gaps]]
----
* [[Bootstrapping methods for productive nanosystems]]
* [[Bootstrapping atomic precision]]
----
* [[Automated research]]
----
* '''[[Thermally driven self assembly]]'''
* [[Termination control]]
----
* '''[[Foldamer technology stiffness nesting]]'''
* '''[[Stiffness focusing]]'''
----
* [[Microfluidics]] & [[Transflooder]] & [[Automated research]]

== External links ==

* Slides: "Toward Modular Molecular Composite Nanosystems" -- K. Eric Drexler, PhD -- U.C. Berkeley -- 26 April 2009 -- [http://metamodern.com/b/wp-content/uploads/2009/05/Molecular_Nanosystems_Berkeley.pdf]

== References ==

<references />

[[Category:General]]
[[Category:Disquisition]]

[[category:Incremental path]]

Incremental path

2026-10-09T07:47:36Z

Apm: /* Why necessarily early – fist climbing hierarchical self-assembly – then climbing technology levels */

{| class="wikitable" style="float:right; margin-left: 10px; text-align: center"
! colspan = "2"|Technology levels and steps of the incremental path
|-
| [[Technology level 0|Level 0]]
| [[side products of technology level 0|side products]]
|-
| [[Introduction of total positional control]]
| xxx
|-
| [[Technology level I|Level I]]
| [[side products of technology level I|side products]]
|-
| [[switch-over to stiffer materials]]
| xxx
|-
| [[Technology level II|Level II]]
| [[side products of technology level II|side products]]
|-
| [[introduction of practically perfect vacuum]]
| xxx
|-
| [[Technology level III|Level III]]
| [[diamondoid metamaterials|basis for products]] [[further improvement at technology level III|advanced products]] [[most speculative potential applications| maybe-products]]
|}
[[File:Incremental path - MMCS Modular Molecular Composite Nanosystems.svg|500px|thumb|right|'''Very crude conceptual example of part of an MMCN.''' Red may represent proteins, Blue dots may represent binding sites/active sites. Dark grey blocks and grid of black may represent bigger structures (maybe [[structural DNA nanotechnology]]). Yellow way represent a gold contact on a chip for electrostatic interaction. White outline: A hinge. ... Moe details on page: [[Modular molecular composite nanosystem]].]]
Up: [[Pathways to advanced APM systems]] 
{{Wikitodo|Collage and add image of sequence of material classes. DNA/RNA, peptide/protein, artificial foldamer, spiroligomer, solvent gem (CeO2), vacuum gem (diamond)}}

The '''incremental path''' towards advanced APM systems describes a desired process of slowly increasing technological capabilities (tools making better tools) with avoidance of loss of a strong orientation towards the far term goal of the [[stiffness|stiff nanomachinery]] in [[In-vacuum gem-gum technology|gem-gum technology]].
This translates into starting off by using [[soft nanomachines]] to the fullest to get away from soft nanomachines ASAP.

The '''incremental path''' towards advanced APM systems is complementary to the [[direct path]].
The direct path to advanced APM systems in comparison describes a desired process of jumping to the advanced far term goal ASAP without significant detours. It is specifically focused on early usage of scanning probe microscopy for [[mechanosynthesis]] of diamond (or silicon) with throughput levels that are significant enough for the bootstrapping of a [[gem-gum factory]]. Following the [[direct path]] alone may be problematic.

* Sometimes a direction that on first inspection looks like it would lead fast to the goal actually does lead to it very slowly (or even not at all).
* Sometimes a direction that on first inspection looks as if it would lead only very slowly to the goal actually would lead to the goal fastest (which might still be slow).

This was the reason for the introduction of the distinction between direct path and incremental path. 
Details on the critics towards the direct path will be located on the "[[direct path]]"-page.

As historical note there is also the '''[[Feynman path]]''' but as-is in its unmodified version 
it is clearly not practical for several reasons 
elucidated on the dedicated page linked above.

== Dodge the trapdoors ==

'''Do not be fooled by the symmetry and scale of artificial self assembled molecule crystals!''' 
'''What matters most is [[termination control]].''' Especially on surfaces. 
This is a way better (but less visually conspicuous and stunning) measure for technological progress.

This is in analogy to metallic or mineral nanoparticles. 
Despite them having an atomically precise interior crystal structure they 
are not being considered atomically precise because their surface geometry is usually a combination of ...
* a statistical distribution and
* a predetermined shape (usually simple convex polyhedra, sometimes constrained to 2D sheets or even 1D rods).

Also note: Self assembly of an arc into a full circle 
can be considered as absence of termination control in angular direction 
as angles are constrained to 360° by nature already. 
When averting hitting the start when going around by 360° and thus going helical 
a lack of termination control becomes trivially obvious if present.

== High level map for the incremental path ==

[[File:APM-EarlyDevelopmentPaths.jpg|500px|thumb|right|Possible map for the incremental path. Left axis: [[technology levels]] Right axis see: [[convergent assembly comparison]] and [[hierarchical self-assembly]].]]

This map here plots:
* '''technology levels''' by use/control of material and means of assembly against ...
* '''assembly levels''' as in the degree to which [[hierarchical selfassembly]] has been achieved.

The starting-point of technological development/progression is the bottom-most asterisk-star. 
Green asterisks mark ares where some results have already been achieved.

=== The window of escape ===

The argument this map-diagram here is trying to justify is that there might be kind of a 
'''[[window of escape]]''' between the blockades in pathways of development (red, orange, and yellow) .

'''Blockades:'''
* The red, orange, and yellow stars tagged with "redundant" mean: Everything that positional assembly can do here selfassembly can do equally well (yellow) or better (red).
* The red, orange, and yellow stars tagged with "too big to diffuse" means: [[Thermally driven selfassembly]] faces increasing problems due larger parts moving slower.

Starting out to the left right away is both
* technically hardly possible (noncomposable primitive selfassemblies hardly can introduce positional assembly) and
* economically not at all motivatable (due to the [[positional assembly redundancy blockade]] mentioned above)

=== Degree of directness of the indirect path ===

Note that there is kind of a degree of directness in the indirect path. 
Directness in the sense of:
* How early/aggressively one attempts to take a hard tun left in the map-diagram.
* How early/aggressively one attempts to get to a [[positional assembly kinematic loop]] with proper [[separation of concerns]]
* How tightly one attempts to circumnavigate the '''[[positional assembly redundancy blockade]]'''.
* How far to run up against the '''[[diffusion slowdown blockade]]''' before taking the left-turn

Depending on the directness of the indirect path further sub approaches of the indirect path can be identified:
* Early-most leftward-turn: [[Catalysis construction kit approach]]
* Later leftward-turn: [[Printer approach]] (See: [[Foldamer printer]])
* Very late leftward-turn: [[Robo approach]] (See: [[Modular molecular composite nanosystem]] MMCN)

== System complexity – Climbing [[hierarchical self-assembly]] levels ==

Or more generally: Increasing essential system complexity by expanding on [[noncyclic termination contol]] capabilities.

=== Why necessarily early – fist climbing [[hierarchical self-assembly]] – then climbing [[technology levels]] ===

Scaling of essential system complexity before starting climbing the technology level ladder of increasingly better materials. 
is critically needed to gain sufficient [[separation of concerns]] to get engineerability of systems capable to do the climbing. 

Specifically scaling of essential system complexity is needed for [[expanding the kinematic loop]]. 

Trying to climb the technology level ladder to better materials early 
gives insufficient [[separation of concerns]] and sends one straight into [[fat finger problem]]. 

As a more concrete example (based on some personal startup company participation experience of this wikis author) 
Trying to gain side functions like small molecule binding (or catalysis) for for-profit sellable products too early. 
Is much like trying to climb the technology level ladder to better materials too early. 

This is the [[Functional block construction kit approach]] for binding 
or the even more challenging [[Catalysis construction kit approach]] for catalysis. 
This is not to confuse with conventional protein engineering for binding and/or catalysis, 
which is more like singe protein holistic systems that need AI or better even quantum computers for one off solutions. 

This is about trying to beat that with systematic engineerable cominatorics at a (too) early point 
still (too) low in the capabilities of 
– [[noncyclic termination control]] 
– [[essential system complexity]] 
– [[hierarchical assembly]] 

From the technology perspective (but not from the funding perspective) the best path seems 
– [[Robo approach (incremental path)]] … just a focus on scaling [[hierarchical assembly]] 
– [[MMCNs]] … proteins joining in on [[noncyclic termination control]] 
– [[Foldamer printer approach (incremental path)]] as [[MMCN]] subsystems … finally getting to [[technology level climbig capability]] 

----
Side-note: The [[direct path]] has the opposite order. 
There the fist blocker/challenge is to get [[vacuum gemstone]] [[force applying mechanosynthesis]] 
of (eventually surface separable) 3D structures to work at all before any kind of scaling can begin. 
There the analog to [[hierarchical self assembly]] is called [[convergent positional assembly]]. 
Different names as the names emerged from different contexts. 

=== Quantification ===

A main early blocker/challenge along the incremental path is increasing the essential useful system complexity. 
This must not be confused with system size. 

It is easier but much less useful to 
(A) have really large periodic structures than to 
(B) have small ones with precisely controlled termination of self assembly. 
See page "[[Noncyclic termination control]]" which describes the principle of core importance. 
There is no essential system complexity beyond the base period. 

(A) has been done with both structural DNA and proteins {{wikitodo|reference examples}} 
(B) is still mostly reserved to structural DNA alone (as of 2026) 
(protein capsid like structures are merely cyclically terminating which in limited useful) 

Out of this reason in the critical regard of scaling of system complexity structural DNA seems ahead of proteins as of 2026. 
And that despite the big downside of DNA severely lacking stiffness compared to protein assemblies. 

There are at least two variants of proper [[noncyclic termination control]]: 
– Full voxel canvas adressability (like in [[structural DNA nanotechnology]]) 
– [[Algorithmic selv assembly]] 
These can serve as a basis for quantization of [[essential system complexity]] 
via entropy i.e. log of number of possible encodable states. 

{{wikitodo|Below are older subsection to better integrate.}}

=== State of progress of [[self assembly]] ===

A good place to look at is [[foldamer R&D]] specifically [[structural DNA nanotechnology]]. 
Several [[reached milestones in foldamer R&D|noteworthy milestones]] have already been reached.

=== Metrics for progress ===

'''Bad metrics for progress (superficially impressive):'''
* symmetry of self-assembles
* size of self-assemblies

'''Good metrics for progress (more subtle):'''
* degree of [[termination control]]
* stiffness originating from geometry of formed structures '''persistence length''' but in relative terms: [https://en.wikipedia.org/wiki/Persistence_length (wikipedia)]

=== Pushing against the limits of artificial self-assembly ===

'''What are the limitations to scaling up selfassembly?'''
* (A) more blocks taking more time to find each other
* (B) bigger blocks diffusing more slowly – The [[diffusion slowdown blockade]]
* (C) limits in implementability of sets of complementary interfaces where correct pair bind well but wrong pairs do not
* (D) wrong assembles not coming apart again – [[kinetic traps]]
* ... and certainly more

'''Counterstrategies:'''
* (1) using longer chain molecules to increase local [[effective concentration]] – so done in some forms of [[SDN]] and always present in single chain [[self folding]].
* (2) [[Squigglesembly]] – using [[iterative self-assembly]] to getaway with small sets of complementary interfaces
* (3) [[Circumsembly]] – using parallel selfassembly pathways to circumvent selfassembly errors (that may be tolerable)
* (4) algorithmic selfassembly ...
* (5) going for [[nonthermal self-assembly]] at larger scales
* ... and certainly more

== Base material – Climbing '''technology levels''' ==

The recently developed self assembling [[structural DNA nanotechnology]] and similar reliably designable foldamer structures might be a good starting point from [[technology level 0]]. 
* By [[Method of assembly#Loose stereotactic control with self assisted assembly|introducing robotic (more precisely stereotactic) control]] one could reach something like a "''block level precision robotic technology''" [[technology level I]] from there in a first step. 
* In a second step one could change to e.g. Pyrite or Silica [[technology level II]] as building material to increase structural stiffness, reduce vibration amplitudes and get thus more placing accuracy. 
* And finally in a third step one could switch from fluid phase to vacuum so that carbon and silicon can be assembled [[technology level III]].

This very crude temporal outline is by no means the only possible way to go to eventually arrive at [[positional atomic precision]]. 
There may be shortcuts or other paths. (See: [[Direct path]]) 

=== Literature ===

In Appendix II of the book "[[Radical Abundance]]" <ref name="RA">Radical Abundance: How a Revolution in Nanotechnology Will Change Civilization - by K. Eric Drexler</ref> it is proposed to go through several levels of APM technology to reach advanced ([[positional atomic precision]] & diamondoid) APM.
These levels will serve as a rough guideline for the structuring of this Wiki.
In "Nanosystems" <ref name="nasy">[[Nanoystems|Nanosystems: Molecular Machinery, Manufacturing, and Computation - by K. Eric Drexler]]</ref> technology stages are mentioned beginning with section 16.5.2. (written before the emergence of structural DNA nanotechnology). 

== Combining the best of different selfassembly technologies ==

[[File:Foldeamer-printer-stiffness-adapters.jpg|thumb|right|350px|'''Left:''' Adding small inserts that can be made stiffer in a lower stiffness background framework that can be made bigger. '''Right:''' Application of such a combining of self-assembly technologies technology demonstrated in the context of the [[foldamer printer]] concept.]]

Combining self assembly technologies could perhaps boost progress. 
See main page: '''[[Combining advantages of different selfassembly technologies]]'''

== Why positional control must be introduced before switchover to stiffest materials ==

For water synthesizable gemstone materials every crystal site looks exactly the same. Sites are featureless. 
So to add atoms (or [[AP]] groups thereof) to such a crystal at desired locations (and there only), 
the one single option available is [[positional assembly]]. 
The same holds for materials made out of many identical small organic molecules.

'''Details:'''
* [[switch-over to stiffer materials]] at some point is critically dependent on
* [[introduction of total positional control]] ...
... this is because stiffer materials cannot afford to '''encode the position of their constitute parts within the shape of their constitute parts''' which is what [[selfassembly]] mandates as fundamental prerequisite. 
Such '''position in shape encoding''' forces a minimum size of constitute parts and bonds weak enough to be suitable for thermal annealing averting [[kinetic traps]].

'''But what about Biomineralization?''' 
Does it not work without positional assembly? 

In biology biomineralization is likely not atomically precise. Bones & teeth (apatite or calcium-phosphate), shells (calcite or calcium-carbonate), diatoms (silica) all have no need to be atomically precise. Variously sized batches of phosphate, carbonate, silicate, sulfate, ions are probably just dumped in the general location to push the concentration locally to levels of where percipitation starts happening. 
{{todo|verify lack of [[AP]] in biomineralization}}

Yes, there is biomineral with atomic precision in the active center of some proteins, but this is usually just a few unit-cells. 
The protein provides a one-off specialized solution for this exact nano-crystal.

== Atomically precise positional control requires positional atomic precision ==

Attaining [[positional control]] mandates going from mere [[topological atomic precision]] (no errors in what links to what) to actual proper [[positional atomic precision]] (sub building block sized resolution – possibly subatomic resolution).

Weaker: Placing super-atomar blocks (small molecules, stiff compact de-novo-proteins) only requites block level precision. 
See: [[Lattice scaled stiffness]]

== Terminology ==

Since a [[nanofactory]] at the endpoint of an incremental path will inherit the capability of handling at least the materials of one generation before it, it may be better to call the products '''gemoid''' instead of '''diamondoid''' this terminology would make it more clear that gemstone like bio-minerals like quartz are included.

== Paths that are treated separately because its harder to find a concrete goal for them ==

Note that the behavior of mobile electrons at the nanoscale is not as easily predictable as the behavior of mechanics at the same scale thus there's less [[exploratory engineering]] for nanoelectronics than nanomechanics.
See:

* [[non mechanical technology path]] (including nanoelectronics)
* [[brownian technology path]]. (including things like synthetic biology)

['''Todo:''' improve article quality]

== Terminology for early systems ==

In [[Erics blog]] (2018-11-10) early foldamer based systems were referred to as: 
'''"modular molecular composite nanosystems (MMCNs)"''' 
One could also perhaps call them: 
'''"coarse-block atomically precise systems"''' 

== Related ==

* '''[[Technology levels]]''' (axis to the left in diagram)
* '''[[Hierarchical self-assembly]] levels''' (axis to the right in diagram)
* [[Pathways to advanced APM systems]]
* [[Pathway controversy]]
* [[Bridging the gaps]]
----
* [[Bootstrapping methods for productive nanosystems]]
* [[Bootstrapping atomic precision]]
----
* [[Automated research]]
----
* '''[[Thermally driven self assembly]]'''
* [[Termination control]]
----
* '''[[Foldamer technology stiffness nesting]]'''
* '''[[Stiffness focusing]]'''
----
* [[Microfluidics]] & [[Transflooder]] & [[Automated research]]

== External links ==

* Slides: "Toward Modular Molecular Composite Nanosystems" -- K. Eric Drexler, PhD -- U.C. Berkeley -- 26 April 2009 -- [http://metamodern.com/b/wp-content/uploads/2009/05/Molecular_Nanosystems_Berkeley.pdf]

== References ==

<references />

[[Category:General]]
[[Category:Disquisition]]

[[category:Incremental path]]

Incremental path

2026-10-09T07:47:12Z

Apm: huge additions == System complexity – Climbing hierarchical assembly levels ==

{| class="wikitable" style="float:right; margin-left: 10px; text-align: center"
! colspan = "2"|Technology levels and steps of the incremental path
|-
| [[Technology level 0|Level 0]]
| [[side products of technology level 0|side products]]
|-
| [[Introduction of total positional control]]
| xxx
|-
| [[Technology level I|Level I]]
| [[side products of technology level I|side products]]
|-
| [[switch-over to stiffer materials]]
| xxx
|-
| [[Technology level II|Level II]]
| [[side products of technology level II|side products]]
|-
| [[introduction of practically perfect vacuum]]
| xxx
|-
| [[Technology level III|Level III]]
| [[diamondoid metamaterials|basis for products]] [[further improvement at technology level III|advanced products]] [[most speculative potential applications| maybe-products]]
|}
[[File:Incremental path - MMCS Modular Molecular Composite Nanosystems.svg|500px|thumb|right|'''Very crude conceptual example of part of an MMCN.''' Red may represent proteins, Blue dots may represent binding sites/active sites. Dark grey blocks and grid of black may represent bigger structures (maybe [[structural DNA nanotechnology]]). Yellow way represent a gold contact on a chip for electrostatic interaction. White outline: A hinge. ... Moe details on page: [[Modular molecular composite nanosystem]].]]
Up: [[Pathways to advanced APM systems]] 
{{Wikitodo|Collage and add image of sequence of material classes. DNA/RNA, peptide/protein, artificial foldamer, spiroligomer, solvent gem (CeO2), vacuum gem (diamond)}}

The '''incremental path''' towards advanced APM systems describes a desired process of slowly increasing technological capabilities (tools making better tools) with avoidance of loss of a strong orientation towards the far term goal of the [[stiffness|stiff nanomachinery]] in [[In-vacuum gem-gum technology|gem-gum technology]].
This translates into starting off by using [[soft nanomachines]] to the fullest to get away from soft nanomachines ASAP.

The '''incremental path''' towards advanced APM systems is complementary to the [[direct path]].
The direct path to advanced APM systems in comparison describes a desired process of jumping to the advanced far term goal ASAP without significant detours. It is specifically focused on early usage of scanning probe microscopy for [[mechanosynthesis]] of diamond (or silicon) with throughput levels that are significant enough for the bootstrapping of a [[gem-gum factory]]. Following the [[direct path]] alone may be problematic.

* Sometimes a direction that on first inspection looks like it would lead fast to the goal actually does lead to it very slowly (or even not at all).
* Sometimes a direction that on first inspection looks as if it would lead only very slowly to the goal actually would lead to the goal fastest (which might still be slow).

This was the reason for the introduction of the distinction between direct path and incremental path. 
Details on the critics towards the direct path will be located on the "[[direct path]]"-page.

As historical note there is also the '''[[Feynman path]]''' but as-is in its unmodified version 
it is clearly not practical for several reasons 
elucidated on the dedicated page linked above.

== Dodge the trapdoors ==

'''Do not be fooled by the symmetry and scale of artificial self assembled molecule crystals!''' 
'''What matters most is [[termination control]].''' Especially on surfaces. 
This is a way better (but less visually conspicuous and stunning) measure for technological progress.

This is in analogy to metallic or mineral nanoparticles. 
Despite them having an atomically precise interior crystal structure they 
are not being considered atomically precise because their surface geometry is usually a combination of ...
* a statistical distribution and
* a predetermined shape (usually simple convex polyhedra, sometimes constrained to 2D sheets or even 1D rods).

Also note: Self assembly of an arc into a full circle 
can be considered as absence of termination control in angular direction 
as angles are constrained to 360° by nature already. 
When averting hitting the start when going around by 360° and thus going helical 
a lack of termination control becomes trivially obvious if present.

== High level map for the incremental path ==

[[File:APM-EarlyDevelopmentPaths.jpg|500px|thumb|right|Possible map for the incremental path. Left axis: [[technology levels]] Right axis see: [[convergent assembly comparison]] and [[hierarchical self-assembly]].]]

This map here plots:
* '''technology levels''' by use/control of material and means of assembly against ...
* '''assembly levels''' as in the degree to which [[hierarchical selfassembly]] has been achieved.

The starting-point of technological development/progression is the bottom-most asterisk-star. 
Green asterisks mark ares where some results have already been achieved.

=== The window of escape ===

The argument this map-diagram here is trying to justify is that there might be kind of a 
'''[[window of escape]]''' between the blockades in pathways of development (red, orange, and yellow) .

'''Blockades:'''
* The red, orange, and yellow stars tagged with "redundant" mean: Everything that positional assembly can do here selfassembly can do equally well (yellow) or better (red).
* The red, orange, and yellow stars tagged with "too big to diffuse" means: [[Thermally driven selfassembly]] faces increasing problems due larger parts moving slower.

Starting out to the left right away is both
* technically hardly possible (noncomposable primitive selfassemblies hardly can introduce positional assembly) and
* economically not at all motivatable (due to the [[positional assembly redundancy blockade]] mentioned above)

=== Degree of directness of the indirect path ===

Note that there is kind of a degree of directness in the indirect path. 
Directness in the sense of:
* How early/aggressively one attempts to take a hard tun left in the map-diagram.
* How early/aggressively one attempts to get to a [[positional assembly kinematic loop]] with proper [[separation of concerns]]
* How tightly one attempts to circumnavigate the '''[[positional assembly redundancy blockade]]'''.
* How far to run up against the '''[[diffusion slowdown blockade]]''' before taking the left-turn

Depending on the directness of the indirect path further sub approaches of the indirect path can be identified:
* Early-most leftward-turn: [[Catalysis construction kit approach]]
* Later leftward-turn: [[Printer approach]] (See: [[Foldamer printer]])
* Very late leftward-turn: [[Robo approach]] (See: [[Modular molecular composite nanosystem]] MMCN)

== System complexity – Climbing [[hierarchical self-assembly]] levels ==

Or more generally: Increasing essential system complexity by expanding on [[noncyclic termination contol]] capabilities.

=== Why necessarily early – fist climbing [[hierarchical self-assembly]] – then climbing [[technology levels]] ===

Scaling of essential system complexity before starting climbing the technology level ladder of increasingly better materials. 
is critically needed to gain sufficient [[separation of concerns]] to get engineerability of systems capable to do the climbing. 

Specifically scaling of essential system complexity is needed for [[expanding the kinematic loop]]. 

Trying to climb the technology level ladder to better materials early 
gives insufficient [[separation of concerns]] and sends one straight into [[fat finger problem]]. 

As a more concrete example (based on some personal startup company participation experience of this wikis author) 
Trying to gain side functions like small molecule binding (or catalysis) for for-profit sellable products too early. 
Is much like trying to climb the technology level ladder to better materials too early. 

This is the [[Functional block construction kit approach]] for binding 
or the even more challenging [[Catalysis construction kit approach]] for catalysis. 
This is not to confuse with conventional protein engineering for binding and/or catalysis, 
which is more like singe protein holistic systems that need AI or better even quantum computers for one off solutions. 

This is about trying to beat that with systematic engineerable cominatorics at a (too) early point 
still (too) low in the capabilities of 
– [[noncyclic termination control]] 
– [[essential system complexity]] 
– [[hierarchical assembly]] 

From the technology perspective (but not from the funding perspective) the best path seems 
– [[Robo approach (incremental path)]] … just a focus on scaling [[hierarchical assembly]] 
– [[MMCNs]] … proteins joining in on [[noncyclic termination control]] 
– [[Foldamer printer approach (incremental path)]] as [[MMCN]] subsystems … finally getting to [[technology level climbig capability]] 

Side-note: The [[direct path]] has the opposite order. 
There the fist blocker/challenge is to get [[vacuum gemstone]] [[force applying mechanosynthesis]] 
of (eventually surface separable) 3D structures to work at all before any kind of scaling can begin. 
There the analog to [[hierarchical self assembly]] is called [[convergent positional assembly]]. 
Different names as the names emerged from different contexts. 

=== Quantification ===

A main early blocker/challenge along the incremental path is increasing the essential useful system complexity. 
This must not be confused with system size. 

It is easier but much less useful to 
(A) have really large periodic structures than to 
(B) have small ones with precisely controlled termination of self assembly. 
See page "[[Noncyclic termination control]]" which describes the principle of core importance. 
There is no essential system complexity beyond the base period. 

(A) has been done with both structural DNA and proteins {{wikitodo|reference examples}} 
(B) is still mostly reserved to structural DNA alone (as of 2026) 
(protein capsid like structures are merely cyclically terminating which in limited useful) 

Out of this reason in the critical regard of scaling of system complexity structural DNA seems ahead of proteins as of 2026. 
And that despite the big downside of DNA severely lacking stiffness compared to protein assemblies. 

There are at least two variants of proper [[noncyclic termination control]]: 
– Full voxel canvas adressability (like in [[structural DNA nanotechnology]]) 
– [[Algorithmic selv assembly]] 
These can serve as a basis for quantization of [[essential system complexity]] 
via entropy i.e. log of number of possible encodable states. 

{{wikitodo|Below are older subsection to better integrate.}}

=== State of progress of [[self assembly]] ===

A good place to look at is [[foldamer R&D]] specifically [[structural DNA nanotechnology]]. 
Several [[reached milestones in foldamer R&D|noteworthy milestones]] have already been reached.

=== Metrics for progress ===

'''Bad metrics for progress (superficially impressive):'''
* symmetry of self-assembles
* size of self-assemblies

'''Good metrics for progress (more subtle):'''
* degree of [[termination control]]
* stiffness originating from geometry of formed structures '''persistence length''' but in relative terms: [https://en.wikipedia.org/wiki/Persistence_length (wikipedia)]

=== Pushing against the limits of artificial self-assembly ===

'''What are the limitations to scaling up selfassembly?'''
* (A) more blocks taking more time to find each other
* (B) bigger blocks diffusing more slowly – The [[diffusion slowdown blockade]]
* (C) limits in implementability of sets of complementary interfaces where correct pair bind well but wrong pairs do not
* (D) wrong assembles not coming apart again – [[kinetic traps]]
* ... and certainly more

'''Counterstrategies:'''
* (1) using longer chain molecules to increase local [[effective concentration]] – so done in some forms of [[SDN]] and always present in single chain [[self folding]].
* (2) [[Squigglesembly]] – using [[iterative self-assembly]] to getaway with small sets of complementary interfaces
* (3) [[Circumsembly]] – using parallel selfassembly pathways to circumvent selfassembly errors (that may be tolerable)
* (4) algorithmic selfassembly ...
* (5) going for [[nonthermal self-assembly]] at larger scales
* ... and certainly more

== Base material – Climbing '''technology levels''' ==

The recently developed self assembling [[structural DNA nanotechnology]] and similar reliably designable foldamer structures might be a good starting point from [[technology level 0]]. 
* By [[Method of assembly#Loose stereotactic control with self assisted assembly|introducing robotic (more precisely stereotactic) control]] one could reach something like a "''block level precision robotic technology''" [[technology level I]] from there in a first step. 
* In a second step one could change to e.g. Pyrite or Silica [[technology level II]] as building material to increase structural stiffness, reduce vibration amplitudes and get thus more placing accuracy. 
* And finally in a third step one could switch from fluid phase to vacuum so that carbon and silicon can be assembled [[technology level III]].

This very crude temporal outline is by no means the only possible way to go to eventually arrive at [[positional atomic precision]]. 
There may be shortcuts or other paths. (See: [[Direct path]]) 

=== Literature ===

In Appendix II of the book "[[Radical Abundance]]" <ref name="RA">Radical Abundance: How a Revolution in Nanotechnology Will Change Civilization - by K. Eric Drexler</ref> it is proposed to go through several levels of APM technology to reach advanced ([[positional atomic precision]] & diamondoid) APM.
These levels will serve as a rough guideline for the structuring of this Wiki.
In "Nanosystems" <ref name="nasy">[[Nanoystems|Nanosystems: Molecular Machinery, Manufacturing, and Computation - by K. Eric Drexler]]</ref> technology stages are mentioned beginning with section 16.5.2. (written before the emergence of structural DNA nanotechnology). 

== Combining the best of different selfassembly technologies ==

[[File:Foldeamer-printer-stiffness-adapters.jpg|thumb|right|350px|'''Left:''' Adding small inserts that can be made stiffer in a lower stiffness background framework that can be made bigger. '''Right:''' Application of such a combining of self-assembly technologies technology demonstrated in the context of the [[foldamer printer]] concept.]]

Combining self assembly technologies could perhaps boost progress. 
See main page: '''[[Combining advantages of different selfassembly technologies]]'''

== Why positional control must be introduced before switchover to stiffest materials ==

For water synthesizable gemstone materials every crystal site looks exactly the same. Sites are featureless. 
So to add atoms (or [[AP]] groups thereof) to such a crystal at desired locations (and there only), 
the one single option available is [[positional assembly]]. 
The same holds for materials made out of many identical small organic molecules.

'''Details:'''
* [[switch-over to stiffer materials]] at some point is critically dependent on
* [[introduction of total positional control]] ...
... this is because stiffer materials cannot afford to '''encode the position of their constitute parts within the shape of their constitute parts''' which is what [[selfassembly]] mandates as fundamental prerequisite. 
Such '''position in shape encoding''' forces a minimum size of constitute parts and bonds weak enough to be suitable for thermal annealing averting [[kinetic traps]].

'''But what about Biomineralization?''' 
Does it not work without positional assembly? 

In biology biomineralization is likely not atomically precise. Bones & teeth (apatite or calcium-phosphate), shells (calcite or calcium-carbonate), diatoms (silica) all have no need to be atomically precise. Variously sized batches of phosphate, carbonate, silicate, sulfate, ions are probably just dumped in the general location to push the concentration locally to levels of where percipitation starts happening. 
{{todo|verify lack of [[AP]] in biomineralization}}

Yes, there is biomineral with atomic precision in the active center of some proteins, but this is usually just a few unit-cells. 
The protein provides a one-off specialized solution for this exact nano-crystal.

== Atomically precise positional control requires positional atomic precision ==

Attaining [[positional control]] mandates going from mere [[topological atomic precision]] (no errors in what links to what) to actual proper [[positional atomic precision]] (sub building block sized resolution – possibly subatomic resolution).

Weaker: Placing super-atomar blocks (small molecules, stiff compact de-novo-proteins) only requites block level precision. 
See: [[Lattice scaled stiffness]]

== Terminology ==

Since a [[nanofactory]] at the endpoint of an incremental path will inherit the capability of handling at least the materials of one generation before it, it may be better to call the products '''gemoid''' instead of '''diamondoid''' this terminology would make it more clear that gemstone like bio-minerals like quartz are included.

== Paths that are treated separately because its harder to find a concrete goal for them ==

Note that the behavior of mobile electrons at the nanoscale is not as easily predictable as the behavior of mechanics at the same scale thus there's less [[exploratory engineering]] for nanoelectronics than nanomechanics.
See:

* [[non mechanical technology path]] (including nanoelectronics)
* [[brownian technology path]]. (including things like synthetic biology)

['''Todo:''' improve article quality]

== Terminology for early systems ==

In [[Erics blog]] (2018-11-10) early foldamer based systems were referred to as: 
'''"modular molecular composite nanosystems (MMCNs)"''' 
One could also perhaps call them: 
'''"coarse-block atomically precise systems"''' 

== Related ==

* '''[[Technology levels]]''' (axis to the left in diagram)
* '''[[Hierarchical self-assembly]] levels''' (axis to the right in diagram)
* [[Pathways to advanced APM systems]]
* [[Pathway controversy]]
* [[Bridging the gaps]]
----
* [[Bootstrapping methods for productive nanosystems]]
* [[Bootstrapping atomic precision]]
----
* [[Automated research]]
----
* '''[[Thermally driven self assembly]]'''
* [[Termination control]]
----
* '''[[Foldamer technology stiffness nesting]]'''
* '''[[Stiffness focusing]]'''
----
* [[Microfluidics]] & [[Transflooder]] & [[Automated research]]

== External links ==

* Slides: "Toward Modular Molecular Composite Nanosystems" -- K. Eric Drexler, PhD -- U.C. Berkeley -- 26 April 2009 -- [http://metamodern.com/b/wp-content/uploads/2009/05/Molecular_Nanosystems_Berkeley.pdf]

== References ==

<references />

[[Category:General]]
[[Category:Disquisition]]

[[category:Incremental path]]

Separation of concerns

2026-10-05T09:46:59Z

Apm: /* In design of artificial advanced productive nanosystems */

{{stub}}

== In protein folding ==

=== At least three competing purposes for protein side-chains ===

* internal cohesion (hydrophobic side-chains in aqueous solution tend to nestle inside; lack of that gives intrinsically disordered proteins or worse)
* inter protein binding (protein quarternary structure; larger interfaces needed for decently controllable and stiff binding angles)
* outer functionality (binding small molecules and possibly catalyzing reactions between them)
* (allosteric long range motion transmission effects – when looking beyond stiff proteins as building blocks)

Related: [[Orthogonal set of protein binding interfaces]]

=== Holistic behavior on single side chain changes ===

Changing one side-chain on a protein to change a specific function 
can often change conformation and function of the protein at a completely different site. 
This is either ...
* ... a case of bad separation of concerns (that is tolerable for the host organisms species survival) or
* ... a case of separation of concerns at a higher level of abstraction that we do non yet understand

Both cases can pose interesting research problems but 
neither case is useful for fast targeted development.

That is why stiff predictable folding protein motifs are of especial interest. 
Protein that are rather insensitive to local changes. 
See: [[De-novo protein engineering]]

Related: [[Fat finger problem]]

== In design of artificial [[advanced productive nanosystem]]s ==

Separation of concerns is highly desirable for
* better testability that is: easier narrowing down of bugs and
* better system comprehesability

=> Well distributed well debugable systems 
rather than (outdated) ultra compact self replication monolitic[[molecular assemblers]] following the biological cell analogy. 

Both for [[bootstrapping]] ([[Modular molecular composite nanosystem]]s, [[early diamondoid nanosystem pixel (direct path)]]) 
and for [[advanced productive nanosystem]]s ([[gemstone metamaterial on chip factory]]). 

== In design of "early" nanosystems ==

The strong separation into one-task-only units in the cases of: 
* [[2D rail-frame based distributed modular pick-place assembly system]]
* [[Early diamondoid nanosystem pixel (direct path)]]
* [[Modular molecular composite nanosystem]]s

== In evolution and life ==

See: [[Decompression chain#Philosophical]]

== Related ==

* [[Decompression chain]]
* [[Fat fingers]] & [[Floppy fingers]] – ([[Finger problems]])
* [[Expanding the kinematic loop]]
* better system extendability by compsability of smaller predictably behaving sub building-blocks Thus there is no need for investing again and again in fom-near-scratch-one-off-research-effort for every new product.

== External links ==

* Wikipedia: [https://en.wikipedia.org/wiki/Separation_of_concerns Separation of concerns]

=== Generally in research and engineering ===

In cases where there … 
– too many parameters that can be adjusted (for debugging and/or optimization) and 
– it takes too much time/effort/money for one single of these many tests/experiments 
Clear separation-of-concerns and changing just one parameter at a time is no longer a viable option. 
Then there are available statistical methods that can help. 
* Youtube video: [https://www.youtube.com/watch?v=5oULEuOoRd0 Test Multiple Variables at Once to Optimize Anything – by NightHawkInLight] (Taguchi arrays)
* Wikipedia: [https://en.wikipedia.org/wiki/Taguchi_methods Taguchi_methods] ([https://de.wikipedia.org/wiki/Taguchi-Methode German page with other info ~ i.e. more concrete as of 2024-03])
* Wikipedia: [https://en.wikipedia.org/wiki/Design_of_experiments Design of experiments (DOE)] ([https://de.wikipedia.org/wiki/Statistische_Versuchsplanung German page "statistical experiment-planning"])

[[Category: Incremental path]]

Separation of concerns

2026-10-05T09:45:57Z

Apm: /* In design of "early" nanosystems */ * Modular molecular composite nanosystems

{{stub}}

== In protein folding ==

=== At least three competing purposes for protein side-chains ===

* internal cohesion (hydrophobic side-chains in aqueous solution tend to nestle inside; lack of that gives intrinsically disordered proteins or worse)
* inter protein binding (protein quarternary structure; larger interfaces needed for decently controllable and stiff binding angles)
* outer functionality (binding small molecules and possibly catalyzing reactions between them)
* (allosteric long range motion transmission effects – when looking beyond stiff proteins as building blocks)

Related: [[Orthogonal set of protein binding interfaces]]

=== Holistic behavior on single side chain changes ===

Changing one side-chain on a protein to change a specific function 
can often change conformation and function of the protein at a completely different site. 
This is either ...
* ... a case of bad separation of concerns (that is tolerable for the host organisms species survival) or
* ... a case of separation of concerns at a higher level of abstraction that we do non yet understand

Both cases can pose interesting research problems but 
neither case is useful for fast targeted development.

That is why stiff predictable folding protein motifs are of especial interest. 
Protein that are rather insensitive to local changes. 
See: [[De-novo protein engineering]]

Related: [[Fat finger problem]]

== In design of artificial [[advanced productive nanosystem]]s ==

Separation of concerns is highly desirable for
* better testability that is: easier narrowing down of bugs and
* better system comprehesability

=> Well distributed well debugable systems 
rather than (outdated) ultra compact self replication monolitic[[molecular assemblers]] following the biological cell analogy. 

Both for [[bootstrapping]] ([[MMCN]]s, [[early diamondoid nanosystem pixel (direct path)]]) 
and for [[advanced productive nanosystem]]s ([[gemstone metamaterial on chip factory]]). 

== In design of "early" nanosystems ==

The strong separation into one-task-only units in the cases of: 
* [[2D rail-frame based distributed modular pick-place assembly system]]
* [[Early diamondoid nanosystem pixel (direct path)]]
* [[Modular molecular composite nanosystem]]s

== In evolution and life ==

See: [[Decompression chain#Philosophical]]

== Related ==

* [[Decompression chain]]
* [[Fat fingers]] & [[Floppy fingers]] – ([[Finger problems]])
* [[Expanding the kinematic loop]]
* better system extendability by compsability of smaller predictably behaving sub building-blocks Thus there is no need for investing again and again in fom-near-scratch-one-off-research-effort for every new product.

== External links ==

* Wikipedia: [https://en.wikipedia.org/wiki/Separation_of_concerns Separation of concerns]

=== Generally in research and engineering ===

In cases where there … 
– too many parameters that can be adjusted (for debugging and/or optimization) and 
– it takes too much time/effort/money for one single of these many tests/experiments 
Clear separation-of-concerns and changing just one parameter at a time is no longer a viable option. 
Then there are available statistical methods that can help. 
* Youtube video: [https://www.youtube.com/watch?v=5oULEuOoRd0 Test Multiple Variables at Once to Optimize Anything – by NightHawkInLight] (Taguchi arrays)
* Wikipedia: [https://en.wikipedia.org/wiki/Taguchi_methods Taguchi_methods] ([https://de.wikipedia.org/wiki/Taguchi-Methode German page with other info ~ i.e. more concrete as of 2024-03])
* Wikipedia: [https://en.wikipedia.org/wiki/Design_of_experiments Design of experiments (DOE)] ([https://de.wikipedia.org/wiki/Statistische_Versuchsplanung German page "statistical experiment-planning"])

[[Category: Incremental path]]

Separation of concerns

2026-10-05T09:44:58Z

Apm: /* In design of artificial advanced productive nanosystems */ added short conclusionsdiscussion

{{stub}}

== In protein folding ==

=== At least three competing purposes for protein side-chains ===

* internal cohesion (hydrophobic side-chains in aqueous solution tend to nestle inside; lack of that gives intrinsically disordered proteins or worse)
* inter protein binding (protein quarternary structure; larger interfaces needed for decently controllable and stiff binding angles)
* outer functionality (binding small molecules and possibly catalyzing reactions between them)
* (allosteric long range motion transmission effects – when looking beyond stiff proteins as building blocks)

Related: [[Orthogonal set of protein binding interfaces]]

=== Holistic behavior on single side chain changes ===

Changing one side-chain on a protein to change a specific function 
can often change conformation and function of the protein at a completely different site. 
This is either ...
* ... a case of bad separation of concerns (that is tolerable for the host organisms species survival) or
* ... a case of separation of concerns at a higher level of abstraction that we do non yet understand

Both cases can pose interesting research problems but 
neither case is useful for fast targeted development.

That is why stiff predictable folding protein motifs are of especial interest. 
Protein that are rather insensitive to local changes. 
See: [[De-novo protein engineering]]

Related: [[Fat finger problem]]

== In design of artificial [[advanced productive nanosystem]]s ==

Separation of concerns is highly desirable for
* better testability that is: easier narrowing down of bugs and
* better system comprehesability

=> Well distributed well debugable systems 
rather than (outdated) ultra compact self replication monolitic[[molecular assemblers]] following the biological cell analogy. 

Both for [[bootstrapping]] ([[MMCN]]s, [[early diamondoid nanosystem pixel (direct path)]]) 
and for [[advanced productive nanosystem]]s ([[gemstone metamaterial on chip factory]]). 

== In design of "early" nanosystems ==

The strong separation into one-task-only units in the cases of: 
* [[2D rail-frame based distributed modular pick-place assembly system]]
* [[Early diamondoid nanosystem pixel (direct path)]]

== In evolution and life ==

See: [[Decompression chain#Philosophical]]

== Related ==

* [[Decompression chain]]
* [[Fat fingers]] & [[Floppy fingers]] – ([[Finger problems]])
* [[Expanding the kinematic loop]]
* better system extendability by compsability of smaller predictably behaving sub building-blocks Thus there is no need for investing again and again in fom-near-scratch-one-off-research-effort for every new product.

== External links ==

* Wikipedia: [https://en.wikipedia.org/wiki/Separation_of_concerns Separation of concerns]

=== Generally in research and engineering ===

In cases where there … 
– too many parameters that can be adjusted (for debugging and/or optimization) and 
– it takes too much time/effort/money for one single of these many tests/experiments 
Clear separation-of-concerns and changing just one parameter at a time is no longer a viable option. 
Then there are available statistical methods that can help. 
* Youtube video: [https://www.youtube.com/watch?v=5oULEuOoRd0 Test Multiple Variables at Once to Optimize Anything – by NightHawkInLight] (Taguchi arrays)
* Wikipedia: [https://en.wikipedia.org/wiki/Taguchi_methods Taguchi_methods] ([https://de.wikipedia.org/wiki/Taguchi-Methode German page with other info ~ i.e. more concrete as of 2024-03])
* Wikipedia: [https://en.wikipedia.org/wiki/Design_of_experiments Design of experiments (DOE)] ([https://de.wikipedia.org/wiki/Statistische_Versuchsplanung German page "statistical experiment-planning"])

[[Category: Incremental path]]

Conflation of concerns

2026-10-05T09:38:42Z

Apm: Redirected page to Separation of concerns

#REDIRECT [[Separation of concerns]]

Separation of concerns

2026-10-05T09:37:04Z

Apm: /* At least three competing purposes for protein side-chains */

{{stub}}

== In protein folding ==

=== At least three competing purposes for protein side-chains ===

* internal cohesion (hydrophobic side-chains in aqueous solution tend to nestle inside; lack of that gives intrinsically disordered proteins or worse)
* inter protein binding (protein quarternary structure; larger interfaces needed for decently controllable and stiff binding angles)
* outer functionality (binding small molecules and possibly catalyzing reactions between them)
* (allosteric long range motion transmission effects – when looking beyond stiff proteins as building blocks)

Related: [[Orthogonal set of protein binding interfaces]]

=== Holistic behavior on single side chain changes ===

Changing one side-chain on a protein to change a specific function 
can often change conformation and function of the protein at a completely different site. 
This is either ...
* ... a case of bad separation of concerns (that is tolerable for the host organisms species survival) or
* ... a case of separation of concerns at a higher level of abstraction that we do non yet understand

Both cases can pose interesting research problems but 
neither case is useful for fast targeted development.

That is why stiff predictable folding protein motifs are of especial interest. 
Protein that are rather insensitive to local changes. 
See: [[De-novo protein engineering]]

Related: [[Fat finger problem]]

== In design of artificial [[advanced productive nanosystem]]s ==

Separation of concerns is highly desirable for
* better testability that is: easier narrowing down of bugs and
* better system comprehesability

== In design of "early" nanosystems ==

The strong separation into one-task-only units in the cases of: 
* [[2D rail-frame based distributed modular pick-place assembly system]]
* [[Early diamondoid nanosystem pixel (direct path)]]

== In evolution and life ==

See: [[Decompression chain#Philosophical]]

== Related ==

* [[Decompression chain]]
* [[Fat fingers]] & [[Floppy fingers]] – ([[Finger problems]])
* [[Expanding the kinematic loop]]
* better system extendability by compsability of smaller predictably behaving sub building-blocks Thus there is no need for investing again and again in fom-near-scratch-one-off-research-effort for every new product.

== External links ==

* Wikipedia: [https://en.wikipedia.org/wiki/Separation_of_concerns Separation of concerns]

=== Generally in research and engineering ===

In cases where there … 
– too many parameters that can be adjusted (for debugging and/or optimization) and 
– it takes too much time/effort/money for one single of these many tests/experiments 
Clear separation-of-concerns and changing just one parameter at a time is no longer a viable option. 
Then there are available statistical methods that can help. 
* Youtube video: [https://www.youtube.com/watch?v=5oULEuOoRd0 Test Multiple Variables at Once to Optimize Anything – by NightHawkInLight] (Taguchi arrays)
* Wikipedia: [https://en.wikipedia.org/wiki/Taguchi_methods Taguchi_methods] ([https://de.wikipedia.org/wiki/Taguchi-Methode German page with other info ~ i.e. more concrete as of 2024-03])
* Wikipedia: [https://en.wikipedia.org/wiki/Design_of_experiments Design of experiments (DOE)] ([https://de.wikipedia.org/wiki/Statistische_Versuchsplanung German page "statistical experiment-planning"])

[[Category: Incremental path]]

Separation of concerns

2026-10-05T09:36:38Z

Apm: /* In protein folding */ added section === At least three competing purposes for protein side-chains === & === Holistic behavior on single side chain changes ===

{{stub}}

== In protein folding ==

=== At least three competing purposes for protein side-chains ===

* internal cohesion (hydrophobic side-chains in aqueous solution tend to nestle inside; lack of that gives intrinsically disordered proteins or worse)
* inter protein binding (protein quarternary structure; larger interfaces needed for decently controllable and stiff binding angles)
* outer functionality (binding small molecules and possibly catalyzing reactions between them)
* (allosteric long range motion transmission effects looking beyond stiff proteins as building blocks)

Related: [[Orthogonal set of protein binding interfaces]]

=== Holistic behavior on single side chain changes ===

Changing one side-chain on a protein to change a specific function 
can often change conformation and function of the protein at a completely different site. 
This is either ...
* ... a case of bad separation of concerns (that is tolerable for the host organisms species survival) or
* ... a case of separation of concerns at a higher level of abstraction that we do non yet understand

Both cases can pose interesting research problems but 
neither case is useful for fast targeted development.

That is why stiff predictable folding protein motifs are of especial interest. 
Protein that are rather insensitive to local changes. 
See: [[De-novo protein engineering]]

Related: [[Fat finger problem]]

== In design of artificial [[advanced productive nanosystem]]s ==

Separation of concerns is highly desirable for
* better testability that is: easier narrowing down of bugs and
* better system comprehesability

== In design of "early" nanosystems ==

The strong separation into one-task-only units in the cases of: 
* [[2D rail-frame based distributed modular pick-place assembly system]]
* [[Early diamondoid nanosystem pixel (direct path)]]

== In evolution and life ==

See: [[Decompression chain#Philosophical]]

== Related ==

* [[Decompression chain]]
* [[Fat fingers]] & [[Floppy fingers]] – ([[Finger problems]])
* [[Expanding the kinematic loop]]
* better system extendability by compsability of smaller predictably behaving sub building-blocks Thus there is no need for investing again and again in fom-near-scratch-one-off-research-effort for every new product.

== External links ==

* Wikipedia: [https://en.wikipedia.org/wiki/Separation_of_concerns Separation of concerns]

=== Generally in research and engineering ===

In cases where there … 
– too many parameters that can be adjusted (for debugging and/or optimization) and 
– it takes too much time/effort/money for one single of these many tests/experiments 
Clear separation-of-concerns and changing just one parameter at a time is no longer a viable option. 
Then there are available statistical methods that can help. 
* Youtube video: [https://www.youtube.com/watch?v=5oULEuOoRd0 Test Multiple Variables at Once to Optimize Anything – by NightHawkInLight] (Taguchi arrays)
* Wikipedia: [https://en.wikipedia.org/wiki/Taguchi_methods Taguchi_methods] ([https://de.wikipedia.org/wiki/Taguchi-Methode German page with other info ~ i.e. more concrete as of 2024-03])
* Wikipedia: [https://en.wikipedia.org/wiki/Design_of_experiments Design of experiments (DOE)] ([https://de.wikipedia.org/wiki/Statistische_Versuchsplanung German page "statistical experiment-planning"])

[[Category: Incremental path]]

Casting crystolecules

2026-10-05T09:22:35Z

Apm: Size of cast crystolecules

{{stub}}
[[File:Images large oc4c01826 0007.jpeg|268px|thumb|righ|Here [https://pubs.acs.org/doi/10.1021/acscentsci.4c01826 (leave to paper)] de-novo proteins are used to regulate the size of CdS nanoscystals. The proteins make a sort of casting shell for the crystal growth defining and delimiting it's shape. Not quite atomically precise but well beyond the capabilities of free space thermodynamically grown nanocrystals. This example is still quite simple and primitive. Casting bigger more complex structures will need improvements on [[noncyclic termination control]] for [[de-novo protein engineering]].]]

'''Casting crystolecules'''. Or more accurately '''"in nano-mold crystallization"'''. 
The basic idea here is to use a mold for that inside has surfaces that temlates crystal seed formation 
that initiate crystallization but also a compartment with small enough openings that terminate crystal growth (presumably). 

This only works for in-solvent-crystallizable gemstones. 
In particular clearly excluding diamond and it's hexagonal version [[lonsdaleite]], also likely excluding [[moissanite]] and many semiconductor diamondoid structure gemstones. 
Some salot of oxoacid gemstones may be viable. Iron based gems like hematite, magnetite, pyrite seem viable. 

== Questions ==

* limits on atomic precison in surfaces (and in the interior crystal structure)
* removability of the mold

== Nature of the mold ==

* In early incremental path technology this may protein based molds. 
* In advanced [[gem based APM]] the molds themselves could possibly be made from [[crystolecules]]. 

== Size of cast crystolecules ==

Since achieving atomic precision of surfaces via this approach is questionable 
to still get decently well defined shapes somewhat bigger sizes for the hollow casting structures will be needed. 
Somewhat bigger than the typical size of [[crystolecules]] expectable via [[force applying mechanosynthesis]]. 
Casting such bigger more complex structures will need improvements on [[noncyclic termination control]] for [[de-novo protein engineering]]. 

Actually [[noncyclic termination control]] for [[de-novo protein engineering]] 
is an obstacle that is generally present of the [[incremental path]]. 
Particularly for scaling of [[hierarchical self-assembly]] to expand the [[kinematic loop]] disentangle [[conflation of concerns]] 
and thereby provide a basis to make starting climbing of the [[technology levels]] more feasible. 

== Related ==

* [[Amorphous structures]]
* [[Inter technology binding]]

== External links ==

* Youtube Foresight Institute: '''[https://www.youtube.com/watch?v=16-OB2Q9WoY 2025 – Amijai Saragovi | Functional Protein-Semiconductor Nanotechnology in Microbial Factories]'''

* Good graphic on nucleation barrier in Gibbs free energy used on German wikipedia: '''[https://de.wikipedia.org/wiki/Datei:CNT_barrier.png CNT barrier]''' [https://de.wikipedia.org/wiki/Keimbildung Keimbildung (de)]
* https://en.wikipedia.org/wiki/Nucleation
* https://en.wikipedia.org/wiki/Classical_nucleation_theory
* https://en.wikipedia.org/wiki/Crystal_growth
* https://en.wikipedia.org/wiki/Gibbs_free_energy

Casting crystolecules

2026-10-05T09:08:45Z

Apm: added relevant image and adjusted the carried over description for the local context here

{{stub}}
[[File:Images large oc4c01826 0007.jpeg|268px|thumb|righ|Here [https://pubs.acs.org/doi/10.1021/acscentsci.4c01826 (leave to paper)] de-novo proteins are used to regulate the size of CdS nanoscystals. The proteins make a sort of casting shell for the crystal growth defining and delimiting it's shape. Not quite atomically precise but well beyond the capabilities of free space thermodynamically grown nanocrystals. This example is still quite simple and primitive. Casting bigger more complex structures will need improvements on [[noncyclic termination control]] for [[de-novo protein engineering]].]]

'''Casting crystolecules'''. Or more accurately '''"in nano-mold crystallization"'''. 
The basic idea here is to use a mold for that inside has surfaces that temlates crystal seed formation 
that initiate crystallization but also a compartment with small enough openings that terminate crystal growth (presumably). 

This only works for in-solvent-crystallizable gemstones. 
In particular clearly excluding diamond and it's hexagonal version [[lonsdaleite]], also likely excluding [[moissanite]] and many semiconductor diamondoid structure gemstones. 
Some salot of oxoacid gemstones may be viable. Iron based gems like hematite, magnetite, pyrite seem viable. 

== Questions ==

* limits on atomic precison in surfaces (and in the interior crystal structure)
* removability of the mold

== Nature of the mold ==

* In early incremental path technology this may protein based molds. 
* In advanced [[gem based APM]] the molds themselves could possibly be made from [[crystolecules]].

== Related ==

* [[Amorphous structures]]
* [[Inter technology binding]]

== External links ==

* Youtube Foresight Institute: '''[https://www.youtube.com/watch?v=16-OB2Q9WoY 2025 – Amijai Saragovi | Functional Protein-Semiconductor Nanotechnology in Microbial Factories]'''

* Good graphic on nucleation barrier in Gibbs free energy used on German wikipedia: '''[https://de.wikipedia.org/wiki/Datei:CNT_barrier.png CNT barrier]''' [https://de.wikipedia.org/wiki/Keimbildung Keimbildung (de)]
* https://en.wikipedia.org/wiki/Nucleation
* https://en.wikipedia.org/wiki/Classical_nucleation_theory
* https://en.wikipedia.org/wiki/Crystal_growth
* https://en.wikipedia.org/wiki/Gibbs_free_energy

Inter technology binding

2026-10-05T09:02:13Z

Apm: fixed typos in image description

{{site specific term}}
{{stub}}
[[File:Images large oc4c01826 0007.jpeg|268px|thumb|righ|Here [https://pubs.acs.org/doi/10.1021/acscentsci.4c01826 (leave to paper)] de-novo proteins are used to regulate the size of CdS nanoscystals, But once one has the capability of [[force applying mechanosynthesis]] then one (reversely) could mechanosynthsize nano-cystals with a shape that nicely binds to the de-novo proteins. Giving one a [[stiff]] interface between the two material technologies.]]

{{Wikitodo|Add main text.}}

== Related ==

* '''[[Mixed path]]''', [[Incremental path]], [[Direct path]], [[Pathways]]
* [[Technology levels]]

== Externa links ==

=== Protein <=> Nanocrystal ===

* [https://pubs.acs.org/doi/10.1021/acscentsci.4c01826 2025 – De Novo Proteins Template the Formation* of Semiconductor Quantum Dots]

=== DNA <=> Protein ===

* [https://en.wikipedia.org/wiki/Category:DNA-binding_proteins Category:DNA-binding_proteins]
* [https://en.wikipedia.org/wiki/DNA-binding_protein DNA-binding protein]
* [https://en.wikipedia.org/wiki/DNA-binding_domain DNA-binding domain]
* [https://en.wikipedia.org/wiki/Histone-like_DNA-binding_protein Histone-like DNA-binding protein]
* [https://en.wikipedia.org/wiki/Histone Wikipedia: Histone]
----
* [https://pdb101.rcsb.org/motm/7 Molecule of the Month: Nucleosome]
Some random PDB entries of nucleosomes with histones:
* [https://www.rcsb.org/structure/7XVL 7XVL – Crystal Structure of Nucleosome-H1.0 Linker Histone Assembly (sticky-169an DNA fragment)]
* [https://www.rcsb.org/structure/7XVM 7XVM – Crystal Structure of Nucleosome-H5 Linker Histone Assembly (sticky-169a DNA fragment)]
* [https://www.rcsb.org/structure/8T9F 8T9F – Crystal Structure of Nucleosome-H1.0 Linker Histone Assembly (sticky-169an DNA fragment)]
* [https://www.rcsb.org/structure/8U13 8U13 – Cryo-EM structure of the human nucleosome core particle ubiquitylated at histone H2A lysine 15 in complex with RNF168-UbcH5c (class 1)]
* [https://www.ebi.ac.uk/pdbe/entry/pdb/5gt3?activeTab=summary 5gt3 – Crystal structure of nucleosome particle in the presence of human testis-specific histone variant, hTh2b]
* [https://www.ebi.ac.uk/pdbe/entry/pdb/5GSU?activeTab=summary 5gsu – Crystal structure of nucleosome core particle consisting of human testis-specific histone variants, Th2A and Th2B]
* [https://www.ebi.ac.uk/pdbe/entry/pdb/3ayw?activeTab=summary 3ayw – Crystal Structure of Human Nucleosome Core Particle Containing H3K56Q mutation]
----
* [https://www.uniprot.org/uniprotkb/Q09028/entry Histone-binding protein RBBP4]

Casting crystolecules

2026-10-05T09:00:03Z

Apm: added link to * Inter technology binding

{{stub}}

'''Casting crystolecules'''. Or more accurately '''"in nano-mold crystallization"'''. 
The basic idea here is to use a mold for that inside has surfaces that temlates crystal seed formation 
that initiate crystallization but also a compartment with small enough openings that terminate crystal growth (presumably). 

This only works for in-solvent-crystallizable gemstones. 
In particular clearly excluding diamond and it's hexagonal version [[lonsdaleite]], also likely excluding [[moissanite]] and many semiconductor diamondoid structure gemstones. 
Some salot of oxoacid gemstones may be viable. Iron based gems like hematite, magnetite, pyrite seem viable. 

== Questions ==

* limits on atomic precison in surfaces (and in the interior crystal structure)
* removability of the mold

== Nature of the mold ==

* In early incremental path technology this may protein based molds. 
* In advanced [[gem based APM]] the molds themselves could possibly be made from [[crystolecules]].

== Related ==

* [[Amorphous structures]]
* [[Inter technology binding]]

== External links ==

* Youtube Foresight Institute: '''[https://www.youtube.com/watch?v=16-OB2Q9WoY 2025 – Amijai Saragovi | Functional Protein-Semiconductor Nanotechnology in Microbial Factories]'''

* Good graphic on nucleation barrier in Gibbs free energy used on German wikipedia: '''[https://de.wikipedia.org/wiki/Datei:CNT_barrier.png CNT barrier]''' [https://de.wikipedia.org/wiki/Keimbildung Keimbildung (de)]
* https://en.wikipedia.org/wiki/Nucleation
* https://en.wikipedia.org/wiki/Classical_nucleation_theory
* https://en.wikipedia.org/wiki/Crystal_growth
* https://en.wikipedia.org/wiki/Gibbs_free_energy

Form factors of gem-gum factories

2026-10-05T08:58:48Z

Apm: added image with contents in the desktop device

[[File:C00-HomeScaleAssemblySystems.jpg|400px|thumb|right|Collage of some AI-art & a hand-sketch. Illustrating how a portable desktop living-room nanofactory device could look like. And illustrating larger scales too. Though at larger scales in-place-prodcution for visibly large scales (as is depicted for a car and a ship) grows increasingly unlikely. For car scale more likely is the use of macroscale fairy-hand-tentacle-manipulators (as depicted) and organic looking crane like manipulators for ship & building scale (not depicted). Also at ship scale quite likely is the use of several disjoint nanofactory chips rather than the extremely big on (as is depicted). All macroscale manipulators possible dynamically deployed as needed.]]

[[File:PortableLivingroomNanofactory.jpg|300px|thumb|right|One possible form factor is similar to today's tablet computers. The protective hood could be dynamical deployed making it very backpack-portable. A cable for supply with resources and/or power would be needed. Not depicted here. Related: [[Operation modes of a gem-gum factory]].]]

[[File:Gem-gum-factory-with-shoe-product-and-anemone-arm-fairy-hand-end-effectors.jpg|thumb|right|300px|A personal [[Nanofactory|gem-gum factory]] here in tablet format dynamically deploying a clean-room hood [[Gem-gum anemone-arm fairy-hand manipulator]]s and thst are doing some final touches (tying retro-style laces) on the fully "extruded" product.]]

[[File:Photo of a iridescent friendly futuristic organically shaped telephone booth standing beside a path in a park in summer photo.jpeg|300px|thumb|right|Public terminal concept art. More on that on page: [[Global microcomponent redistribution system]].]]

= Generally =

* Bigger devices may stay permanently connect to the [[global microcomponent redistribution system]].
* Smaller devices for mobile uses may be connected too or used in conjunction with [[resource cartridges]].
Special form-factors may be present for special tasks like e.g.
* extending or culling back on the [[global microcomponent redistribution system]]
* extending or culling back on a gem-gum street transport network
* very large scale construction of houses, ships, and structures in space

Smaller ones (up to garage door size maybe) could be called '''"personal gem-gum factories"''' 
larger community controlled ones ones in analogy '''"mainframe gem-gum factories"''' 
Related topic: [[Private ownership]]

= Some thought about various form factors =

== Tablet (portable keyless computer) form-factor ==

Basically the size of a tablet or a laptop or a school notebook of some sort. 
The main point is portability. 
A form factor that allows for convenient transport in backpacks.

Usage will often be unplugged. 
So one might want to charge up and lug around additional [[resource cartridges]]. 
These may have the same rectangular form factor except greater thickness to pack more stuff in. 
Thick and heavy like a massive book.

[[Folding gem-gum factories|Designs that fold up]] to provide bigger area should be possible 
if some more design effort is invested.

=== Phablet (big smartphone) form-factor ===

Like the Tablet one just a bit smaller. 
For people who want to carry their device in their pants pockets. 
This may be sufficiently big for Making some shoes.

This form factor could be called: '''"Pants-pockets gem-gum factory"'''.

== Standalone photocopier form-factor ==

These would be located:
* in every home in one of the main rooms like the living room, the kitchen or an office
* in public on the side of walkways and streets
All directly and permanently connected to the [[global microcomponent redistribution system]]

This direct connection means a vide variety of preassembled microcomponents is readily available leading to
very high assembly speeds for all non exotic non super novel products.
In cases maybe practically instant assembly for human senses.

Of course one could make just plain faucets for the [[global microcomponent redistribution system]].
But almost everywhere will be enough space to add a photocopier sized terminal.
If not a standanlone photocopier sized one than at least a tablet/laptop sized one.
And if not that than at least the some means for spaning one at the endpoint.
like a nametag keyfob form-factor one.
This "leaf" may double as kind of a "seed". See further down.

There is also the gem-gum factory that assembled the branch of the [[microcomponent redistribution system]] in the first place. But that one might be special in that it has a very different long cylindrical form factor especially optimized for construction of [[capsule transport]] wires and digging on the other end.
And one might want to remove it / retract it / "suck" it in after wire laying work work is finished to the final branch tips.

== Nametag keyfob form-factor ==

Given the small size and mass there is no harm in carrying such small a device around
additionally to one of the tablet form factor ones.

=== Product size limitations ===

Unless it's not a foldable or otherwise stretching design
the size of the immediate products are quite limited.

Of course it's possible to first assemble bigger (longer) one and proceed with that.

Possible direct products of keyfob form-factor gem-gum factories could include: 
(highly random list) 
* smart glasses, small hand input devices
* knives, spoons, forks, bottle openers
* writing pens, laser pointers, small hand tools
* shoe laces, small short ropes and wires
* jewellery

=== Energy supply limitations ===

More critically than size restrictions on products the [[resource cartridges]] for raw material and energy may be in-proportionally big. If [[air as a resource]] is used to avoid the need for a big cartridge then it will be necessary to procure and supply a considerable amount of energy from local resources.

Quite big but very thin and flexible fold up solar panels could be integrated for providing that energy off grid.
Think: small fold up frisbee or very small umbrella.
Given the intended location of usage is sufficiently sunny. Ideally direct an high up sun. This will be slow.

Of course it's possible to first very slowly assemble bigger gem-gum factory and much more solar cell area
and then proceed with that with much more solar power and speed even in areas that are overclouded/shaddowy.
Doing that multistage yields an exponential speedup. That only works to some limit though.
If it's simply too dark (completely clouded, underground, in polar night, …) or there is not enough area available for lay out of (self anchoring?) solar cell foil then one obviously needs to look for other energy sources.

* Manual cranking. This manufacturing keyfob is supposed to be carried by humans after all.
* Wind power. Seems quite hard to pack something like that down into kefob size. But who knows.
* Thermal differences. Having some micro-robots (not nano-robots) driving a thin needle into the ground. (low friction solid state heatpump)
* Exotic inverse solar panels? Exploiting that fact that the cosmic background has a cold temperature of just ~3K

Many of these may make more sense only after a second scaleup-stage 
only after some initial scale-up powered by hand-cranking.

All this is especially relevant for a scenario with a more or less global catastrophe where
a bunch of geocached gem-gum factories of this form factor could provide a [[save point]] for technology.

== Bigger ==

* Garage form-factor
* Shipyard form-factor
* Housing construction
* Space construction

= Related =

* [[Gemstone metamaterial on chip factory]]
----
* [[Microcomponent redistribution system]]
* [[Large scale construction]]
----
* [[Gem-gum fairy-hand-tentacle manipulator]] (and [[organically shaped truss crane]])

[[Category:Large scale construction]]
[[Category:Far term target]]

Pathways to advanced APM systems

2026-10-04T19:26:12Z

Apm: Added the pathways graphic as it was sorely missing here.

{{stub}}
[[File:APM-EarlyDevelopmentPaths.jpg|600px|thumb|right|A possible map for [[incremental path]]ways and [[mixed path]]ways. Left axis: [[technology levels]] Right axis see: [[convergent assembly comparison]] and [[hierarchical self-assembly]]. The [[direct path]] starts top left (3,0) right away facing the challenge of more difficult [[scaling of system complexity]] rather than getting the challenge to get to better i.e. stiffer materials. The red stars indicate challenging blockades: (1,0) [[Positional assembly redundancy blockade]] and (0,5) [[Thermal driven selfassembly diffusion speed slowdown blockade]].]]
[[File:Rock_climber_on_the_Main_Wall_Trowbarrow.jpg|400px|thumb|right|the steep direct path]]
[[File:Stone_path_on_Fan_Brycheiniog.jpg|400px|thumb|right|the long incremental path]]
* The [[Incremental path]]
* The [[Direct path]]
* The [[Mixed path]]
* The historic [[Feynman path]]
* The paths that aren't paths: [[Brownian Path]] => [[Accidental Path]]
[[Category:General]]
[[Category:Disquisition]]
{{wikitodo|Needs a basic introduction.}}

Its not a binary either or question whether the direct or the incremental path will be taken its more that the two represent extreme ends of a spectrum of possible development progressions.
Both types of paths will likely heavily borrow from the [[non mechanical technology path]].

There seems to be a peaceful internal conflict. 
See also: [[Pathway controversy]].

== Views of the paths from the proponents of different viewpoints ==

Critiques:
* incremental path (Ralph Merkle & co): slow and aimless little targeted effort ... {{wikitodo|collect their arguments}}
* direct path (E.Drexler & co): too hard to access experimentally, slow experimental progress, little research motivation (funds)

== Relation to speed of introduction of advanced productive nanosystems ==

It seems any bets are off here.
It is worth to note that the usual association of the direct path with sudden and rapid changes and the indirect path with slow and progressive changes
might be not incorrect.
* {{wikitodo|treat benefits and risks of fast vs slow changes}}

== Related ==

* [[Bootstrapping methods for productive nanosystems]]
* [[Spectrum of pathways]]
* [[Pathway controversy]]
* [[Bridging the gaps]]
* '''Up: [[Where to start targeted development]]'''
----
{{wikitodo|These following pages need some review.}}
* [[Non mechanical technology path]]
* [[Brownian technology path]]

== External links ==

Citation from the article "[http://crnano.typepad.com/crnblog/2006/09/from_here_to_na.html From Here to Nanofactories]" (crnano blog – Posted on September 24, 2006): 
"..., advances in one dimension will synergize with advances in other dimensions, so it may be more efficient to go straight to a new technology that makes bigger leaps forward in several dimensions at once. But if such a technology can't be found for a particular leap, it can be done in a series of incremental steps. ..."

[[category:Incremental path]]
[[category:Direct path]]

Convergent assembly

2026-10-04T18:39:42Z

Apm: /* Related */ * Optimal sublayernumber for minimal friction

[[File:0609factory700x681.jpg|thumb|400px|Note that '''in a practical design the size steps would be much bigger than mere doubling steps''' also '''it is not a necessity that the topmost convergent assembly levels have the same size as the whole factory device''' - like shown here. - Devices can be made thin and flat. - Coplanar layers are natural when equal operation speeds in all assembly levels are present.]]
[[File:NanosystemsNotAProposedDesignConvergentAssembly.jpg|400px|thumb|right|'''THIS IS NOT A PROPOSED DESIGN (so explicitly stated in [[Nanosystems]])'''. Just an example of a non-planar [[convergent assembly]] topology and geometry (or morphology as in biology). '''More or less planar [[assembly layers]] likely match natural scaling laws applied to the problem domain much better.''' {{wikitodo|Add Josh Halls analytic math comparison to scaling laws in bio-systems too. Plus his picture.}}]]
[[File:productive-nanosystems-video-snapshot.png|thumb|400px|Cross section through a nanofactory. Image taken from [[Productive Nanosystems From molecules to superproducts]] video. '''This here is an actually proposed design''' for convergent [[assembly level]]s in the form of convergent [[assembly layer]]s. Note that the most part of the stack are the bottom nanoscale [[sub-layer]]s all of same size. Further convergent assembly in the naive form (shown in the first image on the page here) is optional (replacing product assemblers) at the top and not present here at all.]]

In [[nanofactory|advanced gemstone based atomically precise manufacturing systems]] convergent assembly (Or hierarchical assembly or confluent assembly) is the general process of taking small parts and putting them together to bigger parts and then taking those bigger parts and putting them together to even bigger parts and so on.

Convergent assembly must not be confused with [[exponential assembly]] 
A concept for bootstrapping [[APM|AP manufacturing]]. 
Convergent assembly is also exponential due to its tree structure. Describable by geometric series. This might be a source of potential confusion. 

'''For related math see: [[Math of convergent assembly]]'''

= Motivations for convergent assembly =

* '''Avoiding unnecessary disassembly''' when reconfiguring already produced products in a way that just swaps big chunks.
* Allowing to assemble unstable overhangs or impossible undercuts without scaffolds. (stalactite like structures)
* The possibility to keep everything in a vacuum/cleanroom till the final product release - this should not be necessary and may decrease the incentive for the creation of systems that are capable of [[recycling]].
* Nontrivial effects on speed.

= General =

Convergent assembly is possible in both: [[positional assembly]] and [[self assembly]]. 
{{wikitodo|Cover the selfassembly side too in this introductory general article – [[selfassembly level]]s}}

In an advanced [[nanofactory|gem-gum-factory]] the '''convergent assembly levels''' can be identified with the abstract [[assembly levels]]. 
Note that those are not tied to any specific geometric layout like e.g. stacked coplanar [[assembly layers]].

Stacking those levels to [[nanofactory layers|layers]] as a concrete implementation
is a good first approximation (especially in the mid range size levels where scale invariant design holds for a decent range of orders of magnitudes)
it creates a [[nanofactory]] which is practical and conveniently also reasonably easy to analyze.
For optimal performance (in efficiency or throughput) deviations from a design with coplanar layers may be necessary.

Both at the very small scales and at the very large scales a highly optimized nanofactroy design may strongly deviate from [[Nanofactory layers|a simple stack of layers]].

Some new factors that come into effect at large scales are:
* The production facilities own mass under earths (or other planetary) gravity
* At very large scales even abundant materials can get scarce.
* {{speculativity warning}} At very very large scales production facilies would act as "planetoid" attracting the outer parts of its structure to its center.

Related: [[Look of large scale gem-gum factories]]

= Degree, stepsize, fillfactor, ... =

There are at least three important parameters to characterize convergent assembly. 

* The '''"degree" or "[[convergent assembly depth]]"''' of convergent assembly, in terms of number of '''convergent assembly levels across the whole stack'''. Stacks of chambers of the same are counted as one layer! Such stacks need means to transport finished parts to the top. Convergent assembly depth has little effect on maximal throughput! But not none.

* The '''"stepsize" or "[[branching factor]]"''' of (convergent) assembly, in terms of the '''ratio of product-size to resource-size''' in each assembly step, has a huge effect on speed. Note though that this parameter is present for all "degrees" of convergent assembly even degree one or zero. Meaning it is also present in productive nanosystems that lack convergent assembly. (In systems with more than one convergent assembly layer unequal stepsizes can occur.)

* The '''"fillfactor" or "[[chamber to part size ratio]]"'''. This is relevant for when the convergent assembly does not lead all the way up to a single macroscopic chamber but instead stops sooner. The topmost layer has to fill a dense volume unlike the layers below. If the topmost layer indeed assembles a dense product then this will slow it down (if not compensated by more and/or faster working sub-chambers in the layer below).

= Topology and Geometry =

The optimal branching topology (given by physics) can impose strong constraints on the geometry of the [[assembly levels]] of convergent assembly. 
For artificial on chip gemstone based systems an organization into coplanar [[assembly layers]] seems to be a good baseline starting point. 

Natural systems are quite different. They tend to
* fill up whole macroscopic volumes with productive nanomachinery
* form dentridic 3D tree like systems. Like e.g. vascular systems, lungs, lymph systems, trachea systems in insects, …

= Influence of the degree of convergent assembly on throughput speed =

Convergent assembly per se is not faster than if one would just use the highly parallel bottom layer(s) to assemble final product in one fell swoop.
Assembling the final product in one fell swoop right from a naive general purpose highly parallel bottom-most layer would be just as fast as a system with the same bottom-layer that has a convergent assembly hierarchy stacked on top.
There are indirect aspects of convergent assembly that provide speedup though. Including avoiding unnecessary energy turnover.

Especially [[recycling]] of already produced [[microcomponents]] in the higher [[assembly level]]s should be able to give a massive speed boost.

== Speedup of recycling (recomposing product updates) by enabling partial top down disassembly ==

* Simpler decomposition into standard assembly-groups that can be put together again in completely different ways.
* Automated management of bigger logical assembly-groups

Full convergent assembly all the way up to the macro-scale allows one to perform rather trivial automated macroscopic reconfigurations with the available macroscopic manipulators. Otherwise it would be necessary to fully disassemble the product almost down to the molecular level which would be wasteful in energy and time. In short: just silly.

Especially doing full disassembly at the lowest assembly levels makes the surface area explode and number of strong interfaces that need to be broken and reformed explode. Each step with a ''potentially very low'' but still existent efficiency penality. Getting energy in and waste heat out can limit operation speed.

Choosing to leave out just the topmost one to three convergent assembly layers could provide the huge portability benefit of a flat form factor (without significant loss of reconfiguration speed).
Alternatively with a bit more design effort the topmost convergent layers could be made collapsible/foldable.

== Convergent assembly makes low level specialization possible => speedup ==

Putting the first convergent assembly layers right above the bottom layers allows for specialized production units ([[mechanosynthesis core]]s specialized to specific [[crystolecule|molecular machine elements]]) that can operate faster than general purpose production units.
The pre-produced standard-parts get redistributed ''form where they are made to where they are needed'' by an intermediary [[routing layer]] and then assembled by the next layer in the convergent assembly hierarchy.

=== Component routing logistics ===

Between the layers of convergent assembly there is the opportunity to nestle [[routing layer]]s that are potentially non local.

If necessary the products outputted by the small assembly cells below the one bigger associated upper assembly cell may be routed beyond the limits of this associated assembly cell that lies directly above them. That is if the geometric layout decisions allow this (this seems e.g. relatively easy the case in a stratified nanofactory design). This allows the upper bigger assembly cells to receive more part types than the limited number of associated lower special purpose mill outputs would allow.
The low lying [[diamondoid molecular element|crystolecule]] routing layer is especially critical in this regard.

=== Comparison to specialization on the macroscale ===

In today's industry of non atomically precise production convergent assembly is the rule but in most cases it is just not fully automated. An example is the path from raw materials to electronic parts to printed circuit boards and finally to complete electronic devices. The reason for convergent assembly here is that for the separate parts there are many specialized production places necessary. The parts just can't be produced directly in place in the final product.

Usually one needs '''a welter of completely identical building components in a product'''.
Connection pins are a good example.
'''Single atoms are completely identical but they lack in variety''' in their independent function.
Putting together standard parts in place with a freely programmable general purpose manipulator amounts to a waste of space and time. General purpose manipulators are misused that way.

Even in general purpose computer architectures there are - if one takes a closer look - specially optimized areas for special tasks. '''Specialization on a higher abstraction level is usually removed from the hardware and put into software.'''

(In a physically producing personal fabricator there's a far wider palette of possibilities for physical specialization than in a data shuffling microprocessor since there are so many possible [[diamondoid molecular elements]] that can be designed.)

'''Bigger assembly groups provide more design freedom''' and for the better or the worse the freedom of format proliferation.
Here the speed gain from specialization drops and the space usage explodes exponentially because of the combinatoric possibilities.
Out of this reason '''this is the place where to switch hardware generalization compensated by newly introduced software specialization.'''

Thus In a personal fabricator the most if not '''all the specialization is distributed in the bottom-most layers'''. Further up the assembly levels specialization is not a motivation for convergent assembly anymore. Some of the other motivations may prevail.
Higher convergent assembly levels (layers) quickly loose their logistic importance (the relative transport distances to the part sizes shrink).
The main distribution action takes place in the first three logistic layers.

Side-notes:
* In the [[Molecular assembler|'''obsolete''' assembler concept]] all parts of a product where thought to be [[mechanosynthesis|mechanosynthesized]] right at their final place in the product.
* Consumer side preferences in possibility space may drive higher level physical specialization in [[further improvement at technology level III|beyond advanced APM systems]].

= Characterization of convergent assembly =

'''See: [[Math of convergent assembly]]'''

Convergent assembly can follow different scaling laws and follow different topology. 
Depending on that, the embedding of convergent assembly into 3D space sometimes necessarily need to change.

For artificial [[machine phase]] systems an organization of [[assembly levels]] into [[assembly layers]] seems to be the obvious starting point for design. When liquid or gas phase is involved then dendridic tree like designs that have too much branching to match a layered design might be the better choice.

= Relation to the [[incremental path]] =

[[File:APM-EarlyDevelopmentPaths.jpg|500px|thumb|right| '''Convergent [[assembly level]]s''' are plotted to the right for all [[technology levels]] that are [[positional assembly]]. For the fist technology level that is unentabgably intertwined with [[selfassembly]] they are called [[hierarchical selfassembly]] levels.]]

'''Convergent [[assembly level]]s''' are plotted to the right for the but only for the higher [[technology level]]s that already feature [[positional assembly]]. In the case of selfassembly the analog to converget assembly is called [[hierarchical selfassembly]] (historic reasons). Details on bootstrapping callenge on page: [[Positional assembly kinematic loop]] & also on page [[Introduction of total positional control]].

= Related =

* '''[[Gemstone metamaterial on chip factory]]'''
* [[Math of convergent assembly]]
* [[Convergent self assembly]]
* [[Visualization methods for gemstone metamaterial factories]] In particular: [[Distorted visualization methods for convergent assembly]]
* [[Level throughput balancing]]
* '''[[Assembly levels]]''' – [[Selfassembly level]]
* Assembly levels in the geometry of layers are: '''[[Assembly layers]]'''
* [[Multilayer assembly layers]]
* [[Fractal growth speedup limit]]
* relation to data packages in electronic networks
----
* '''[[Higher throughput of smaller machinery]]''' When convergent assembly is illustrated in a naive [[scale invariance|scale invariant]] way it is the natural way to illustrate this scaling law.
----
* '''[[Hierarchical selfassembly]]''' – The [[incremental path]] [[foldamer]] [[self assembly]] analogy to [[positional assembly]] convergent assembly process here.
----
* [[In place assembly]]
----
* '''[[Optimal sublayernumber for minimal friction]]'''

{{todo | investigate various forms of self assembly further}}

= External links =

* [http://e-drexler.com/p/04/04/0507molManConvergent.html Convergent assembly can quickly build large products from nanoscale parts] (from K. Eric Drexlers website)
* Illustrations: http://e-drexler.com/p/04/05/0609factoryImages.html
----
* https://en.wikipedia.org/wiki/Max-flow_min-cut_theorem and https://en.wikipedia.org/wiki/Approximate_max-flow_min-cut_theorem
* https://en.wikipedia.org/wiki/Maximum_flow_problem
* https://en.wikipedia.org/wiki/Flow_network
* https://en.wikipedia.org/wiki/Circulation_problem
* https://en.wikipedia.org/wiki/Mathematical_optimization
----
* http://www.zyvex.com/nanotech/convergent.html

[[Category:General]]
[[Category:Nanofactory]]
[[Category:Far term target]]

Motor-muscle

2026-10-04T15:14:25Z

Apm: /* Thin sheet and balloon muscle-motor mocles */ added sub-headline & note on force density

{{Template:Site specific definition}}
[[file:Crystal molecule - redundant fractal design - 342x640.png |thumb|250px|Fractal structuring of metamaterials can avoid linear increase of actuation range loss due to e.g. [[radiation damage|radiation induced damage]]. [http://apm.bplaced.net/w/images/a/a1/Crystal_muscle_-_redundant_fractal_design.svg SVG] ]]

'''Artificial motor-muscles''' (suggestion: '''Mokels''') are actuators out of an active [[diamondoid metamaterial]] that '''can perform pull but also push action''' with '''high energy densities''' beyond the ones seen in biological muscles tissue and even beyond combustion engines [[power density|like it's typical '''[add ref]''' for all AP technologies]] of [[technology level III|technology level III]].
On the small scale they resemble some form of motors but on the large scale they seem sort of like a crystalline muscle thus the term ''motor-muscle''.

The material consists out of many minimal sized active units. Each of them contains one or more [[electromechanical converter|electromechanical]] or [[Chemomechanical converters|chemomechanical]] motors that extend or shrink the units length. For fault tolerance a the units must be connected parallel and serial in a hierarchical fractal fashion '''[TODO add [http://www.thingiverse.com/thing:404286 info-graphic]]'''.

When a mokel metamaterial is actuated a volume changing extension or shrinkage takes place.
This is in contrast to '''[[interfacial drive]]s''' (which are essentially [[infinitesimal bearing]]s with motor/generator cells included)
where only a shear deformation is present which does not change the actuators volume.

With motor-muscles built out of modular [[microcomponents]] beside [[electromechanical converters]] or [[chemomechanical converter]]s other microcomponents like [[energy storage cells]] could directly be incorporated (possibly in a choosable ratio) instead of feeding the energy in from an external source. This way one can trade efficiency (through lowering of power transport distance) for maximal force and power density.

All the power-supply infrastructure for the motors must be incorporated making the design quite complex.
Combining mokel with [[metamaterial]] [[emulated elasticity|elasticity]] in the directions normal to the pulling action (transversal directions) and making the mokel long and thin one gains some kind of '''active rope'''.

Mokel would undoubtedly provide a boost for robotic engineering.

Due to their high power density mokel can be distributed sparsely into active materials.
Chemical energy storage in contrast has high volume but can be located far off sight since with AP technology [[energy transmission]] is easy.

== Thin sheet and balloon muscle-motor mocles ==

Due to high power an force densities 
the macroscale analogy to a biological muscle in performance 
could be just a thin stripe pf material. 
Rooled up it could be a possible high pressure gas inflated hollow tubular "balloon". 
See page: [[Gem-gum balloon products]] 

=== [[Chemomechanical converter]]s as nanomotors ===

'''Caveat: Connection to the chemical energy transportation as a bottleneck for power density.'''

Unlike [[power density]] chemical energy density is already almost at the physical limit 
with today's liquid hydrocarbons like gasoline, ethanol, and whatnot. 
Future chemical energy storages used by efficiency optimized [[chemomechanical converter]] metamaterials 
will most likely have a bit lower energy density than above listed liquid fuels. 

To keep the mocle muscle-motor thin-film and separate from the energy storage, 
the energy needs to be long range macroscale distance transported 
into the mocle muscle-motor to there be chemomechanicaly converted 
to mechanical motion inside of cheomechanical motors (e.g. covalent bond zippers). 

For high power density applications that transport might become a bottleneck. 
Thereby motivating the inclusion of energy storage metamatrial right into the mocle muscel-motor metamaterial. 
A combined chemical energy storage and chemomechanical conversion metamaterial. 
Loosing some seperatiion of concerns. 

The big disadvantage with this is that this would massively increase its volume and mass of the "energy-storage-mocle" metamaterial. 
Moving mass that is not the payload is usually what one will want to avoid. 
It might be ok for some special niche applications. Low speed high force high power density. 

The desire to keep mocle muscle-motors light by implies the need for 
'''long range macrocale transportation in the chemical material into the mokel and depleted carriers out again.''' 
But this limits the power density. 

There is an option to escape this dilemma. 

=== [[Electromechanical converter]]s as nanomotors ===

For really high power applications fro which mechanical transport of chemical energy storage material become a bottleneck. 
Go for an extra detour over electrical energy. 
chemomechnical => mechanoelectical => electomechanical 
and the reverse for recuperation 
all that completely free of any wear 

But likely not directly [[electrochemically]]. 
At least not as in today's batteries that are subject to a lot of wear. 
Typically a few 10000 cycles till badly damaged. 

Nanotubes can provide superb conductivity beyond copper and silver. 
Perhaps some high critical current supercunductive solutions will be found. 
Active cooling plus novel superinsualtion metamateruals and or higher critical temperatures. 

One possible disadvantage is lower maximal force density compared to chemomechanical converters. 
Perhaps not so much an issue for mocle muscle-motors, 
but more an issue for driving mechanochemical reactions in productive nanosystems. 
Some form of mechanical advantage mechanisms needed to get back to higher force density (pulling/pushing stress). 

== Extremes ==

=== Very high efficiency by nature ===

Since actuation speeds add up incrementally in a muscle like structure 
a macroscale speed of 1m/s at the scale of 1m (human arm) or 
a macroscale speed of 100mm/s at the scale of 100mm (FFF 3D printer) 
translates down to an extremely slow sped of 10nm/s across 10nm. 
This allows these devices to operate in extremely high efficiency regimes. 
The as of 2026 here explored friction models: [[Friction in gemstone metamaterial technology]] … 
(That is: Models giving quadratically with speed scaling friction power losses) 
… might break down in these regimes and scale differently. 
Worse, better, or unchanged. It remains to be determined. 

Maybe one get truly zero static friction and remains pretty much in that static friction regime? 
See: [[Supercritically superlubric]] – {{speculativity warning}} 

=== Maximal speed ===

The other way around: 
Proposed speeds for productive nanosystems are around 4nm/s at 10nm scale. 
A lot faster is possible but this increasingly leads to coolability problems. 
I.e. only short intermittent burst with long cooling pauses remain possible for the bulk meta-material. 

Adding (4nm/s)/10nm up in a motor-muscle metamaterial 
would lead to an extreme speed of 400m/s at 1mm length of the motor muscle metamaterial already. 

* The driving force might give out before
* Very loud sound (possibly dangerous) sound shockwaves shoud be generatable (safety and weapons concern)
* Going even faster inertial forces from accelerations might exceed the tensile strength of any physically possible material. Somewhat related topic: [[Unsupported rotating ring speed limit]]

== Related ==

* [[Resilience boost by fractal design]]
* [[Fractals in gem-gum nanomachinery]]
* [[Nanoscale actuators]]
----
* [[Infinitesimal bearing]] … possible a good base metamaterial good base for shear mocles
----
* [[Gem-gum balloon products]]
* [[Multi limbed sensory equipped shells]]

[[Category:Technology level III]]
[[Category:Site specific definitions]]

Motor-muscle

2026-10-04T13:17:59Z

Apm: /* Caveat: Connection to the chemical energy storage as a bottleneck for power density */ small changes

{{Template:Site specific definition}}
[[file:Crystal molecule - redundant fractal design - 342x640.png |thumb|250px|Fractal structuring of metamaterials can avoid linear increase of actuation range loss due to e.g. [[radiation damage|radiation induced damage]]. [http://apm.bplaced.net/w/images/a/a1/Crystal_muscle_-_redundant_fractal_design.svg SVG] ]]

'''Artificial motor-muscles''' (suggestion: '''Mokels''') are actuators out of an active [[diamondoid metamaterial]] that '''can perform pull but also push action''' with '''high energy densities''' beyond the ones seen in biological muscles tissue and even beyond combustion engines [[power density|like it's typical '''[add ref]''' for all AP technologies]] of [[technology level III|technology level III]].
On the small scale they resemble some form of motors but on the large scale they seem sort of like a crystalline muscle thus the term ''motor-muscle''.

The material consists out of many minimal sized active units. Each of them contains one or more [[electromechanical converter|electromechanical]] or [[Chemomechanical converters|chemomechanical]] motors that extend or shrink the units length. For fault tolerance a the units must be connected parallel and serial in a hierarchical fractal fashion '''[TODO add [http://www.thingiverse.com/thing:404286 info-graphic]]'''.

When a mokel metamaterial is actuated a volume changing extension or shrinkage takes place.
This is in contrast to '''[[interfacial drive]]s''' (which are essentially [[infinitesimal bearing]]s with motor/generator cells included)
where only a shear deformation is present which does not change the actuators volume.

With motor-muscles built out of modular [[microcomponents]] beside [[electromechanical converters]] or [[chemomechanical converter]]s other microcomponents like [[energy storage cells]] could directly be incorporated (possibly in a choosable ratio) instead of feeding the energy in from an external source. This way one can trade efficiency (through lowering of power transport distance) for maximal force and power density.

All the power-supply infrastructure for the motors must be incorporated making the design quite complex.
Combining mokel with [[metamaterial]] [[emulated elasticity|elasticity]] in the directions normal to the pulling action (transversal directions) and making the mokel long and thin one gains some kind of '''active rope'''.

Mokel would undoubtedly provide a boost for robotic engineering.

Due to their high power density mokel can be distributed sparsely into active materials.
Chemical energy storage in contrast has high volume but can be located far off sight since with AP technology [[energy transmission]] is easy.

== Thin sheet and balloon muscle-motor mocles ==

Due to high power an force densities 
the macroscale analogy to a biological muscle in performance 
could be just a thin stripe pf material. 
Rooled up it could be a possible high pressure gas inflated hollow tubular "balloon". 
See page: [[Gem-gum balloon products]] 

=== Caveat: Connection to the chemical energy transportation as a bottleneck for power density ===

Unlike [[power density]] chemical energy density is already almost at the physical limit 
with today's liquid hydrocarbons like gasoline, ethanol, and whatnot. 
Future chemical energy storages used by efficiency optimized [[chemomechanical converter]] metamaterials 
will most likely have a bit lower energy density than above listed liquid fuels. 

To keep the mocle muscle-motor thin-film and separate from the energy storage, 
the energy needs to be long range macroscale distance transported 
into the mocle muscle-motor to there be chemomechanicaly converted 
to mechanical motion inside of cheomechanical motors (e.g. covalent bond zippers). 

For high power density applications that transport might become a bottleneck. 
Thereby motivating the inclusion of energy storage metamatrial right into the mocle muscel-motor metamaterial. 
A combined chemical energy storage and chemomechanical conversion metamaterial. 
Loosing some seperatiion of concerns. 

The big disadvantage with this is that this would massively increase its volume and mass of the "energy-storage-mocle" metamaterial. 
Moving mass that is not the payload is usually what one will want to avoid. 
It might be ok for some special niche applications. Low speed high force high power density. 

The desire to keep mocle muscle-motors light by implies the need for 
'''long range macrocale transportation in the chemical material into the mokel and depleted carriers out again.''' 
But this limits the power density. 

There is an option to escape this dilemma. 

For really high power applications fro which mechanical transport of chemical energy storage material become a bottleneck. 
Go for an extra detour over electrical energy. 
chemomechnical => mechanoelectical => electomechanical 
and the reverse for recuperation 
all that completely free of any wear 

But likely not directly [[electrochemically]]. 
At least not as in today's batteries that are subject to a lot of wear. 
Typically a few 10000 cycles till badly damaged. 

Nanotubes can provide superb conductivity beyond copper and silver.
Perhaps some high critical current supercunductive solutions will be found.
Active cooling plus novel superinsualtion metamateruals and or higher critical temperatures.

== Extremes ==

=== Very high efficiency by nature ===

Since actuation speeds add up incrementally in a muscle like structure 
a macroscale speed of 1m/s at the scale of 1m (human arm) or 
a macroscale speed of 100mm/s at the scale of 100mm (FFF 3D printer) 
translates down to an extremely slow sped of 10nm/s across 10nm. 
This allows these devices to operate in extremely high efficiency regimes. 
The as of 2026 here explored friction models: [[Friction in gemstone metamaterial technology]] … 
(That is: Models giving quadratically with speed scaling friction power losses) 
… might break down in these regimes and scale differently. 
Worse, better, or unchanged. It remains to be determined. 

Maybe one get truly zero static friction and remains pretty much in that static friction regime? 
See: [[Supercritically superlubric]] – {{speculativity warning}} 

=== Maximal speed ===

The other way around: 
Proposed speeds for productive nanosystems are around 4nm/s at 10nm scale. 
A lot faster is possible but this increasingly leads to coolability problems. 
I.e. only short intermittent burst with long cooling pauses remain possible for the bulk meta-material. 

Adding (4nm/s)/10nm up in a motor-muscle metamaterial 
would lead to an extreme speed of 400m/s at 1mm length of the motor muscle metamaterial already. 

* The driving force might give out before
* Very loud sound (possibly dangerous) sound shockwaves shoud be generatable (safety and weapons concern)
* Going even faster inertial forces from accelerations might exceed the tensile strength of any physically possible material. Somewhat related topic: [[Unsupported rotating ring speed limit]]

== Related ==

* [[Resilience boost by fractal design]]
* [[Fractals in gem-gum nanomachinery]]
* [[Nanoscale actuators]]
----
* [[Infinitesimal bearing]] … possible a good base metamaterial good base for shear mocles
----
* [[Gem-gum balloon products]]
* [[Multi limbed sensory equipped shells]]

[[Category:Technology level III]]
[[Category:Site specific definitions]]

Motor-muscle

2026-10-04T13:14:13Z

Apm: /* Very high efficiency by nature */ Supercritically superlubric

{{Template:Site specific definition}}
[[file:Crystal molecule - redundant fractal design - 342x640.png |thumb|250px|Fractal structuring of metamaterials can avoid linear increase of actuation range loss due to e.g. [[radiation damage|radiation induced damage]]. [http://apm.bplaced.net/w/images/a/a1/Crystal_muscle_-_redundant_fractal_design.svg SVG] ]]

'''Artificial motor-muscles''' (suggestion: '''Mokels''') are actuators out of an active [[diamondoid metamaterial]] that '''can perform pull but also push action''' with '''high energy densities''' beyond the ones seen in biological muscles tissue and even beyond combustion engines [[power density|like it's typical '''[add ref]''' for all AP technologies]] of [[technology level III|technology level III]].
On the small scale they resemble some form of motors but on the large scale they seem sort of like a crystalline muscle thus the term ''motor-muscle''.

The material consists out of many minimal sized active units. Each of them contains one or more [[electromechanical converter|electromechanical]] or [[Chemomechanical converters|chemomechanical]] motors that extend or shrink the units length. For fault tolerance a the units must be connected parallel and serial in a hierarchical fractal fashion '''[TODO add [http://www.thingiverse.com/thing:404286 info-graphic]]'''.

When a mokel metamaterial is actuated a volume changing extension or shrinkage takes place.
This is in contrast to '''[[interfacial drive]]s''' (which are essentially [[infinitesimal bearing]]s with motor/generator cells included)
where only a shear deformation is present which does not change the actuators volume.

With motor-muscles built out of modular [[microcomponents]] beside [[electromechanical converters]] or [[chemomechanical converter]]s other microcomponents like [[energy storage cells]] could directly be incorporated (possibly in a choosable ratio) instead of feeding the energy in from an external source. This way one can trade efficiency (through lowering of power transport distance) for maximal force and power density.

All the power-supply infrastructure for the motors must be incorporated making the design quite complex.
Combining mokel with [[metamaterial]] [[emulated elasticity|elasticity]] in the directions normal to the pulling action (transversal directions) and making the mokel long and thin one gains some kind of '''active rope'''.

Mokel would undoubtedly provide a boost for robotic engineering.

Due to their high power density mokel can be distributed sparsely into active materials.
Chemical energy storage in contrast has high volume but can be located far off sight since with AP technology [[energy transmission]] is easy.

== Thin sheet and balloon muscle-motor mocles ==

Due to high power an force densities 
the macroscale analogy to a biological muscle in performance 
could be just a thin stripe pf material. 
Rooled up it could be a possible high pressure gas inflated hollow tubular "balloon". 
See page: [[Gem-gum balloon products]] 

=== Caveat: Connection to the chemical energy storage as a bottleneck for power density ===

Unlike [[power density]] chemical energy density is already almost at the physical limit 
with today's liquid hydrocarbons like gasoline, ethanol, and whatnot. 
Future chemical energy storages used by efficiency optimized [[chemomechanical converter]] metamaterials 
will most likely have a bit lower energy density than above listed liquid fuels. 

Energy needs to be long range macroscale distance transported 
into the mocle muscle-motor to there be chemomechanicaly converted 
to mechanical motion inside of cheomechanical motors (e.g. covalent bond zippers). 
For high power density applications that transport might become a bottleneck. 
Theeby motivating the inclusion of energy storage metamatrial right into the mocle muscel-motor metamaterial. 
A combined chemical energy storage and chemomechanical conversion metamaterial. 
Loosing some seperatiion of concerns. 

The big disadvantage with this is that this would massively increase its volume and mass of the "energy-storage-mocle" metamaterial. 
Moving mass that is not the payload is usually what one will want to avoid. 
It might be ok for some special niche applications. Low speed high force high power density. 

The desire to keep mocle muscle-motors light by implies the need for 
'''long range macrocale transportation in the chemical material into the mokel and depleted carriers out again.''' 
But this limits the power density. 

There is an option to escape this dilemma. 

For really high power applications fro which mechanical transport of chemical energy storage material become a bottleneck. 
Go for an extra detour over electrical energy. 
chemomechnical => mechanoelectical => electomechanical 
and the reverse for recuperation 
all that completely free of any wear 

But likely not directly [[electrochemically]]. 
At least not as in today's batteries that are subject to a lot of wear. 
Typically a few 10000 cycles till badly damaged. 

Nanotubes can provide superb conductivity beyond copper and silver.
Perhaps some high critical current supercunductive solutions will be found.
Active cooling plus novel superinsualtion metamateruals and or higher critical temperatures.

== Extremes ==

=== Very high efficiency by nature ===

Since actuation speeds add up incrementally in a muscle like structure 
a macroscale speed of 1m/s at the scale of 1m (human arm) or 
a macroscale speed of 100mm/s at the scale of 100mm (FFF 3D printer) 
translates down to an extremely slow sped of 10nm/s across 10nm. 
This allows these devices to operate in extremely high efficiency regimes. 
The as of 2026 here explored friction models: [[Friction in gemstone metamaterial technology]] … 
(That is: Models giving quadratically with speed scaling friction power losses) 
… might break down in these regimes and scale differently. 
Worse, better, or unchanged. It remains to be determined. 

Maybe one get truly zero static friction and remains pretty much in that static friction regime? 
See: [[Supercritically superlubric]] – {{speculativity warning}} 

=== Maximal speed ===

The other way around: 
Proposed speeds for productive nanosystems are around 4nm/s at 10nm scale. 
A lot faster is possible but this increasingly leads to coolability problems. 
I.e. only short intermittent burst with long cooling pauses remain possible for the bulk meta-material. 

Adding (4nm/s)/10nm up in a motor-muscle metamaterial 
would lead to an extreme speed of 400m/s at 1mm length of the motor muscle metamaterial already. 

* The driving force might give out before
* Very loud sound (possibly dangerous) sound shockwaves shoud be generatable (safety and weapons concern)
* Going even faster inertial forces from accelerations might exceed the tensile strength of any physically possible material. Somewhat related topic: [[Unsupported rotating ring speed limit]]

== Related ==

* [[Resilience boost by fractal design]]
* [[Fractals in gem-gum nanomachinery]]
* [[Nanoscale actuators]]
----
* [[Infinitesimal bearing]] … possible a good base metamaterial good base for shear mocles
----
* [[Gem-gum balloon products]]
* [[Multi limbed sensory equipped shells]]

[[Category:Technology level III]]
[[Category:Site specific definitions]]

Motor-muscle

2026-10-04T13:06:15Z

Apm: /* Thin sheet and balloon muscle-motor mocles */ === Caveat: Connection to the chemical energy storage as a bottleneck for power density ===

{{Template:Site specific definition}}
[[file:Crystal molecule - redundant fractal design - 342x640.png |thumb|250px|Fractal structuring of metamaterials can avoid linear increase of actuation range loss due to e.g. [[radiation damage|radiation induced damage]]. [http://apm.bplaced.net/w/images/a/a1/Crystal_muscle_-_redundant_fractal_design.svg SVG] ]]

'''Artificial motor-muscles''' (suggestion: '''Mokels''') are actuators out of an active [[diamondoid metamaterial]] that '''can perform pull but also push action''' with '''high energy densities''' beyond the ones seen in biological muscles tissue and even beyond combustion engines [[power density|like it's typical '''[add ref]''' for all AP technologies]] of [[technology level III|technology level III]].
On the small scale they resemble some form of motors but on the large scale they seem sort of like a crystalline muscle thus the term ''motor-muscle''.

The material consists out of many minimal sized active units. Each of them contains one or more [[electromechanical converter|electromechanical]] or [[Chemomechanical converters|chemomechanical]] motors that extend or shrink the units length. For fault tolerance a the units must be connected parallel and serial in a hierarchical fractal fashion '''[TODO add [http://www.thingiverse.com/thing:404286 info-graphic]]'''.

When a mokel metamaterial is actuated a volume changing extension or shrinkage takes place.
This is in contrast to '''[[interfacial drive]]s''' (which are essentially [[infinitesimal bearing]]s with motor/generator cells included)
where only a shear deformation is present which does not change the actuators volume.

With motor-muscles built out of modular [[microcomponents]] beside [[electromechanical converters]] or [[chemomechanical converter]]s other microcomponents like [[energy storage cells]] could directly be incorporated (possibly in a choosable ratio) instead of feeding the energy in from an external source. This way one can trade efficiency (through lowering of power transport distance) for maximal force and power density.

All the power-supply infrastructure for the motors must be incorporated making the design quite complex.
Combining mokel with [[metamaterial]] [[emulated elasticity|elasticity]] in the directions normal to the pulling action (transversal directions) and making the mokel long and thin one gains some kind of '''active rope'''.

Mokel would undoubtedly provide a boost for robotic engineering.

Due to their high power density mokel can be distributed sparsely into active materials.
Chemical energy storage in contrast has high volume but can be located far off sight since with AP technology [[energy transmission]] is easy.

== Thin sheet and balloon muscle-motor mocles ==

Due to high power an force densities 
the macroscale analogy to a biological muscle in performance 
could be just a thin stripe pf material. 
Rooled up it could be a possible high pressure gas inflated hollow tubular "balloon". 
See page: [[Gem-gum balloon products]] 

=== Caveat: Connection to the chemical energy storage as a bottleneck for power density ===

Unlike [[power density]] chemical energy density is already almost at the physical limit 
with today's liquid hydrocarbons like gasoline, ethanol, and whatnot. 
Future chemical energy storages used by efficiency optimized [[chemomechanical converter]] metamaterials 
will most likely have a bit lower energy density than above listed liquid fuels. 

Energy needs to be long range macroscale distance transported 
into the mocle muscle-motor to there be chemomechanicaly converted 
to mechanical motion inside of cheomechanical motors (e.g. covalent bond zippers). 
For high power density applications that transport might become a bottleneck. 
Theeby motivating the inclusion of energy storage metamatrial right into the mocle muscel-motor metamaterial. 
A combined chemical energy storage and chemomechanical conversion metamaterial. 
Loosing some seperatiion of concerns. 

The big disadvantage with this is that this would massively increase its volume and mass of the "energy-storage-mocle" metamaterial. 
Moving mass that is not the payload is usually what one will want to avoid. 
It might be ok for some special niche applications. Low speed high force high power density. 

The desire to keep mocle muscle-motors light by implies the need for 
'''long range macrocale transportation in the chemical material into the mokel and depleted carriers out again.''' 
But this limits the power density. 

There is an option to escape this dilemma. 

For really high power applications fro which mechanical transport of chemical energy storage material become a bottleneck. 
Go for an extra detour over electrical energy. 
chemomechnical => mechanoelectical => electomechanical 
and the reverse for recuperation 
all that completely free of any wear 

But likely not directly [[electrochemically]]. 
At least not as in today's batteries that are subject to a lot of wear. 
Typically a few 10000 cycles till badly damaged. 

Nanotubes can provide superb conductivity beyond copper and silver.
Perhaps some high critical current supercunductive solutions will be found.
Active cooling plus novel superinsualtion metamateruals and or higher critical temperatures.

== Extremes ==

=== Very high efficiency by nature ===

Since actuation speeds add up incrementally in a muscle like structure 
a macroscale speed of 1m/s at the scale of 1m (human arm) or 
a macroscale speed of 100mm/s at the scale of 100mm (FFF 3D printer) 
translates down to an extremely slow sped of 10nm/s across 10nm. 
This allows these devices to operate in extremely high efficiency regimes. 
The as of 2026 here explored friction models: [[Friction in gemstone metamaterial technology]] … 
(That is: Models giving quadratically with speed scaling friction power losses) 
… might break down in these regimes and scale differently. 
Worse, better, or unchanged. It remains to be determined. 

=== Maximal speed ===

The other way around: 
Proposed speeds for productive nanosystems are around 4nm/s at 10nm scale. 
A lot faster is possible but this increasingly leads to coolability problems. 
I.e. only short intermittent burst with long cooling pauses remain possible for the bulk meta-material. 

Adding (4nm/s)/10nm up in a motor-muscle metamaterial 
would lead to an extreme speed of 400m/s at 1mm length of the motor muscle metamaterial already. 

* The driving force might give out before
* Very loud sound (possibly dangerous) sound shockwaves shoud be generatable (safety and weapons concern)
* Going even faster inertial forces from accelerations might exceed the tensile strength of any physically possible material. Somewhat related topic: [[Unsupported rotating ring speed limit]]

== Related ==

* [[Resilience boost by fractal design]]
* [[Fractals in gem-gum nanomachinery]]
* [[Nanoscale actuators]]
----
* [[Infinitesimal bearing]] … possible a good base metamaterial good base for shear mocles
----
* [[Gem-gum balloon products]]
* [[Multi limbed sensory equipped shells]]

[[Category:Technology level III]]
[[Category:Site specific definitions]]

Motor-muscle

2026-10-04T12:12:13Z

Apm: added section == Extremes ==

Power density

2026-10-04T11:44:03Z

Apm: /* Related */ Gem-gum balloon products

Power densities are covered in [[Nanosystems]] in the early chapter about [[scaling law]]s. 
Lower bounds for maximally achievable power densities are [[exploratory engineering|explored]] in 
later chapters covering [[electromechanical converters]]. They are ''very'' high.

What is too often missed though is the 
'''[[limits of power density imposed by limits of cooling]]'''.

Power-densities for [[mechanical energy transmission]] are explored here on this wiki a bit (follow the link).

== SI Units ==

There are two kinds of power densities. 
Per area (areal) and per volume (volumetric).
* areal power densities are relevant for power transmission
* volumetric power densities are relevant for power conversion
----
'''Volumetric power density:'''
* electromechanical conversion: >10^15 W/m³ ([[Nanosystems]] 11.7.3. Motor power and Power density)
* mechanical transmission example: 1.7*10^19 W/m³ (1.0 m/s) ([[Nanosystems]] equation (2.13) 10nN 1nm³)
* mechanical transmission example: 1.7*10^22 W/m³ (1.7 km/s) ([[Nanosystems]] equation (2.13) 10nN 1nm³) - huge dynamic friction!
Example: The power transmitted by a gear divided by its volume. 

Please note that there are lower '''[[limits of power density imposed by limits of cooling]]''' 
for bulk volumes of densely packed nanomachinery running steady state.
----
'''Areal power density:'''
* – W/m² … See: [[Mechanical energy transmission]]

{{todo|How & in how far can the two types be made comparable? And is there a way to get an intuitive grasp on them?}} 
{{todo|If possible get power densities from [[electromechanical converters]] and [[mechanical energy transmission]] in a form that is comparable. Despite different units ...}}

== Ultimate limits & cooling ==

Details in [[Nanosystems]] 11.7.4. Energy dissipation and efficiency

While for
* small volumes and steady state
* big volumes and brief times (burst mode operation)
We already have lower bound [[conservative estimation]] numbers, for
* bigger volumes and longer operation times
waste heart removal becomes the limiting bottleneck. 
Even with very high efficiencies given extreme power densities there will still be produce way too much waste heat.

To get a better handle on the ultimate limits of [[gem-gum system]]s 
lower bounds for ultimate limits for power-densities for waste heat removal need closer investigation. 
That is ultra high performance cooling systems. Likely based on solid state capsules in machine phase. 

== Math for onset of cooling limiting power density by system geometry ==

[[Nanosystems]] only covers:
* cooling systems sufficient for proposes the [[nanofactories]] – 11.5. Convective cooling systems
* cooling for nanomechanical computation – 12.8. Cooling and computational capacity

'''Questions:''' At which size scale does heat removal become the limiting factor for
* a volume (cube or sphere shape)
* a thin layer of specified thickness

'''Volumetric (cube) case:'''
* P_in = Q_V * V = Q_V * s³
* P_out = Q_A * 6A = Q_A * s²
* P_in = P_out
* s = 6Q_A / Q_V
This gives a maximal cube side-length. 
Spherical case is left as exercise for the so inclined reader.

'''Thin layer case (s >> t):'''
* P_in = Q_V * (A*t) = Q_V * (s²*t)
* P_out = Q_A * (2*A + 4*s*t) ~ Q_A * (2*s²+0)
* P_in = P_out
* t = 2Q_A / Q_V
This gives a maximal layer thickness. 
The layer side-length s can be arbitrarily large.

----

'''TODO:''' That leaves Q_A for to be determined. 
A lower bound for the maximally achievable heat removal power density.

'''Complications:'''
* Thin layer case: Heat conduction alone does not work. When assuming s as infinitely large then the carry-heat-away power density never drops with distance to the layer and the longer the (not widening) carry-heat-away-path gets the higher the cumulative thermal resistance gets. Thus active heat removal (material with heat capacity moving cold in & hot out) is a necessity. E.g. Boosted heat removal by fast active motion of thermal mass capsules.
* volumetric case: The heat gradient is nonlinear since spherical hear flow. Thermal resistance integral to infinite radius is finite though.
----
* Going too far to the limits the heat removal system will itself start to produce waste heat complicating the analysis more.
----
* Analyzing '''[[burst mode operation]]''' it gets even more complicated needing additional assumptions on heat capacity of the power conversion machinery itself.

== Related ==

* [[Energy conversion]] – There's an especially high lower bound for the maximal power density in [[electromechanical converters]]
* [[Energy density]]

High power [[energy transmission]] as a combination of:
* [[Chemical energy transmission]]
* [[Mechanical energy transmission]]
* [[Entropic energy transmission]]
* [[Thermal energy transmission]] – other quite different constraints here
-----
* [[Higher throughput of smaller machinery]]
* [[High performance of gem-gum technology]]
----
* '''[[Limits of power density imposed by limits of cooling]]'''
----
* [[Gem-gum balloon products]] … as consequence of possible high power density.

== External Links ==

Wikipedia
* [https://en.wikipedia.org/wiki/Surface_power_density Surface power density] – W/m²
* [https://en.wikipedia.org/wiki/Power_density Power density] – W/m³

[[Category:Pages with math]]

Gem-gum balloon products

2026-10-04T11:42:39Z

Apm: /* Related */ power density

Many [[gem-gum products]] may come in the form of strong high pressure air inflated tube and similar shaped balloons
Think: balloon-tent (but actuated by nanomachinery within the hulls) – {{wikitodo|add illustration}}

'''This is concept introduced as "balloon robots" by Josh Hall (better known as the inventor of [[utility fog]]).'''

As mentioned on the "[[gemstone based metamaterial]]" page in [[further improvement at technology level III|products of advanced atomically precise technology]] 
actuators for reasonable forces use up only a rather tiny fraction of the product volume since they can run at very high [[power density|power densities]]. 
It should thus be possible to make various kinds of active structures that are inflatable and integrate actuators such as [[motor-muscle]]s, 
[[shearing drive]]s and or other stuff.

'''Note:''' Gem-gum balloon products are not to confuse with: [[robust metamaterial balloons|Aeronautic balloons out of robust metamaterials]]

== Balloon robots – A concept introduced by Josh Storrs Hall ==

A [[diamondoid]]/[[gemstone]] nanotechnology based analogy to biological muscles. 
But due to the expectable much higher possible power and force density (at same efficiency or perhaps even better efficiency) 
just as thin shelled hollow tubular balloons rather than slid muscle material. 

'''Releated pages to this:'''
* Down: [[Motor-muscle]] (mocle) & [[infinitesimal bearing]] … the metamaterial basis to build on
* Up: [[multi limbed sensory equipped shells]] … some stuff that could could be built atom the bases

=== Extending on the idea ===

High pressure balloons come with the challenge of that mobile angle joints usually lead to a volume change and thus a big counter-force. 
A problem well known from space suit engineering. 
( napkin math: ΔE = W = F·s => F = W/s and ΔE = p·(V2-V1) for easy isotherm case, though often more adiabatic ) 
A possible workaround for this might be to add complex tendon like internal cross-bracings generated via generative design software. 

=== Diverging from the idea (no longer balloons) ===

Rather than gas inflated balloons, instead go for 
'''thin wide stripes "belt motor muscles (belt-mocels)"''' 
Stiffening then needs to be provided by other (more conventional) means of a structural frame. 
In analogy to bones (and tendons) of skeleton when keeping with the bio-analogy. 

Why not cylindrical cables instead of belts? They would … 
★ give more concentrated pressure on supports. 
★ be worse for cooling 
Well, the latter only matters when hitting the limits which will be rare) 

When hitting the cooling limits then less thin-sheet-belt-like-designs may force 
the difficult design of a more complex metamaterial for both actuation and cooling in the same volume. 
Whereas more thin-sheet-belt-like-designs may allow to keep-with/stick-with 
macroscopically separate materials for actuation and cooling. 
And maybe a metamaterial for connecting between the two. 
Related: [[Separation of concerns]] 

== Detail thoughts to "balloon products" ==

=== Compartments ===

Micro sized compartmentisation (similar to the ones that may be found in [[diamondoid heat pump system]] 
or [[entropomechanical converter]] but maybe bigger and softer due to lower pressure) 
should allow for safe use of high pressures without explosion hazard. 
Internal (possibly tree like spreading) tensioning structures (e.g. cables) can define the outer structure. 

=== Compression heat ===

To partly avoid thermal losses when compressing air for a fill of an inflatable structure 
the air can first be compressed into a small high surface area pre-chamber with target pressure. 
An [[entropomechanical converter]] system can be used to catch as much as possible from the free energy from the produced temperature difference. 

=== Recycling ===

It may be to note that when such structures aren't filled to liquid densities 
(these are around 1000bar at room temperature, normally some 10 bar should suffice) 
in some sense one leaves the [[machine phase]] a bit. 

Especially when non stiff inflatable structures are deflated new degrees of freedom are introduced. 
(Remotely related: [[atomically precise positioning]]; the products are still [[topological atomic precision|topologically atomically precise]] tough.) 
Very floppy structures must be brought back to microcomponent-level-[[machine phase]] 
(rolling the stuff up in a tensioned ordered state removing creases and tangles) 
before their [[microcomponent]]s can be [[recycling|recycled]]. 
(See: management of [[soft cables and sheets]]) 

{{todo|Do more rewriting here for better comprehensability.}}

=== Use in Space ===

In very cold environments below the boiling point of air (~ liquid nitrogen) like in the outer solar system either heating and [[thermal isolation|isolating]] is needed or hydrogen can be used as filling gas.

== Wild scenario: Inflatable vehicles ==

Use of "gem-gum balloon products" as collapsible transport vehicles. 
Think: inflatable cars, planes, boats, … 

If human powered like a bicycle and not live connection powered from a street that can provide power continuously along its length. 
Then the vehicle needs no heavy energy storage and might turn out too lightweight and need ballast mass material. 
Otherwise the vehicle needs energy storage (as a meta-material) that unlike the motors can not be hugely collapsed in volume. 
Energy storage is inherently not-so-compact and light. 

Both ballast mass material and energy storage metamaterial 
(the latter pre-assembled to various degree in size to [[chemomechanical]] or [[entropomechanical]] batteries rather than today's [[electrochemical]] ones) 
could be taken/tapped from a [[global microcomponent redistribution system]] (GMRS) and water lines 
embedded in future [[upgraded street infrastructure]]) respectively. 

Ballast mass could be as simple as just water or someting fancy like 
safely packaged high density heavy lead compounds. 

'''As a wild scenario:''' 
The vehicle can deflate in a suitcase size. 
The energy storage "battery" metamaterial being dumped into the [[GMRS]] takes the place of a garage for the vehicle. 
And even that is that's only needed when going driving of a gemstone metamaterial technology road. 

== Related ==

* [[Origami]]
* use in [[upgraded street infrastructure]] and advanced modular housing
----
* use for diverse robotic applications including '''[[multi limbed sensory equipped shells]]'''
* [[Motor-muscle]] (mocle)
----
* high [[power density]] => small volume of actuators

[[Category:Technology level III]]
[[Category:Surprising facts]]

Friction in gemstone metamaterial technology

2026-10-04T10:14:35Z

Apm: /* Related */ * Reciprocative dissipation mechanisms in gem-gum technology & * Macroscale mechanical bearings

{{wikitodo|This page needs major cleanup - several parts need to be merged and completed and factored out}} 
[[File:Superlubricity scaling chart.png|800px|thumb|right|Double logarithmic chart of several estimations for [[superlubricity|superlubric friction]] and its quadratic scaling. Note that at moderate speeds like 1m/s it is actually quite high but it quickly drops off going to lower (proposed) speeds around ~1mm/s. The black line (way higher up than all the others) is not superlubric friction but dynamic friction in fluids for comparison. '''This does not cover [[reciprocative dissipation mechanism]]s modes''' which can be significant and can't be co-plotted without a number of (at this point in 2025 still too difficult to pin down) assumptions.]]
Up: [[Energy dissipation in gemstone metamaterial technology]] 
Up: [[Friction]]

'''[[Macroscale style machinery at the nanoscale]]''' has in the past received some seriously bad reputation
because it comes with a bunch of [[common misconceptions|mental trapdoors]] that led a a number of very smart reputational and vocal people to bad conclusions.
One of these bad conclusions is that macroscale style machinery at the nanoscale would lead to exorbitant amounts of friction. A very wrong conclusion, as I will try to show below.
(There are other misled criticisms to the idea beside the false conclusion of exorbitant friction. For a discussion of those you may want to check out the main page about [[macroscale style machinery at the nanoscale]].)

= To the doubly logarithmic friction chart =

The chat is meant as …
* a common comparing ground for a broad set different results.
* a starting point to be improved on.

In particular:
* (A) Eventually adding more lines from more suitable data sources eventually.
* (B) Finding the high speed and low speed limits where the quadratic scaling breaks down and gives way to other scaling laws (or destructive end) eventually.

For now in the chart beside results only the book [[Nanosystems]] a source 
there is also one second independent source at least. This one is also theoretical though. {{Wikitodo|Check if fully true.}} 
The second source: [https://pubs.rsc.org/en/content/articlehtml/2017/me/c7me00021a 2017 Evaluating the Friction of Rotary Joints in Molecular Machines] [https://arxiv.org/abs/1701.08202 (arxiv)]

A big problem with current day (2026) experimental results is that 
experimental limitations introduce uncontrollable side effects that overshadow 
what one would get with atomically precise surfaces sliding in an advanced much cleaner not yet preparable setup. 
{{Wikitodo|Elaborate on that eventually. This may deserve a dedicated page. Add papers and explain associated concrete issues with them.}} 

= Dodge the trapdoors =

* '''Yes, It is true that physics changes when the size-scale changes.''' But who says it changes for the worse when it comes to [[macroscale style machinery at the nanoscale]]?
* '''Yes, It is true that [[rising surface area|surface area grows with shrinking structure sizes]], and that this contributes to friction.''' But there are other effects that overcompensate growing surface area and these are very often overlooked.
* '''Yes, It is true that unlike diffusion transport there is friction all the time along the whole way.''' But it's often overlooked that diffusion must devaluate chunks of energy at its "pit-stops" to prevent transport from running backwards and that the "change money" energy that gets left over at these "pit-stops" cannot be kept for later usage. Whereas in [[machine phase system]]s keeping and reuseing the energetic change money may be possible.
* '''Yes, It is true that there is no natural example of macro style machinery at the nanoscale (similar to the one proposed).''' But concluding from that that it's not possible or a worse solution is a fallacy. There are plenty of human invented things that exceed capabilities of nature by orders of magnitude. To give just a few examples: Bicycles, combustion engines (spaceships), copper wires (superconductors), wheels and streets, ...
* '''Yes, It is true that MEMS (microelectromechanical systems) have high friction (and bad wear from "stiction").''' But in case of MEMS this is due to MEMS not having atomically precise [[superlubricity|suberbublicating]] bearings but instead having a really bad signal to noise ratio in their geometry due to them being manufactured top-down.

= Main sources of friction and countermeasures =

Friction in [[gem-gum-tec|gemstone based nanomachinery]] is mainly caused by:
* (1) band-stiffness scattering drag and
* (2) shear-reflection drag
Source: [[Nanosystems]] 10.4.6. Mechanisms of Energy dissipation f. Summary 
{{todo|find and add an intuitively comprehensible explanation for these two [[phonon interaction based dissipation mechanisms]]}}

Furthermore there are energy dissipation mechanisms that are specific to reciprocative motion. 
'''See page: [[Reciprocative friction in gem-gum technology]]'''

== Tuning for superlubricity against band-stiffness scattering drag ==

Only (1) can be reduced by tuning for [[superlubricity]] till (2) gets dominant. 
'''Maybe about x100 lower friction possible tuned vs untuned?'''

== Cranking up "compenslow" to reduce friction overall ==

Both (1) and (2) can be reduced cranking up the "[[compenslow]]" design parameter. 
Higher "compenslow" means an increased amount of nanomachinery that all runs at a slower absolute speed. 
"Compenslow" is a portemonteau for "by more machinery compensated slowdown"

'''When doubling the compenslow:'''
* The total throughput per chip area (areal throughput density) stays unchanged!
* Friction losses are cut in half.
* The thickness of the nanomachinery layer doubles. (this is not an issue)
* the internal bearing area per chip area doubles and speeds are cut in half.

'''Increasing compenslow can reduce losses from friction by many orders of magnitude.''' 

=== Limits to optimization by increase of "compenslow" ===

At some point friction from fast transport motions becomes relevant. 
Only the assembly motions are slowed down but assembly motions make up most of the distance the robotics travels. 
Once transport motions get similar in length to the assembly motions. Increasing compenslow is no longer a viable optimization option.

Also:
* the more parts are assembled per [[assembly cycle]] across an [[assembly level]]
* the more there is potential for reduction of friction by increase of compenslow across that assembly level

== Don't over-optimize friction way below mechanochemical losses ==

For systems that perform [[piezochemical mechanosynthesis]] and or [[chemomechanical conversion]] 
it's only sensible to tune friction down so far that [[losses from mechanochemical reactions]] become clearly dominant. 
Note that the increased amount of nanomachinery that results from for standard parts specialized subsystems 
already leads to some minimal compenslow.

For systems that do not perform any mechanochemical conversions like e.g. [[microcomponent recomposer]]s 
losses from friction may become the remaining dominant factor. Relevant in the context of [[recycling]]. 
So here going all out on minimizing friction may really pay off.

= Employing scaling laws against friction =

'''Overcompensating increased friction from increased bearing area''' 
'''See main page: [[How friction diminishes at the nanoscale]]'''

=== The two core physical facts that provide the lion-share of lowering friction ===

[[File:NongrowingAreaInConvergentAssembly.png|thumb|400px|In simple [[convergent assembly]] all layers feature the same total bearing area. So the bottommost nanomachinery has no more bearing surface area than the topmost macromachinery (despite [[higher bearing surface area of smaller machinery]]). Furthermore for practical jumps of scale (x32?) there are only a few layers of convergent assembly.]]

* [[higher throughput of smaller machinery]] Halving the size of the robotics has doubles the throughput per volume when robotic keeping speeds (NOT frequencies) constant. This means that in a naive first approximation the total bearing area of nanomchinery in a [[gem-gum factory]] is no bigger than the bearing area of macromachinery. It's desirable to deviate quite a bit from that first approximation, but as it turns out that only drops friction even further despite increasing bearing area.
* [[power losses from friction scale quadratic with speed]] that is: 1/2 the speed of the machinery => 1/4th friction power losses

=== The two main tricks that apply and combine these physical facts to great avail ===

[[File:ReducingFrictionByDeliberateSlowdown.png|thumb|left|400px|'''The first trick:''' Friction can be reduced by a lot by slowing down the speed of operation of (bottom-most) nanomachinery. In order to not loose throughput capacity [[Multilayer assembly layers|just add more nanomachinery compensating the slowdown]]. This still remains an imperceptibly thin layer on the [[gem-gum factory]] chip due to the [[higher throughput of smaller machinery|high throughput density of nanomachinery]]. '''Total friction losses falls despite rising bearing area!!''']]

[[File:Infinitesimal-bearing-sketch.png|thumb|right|250px|speed distributions from conventional to infinitesimal bearing|frame|'''The second trick:''' [[Infinitesimal bearings]]: 2x the number of layers => 1/2x the friction. This is because the drop in friction from reduced speed (x1/4) overcompensates the rise in friction from increased bearing area (x2). This is only applicable at the higher assembly levels with larger scale machinery.]]

* Distribute productive activity over a lot more layers of nanomachinery (there is more than sufficient space to do so. See [[multilayer assembly layers]])
* [[Infinitesimal bearings|Distribute speed differences over multiple coplanar surfaces]] (there is ore than sufficient space to do so)
----
* In both cases there is more then sufficient space available to do so.
* In both cases speed falls linearly with the number of bearing layers. This gives simultaneously a linear increase (more bearing area) and a quadratic fall (less bearing speed) of friction losses. That is: overall a linear fall of friction losses.
----
* The first case is relevant for the bottom-most layer of [[convergent assembly]] in [[gemstone metamaterial on-chip factories]]
* The second case is relevant for higher up layers of [[convergent assembly]] where larger scale bearings are possible.

== Smaller contributions ==

* Bearing can be tuned for good [[superlubricity]]
* minimization of travel-distance needed per chemical synthesis operation dissipation falls linearly with the path traveled

Minimization of travel-distance leads towards the nanofactory design and away from the molecular assembler design. 
{{wikitodo|elaborate on that}}

= Quantitatively (Math and Numbers) =

== Dynamic drag in superlubricating gemstone bearings - vs - viscous drag in liquids ==

'''There is at least 2,000.0 to 100,000.0 times less friction in gemstone bearings compared to movement at the same speed in water.''' 

So when it comes to peak performance parameters 
soft nanotechnologies and artificial [[synthetic biology]] derived from molecular biology, 
is fundamentally massively inferior to [[gemstone metamaterial technology]]

Yes, this much lower friction is still more than the zero friction that is as present in diffusion transport. 
But this misses a crucial point. 
For diffusion transport to happen it still needs to "expend" energy (still needs to devaluate free energy). 
It is just that the free energy expense need to be payed up at the pitstops (when crossing cell- and vesticle-membranes) rather than during the transport motion. (see external links)

So: 
'''Diffusion transport driven by concentration gradients does NOT make biological nanosystems fundamentally more efficient than conveyorbelt style transport in stiff dry artificial nanosystems in a vacuum.'''

=== Associated math ===

Source: <ref name="phononvsviscousdrag"> '''Eric Drexlers former homepage (webarchive):''' [https://web.archive.org/web/20160305212101/http://e-drexler.com/p/04/03/0322drags.html Phonon drag in sleeve bearings can be orders of magnitude smaller than viscous drag in liquids]</ref>

'''Rotating sphere in Water:''' (Source: <ref name="viscdrag"> '''Viscous torque on a sphere:''' Landau, L, and Lifshitz, E (1987) Fluid Mechanics, 2nd ed. Pergamon Press p.91.</ref>)
* <math> \omega = v/R </math>
* Drag-torque: <math> M_{flow} = -8 \pi \eta R^3 \omega </math>
* Dissipation: <math> P_{flow} = M_{flow} \omega = 8 \pi \eta R v^2 </math>
With: <math> \eta \approx 10 \times 10^{-3} Pa \cdot s </math> and <math> R = 2nm </math>
* Dissipation: <math> P_{flow} \approx 5 \times 10^{-11} v^2 W = 5 \times 10^{-11} W/(m/s)^2</math>

----
'''Gemstone sleeve nearing:''' (Source: <ref name="pdrag"> '''Drag mechanisms in symmetrical sleeve bearings:''' Drexler, K. E. (1992) ''[[Nanosystems]]: Molecular Machinery, Manufacturing, and Computation.'' Wiley/Interscience, pp.290–293.</ref>)
* <math> P_{drag} = 5.8 \times 10^{-16} W/(m/s)² -- \Delta k_a / k_a = 0.003</math>
* <math> P_{drag} = 2.7 \times 10^{-14} W/(m/s)² -- \Delta k_a / k_a = 0.4 </math>
----
'''Ratio:'''
* <math> P_{flow} / P_{drag} \approx 2000 … 100000</math>

== Despite superlubricity dynamic drag can be significant ==

{{wikitodo|add doublelog gnulot plot of examples}}

While static friction in superlubricity falls to nigh zero, 
'''Dynamic (speed dependent) friction can be quite significant for higher speeds.'''

For higher speeds and bearings that do not resort to:
* [[levitation|some mean of levitation]] ( only possible for low loads ) or
* [[infinitesimal bearings|bearing stratification]] ( only possible for bigger nearings )
... the friction per area can actually get quite high for higher speeds.

{| class="wikitable left" style="margin-left: auto; margin-left: 0px;"
|-
| v=100µm/s
| '''v=1mm/s''' (proposed speed)
| '''v=10mm/s''' (proposed speed)
| v=100mm/s
| v=1m/s
| v=10m/s
|-
| 230nW/m² to 10µW/m²
| 23µW/m² to 1mW/m²
| 2.3mW/m² to 100mW/m²
| 230mW/m² to 10W/m²
| 23W/m² to 1kW/m²
| 2.3kW/m² to 100kW/m²
|}
* <math> P_{drag} = 23 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.003</math>
* <math> P_{drag} = 1080 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.4 </math>
Source: [[Nanosystems]] Equation (10.27) <ref name="pdrag"/> --
But here calculated backwards to friction per area from friction per bearing. 
'''Note:''' These are highly conservative estimates. Real values should be quite a bit lower.

Halving the linear speed (in units of m/s) quaters the friction losses. 
And going down from 1m/s to 1mm/s the friction losses fall by a factor of a million (1,000,000). 
More technically: Dynamic friction for crystolecules scales quadratically with speed. 

=== Why significant dynamic drag at higher speeds is this is not a problem ===

 Note: This section is redundant but provides a different formulation.
Skip ahead if the everything so far was clear.

==== Worry #1: Looking at the table friction per area for small speeds like 1m/s is quite high. ====

Friction can be ''massively'' massively reduced by reducing the linear speed of motions (speed in units m/s NOT Hz!). 
And '''we can totally afford to reduce the linear speed of motion in [[advanced productive nanosystem]]s because all the machinery that is needed for practical levels of throughput fits in a super thin layer at the very bottom of the [[convergent assembly]] of a [[gem-gum factory]] chip.''' 
(Reason: [[Higher throughput of smaller machinery]] - things scale favorably here)

We just need to make the bottom layer [[gem-gum factory]] chip a bit thicker 
to compensate for the loss of speed and we are back at the original throughput. 
(We want to do that anyway because many different specialized assembly lines need space.)

One totally can afford to slow down so much in advanced productive nanosystems like [[gem-gum factories]] 
because there is plenty of space to compensate by just adding more nanomachinery.

'''Q:''' '''But what about the additional bearing area?''' 
'''A:''' Yes, the total bearing area increases. 
But while 10x the amount of nanomachinery gives 10x the bearing area 
the friction per area falls by 100x due to 1/10th the speed. 
So overall friction falls by 10x.

PS: Also note that the table above gives conservative (pessimistic) estimates on levels of friction.

==== Worry #2: Nanotech has a lot of surface area per volume. Won't that cause friction to become excessive? ====

'''Q:''' Shouldn't there be massive amounts of bearing surface area? 
It's nanomachinery after all, and and for nanotechnology the surface to volume ratio gets extremely high? 
'''A:''' Surface per volume is indeed high. BUT: '''We barely need any volume to achieve practical levels of throughput.''' 
(Reason: [[Higher throughput of smaller machinery]] - things scale favorably here)

Looking at [[convergent assembly]] in a first naive approximation every layer has exactly the same bearing area. 
So the bottom-most nanomachinery layer has exactly the same bearing area as the topmost macroscale assembly chamber. 
In practice one would want to deviate form naive [[convergent assembly]] by making the bottom layer thicker, 
which, as described above, only improves the situation with friction losses from dynamic drag.

As for the bearing area of the convergent assembly layers higher up:
* (1) There are only a few convergent assembly layers present (take 32nm chambers times 32 four times and you are at 32mm).
* (2) Bigger bearings can [[nest many layers|infinitesimal bearings]]. Again. Same trick. Area x10 & speed x1/10 => overall friction x1/10.

== Highly conservative form Nanosystems {{wikitodo|check and merge this section}} ==

'''Assumed:'''
* A [[crystolecule]] bearing with 2nm radius and 2nm length
* Bearing stiffness k = 1000N/m
* Bearing bumpiness [[superlubricity|incommensurability]]: R = abs(m/(m-n)) = 10
* Bearing operating temperature: Roomtemperature 300K

The dominant power loss contributions (Nanosystems 10.4.6.f.) give: 
* P = 2.7*10⁻14 W / (m/s)^2 -- (for Δka/ka = 0.4) or
* P = 5.8*10⁻16 W / (m/s)^2 -- (for Δka/ka = 0.003)

So how much waste heat would one get for a reasonable desktop [[gemstone metamaterial on-chip factory]]? 
It is not calculated in [[Nanosystems]] since energy recuperation inefficiencies
* in force applying mechanosynthesis and
* "covalent welding" block assembly
likely dominates.

But let's confirm that: 
The proposed [[nanofactory]] convergent assembly system architecture (Nanosystems Table 14.1.)
lists (as reasonable) a few times 10^17 units at the lowest [[assembly levels]].
Nanosystems provides no info about how many bearings per unit to assume.
But Let's assume 100 bearings per unit. This kinda seems like a reasonable
(that is pessimistic and on the safe side) assumption. (applied [[Exploratory engineering]])
This gives:
* P = TODO
* P = TODO

Note that this is (on purpose) a rather pessimistic ("conservative") estimation.

Also the assumed 1019 bearings give ''a total internal bearing sliding surface area of about: 
S = 200m^2''' -- Which intuitively feels like quite a lot but not overly excessive.

=== Side-notes regarding the Numbers given above ===

In [[Nanosystems]] 10.4.6. some examples are calculated for 1m/s sliding speed (it gives about 80MHz for the r=2nm l=2nm bearing).
It's worth to note that a sliding speed of 1m/s is already quite fast.
The actually proposed speeds are more on the order of about 1mm/s (1000 times slower).
This makes power losses no less than one million times lower (since the two dominant drag mechanisms scales quadratically with speed).

According to [[Nanosystems]] 10.4.6.f. the two dominating effects of for friction in [[crystolecule]] bearings (at speeds of interest ) are:
* band-stiffness scallering and
* shear-reflection drag
Other drag mechanisms (acoustic radiation, band-flutter scattering, thermoelastic damping)
all give negligible contributions (at least for the speeds of interest).

= Numbers from papers -- less safe (since more optimistic) =

For much more optimistic but less absolutely certainly on the safe side numbers there is work on coaxial carbon nanotubes:
Also in contrast to crystolecule bearings nanotube bearings are already somewhat accessible to experiments.

The following is from the paper: 
"Evaluating the Friction of Rotary Joints in Molecular Machines"

'''Assumed:'''
* A nanotube bearing with 0.6nm radius and 5nm length
* Bearing operating temperature: Roomtemperature 300K
* Simulation was done at the rather high speed of 30m/s ~ 8GHz

* P = 2.9(+-1.5)*10^-33 W/(rad/s)^2
Or converted into the same units as used in Nanosystems :
* P = 7.25*10^-12 W/(m/s)^2

For the above assumed 10^19 bearings this gives:
* P = TODO

= '''TODO''' update chapters below =

=== Flawless surfaces drop friction significantly ===

In contrast to etched micro-systems where the relative manufacturing error gets bigger with shrinking size.
Atomically precise machinery has no error
allow [[superlubrication]] which drops friction at least three orders of magnitude

== Evolved molecular biology is not a proof that diffusion transport is the ideal solution with minimal losses ==

With those aforementioned effects cog-and-gear nanomachinery could potential feature smaller losses than diffusion driven natural systems (more on that comparison further down). To quantify that more in depth investigations are needed.

=== The issue ===

Nature is often (probably mostly out of psychological reasons) seen as unsurpassable.
But actually it is completely unknowable whether nature as a whole will be "surpassed" by artificial technology in the far future ([[nature vs technology|get side-tracked]]).
Regardless of that, specific aspects of nature definitively can (and have been) surpassed by artificial technologies
(there are [[technology exceeding nature in performance|countless examples]]).

Evolution ended up with diffusion transport and not cog-and-gear-machinery.
Taken the former in to consideration that does by no means imply that this is the best or only solution.
Actually evolution is facing severe [[Evolution#Limits_of_natural_evolution|limitations]] (lock-in-effect, incrementalism, ...).

(This is only one of the many cases where [[misconceptions|bio-analogies]] can have a problematic effect on perception.)

=== Why cog-and-gear transport may be more efficient ===

While diffusion transport features no friction during the transport process itself
diffusion transport is not at all lossless.
At intermediate passing stations some energy always needs to be converted to heat (tech term: dissipated).
Otherwise the chemical reactions would not have a preferred direction to go and all the molecular "machinery" would cease to do anything.

Of course cog-and gear nanomachinery has exactly the same requirement.
The big difference is that in biological systems energy often comes in discrete disconnected chunks.
If ther's more than needed the excess is dissipated without being used for some desired effect.
In a crude analogy it's like being unable to accept the change money.

In cog-and-gear nanomachinery everything is linked together in one big [[machine phase]]
There energy can be drawn in a continuous rather than discrete fashion.
The dissipation necessary for forward moving operation (arrow of time) can be
balanced and minimized further down to the absolutely unconditionally required minimum.
See main article: "[[Low speed efficiency limit]]"

== Proposed machine speeds are WAY below speeds of thermal motion ==

In gemstone based nanomachinery one usually wants the operation frequencies to be well below the thermal motion frequencies. Otherwise the mechanical motions couple too strongly into thermal motions and things will get very hot very quickly. The frequencies of thermal motions can be seen in oscillation infrared spectra. Typical covalent bonds are located in the wavelength range of 3µm-30µm. This corresponds to 10THz-0.1PHz.

Related: [[Stroboscopic illusion in animations of diamondoid molecular machine elements]]

== Typical operation frequencies ==

This is strongly depending on the method of bearing ([[superlubrication]] / single sp3 bonds as bearings / some for m of levitation / ... ) and efficiency of operations.

* For mechanosynthetic mills in a [[nanofactory]] where larger forces are present and potentially slightly inefficient mechanosynthesis is performed the low MHz range is a good target.
* For low friction bearings (like in [[nanomechanical computing]]) one can go up into the high MHz to low GHz range. This still leaves a gap of three orders of magnitude to the oszillative thermal motion DOFs.

== Less soft nanomachinery => less drag ==

Unlike compliant bio-molecules in water [[stiffness|stiff structures]] like carbon nanotubes (or bearings out of gemstone) in dry vacuum do not provide low energy low frequency rotative degrees of freedom (DOFs) to couple into. Those DOFs could (if they where present like in water) go down all the way to the microwave range: ~ 3cm & 10GHz. So overlap of mechanical motion with rotative thermal motion isn't so much of a problem
even at higher operation frequencies.

Note that existing simulations of [[crystolecule]]s can show a
a '''stroboscopic effect'''. That can lead one to believe
machine motion and thermal motion lie very close together and that consequently friction would be horrendous.
This is not the case. It's just an artifact of the simulation.

== Related ==

* '''[[Friction]]'''
* The myth that [[diffusion transport]] does not need to dissipate energy or is fundamentally more efficient.
* [[Superlubricity]]
* [[Levitation]]
* [[Crystolecule]]s
* [[How friction diminishes at the nanoscale]]
* [[Atomically precise bearings]] – especially [[Atomically precise slide bearing]]s
* '''[[Mesoscale friction]]'''
* [[Macroscale mechanical bearings]]
----
* [[Reciprocative dissipation mechanisms in gem-gum technology]]

[[Nanosystems]] – Chapter 7 – Energy Dissipation – (page 161 to 190)
----
* [[Losses from mechanochemical reactions]]
----
* '''[[Wear]]'''

== External links ==

* {{todo|Add ref's to relevant chapters in "Nanosystems"}}
----
* Paper: [https://www.mse.ncsu.edu/CompMatSci/papers/TTN4_p9700_1.pdf Molecular-dynamics simulations of atomic-scale friction of diamond surfaces]
----
* Wikipedia: [https://en.wikipedia.org/wiki/Rotational_spectroscopy Rotational spectroscopy]
* Wikipedia: [https://en.wikipedia.org/wiki/Rotational%E2%80%93vibrational_spectroscopy Rotational–vibrational spectroscopy]
* Wikipedia: [https://en.wikipedia.org/wiki/Infrared_spectroscopy Infrared spectroscopy] & [https://en.wikipedia.org/wiki/Thermal_infrared_spectroscopy Thermal infrared spectroscopy]
----
* https://sci-nanotech.com/index.php?thread/43-a-closer-look-at-friction-in-cog-gear-style-stiff-nanomachinery/
----
* [https://pubs.rsc.org/en/content/articlehtml/2017/me/c7me00021a 2017 Evaluating the Friction of Rotary Joints in Molecular Machines] [https://arxiv.org/abs/1701.08202 (arxiv)]

[[Category:Surprising facts]]

= References =

<references/>

Distorted visualization methods for convergent assembly

2026-09-29T23:48:16Z

Apm: /* Related */ * Convergent assembly

[[File:LogPolarMapping3DwithMolecularMills.jpg|480px|thumb|right|Here mapped is both a c coordinate grid and molecular mill rotors analog to the ones seen in: "Productive Nanosystems from Molecules to Superproducts". Note that in non-transformed coordinates the grey wall sits on xy-plane partly above partly below. Thus it gets curls both ways in the magnifying log polar coordinates. The wide bottom is a small cutout around (0,0,0) that's necessary as nearing zero everything gets exponentially magnified.]]

[[File:LogPolarMapping3DacrossTwoAssemblyLayers.png|200px|thumb|right|Generalized log polar mapping across two assembly layers. This should be extendable to more. Big caveat here is that assembly layers need to be roughly same sub-layer number which is not at all the case for the lowermost assembly layers. Hard coded assembly lines makes for very many sub-layers.]]

To get a complete picture of the physical layout of all the [[assembly levels]] of the [[convergent assembly]] in a [[nanofactory]] (which might be organized in a stack of coplanar [[nanofactory layers|layers]]) and see all of this in one single image at one glance one needs to project space in a nonlinear way. 
Normal perspective (a linear projection) is unsuitable since it compresses most details towards the horizon.
Instead a nonlinear polar logarithmic mapping is the best fit.

An additional difficulty is that a nanofactory as opposed to a map is inherently three dimensional so some cross cut has to be chosen. Whether that cross cut can be simply planar or not depends on the exact design choices taken in a concrete nanofactories design.

{{wikitodo| add image [http://i.imgur.com/GFGJU.jpg] -- license?}}

== Displaying many scales and their relation simultaneously ==

This can be done by '''generalizing log polar mapping to 3D''' like so:
* x'(x,y,z) = pi/2 - atan2( z, sqrt(pow(x,2) + pow(y,2)) ) * cos(atan2(y,x)))
* y'(x,y,z) = pi/2 - atan2( z, sqrt(pow(x,2) + pow(y,2)) ) * sin(atan2(y,x)))
* z'(x,y,z) = log( sqrt(pow(x,2) + pow(y,2) + pow(z,2)) ) / log(base)

== Related ==

Distorted visualization methods (like e.g. the 3D log polar mapping visualization method) may also be useful to keep oriented in the visualizations of 
abstract spaces other than concrete physical space. E.g. circuitry topology in very large software systems.
----
* More generally: [[Visualization methods for gemstone metamaterial factories]]
* [[Challenges in the visualization of gem-gum factories]]
----
* Visualizing the stratified [[nanofactory layers]] or other geometries that implements [[assembly levels]].
----
* Showing only what is needed at anyone time. Related: The software interface principle of "[[progressive disclosure]]".
* Drifting off-topic: [[General software issues]]

== Hyperbolic geometry and Escher disks ==

Related to this: https://en.wikipedia.org/wiki/Circle_Limit_III

'''Problem #1:''' 
Not all scales are treated the same. More precisely: 
The mapping does not transform scale invariance into translational symmetry (as log polar does). 
Infinitely big things get crunched into finite space. A singularity at the perimeter. Even when exponentially/geometrically growing. 
(Not sure if you can explode the rim when growing uber expeonentially with an essential singularity, doubt so even then, fascinating math problem but beside the practical focus here.)

'''Problem #1:''' The depiction is inherently 2D.

'''Vertical cut:''' 
Projecting to an Escher disk a vertical cut through exponentially growing assembly levels with bottom at the disks center
this would give only the top half of a disk. Above the center shrinking down the growing size layers but soon too much.
Sideways already small things get shrunk down too pointlessly. 
So overall not a particularly good choice for a coordinate transformation.

'''Horizontal single plane cut through already log polar transformed coordinates:''' 
This gives a disk looking similar to an Escher disk but it would be very different in nature. 
Transforming a planar disk from log polar back to original coordinates gives an spherical (half)shell. 
With exponentially shrinking assembly levels nearing the xy-plane there is much stuff compressed to near the edges of the disks. 
Well limited by the smallest assembly level of course as we have physics not pure math. 
This is really not suitable for showing thinsg at multiple scales simultaneously. 
Also note that the observation angle within a deisk changes like on a sphere as well in the original coordinates we are on a sphere 
(nonequidistantly sampled sphere to highlight peculiarity). 

== External Links ==

* Wikipedia on log polar mapping: [https://en.wikipedia.org/wiki/Log-polar_coordinates Log-polar coordinates]
* Wikipedia on the Mercator projection which becomes log polar near both poles: [https://en.wikipedia.org/wiki/Mercator_projection Mercator projection]
----
* An interactive online map spanning a wide range of scales: [http://mrgris.com/projects/merc-extreme/ '''mercator extreme'''] The mercator projection cut off much closer to the poles whose location can be freely chosen.
----
* python scripts to generate log-polar maps from pixelgraphics [https://github.com/dmishin/log-zoom]
* "Detail-In-Context Visualization for Satellite Imagery" [https://www.researchgate.net/publication/30012541_Detail-In-Context_Visualization_for_Satellite_Imagery] "Complex Logarithmic Views for Small Details in Large Contexts" [https://www.researchgate.net/publication/6715574_Complex_Logarithmic_Views_for_Small_Details_in_Large_Contexts] by Joachim Boettinger et. al. Department of Computer and Information Science, University of Konstanz, Germany
* Video showing a manual multi-scale zoom device [http://www.youtube.com/watch?v=rBffRXfNDW0&t=6m42s] the "zoom-scope"
* square grid mapped to show details on all scales equally [https://www.flickr.com/photos/65091269@N08/21137194509/sizes/l]
* More large scale map examples [http://dmishin.blogspot.co.at/2013/12/log-polar-coordinate-system-applied-to.html]

* [http://dmishin.blogspot.co.at/2014/09/logarithmic-zoom-at-palace-square-saint.html Images from Dmitry Shintyakov]

== Keywords ==

distortion lens view; log-polar map; complex logarithmic map, complex logarithmic view, anamorphic mirror, anamorphosis

== Related ==

* [[Visualization methods for gemstone metamaterial factories]]
* [[Visualizations of gemstone metamaterial factories]]
* [[Log polar mapping]]
* [[Convergent assembly]]

[[Category:Far term target]]
[[Category:Surprising facts]]

Energy dissipation in gemstone metamaterial technology

2026-09-29T09:04:02Z

Apm: minimal basic page

{{Stub}}

Beside friction there are also other things that can lead to energy losses 
by eventual conversion to directed free usable energy to statistic motion unusable bound thermal energy (aka energy devaluation or dissipation). 
These include e.g. shaking and back and and forth bending. 

* [[Friction in gemstone metamaterial technology]]
* [[Reciprocative dissipation mechanisms in gem-gum technology]]

Friction in gemstone metamaterial technology

2026-09-29T08:58:25Z

Apm: added link to yet unwritten page Energy dissipation in gemstone metamaterial technology

{{wikitodo|This page needs major cleanup - several parts need to be merged and completed and factored out}} 
[[File:Superlubricity scaling chart.png|800px|thumb|right|Double logarithmic chart of several estimations for [[superlubricity|superlubric friction]] and its quadratic scaling. Note that at moderate speeds like 1m/s it is actually quite high but it quickly drops off going to lower (proposed) speeds around ~1mm/s. The black line (way higher up than all the others) is not superlubric friction but dynamic friction in fluids for comparison. '''This does not cover [[reciprocative dissipation mechanism]]s modes''' which can be significant and can't be co-plotted without a number of (at this point in 2025 still too difficult to pin down) assumptions.]]
Up: [[Energy dissipation in gemstone metamaterial technology]] 
Up: [[Friction]]

'''[[Macroscale style machinery at the nanoscale]]''' has in the past received some seriously bad reputation
because it comes with a bunch of [[common misconceptions|mental trapdoors]] that led a a number of very smart reputational and vocal people to bad conclusions.
One of these bad conclusions is that macroscale style machinery at the nanoscale would lead to exorbitant amounts of friction. A very wrong conclusion, as I will try to show below.
(There are other misled criticisms to the idea beside the false conclusion of exorbitant friction. For a discussion of those you may want to check out the main page about [[macroscale style machinery at the nanoscale]].)

= To the doubly logarithmic friction chart =

The chat is meant as …
* a common comparing ground for a broad set different results.
* a starting point to be improved on.

In particular:
* (A) Eventually adding more lines from more suitable data sources eventually.
* (B) Finding the high speed and low speed limits where the quadratic scaling breaks down and gives way to other scaling laws (or destructive end) eventually.

For now in the chart beside results only the book [[Nanosystems]] a source 
there is also one second independent source at least. This one is also theoretical though. {{Wikitodo|Check if fully true.}} 
The second source: [https://pubs.rsc.org/en/content/articlehtml/2017/me/c7me00021a 2017 Evaluating the Friction of Rotary Joints in Molecular Machines] [https://arxiv.org/abs/1701.08202 (arxiv)]

A big problem with current day (2026) experimental results is that 
experimental limitations introduce uncontrollable side effects that overshadow 
what one would get with atomically precise surfaces sliding in an advanced much cleaner not yet preparable setup. 
{{Wikitodo|Elaborate on that eventually. This may deserve a dedicated page. Add papers and explain associated concrete issues with them.}} 

= Dodge the trapdoors =

* '''Yes, It is true that physics changes when the size-scale changes.''' But who says it changes for the worse when it comes to [[macroscale style machinery at the nanoscale]]?
* '''Yes, It is true that [[rising surface area|surface area grows with shrinking structure sizes]], and that this contributes to friction.''' But there are other effects that overcompensate growing surface area and these are very often overlooked.
* '''Yes, It is true that unlike diffusion transport there is friction all the time along the whole way.''' But it's often overlooked that diffusion must devaluate chunks of energy at its "pit-stops" to prevent transport from running backwards and that the "change money" energy that gets left over at these "pit-stops" cannot be kept for later usage. Whereas in [[machine phase system]]s keeping and reuseing the energetic change money may be possible.
* '''Yes, It is true that there is no natural example of macro style machinery at the nanoscale (similar to the one proposed).''' But concluding from that that it's not possible or a worse solution is a fallacy. There are plenty of human invented things that exceed capabilities of nature by orders of magnitude. To give just a few examples: Bicycles, combustion engines (spaceships), copper wires (superconductors), wheels and streets, ...
* '''Yes, It is true that MEMS (microelectromechanical systems) have high friction (and bad wear from "stiction").''' But in case of MEMS this is due to MEMS not having atomically precise [[superlubricity|suberbublicating]] bearings but instead having a really bad signal to noise ratio in their geometry due to them being manufactured top-down.

= Main sources of friction and countermeasures =

Friction in [[gem-gum-tec|gemstone based nanomachinery]] is mainly caused by:
* (1) band-stiffness scattering drag and
* (2) shear-reflection drag
Source: [[Nanosystems]] 10.4.6. Mechanisms of Energy dissipation f. Summary 
{{todo|find and add an intuitively comprehensible explanation for these two [[phonon interaction based dissipation mechanisms]]}}

Furthermore there are energy dissipation mechanisms that are specific to reciprocative motion. 
'''See page: [[Reciprocative friction in gem-gum technology]]'''

== Tuning for superlubricity against band-stiffness scattering drag ==

Only (1) can be reduced by tuning for [[superlubricity]] till (2) gets dominant. 
'''Maybe about x100 lower friction possible tuned vs untuned?'''

== Cranking up "compenslow" to reduce friction overall ==

Both (1) and (2) can be reduced cranking up the "[[compenslow]]" design parameter. 
Higher "compenslow" means an increased amount of nanomachinery that all runs at a slower absolute speed. 
"Compenslow" is a portemonteau for "by more machinery compensated slowdown"

'''When doubling the compenslow:'''
* The total throughput per chip area (areal throughput density) stays unchanged!
* Friction losses are cut in half.
* The thickness of the nanomachinery layer doubles. (this is not an issue)
* the internal bearing area per chip area doubles and speeds are cut in half.

'''Increasing compenslow can reduce losses from friction by many orders of magnitude.''' 

=== Limits to optimization by increase of "compenslow" ===

At some point friction from fast transport motions becomes relevant. 
Only the assembly motions are slowed down but assembly motions make up most of the distance the robotics travels. 
Once transport motions get similar in length to the assembly motions. Increasing compenslow is no longer a viable optimization option.

Also:
* the more parts are assembled per [[assembly cycle]] across an [[assembly level]]
* the more there is potential for reduction of friction by increase of compenslow across that assembly level

== Don't over-optimize friction way below mechanochemical losses ==

For systems that perform [[piezochemical mechanosynthesis]] and or [[chemomechanical conversion]] 
it's only sensible to tune friction down so far that [[losses from mechanochemical reactions]] become clearly dominant. 
Note that the increased amount of nanomachinery that results from for standard parts specialized subsystems 
already leads to some minimal compenslow.

For systems that do not perform any mechanochemical conversions like e.g. [[microcomponent recomposer]]s 
losses from friction may become the remaining dominant factor. Relevant in the context of [[recycling]]. 
So here going all out on minimizing friction may really pay off.

= Employing scaling laws against friction =

'''Overcompensating increased friction from increased bearing area''' 
'''See main page: [[How friction diminishes at the nanoscale]]'''

=== The two core physical facts that provide the lion-share of lowering friction ===

[[File:NongrowingAreaInConvergentAssembly.png|thumb|400px|In simple [[convergent assembly]] all layers feature the same total bearing area. So the bottommost nanomachinery has no more bearing surface area than the topmost macromachinery (despite [[higher bearing surface area of smaller machinery]]). Furthermore for practical jumps of scale (x32?) there are only a few layers of convergent assembly.]]

* [[higher throughput of smaller machinery]] Halving the size of the robotics has doubles the throughput per volume when robotic keeping speeds (NOT frequencies) constant. This means that in a naive first approximation the total bearing area of nanomchinery in a [[gem-gum factory]] is no bigger than the bearing area of macromachinery. It's desirable to deviate quite a bit from that first approximation, but as it turns out that only drops friction even further despite increasing bearing area.
* [[power losses from friction scale quadratic with speed]] that is: 1/2 the speed of the machinery => 1/4th friction power losses

=== The two main tricks that apply and combine these physical facts to great avail ===

[[File:ReducingFrictionByDeliberateSlowdown.png|thumb|left|400px|'''The first trick:''' Friction can be reduced by a lot by slowing down the speed of operation of (bottom-most) nanomachinery. In order to not loose throughput capacity [[Multilayer assembly layers|just add more nanomachinery compensating the slowdown]]. This still remains an imperceptibly thin layer on the [[gem-gum factory]] chip due to the [[higher throughput of smaller machinery|high throughput density of nanomachinery]]. '''Total friction losses falls despite rising bearing area!!''']]

[[File:Infinitesimal-bearing-sketch.png|thumb|right|250px|speed distributions from conventional to infinitesimal bearing|frame|'''The second trick:''' [[Infinitesimal bearings]]: 2x the number of layers => 1/2x the friction. This is because the drop in friction from reduced speed (x1/4) overcompensates the rise in friction from increased bearing area (x2). This is only applicable at the higher assembly levels with larger scale machinery.]]

* Distribute productive activity over a lot more layers of nanomachinery (there is more than sufficient space to do so. See [[multilayer assembly layers]])
* [[Infinitesimal bearings|Distribute speed differences over multiple coplanar surfaces]] (there is ore than sufficient space to do so)
----
* In both cases there is more then sufficient space available to do so.
* In both cases speed falls linearly with the number of bearing layers. This gives simultaneously a linear increase (more bearing area) and a quadratic fall (less bearing speed) of friction losses. That is: overall a linear fall of friction losses.
----
* The first case is relevant for the bottom-most layer of [[convergent assembly]] in [[gemstone metamaterial on-chip factories]]
* The second case is relevant for higher up layers of [[convergent assembly]] where larger scale bearings are possible.

== Smaller contributions ==

* Bearing can be tuned for good [[superlubricity]]
* minimization of travel-distance needed per chemical synthesis operation dissipation falls linearly with the path traveled

Minimization of travel-distance leads towards the nanofactory design and away from the molecular assembler design. 
{{wikitodo|elaborate on that}}

= Quantitatively (Math and Numbers) =

== Dynamic drag in superlubricating gemstone bearings - vs - viscous drag in liquids ==

'''There is at least 2,000.0 to 100,000.0 times less friction in gemstone bearings compared to movement at the same speed in water.''' 

So when it comes to peak performance parameters 
soft nanotechnologies and artificial [[synthetic biology]] derived from molecular biology, 
is fundamentally massively inferior to [[gemstone metamaterial technology]]

Yes, this much lower friction is still more than the zero friction that is as present in diffusion transport. 
But this misses a crucial point. 
For diffusion transport to happen it still needs to "expend" energy (still needs to devaluate free energy). 
It is just that the free energy expense need to be payed up at the pitstops (when crossing cell- and vesticle-membranes) rather than during the transport motion. (see external links)

So: 
'''Diffusion transport driven by concentration gradients does NOT make biological nanosystems fundamentally more efficient than conveyorbelt style transport in stiff dry artificial nanosystems in a vacuum.'''

=== Associated math ===

Source: <ref name="phononvsviscousdrag"> '''Eric Drexlers former homepage (webarchive):''' [https://web.archive.org/web/20160305212101/http://e-drexler.com/p/04/03/0322drags.html Phonon drag in sleeve bearings can be orders of magnitude smaller than viscous drag in liquids]</ref>

'''Rotating sphere in Water:''' (Source: <ref name="viscdrag"> '''Viscous torque on a sphere:''' Landau, L, and Lifshitz, E (1987) Fluid Mechanics, 2nd ed. Pergamon Press p.91.</ref>)
* <math> \omega = v/R </math>
* Drag-torque: <math> M_{flow} = -8 \pi \eta R^3 \omega </math>
* Dissipation: <math> P_{flow} = M_{flow} \omega = 8 \pi \eta R v^2 </math>
With: <math> \eta \approx 10 \times 10^{-3} Pa \cdot s </math> and <math> R = 2nm </math>
* Dissipation: <math> P_{flow} \approx 5 \times 10^{-11} v^2 W = 5 \times 10^{-11} W/(m/s)^2</math>

----
'''Gemstone sleeve nearing:''' (Source: <ref name="pdrag"> '''Drag mechanisms in symmetrical sleeve bearings:''' Drexler, K. E. (1992) ''[[Nanosystems]]: Molecular Machinery, Manufacturing, and Computation.'' Wiley/Interscience, pp.290–293.</ref>)
* <math> P_{drag} = 5.8 \times 10^{-16} W/(m/s)² -- \Delta k_a / k_a = 0.003</math>
* <math> P_{drag} = 2.7 \times 10^{-14} W/(m/s)² -- \Delta k_a / k_a = 0.4 </math>
----
'''Ratio:'''
* <math> P_{flow} / P_{drag} \approx 2000 … 100000</math>

== Despite superlubricity dynamic drag can be significant ==

{{wikitodo|add doublelog gnulot plot of examples}}

While static friction in superlubricity falls to nigh zero, 
'''Dynamic (speed dependent) friction can be quite significant for higher speeds.'''

For higher speeds and bearings that do not resort to:
* [[levitation|some mean of levitation]] ( only possible for low loads ) or
* [[infinitesimal bearings|bearing stratification]] ( only possible for bigger nearings )
... the friction per area can actually get quite high for higher speeds.

{| class="wikitable left" style="margin-left: auto; margin-left: 0px;"
|-
| v=100µm/s
| '''v=1mm/s''' (proposed speed)
| '''v=10mm/s''' (proposed speed)
| v=100mm/s
| v=1m/s
| v=10m/s
|-
| 230nW/m² to 10µW/m²
| 23µW/m² to 1mW/m²
| 2.3mW/m² to 100mW/m²
| 230mW/m² to 10W/m²
| 23W/m² to 1kW/m²
| 2.3kW/m² to 100kW/m²
|}
* <math> P_{drag} = 23 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.003</math>
* <math> P_{drag} = 1080 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.4 </math>
Source: [[Nanosystems]] Equation (10.27) <ref name="pdrag"/> --
But here calculated backwards to friction per area from friction per bearing. 
'''Note:''' These are highly conservative estimates. Real values should be quite a bit lower.

Halving the linear speed (in units of m/s) quaters the friction losses. 
And going down from 1m/s to 1mm/s the friction losses fall by a factor of a million (1,000,000). 
More technically: Dynamic friction for crystolecules scales quadratically with speed. 

=== Why significant dynamic drag at higher speeds is this is not a problem ===

 Note: This section is redundant but provides a different formulation.
Skip ahead if the everything so far was clear.

==== Worry #1: Looking at the table friction per area for small speeds like 1m/s is quite high. ====

Friction can be ''massively'' massively reduced by reducing the linear speed of motions (speed in units m/s NOT Hz!). 
And '''we can totally afford to reduce the linear speed of motion in [[advanced productive nanosystem]]s because all the machinery that is needed for practical levels of throughput fits in a super thin layer at the very bottom of the [[convergent assembly]] of a [[gem-gum factory]] chip.''' 
(Reason: [[Higher throughput of smaller machinery]] - things scale favorably here)

We just need to make the bottom layer [[gem-gum factory]] chip a bit thicker 
to compensate for the loss of speed and we are back at the original throughput. 
(We want to do that anyway because many different specialized assembly lines need space.)

One totally can afford to slow down so much in advanced productive nanosystems like [[gem-gum factories]] 
because there is plenty of space to compensate by just adding more nanomachinery.

'''Q:''' '''But what about the additional bearing area?''' 
'''A:''' Yes, the total bearing area increases. 
But while 10x the amount of nanomachinery gives 10x the bearing area 
the friction per area falls by 100x due to 1/10th the speed. 
So overall friction falls by 10x.

PS: Also note that the table above gives conservative (pessimistic) estimates on levels of friction.

==== Worry #2: Nanotech has a lot of surface area per volume. Won't that cause friction to become excessive? ====

'''Q:''' Shouldn't there be massive amounts of bearing surface area? 
It's nanomachinery after all, and and for nanotechnology the surface to volume ratio gets extremely high? 
'''A:''' Surface per volume is indeed high. BUT: '''We barely need any volume to achieve practical levels of throughput.''' 
(Reason: [[Higher throughput of smaller machinery]] - things scale favorably here)

Looking at [[convergent assembly]] in a first naive approximation every layer has exactly the same bearing area. 
So the bottom-most nanomachinery layer has exactly the same bearing area as the topmost macroscale assembly chamber. 
In practice one would want to deviate form naive [[convergent assembly]] by making the bottom layer thicker, 
which, as described above, only improves the situation with friction losses from dynamic drag.

As for the bearing area of the convergent assembly layers higher up:
* (1) There are only a few convergent assembly layers present (take 32nm chambers times 32 four times and you are at 32mm).
* (2) Bigger bearings can [[nest many layers|infinitesimal bearings]]. Again. Same trick. Area x10 & speed x1/10 => overall friction x1/10.

== Highly conservative form Nanosystems {{wikitodo|check and merge this section}} ==

'''Assumed:'''
* A [[crystolecule]] bearing with 2nm radius and 2nm length
* Bearing stiffness k = 1000N/m
* Bearing bumpiness [[superlubricity|incommensurability]]: R = abs(m/(m-n)) = 10
* Bearing operating temperature: Roomtemperature 300K

The dominant power loss contributions (Nanosystems 10.4.6.f.) give: 
* P = 2.7*10⁻14 W / (m/s)^2 -- (for Δka/ka = 0.4) or
* P = 5.8*10⁻16 W / (m/s)^2 -- (for Δka/ka = 0.003)

So how much waste heat would one get for a reasonable desktop [[gemstone metamaterial on-chip factory]]? 
It is not calculated in [[Nanosystems]] since energy recuperation inefficiencies
* in force applying mechanosynthesis and
* "covalent welding" block assembly
likely dominates.

But let's confirm that: 
The proposed [[nanofactory]] convergent assembly system architecture (Nanosystems Table 14.1.)
lists (as reasonable) a few times 10^17 units at the lowest [[assembly levels]].
Nanosystems provides no info about how many bearings per unit to assume.
But Let's assume 100 bearings per unit. This kinda seems like a reasonable
(that is pessimistic and on the safe side) assumption. (applied [[Exploratory engineering]])
This gives:
* P = TODO
* P = TODO

Note that this is (on purpose) a rather pessimistic ("conservative") estimation.

Also the assumed 1019 bearings give ''a total internal bearing sliding surface area of about: 
S = 200m^2''' -- Which intuitively feels like quite a lot but not overly excessive.

=== Side-notes regarding the Numbers given above ===

In [[Nanosystems]] 10.4.6. some examples are calculated for 1m/s sliding speed (it gives about 80MHz for the r=2nm l=2nm bearing).
It's worth to note that a sliding speed of 1m/s is already quite fast.
The actually proposed speeds are more on the order of about 1mm/s (1000 times slower).
This makes power losses no less than one million times lower (since the two dominant drag mechanisms scales quadratically with speed).

According to [[Nanosystems]] 10.4.6.f. the two dominating effects of for friction in [[crystolecule]] bearings (at speeds of interest ) are:
* band-stiffness scallering and
* shear-reflection drag
Other drag mechanisms (acoustic radiation, band-flutter scattering, thermoelastic damping)
all give negligible contributions (at least for the speeds of interest).

= Numbers from papers -- less safe (since more optimistic) =

For much more optimistic but less absolutely certainly on the safe side numbers there is work on coaxial carbon nanotubes:
Also in contrast to crystolecule bearings nanotube bearings are already somewhat accessible to experiments.

The following is from the paper: 
"Evaluating the Friction of Rotary Joints in Molecular Machines"

'''Assumed:'''
* A nanotube bearing with 0.6nm radius and 5nm length
* Bearing operating temperature: Roomtemperature 300K
* Simulation was done at the rather high speed of 30m/s ~ 8GHz

* P = 2.9(+-1.5)*10^-33 W/(rad/s)^2
Or converted into the same units as used in Nanosystems :
* P = 7.25*10^-12 W/(m/s)^2

For the above assumed 10^19 bearings this gives:
* P = TODO

= '''TODO''' update chapters below =

=== Flawless surfaces drop friction significantly ===

In contrast to etched micro-systems where the relative manufacturing error gets bigger with shrinking size.
Atomically precise machinery has no error
allow [[superlubrication]] which drops friction at least three orders of magnitude

== Evolved molecular biology is not a proof that diffusion transport is the ideal solution with minimal losses ==

With those aforementioned effects cog-and-gear nanomachinery could potential feature smaller losses than diffusion driven natural systems (more on that comparison further down). To quantify that more in depth investigations are needed.

=== The issue ===

Nature is often (probably mostly out of psychological reasons) seen as unsurpassable.
But actually it is completely unknowable whether nature as a whole will be "surpassed" by artificial technology in the far future ([[nature vs technology|get side-tracked]]).
Regardless of that, specific aspects of nature definitively can (and have been) surpassed by artificial technologies
(there are [[technology exceeding nature in performance|countless examples]]).

Evolution ended up with diffusion transport and not cog-and-gear-machinery.
Taken the former in to consideration that does by no means imply that this is the best or only solution.
Actually evolution is facing severe [[Evolution#Limits_of_natural_evolution|limitations]] (lock-in-effect, incrementalism, ...).

(This is only one of the many cases where [[misconceptions|bio-analogies]] can have a problematic effect on perception.)

=== Why cog-and-gear transport may be more efficient ===

While diffusion transport features no friction during the transport process itself
diffusion transport is not at all lossless.
At intermediate passing stations some energy always needs to be converted to heat (tech term: dissipated).
Otherwise the chemical reactions would not have a preferred direction to go and all the molecular "machinery" would cease to do anything.

Of course cog-and gear nanomachinery has exactly the same requirement.
The big difference is that in biological systems energy often comes in discrete disconnected chunks.
If ther's more than needed the excess is dissipated without being used for some desired effect.
In a crude analogy it's like being unable to accept the change money.

In cog-and-gear nanomachinery everything is linked together in one big [[machine phase]]
There energy can be drawn in a continuous rather than discrete fashion.
The dissipation necessary for forward moving operation (arrow of time) can be
balanced and minimized further down to the absolutely unconditionally required minimum.
See main article: "[[Low speed efficiency limit]]"

== Proposed machine speeds are WAY below speeds of thermal motion ==

In gemstone based nanomachinery one usually wants the operation frequencies to be well below the thermal motion frequencies. Otherwise the mechanical motions couple too strongly into thermal motions and things will get very hot very quickly. The frequencies of thermal motions can be seen in oscillation infrared spectra. Typical covalent bonds are located in the wavelength range of 3µm-30µm. This corresponds to 10THz-0.1PHz.

Related: [[Stroboscopic illusion in animations of diamondoid molecular machine elements]]

== Typical operation frequencies ==

This is strongly depending on the method of bearing ([[superlubrication]] / single sp3 bonds as bearings / some for m of levitation / ... ) and efficiency of operations.

* For mechanosynthetic mills in a [[nanofactory]] where larger forces are present and potentially slightly inefficient mechanosynthesis is performed the low MHz range is a good target.
* For low friction bearings (like in [[nanomechanical computing]]) one can go up into the high MHz to low GHz range. This still leaves a gap of three orders of magnitude to the oszillative thermal motion DOFs.

== Less soft nanomachinery => less drag ==

Unlike compliant bio-molecules in water [[stiffness|stiff structures]] like carbon nanotubes (or bearings out of gemstone) in dry vacuum do not provide low energy low frequency rotative degrees of freedom (DOFs) to couple into. Those DOFs could (if they where present like in water) go down all the way to the microwave range: ~ 3cm & 10GHz. So overlap of mechanical motion with rotative thermal motion isn't so much of a problem
even at higher operation frequencies.

Note that existing simulations of [[crystolecule]]s can show a
a '''stroboscopic effect'''. That can lead one to believe
machine motion and thermal motion lie very close together and that consequently friction would be horrendous.
This is not the case. It's just an artifact of the simulation.

== Related ==

* '''[[Friction]]'''
* The myth that [[diffusion transport]] does not need to dissipate energy or is fundamentally more efficient.
* [[Superlubricity]]
* [[Levitation]]
* [[Crystolecule]]s
* [[How friction diminishes at the nanoscale]]
* [[Atomically precise bearings]] – especially [[Atomically precise slide bearing]]s
* '''[[Mesoscale friction]]'''

[[Nanosystems]] – Chapter 7 – Energy Dissipation – (page 161 to 190)
----
* [[Losses from mechanochemical reactions]]
----
* '''[[Wear]]'''

== External links ==

* {{todo|Add ref's to relevant chapters in "Nanosystems"}}
----
* Paper: [https://www.mse.ncsu.edu/CompMatSci/papers/TTN4_p9700_1.pdf Molecular-dynamics simulations of atomic-scale friction of diamond surfaces]
----
* Wikipedia: [https://en.wikipedia.org/wiki/Rotational_spectroscopy Rotational spectroscopy]
* Wikipedia: [https://en.wikipedia.org/wiki/Rotational%E2%80%93vibrational_spectroscopy Rotational–vibrational spectroscopy]
* Wikipedia: [https://en.wikipedia.org/wiki/Infrared_spectroscopy Infrared spectroscopy] & [https://en.wikipedia.org/wiki/Thermal_infrared_spectroscopy Thermal infrared spectroscopy]
----
* https://sci-nanotech.com/index.php?thread/43-a-closer-look-at-friction-in-cog-gear-style-stiff-nanomachinery/
----
* [https://pubs.rsc.org/en/content/articlehtml/2017/me/c7me00021a 2017 Evaluating the Friction of Rotary Joints in Molecular Machines] [https://arxiv.org/abs/1701.08202 (arxiv)]

[[Category:Surprising facts]]

= References =

<references/>

Friction in gem-gum technology

2026-09-29T08:48:15Z

Apm: Apm moved page Friction in gem-gum technology to Friction in gemstone metamaterial technology: better to explain gem-gum on different page

#REDIRECT [[Friction in gemstone metamaterial technology]]

Friction in gemstone metamaterial technology

2026-09-29T08:48:15Z

Apm: Apm moved page Friction in gem-gum technology to Friction in gemstone metamaterial technology: better to explain gem-gum on different page

{{wikitodo|This page needs major cleanup - several parts need to be merged and completed and factored out}} 
[[File:Superlubricity scaling chart.png|800px|thumb|right|Double logarithmic chart of several estimations for [[superlubricity|superlubric friction]] and its quadratic scaling. Note that at moderate speeds like 1m/s it is actually quite high but it quickly drops off going to lower (proposed) speeds around ~1mm/s. The black line (way higher up than all the others) is not superlubric friction but dynamic friction in fluids for comparison. '''This does not cover [[reciprocative dissipation mechanism]]s modes''' which can be significant and can't be co-plotted without a number of (at this point in 2025 still too difficult to pin down) assumptions.]]
Up: [[Friction]]

'''[[Macroscale style machinery at the nanoscale]]''' has in the past received some seriously bad reputation
because it comes with a bunch of [[common misconceptions|mental trapdoors]] that led a a number of very smart reputational and vocal people to bad conclusions.
One of these bad conclusions is that macroscale style machinery at the nanoscale would lead to exorbitant amounts of friction. A very wrong conclusion, as I will try to show below.
(There are other misled criticisms to the idea beside the false conclusion of exorbitant friction. For a discussion of those you may want to check out the main page about [[macroscale style machinery at the nanoscale]].)

= To the doubly logarithmic friction chart =

The chat is meant as …
* a common comparing ground for a broad set different results.
* a starting point to be improved on.

In particular:
* (A) Eventually adding more lines from more suitable data sources eventually.
* (B) Finding the high speed and low speed limits where the quadratic scaling breaks down and gives way to other scaling laws (or destructive end) eventually.

For now in the chart beside results only the book [[Nanosystems]] a source 
there is also one second independent source at least. This one is also theoretical though. {{Wikitodo|Check if fully true.}} 
The second source: [https://pubs.rsc.org/en/content/articlehtml/2017/me/c7me00021a 2017 Evaluating the Friction of Rotary Joints in Molecular Machines] [https://arxiv.org/abs/1701.08202 (arxiv)]

A big problem with current day (2026) experimental results is that 
experimental limitations introduce uncontrollable side effects that overshadow 
what one would get with atomically precise surfaces sliding in an advanced much cleaner not yet preparable setup. 
{{Wikitodo|Elaborate on that eventually. This may deserve a dedicated page. Add papers and explain associated concrete issues with them.}} 

= Dodge the trapdoors =

* '''Yes, It is true that physics changes when the size-scale changes.''' But who says it changes for the worse when it comes to [[macroscale style machinery at the nanoscale]]?
* '''Yes, It is true that [[rising surface area|surface area grows with shrinking structure sizes]], and that this contributes to friction.''' But there are other effects that overcompensate growing surface area and these are very often overlooked.
* '''Yes, It is true that unlike diffusion transport there is friction all the time along the whole way.''' But it's often overlooked that diffusion must devaluate chunks of energy at its "pit-stops" to prevent transport from running backwards and that the "change money" energy that gets left over at these "pit-stops" cannot be kept for later usage. Whereas in [[machine phase system]]s keeping and reuseing the energetic change money may be possible.
* '''Yes, It is true that there is no natural example of macro style machinery at the nanoscale (similar to the one proposed).''' But concluding from that that it's not possible or a worse solution is a fallacy. There are plenty of human invented things that exceed capabilities of nature by orders of magnitude. To give just a few examples: Bicycles, combustion engines (spaceships), copper wires (superconductors), wheels and streets, ...
* '''Yes, It is true that MEMS (microelectromechanical systems) have high friction (and bad wear from "stiction").''' But in case of MEMS this is due to MEMS not having atomically precise [[superlubricity|suberbublicating]] bearings but instead having a really bad signal to noise ratio in their geometry due to them being manufactured top-down.

= Main sources of friction and countermeasures =

Friction in [[gem-gum-tec|gemstone based nanomachinery]] is mainly caused by:
* (1) band-stiffness scattering drag and
* (2) shear-reflection drag
Source: [[Nanosystems]] 10.4.6. Mechanisms of Energy dissipation f. Summary 
{{todo|find and add an intuitively comprehensible explanation for these two [[phonon interaction based dissipation mechanisms]]}}

Furthermore there are energy dissipation mechanisms that are specific to reciprocative motion. 
'''See page: [[Reciprocative friction in gem-gum technology]]'''

== Tuning for superlubricity against band-stiffness scattering drag ==

Only (1) can be reduced by tuning for [[superlubricity]] till (2) gets dominant. 
'''Maybe about x100 lower friction possible tuned vs untuned?'''

== Cranking up "compenslow" to reduce friction overall ==

Both (1) and (2) can be reduced cranking up the "[[compenslow]]" design parameter. 
Higher "compenslow" means an increased amount of nanomachinery that all runs at a slower absolute speed. 
"Compenslow" is a portemonteau for "by more machinery compensated slowdown"

'''When doubling the compenslow:'''
* The total throughput per chip area (areal throughput density) stays unchanged!
* Friction losses are cut in half.
* The thickness of the nanomachinery layer doubles. (this is not an issue)
* the internal bearing area per chip area doubles and speeds are cut in half.

'''Increasing compenslow can reduce losses from friction by many orders of magnitude.''' 

=== Limits to optimization by increase of "compenslow" ===

At some point friction from fast transport motions becomes relevant. 
Only the assembly motions are slowed down but assembly motions make up most of the distance the robotics travels. 
Once transport motions get similar in length to the assembly motions. Increasing compenslow is no longer a viable optimization option.

Also:
* the more parts are assembled per [[assembly cycle]] across an [[assembly level]]
* the more there is potential for reduction of friction by increase of compenslow across that assembly level

== Don't over-optimize friction way below mechanochemical losses ==

For systems that perform [[piezochemical mechanosynthesis]] and or [[chemomechanical conversion]] 
it's only sensible to tune friction down so far that [[losses from mechanochemical reactions]] become clearly dominant. 
Note that the increased amount of nanomachinery that results from for standard parts specialized subsystems 
already leads to some minimal compenslow.

For systems that do not perform any mechanochemical conversions like e.g. [[microcomponent recomposer]]s 
losses from friction may become the remaining dominant factor. Relevant in the context of [[recycling]]. 
So here going all out on minimizing friction may really pay off.

= Employing scaling laws against friction =

'''Overcompensating increased friction from increased bearing area''' 
'''See main page: [[How friction diminishes at the nanoscale]]'''

=== The two core physical facts that provide the lion-share of lowering friction ===

[[File:NongrowingAreaInConvergentAssembly.png|thumb|400px|In simple [[convergent assembly]] all layers feature the same total bearing area. So the bottommost nanomachinery has no more bearing surface area than the topmost macromachinery (despite [[higher bearing surface area of smaller machinery]]). Furthermore for practical jumps of scale (x32?) there are only a few layers of convergent assembly.]]

* [[higher throughput of smaller machinery]] Halving the size of the robotics has doubles the throughput per volume when robotic keeping speeds (NOT frequencies) constant. This means that in a naive first approximation the total bearing area of nanomchinery in a [[gem-gum factory]] is no bigger than the bearing area of macromachinery. It's desirable to deviate quite a bit from that first approximation, but as it turns out that only drops friction even further despite increasing bearing area.
* [[power losses from friction scale quadratic with speed]] that is: 1/2 the speed of the machinery => 1/4th friction power losses

=== The two main tricks that apply and combine these physical facts to great avail ===

[[File:ReducingFrictionByDeliberateSlowdown.png|thumb|left|400px|'''The first trick:''' Friction can be reduced by a lot by slowing down the speed of operation of (bottom-most) nanomachinery. In order to not loose throughput capacity [[Multilayer assembly layers|just add more nanomachinery compensating the slowdown]]. This still remains an imperceptibly thin layer on the [[gem-gum factory]] chip due to the [[higher throughput of smaller machinery|high throughput density of nanomachinery]]. '''Total friction losses falls despite rising bearing area!!''']]

[[File:Infinitesimal-bearing-sketch.png|thumb|right|250px|speed distributions from conventional to infinitesimal bearing|frame|'''The second trick:''' [[Infinitesimal bearings]]: 2x the number of layers => 1/2x the friction. This is because the drop in friction from reduced speed (x1/4) overcompensates the rise in friction from increased bearing area (x2). This is only applicable at the higher assembly levels with larger scale machinery.]]

* Distribute productive activity over a lot more layers of nanomachinery (there is more than sufficient space to do so. See [[multilayer assembly layers]])
* [[Infinitesimal bearings|Distribute speed differences over multiple coplanar surfaces]] (there is ore than sufficient space to do so)
----
* In both cases there is more then sufficient space available to do so.
* In both cases speed falls linearly with the number of bearing layers. This gives simultaneously a linear increase (more bearing area) and a quadratic fall (less bearing speed) of friction losses. That is: overall a linear fall of friction losses.
----
* The first case is relevant for the bottom-most layer of [[convergent assembly]] in [[gemstone metamaterial on-chip factories]]
* The second case is relevant for higher up layers of [[convergent assembly]] where larger scale bearings are possible.

== Smaller contributions ==

* Bearing can be tuned for good [[superlubricity]]
* minimization of travel-distance needed per chemical synthesis operation dissipation falls linearly with the path traveled

Minimization of travel-distance leads towards the nanofactory design and away from the molecular assembler design. 
{{wikitodo|elaborate on that}}

= Quantitatively (Math and Numbers) =

== Dynamic drag in superlubricating gemstone bearings - vs - viscous drag in liquids ==

'''There is at least 2,000.0 to 100,000.0 times less friction in gemstone bearings compared to movement at the same speed in water.''' 

So when it comes to peak performance parameters 
soft nanotechnologies and artificial [[synthetic biology]] derived from molecular biology, 
is fundamentally massively inferior to [[gemstone metamaterial technology]]

Yes, this much lower friction is still more than the zero friction that is as present in diffusion transport. 
But this misses a crucial point. 
For diffusion transport to happen it still needs to "expend" energy (still needs to devaluate free energy). 
It is just that the free energy expense need to be payed up at the pitstops (when crossing cell- and vesticle-membranes) rather than during the transport motion. (see external links)

So: 
'''Diffusion transport driven by concentration gradients does NOT make biological nanosystems fundamentally more efficient than conveyorbelt style transport in stiff dry artificial nanosystems in a vacuum.'''

=== Associated math ===

Source: <ref name="phononvsviscousdrag"> '''Eric Drexlers former homepage (webarchive):''' [https://web.archive.org/web/20160305212101/http://e-drexler.com/p/04/03/0322drags.html Phonon drag in sleeve bearings can be orders of magnitude smaller than viscous drag in liquids]</ref>

'''Rotating sphere in Water:''' (Source: <ref name="viscdrag"> '''Viscous torque on a sphere:''' Landau, L, and Lifshitz, E (1987) Fluid Mechanics, 2nd ed. Pergamon Press p.91.</ref>)
* <math> \omega = v/R </math>
* Drag-torque: <math> M_{flow} = -8 \pi \eta R^3 \omega </math>
* Dissipation: <math> P_{flow} = M_{flow} \omega = 8 \pi \eta R v^2 </math>
With: <math> \eta \approx 10 \times 10^{-3} Pa \cdot s </math> and <math> R = 2nm </math>
* Dissipation: <math> P_{flow} \approx 5 \times 10^{-11} v^2 W = 5 \times 10^{-11} W/(m/s)^2</math>

----
'''Gemstone sleeve nearing:''' (Source: <ref name="pdrag"> '''Drag mechanisms in symmetrical sleeve bearings:''' Drexler, K. E. (1992) ''[[Nanosystems]]: Molecular Machinery, Manufacturing, and Computation.'' Wiley/Interscience, pp.290–293.</ref>)
* <math> P_{drag} = 5.8 \times 10^{-16} W/(m/s)² -- \Delta k_a / k_a = 0.003</math>
* <math> P_{drag} = 2.7 \times 10^{-14} W/(m/s)² -- \Delta k_a / k_a = 0.4 </math>
----
'''Ratio:'''
* <math> P_{flow} / P_{drag} \approx 2000 … 100000</math>

== Despite superlubricity dynamic drag can be significant ==

{{wikitodo|add doublelog gnulot plot of examples}}

While static friction in superlubricity falls to nigh zero, 
'''Dynamic (speed dependent) friction can be quite significant for higher speeds.'''

For higher speeds and bearings that do not resort to:
* [[levitation|some mean of levitation]] ( only possible for low loads ) or
* [[infinitesimal bearings|bearing stratification]] ( only possible for bigger nearings )
... the friction per area can actually get quite high for higher speeds.

{| class="wikitable left" style="margin-left: auto; margin-left: 0px;"
|-
| v=100µm/s
| '''v=1mm/s''' (proposed speed)
| '''v=10mm/s''' (proposed speed)
| v=100mm/s
| v=1m/s
| v=10m/s
|-
| 230nW/m² to 10µW/m²
| 23µW/m² to 1mW/m²
| 2.3mW/m² to 100mW/m²
| 230mW/m² to 10W/m²
| 23W/m² to 1kW/m²
| 2.3kW/m² to 100kW/m²
|}
* <math> P_{drag} = 23 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.003</math>
* <math> P_{drag} = 1080 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.4 </math>
Source: [[Nanosystems]] Equation (10.27) <ref name="pdrag"/> --
But here calculated backwards to friction per area from friction per bearing. 
'''Note:''' These are highly conservative estimates. Real values should be quite a bit lower.

Halving the linear speed (in units of m/s) quaters the friction losses. 
And going down from 1m/s to 1mm/s the friction losses fall by a factor of a million (1,000,000). 
More technically: Dynamic friction for crystolecules scales quadratically with speed. 

=== Why significant dynamic drag at higher speeds is this is not a problem ===

 Note: This section is redundant but provides a different formulation.
Skip ahead if the everything so far was clear.

==== Worry #1: Looking at the table friction per area for small speeds like 1m/s is quite high. ====

Friction can be ''massively'' massively reduced by reducing the linear speed of motions (speed in units m/s NOT Hz!). 
And '''we can totally afford to reduce the linear speed of motion in [[advanced productive nanosystem]]s because all the machinery that is needed for practical levels of throughput fits in a super thin layer at the very bottom of the [[convergent assembly]] of a [[gem-gum factory]] chip.''' 
(Reason: [[Higher throughput of smaller machinery]] - things scale favorably here)

We just need to make the bottom layer [[gem-gum factory]] chip a bit thicker 
to compensate for the loss of speed and we are back at the original throughput. 
(We want to do that anyway because many different specialized assembly lines need space.)

One totally can afford to slow down so much in advanced productive nanosystems like [[gem-gum factories]] 
because there is plenty of space to compensate by just adding more nanomachinery.

'''Q:''' '''But what about the additional bearing area?''' 
'''A:''' Yes, the total bearing area increases. 
But while 10x the amount of nanomachinery gives 10x the bearing area 
the friction per area falls by 100x due to 1/10th the speed. 
So overall friction falls by 10x.

PS: Also note that the table above gives conservative (pessimistic) estimates on levels of friction.

==== Worry #2: Nanotech has a lot of surface area per volume. Won't that cause friction to become excessive? ====

'''Q:''' Shouldn't there be massive amounts of bearing surface area? 
It's nanomachinery after all, and and for nanotechnology the surface to volume ratio gets extremely high? 
'''A:''' Surface per volume is indeed high. BUT: '''We barely need any volume to achieve practical levels of throughput.''' 
(Reason: [[Higher throughput of smaller machinery]] - things scale favorably here)

Looking at [[convergent assembly]] in a first naive approximation every layer has exactly the same bearing area. 
So the bottom-most nanomachinery layer has exactly the same bearing area as the topmost macroscale assembly chamber. 
In practice one would want to deviate form naive [[convergent assembly]] by making the bottom layer thicker, 
which, as described above, only improves the situation with friction losses from dynamic drag.

As for the bearing area of the convergent assembly layers higher up:
* (1) There are only a few convergent assembly layers present (take 32nm chambers times 32 four times and you are at 32mm).
* (2) Bigger bearings can [[nest many layers|infinitesimal bearings]]. Again. Same trick. Area x10 & speed x1/10 => overall friction x1/10.

== Highly conservative form Nanosystems {{wikitodo|check and merge this section}} ==

'''Assumed:'''
* A [[crystolecule]] bearing with 2nm radius and 2nm length
* Bearing stiffness k = 1000N/m
* Bearing bumpiness [[superlubricity|incommensurability]]: R = abs(m/(m-n)) = 10
* Bearing operating temperature: Roomtemperature 300K

The dominant power loss contributions (Nanosystems 10.4.6.f.) give: 
* P = 2.7*10⁻14 W / (m/s)^2 -- (for Δka/ka = 0.4) or
* P = 5.8*10⁻16 W / (m/s)^2 -- (for Δka/ka = 0.003)

So how much waste heat would one get for a reasonable desktop [[gemstone metamaterial on-chip factory]]? 
It is not calculated in [[Nanosystems]] since energy recuperation inefficiencies
* in force applying mechanosynthesis and
* "covalent welding" block assembly
likely dominates.

But let's confirm that: 
The proposed [[nanofactory]] convergent assembly system architecture (Nanosystems Table 14.1.)
lists (as reasonable) a few times 10^17 units at the lowest [[assembly levels]].
Nanosystems provides no info about how many bearings per unit to assume.
But Let's assume 100 bearings per unit. This kinda seems like a reasonable
(that is pessimistic and on the safe side) assumption. (applied [[Exploratory engineering]])
This gives:
* P = TODO
* P = TODO

Note that this is (on purpose) a rather pessimistic ("conservative") estimation.

Also the assumed 1019 bearings give ''a total internal bearing sliding surface area of about: 
S = 200m^2''' -- Which intuitively feels like quite a lot but not overly excessive.

=== Side-notes regarding the Numbers given above ===

In [[Nanosystems]] 10.4.6. some examples are calculated for 1m/s sliding speed (it gives about 80MHz for the r=2nm l=2nm bearing).
It's worth to note that a sliding speed of 1m/s is already quite fast.
The actually proposed speeds are more on the order of about 1mm/s (1000 times slower).
This makes power losses no less than one million times lower (since the two dominant drag mechanisms scales quadratically with speed).

According to [[Nanosystems]] 10.4.6.f. the two dominating effects of for friction in [[crystolecule]] bearings (at speeds of interest ) are:
* band-stiffness scallering and
* shear-reflection drag
Other drag mechanisms (acoustic radiation, band-flutter scattering, thermoelastic damping)
all give negligible contributions (at least for the speeds of interest).

= Numbers from papers -- less safe (since more optimistic) =

For much more optimistic but less absolutely certainly on the safe side numbers there is work on coaxial carbon nanotubes:
Also in contrast to crystolecule bearings nanotube bearings are already somewhat accessible to experiments.

The following is from the paper: 
"Evaluating the Friction of Rotary Joints in Molecular Machines"

'''Assumed:'''
* A nanotube bearing with 0.6nm radius and 5nm length
* Bearing operating temperature: Roomtemperature 300K
* Simulation was done at the rather high speed of 30m/s ~ 8GHz

* P = 2.9(+-1.5)*10^-33 W/(rad/s)^2
Or converted into the same units as used in Nanosystems :
* P = 7.25*10^-12 W/(m/s)^2

For the above assumed 10^19 bearings this gives:
* P = TODO

= '''TODO''' update chapters below =

=== Flawless surfaces drop friction significantly ===

In contrast to etched micro-systems where the relative manufacturing error gets bigger with shrinking size.
Atomically precise machinery has no error
allow [[superlubrication]] which drops friction at least three orders of magnitude

== Evolved molecular biology is not a proof that diffusion transport is the ideal solution with minimal losses ==

With those aforementioned effects cog-and-gear nanomachinery could potential feature smaller losses than diffusion driven natural systems (more on that comparison further down). To quantify that more in depth investigations are needed.

=== The issue ===

Nature is often (probably mostly out of psychological reasons) seen as unsurpassable.
But actually it is completely unknowable whether nature as a whole will be "surpassed" by artificial technology in the far future ([[nature vs technology|get side-tracked]]).
Regardless of that, specific aspects of nature definitively can (and have been) surpassed by artificial technologies
(there are [[technology exceeding nature in performance|countless examples]]).

Evolution ended up with diffusion transport and not cog-and-gear-machinery.
Taken the former in to consideration that does by no means imply that this is the best or only solution.
Actually evolution is facing severe [[Evolution#Limits_of_natural_evolution|limitations]] (lock-in-effect, incrementalism, ...).

(This is only one of the many cases where [[misconceptions|bio-analogies]] can have a problematic effect on perception.)

=== Why cog-and-gear transport may be more efficient ===

While diffusion transport features no friction during the transport process itself
diffusion transport is not at all lossless.
At intermediate passing stations some energy always needs to be converted to heat (tech term: dissipated).
Otherwise the chemical reactions would not have a preferred direction to go and all the molecular "machinery" would cease to do anything.

Of course cog-and gear nanomachinery has exactly the same requirement.
The big difference is that in biological systems energy often comes in discrete disconnected chunks.
If ther's more than needed the excess is dissipated without being used for some desired effect.
In a crude analogy it's like being unable to accept the change money.

In cog-and-gear nanomachinery everything is linked together in one big [[machine phase]]
There energy can be drawn in a continuous rather than discrete fashion.
The dissipation necessary for forward moving operation (arrow of time) can be
balanced and minimized further down to the absolutely unconditionally required minimum.
See main article: "[[Low speed efficiency limit]]"

== Proposed machine speeds are WAY below speeds of thermal motion ==

In gemstone based nanomachinery one usually wants the operation frequencies to be well below the thermal motion frequencies. Otherwise the mechanical motions couple too strongly into thermal motions and things will get very hot very quickly. The frequencies of thermal motions can be seen in oscillation infrared spectra. Typical covalent bonds are located in the wavelength range of 3µm-30µm. This corresponds to 10THz-0.1PHz.

Related: [[Stroboscopic illusion in animations of diamondoid molecular machine elements]]

== Typical operation frequencies ==

This is strongly depending on the method of bearing ([[superlubrication]] / single sp3 bonds as bearings / some for m of levitation / ... ) and efficiency of operations.

* For mechanosynthetic mills in a [[nanofactory]] where larger forces are present and potentially slightly inefficient mechanosynthesis is performed the low MHz range is a good target.
* For low friction bearings (like in [[nanomechanical computing]]) one can go up into the high MHz to low GHz range. This still leaves a gap of three orders of magnitude to the oszillative thermal motion DOFs.

== Less soft nanomachinery => less drag ==

Unlike compliant bio-molecules in water [[stiffness|stiff structures]] like carbon nanotubes (or bearings out of gemstone) in dry vacuum do not provide low energy low frequency rotative degrees of freedom (DOFs) to couple into. Those DOFs could (if they where present like in water) go down all the way to the microwave range: ~ 3cm & 10GHz. So overlap of mechanical motion with rotative thermal motion isn't so much of a problem
even at higher operation frequencies.

Note that existing simulations of [[crystolecule]]s can show a
a '''stroboscopic effect'''. That can lead one to believe
machine motion and thermal motion lie very close together and that consequently friction would be horrendous.
This is not the case. It's just an artifact of the simulation.

== Related ==

* '''[[Friction]]'''
* The myth that [[diffusion transport]] does not need to dissipate energy or is fundamentally more efficient.
* [[Superlubricity]]
* [[Levitation]]
* [[Crystolecule]]s
* [[How friction diminishes at the nanoscale]]
* [[Atomically precise bearings]] – especially [[Atomically precise slide bearing]]s
* '''[[Mesoscale friction]]'''

[[Nanosystems]] – Chapter 7 – Energy Dissipation – (page 161 to 190)
----
* [[Losses from mechanochemical reactions]]
----
* '''[[Wear]]'''

== External links ==

* {{todo|Add ref's to relevant chapters in "Nanosystems"}}
----
* Paper: [https://www.mse.ncsu.edu/CompMatSci/papers/TTN4_p9700_1.pdf Molecular-dynamics simulations of atomic-scale friction of diamond surfaces]
----
* Wikipedia: [https://en.wikipedia.org/wiki/Rotational_spectroscopy Rotational spectroscopy]
* Wikipedia: [https://en.wikipedia.org/wiki/Rotational%E2%80%93vibrational_spectroscopy Rotational–vibrational spectroscopy]
* Wikipedia: [https://en.wikipedia.org/wiki/Infrared_spectroscopy Infrared spectroscopy] & [https://en.wikipedia.org/wiki/Thermal_infrared_spectroscopy Thermal infrared spectroscopy]
----
* https://sci-nanotech.com/index.php?thread/43-a-closer-look-at-friction-in-cog-gear-style-stiff-nanomachinery/
----
* [https://pubs.rsc.org/en/content/articlehtml/2017/me/c7me00021a 2017 Evaluating the Friction of Rotary Joints in Molecular Machines] [https://arxiv.org/abs/1701.08202 (arxiv)]

[[Category:Surprising facts]]

= References =

<references/>

Friction in gemstone metamaterial technology

2026-09-29T08:40:47Z

Apm: /* To the doubly logarithmic friction chart */ second source

{{wikitodo|This page needs major cleanup - several parts need to be merged and completed and factored out}} 
[[File:Superlubricity scaling chart.png|800px|thumb|right|Double logarithmic chart of several estimations for [[superlubricity|superlubric friction]] and its quadratic scaling. Note that at moderate speeds like 1m/s it is actually quite high but it quickly drops off going to lower (proposed) speeds around ~1mm/s. The black line (way higher up than all the others) is not superlubric friction but dynamic friction in fluids for comparison. '''This does not cover [[reciprocative dissipation mechanism]]s modes''' which can be significant and can't be co-plotted without a number of (at this point in 2025 still too difficult to pin down) assumptions.]]
Up: [[Friction]]

'''[[Macroscale style machinery at the nanoscale]]''' has in the past received some seriously bad reputation
because it comes with a bunch of [[common misconceptions|mental trapdoors]] that led a a number of very smart reputational and vocal people to bad conclusions.
One of these bad conclusions is that macroscale style machinery at the nanoscale would lead to exorbitant amounts of friction. A very wrong conclusion, as I will try to show below.
(There are other misled criticisms to the idea beside the false conclusion of exorbitant friction. For a discussion of those you may want to check out the main page about [[macroscale style machinery at the nanoscale]].)

= To the doubly logarithmic friction chart =

The chat is meant as …
* a common comparing ground for a broad set different results.
* a starting point to be improved on.

In particular:
* (A) Eventually adding more lines from more suitable data sources eventually.
* (B) Finding the high speed and low speed limits where the quadratic scaling breaks down and gives way to other scaling laws (or destructive end) eventually.

For now in the chart beside results only the book [[Nanosystems]] a source 
there is also one second independent source at least. This one is also theoretical though. {{Wikitodo|Check if fully true.}} 
The second source: [https://pubs.rsc.org/en/content/articlehtml/2017/me/c7me00021a 2017 Evaluating the Friction of Rotary Joints in Molecular Machines] [https://arxiv.org/abs/1701.08202 (arxiv)]

A big problem with current day (2026) experimental results is that 
experimental limitations introduce uncontrollable side effects that overshadow 
what one would get with atomically precise surfaces sliding in an advanced much cleaner not yet preparable setup. 
{{Wikitodo|Elaborate on that eventually. This may deserve a dedicated page. Add papers and explain associated concrete issues with them.}} 

= Dodge the trapdoors =

* '''Yes, It is true that physics changes when the size-scale changes.''' But who says it changes for the worse when it comes to [[macroscale style machinery at the nanoscale]]?
* '''Yes, It is true that [[rising surface area|surface area grows with shrinking structure sizes]], and that this contributes to friction.''' But there are other effects that overcompensate growing surface area and these are very often overlooked.
* '''Yes, It is true that unlike diffusion transport there is friction all the time along the whole way.''' But it's often overlooked that diffusion must devaluate chunks of energy at its "pit-stops" to prevent transport from running backwards and that the "change money" energy that gets left over at these "pit-stops" cannot be kept for later usage. Whereas in [[machine phase system]]s keeping and reuseing the energetic change money may be possible.
* '''Yes, It is true that there is no natural example of macro style machinery at the nanoscale (similar to the one proposed).''' But concluding from that that it's not possible or a worse solution is a fallacy. There are plenty of human invented things that exceed capabilities of nature by orders of magnitude. To give just a few examples: Bicycles, combustion engines (spaceships), copper wires (superconductors), wheels and streets, ...
* '''Yes, It is true that MEMS (microelectromechanical systems) have high friction (and bad wear from "stiction").''' But in case of MEMS this is due to MEMS not having atomically precise [[superlubricity|suberbublicating]] bearings but instead having a really bad signal to noise ratio in their geometry due to them being manufactured top-down.

= Main sources of friction and countermeasures =

Friction in [[gem-gum-tec|gemstone based nanomachinery]] is mainly caused by:
* (1) band-stiffness scattering drag and
* (2) shear-reflection drag
Source: [[Nanosystems]] 10.4.6. Mechanisms of Energy dissipation f. Summary 
{{todo|find and add an intuitively comprehensible explanation for these two [[phonon interaction based dissipation mechanisms]]}}

Furthermore there are energy dissipation mechanisms that are specific to reciprocative motion. 
'''See page: [[Reciprocative friction in gem-gum technology]]'''

== Tuning for superlubricity against band-stiffness scattering drag ==

Only (1) can be reduced by tuning for [[superlubricity]] till (2) gets dominant. 
'''Maybe about x100 lower friction possible tuned vs untuned?'''

== Cranking up "compenslow" to reduce friction overall ==

Both (1) and (2) can be reduced cranking up the "[[compenslow]]" design parameter. 
Higher "compenslow" means an increased amount of nanomachinery that all runs at a slower absolute speed. 
"Compenslow" is a portemonteau for "by more machinery compensated slowdown"

'''When doubling the compenslow:'''
* The total throughput per chip area (areal throughput density) stays unchanged!
* Friction losses are cut in half.
* The thickness of the nanomachinery layer doubles. (this is not an issue)
* the internal bearing area per chip area doubles and speeds are cut in half.

'''Increasing compenslow can reduce losses from friction by many orders of magnitude.''' 

=== Limits to optimization by increase of "compenslow" ===

At some point friction from fast transport motions becomes relevant. 
Only the assembly motions are slowed down but assembly motions make up most of the distance the robotics travels. 
Once transport motions get similar in length to the assembly motions. Increasing compenslow is no longer a viable optimization option.

Also:
* the more parts are assembled per [[assembly cycle]] across an [[assembly level]]
* the more there is potential for reduction of friction by increase of compenslow across that assembly level

== Don't over-optimize friction way below mechanochemical losses ==

For systems that perform [[piezochemical mechanosynthesis]] and or [[chemomechanical conversion]] 
it's only sensible to tune friction down so far that [[losses from mechanochemical reactions]] become clearly dominant. 
Note that the increased amount of nanomachinery that results from for standard parts specialized subsystems 
already leads to some minimal compenslow.

For systems that do not perform any mechanochemical conversions like e.g. [[microcomponent recomposer]]s 
losses from friction may become the remaining dominant factor. Relevant in the context of [[recycling]]. 
So here going all out on minimizing friction may really pay off.

= Employing scaling laws against friction =

'''Overcompensating increased friction from increased bearing area''' 
'''See main page: [[How friction diminishes at the nanoscale]]'''

=== The two core physical facts that provide the lion-share of lowering friction ===

[[File:NongrowingAreaInConvergentAssembly.png|thumb|400px|In simple [[convergent assembly]] all layers feature the same total bearing area. So the bottommost nanomachinery has no more bearing surface area than the topmost macromachinery (despite [[higher bearing surface area of smaller machinery]]). Furthermore for practical jumps of scale (x32?) there are only a few layers of convergent assembly.]]

* [[higher throughput of smaller machinery]] Halving the size of the robotics has doubles the throughput per volume when robotic keeping speeds (NOT frequencies) constant. This means that in a naive first approximation the total bearing area of nanomchinery in a [[gem-gum factory]] is no bigger than the bearing area of macromachinery. It's desirable to deviate quite a bit from that first approximation, but as it turns out that only drops friction even further despite increasing bearing area.
* [[power losses from friction scale quadratic with speed]] that is: 1/2 the speed of the machinery => 1/4th friction power losses

=== The two main tricks that apply and combine these physical facts to great avail ===

[[File:ReducingFrictionByDeliberateSlowdown.png|thumb|left|400px|'''The first trick:''' Friction can be reduced by a lot by slowing down the speed of operation of (bottom-most) nanomachinery. In order to not loose throughput capacity [[Multilayer assembly layers|just add more nanomachinery compensating the slowdown]]. This still remains an imperceptibly thin layer on the [[gem-gum factory]] chip due to the [[higher throughput of smaller machinery|high throughput density of nanomachinery]]. '''Total friction losses falls despite rising bearing area!!''']]

[[File:Infinitesimal-bearing-sketch.png|thumb|right|250px|speed distributions from conventional to infinitesimal bearing|frame|'''The second trick:''' [[Infinitesimal bearings]]: 2x the number of layers => 1/2x the friction. This is because the drop in friction from reduced speed (x1/4) overcompensates the rise in friction from increased bearing area (x2). This is only applicable at the higher assembly levels with larger scale machinery.]]

* Distribute productive activity over a lot more layers of nanomachinery (there is more than sufficient space to do so. See [[multilayer assembly layers]])
* [[Infinitesimal bearings|Distribute speed differences over multiple coplanar surfaces]] (there is ore than sufficient space to do so)
----
* In both cases there is more then sufficient space available to do so.
* In both cases speed falls linearly with the number of bearing layers. This gives simultaneously a linear increase (more bearing area) and a quadratic fall (less bearing speed) of friction losses. That is: overall a linear fall of friction losses.
----
* The first case is relevant for the bottom-most layer of [[convergent assembly]] in [[gemstone metamaterial on-chip factories]]
* The second case is relevant for higher up layers of [[convergent assembly]] where larger scale bearings are possible.

== Smaller contributions ==

* Bearing can be tuned for good [[superlubricity]]
* minimization of travel-distance needed per chemical synthesis operation dissipation falls linearly with the path traveled

Minimization of travel-distance leads towards the nanofactory design and away from the molecular assembler design. 
{{wikitodo|elaborate on that}}

= Quantitatively (Math and Numbers) =

== Dynamic drag in superlubricating gemstone bearings - vs - viscous drag in liquids ==

'''There is at least 2,000.0 to 100,000.0 times less friction in gemstone bearings compared to movement at the same speed in water.''' 

So when it comes to peak performance parameters 
soft nanotechnologies and artificial [[synthetic biology]] derived from molecular biology, 
is fundamentally massively inferior to [[gemstone metamaterial technology]]

Yes, this much lower friction is still more than the zero friction that is as present in diffusion transport. 
But this misses a crucial point. 
For diffusion transport to happen it still needs to "expend" energy (still needs to devaluate free energy). 
It is just that the free energy expense need to be payed up at the pitstops (when crossing cell- and vesticle-membranes) rather than during the transport motion. (see external links)

So: 
'''Diffusion transport driven by concentration gradients does NOT make biological nanosystems fundamentally more efficient than conveyorbelt style transport in stiff dry artificial nanosystems in a vacuum.'''

=== Associated math ===

Source: <ref name="phononvsviscousdrag"> '''Eric Drexlers former homepage (webarchive):''' [https://web.archive.org/web/20160305212101/http://e-drexler.com/p/04/03/0322drags.html Phonon drag in sleeve bearings can be orders of magnitude smaller than viscous drag in liquids]</ref>

'''Rotating sphere in Water:''' (Source: <ref name="viscdrag"> '''Viscous torque on a sphere:''' Landau, L, and Lifshitz, E (1987) Fluid Mechanics, 2nd ed. Pergamon Press p.91.</ref>)
* <math> \omega = v/R </math>
* Drag-torque: <math> M_{flow} = -8 \pi \eta R^3 \omega </math>
* Dissipation: <math> P_{flow} = M_{flow} \omega = 8 \pi \eta R v^2 </math>
With: <math> \eta \approx 10 \times 10^{-3} Pa \cdot s </math> and <math> R = 2nm </math>
* Dissipation: <math> P_{flow} \approx 5 \times 10^{-11} v^2 W = 5 \times 10^{-11} W/(m/s)^2</math>

----
'''Gemstone sleeve nearing:''' (Source: <ref name="pdrag"> '''Drag mechanisms in symmetrical sleeve bearings:''' Drexler, K. E. (1992) ''[[Nanosystems]]: Molecular Machinery, Manufacturing, and Computation.'' Wiley/Interscience, pp.290–293.</ref>)
* <math> P_{drag} = 5.8 \times 10^{-16} W/(m/s)² -- \Delta k_a / k_a = 0.003</math>
* <math> P_{drag} = 2.7 \times 10^{-14} W/(m/s)² -- \Delta k_a / k_a = 0.4 </math>
----
'''Ratio:'''
* <math> P_{flow} / P_{drag} \approx 2000 … 100000</math>

== Despite superlubricity dynamic drag can be significant ==

{{wikitodo|add doublelog gnulot plot of examples}}

While static friction in superlubricity falls to nigh zero, 
'''Dynamic (speed dependent) friction can be quite significant for higher speeds.'''

For higher speeds and bearings that do not resort to:
* [[levitation|some mean of levitation]] ( only possible for low loads ) or
* [[infinitesimal bearings|bearing stratification]] ( only possible for bigger nearings )
... the friction per area can actually get quite high for higher speeds.

{| class="wikitable left" style="margin-left: auto; margin-left: 0px;"
|-
| v=100µm/s
| '''v=1mm/s''' (proposed speed)
| '''v=10mm/s''' (proposed speed)
| v=100mm/s
| v=1m/s
| v=10m/s
|-
| 230nW/m² to 10µW/m²
| 23µW/m² to 1mW/m²
| 2.3mW/m² to 100mW/m²
| 230mW/m² to 10W/m²
| 23W/m² to 1kW/m²
| 2.3kW/m² to 100kW/m²
|}
* <math> P_{drag} = 23 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.003</math>
* <math> P_{drag} = 1080 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.4 </math>
Source: [[Nanosystems]] Equation (10.27) <ref name="pdrag"/> --
But here calculated backwards to friction per area from friction per bearing. 
'''Note:''' These are highly conservative estimates. Real values should be quite a bit lower.

Halving the linear speed (in units of m/s) quaters the friction losses. 
And going down from 1m/s to 1mm/s the friction losses fall by a factor of a million (1,000,000). 
More technically: Dynamic friction for crystolecules scales quadratically with speed. 

=== Why significant dynamic drag at higher speeds is this is not a problem ===

 Note: This section is redundant but provides a different formulation.
Skip ahead if the everything so far was clear.

==== Worry #1: Looking at the table friction per area for small speeds like 1m/s is quite high. ====

Friction can be ''massively'' massively reduced by reducing the linear speed of motions (speed in units m/s NOT Hz!). 
And '''we can totally afford to reduce the linear speed of motion in [[advanced productive nanosystem]]s because all the machinery that is needed for practical levels of throughput fits in a super thin layer at the very bottom of the [[convergent assembly]] of a [[gem-gum factory]] chip.''' 
(Reason: [[Higher throughput of smaller machinery]] - things scale favorably here)

We just need to make the bottom layer [[gem-gum factory]] chip a bit thicker 
to compensate for the loss of speed and we are back at the original throughput. 
(We want to do that anyway because many different specialized assembly lines need space.)

One totally can afford to slow down so much in advanced productive nanosystems like [[gem-gum factories]] 
because there is plenty of space to compensate by just adding more nanomachinery.

'''Q:''' '''But what about the additional bearing area?''' 
'''A:''' Yes, the total bearing area increases. 
But while 10x the amount of nanomachinery gives 10x the bearing area 
the friction per area falls by 100x due to 1/10th the speed. 
So overall friction falls by 10x.

PS: Also note that the table above gives conservative (pessimistic) estimates on levels of friction.

==== Worry #2: Nanotech has a lot of surface area per volume. Won't that cause friction to become excessive? ====

'''Q:''' Shouldn't there be massive amounts of bearing surface area? 
It's nanomachinery after all, and and for nanotechnology the surface to volume ratio gets extremely high? 
'''A:''' Surface per volume is indeed high. BUT: '''We barely need any volume to achieve practical levels of throughput.''' 
(Reason: [[Higher throughput of smaller machinery]] - things scale favorably here)

Looking at [[convergent assembly]] in a first naive approximation every layer has exactly the same bearing area. 
So the bottom-most nanomachinery layer has exactly the same bearing area as the topmost macroscale assembly chamber. 
In practice one would want to deviate form naive [[convergent assembly]] by making the bottom layer thicker, 
which, as described above, only improves the situation with friction losses from dynamic drag.

As for the bearing area of the convergent assembly layers higher up:
* (1) There are only a few convergent assembly layers present (take 32nm chambers times 32 four times and you are at 32mm).
* (2) Bigger bearings can [[nest many layers|infinitesimal bearings]]. Again. Same trick. Area x10 & speed x1/10 => overall friction x1/10.

== Highly conservative form Nanosystems {{wikitodo|check and merge this section}} ==

'''Assumed:'''
* A [[crystolecule]] bearing with 2nm radius and 2nm length
* Bearing stiffness k = 1000N/m
* Bearing bumpiness [[superlubricity|incommensurability]]: R = abs(m/(m-n)) = 10
* Bearing operating temperature: Roomtemperature 300K

The dominant power loss contributions (Nanosystems 10.4.6.f.) give: 
* P = 2.7*10⁻14 W / (m/s)^2 -- (for Δka/ka = 0.4) or
* P = 5.8*10⁻16 W / (m/s)^2 -- (for Δka/ka = 0.003)

So how much waste heat would one get for a reasonable desktop [[gemstone metamaterial on-chip factory]]? 
It is not calculated in [[Nanosystems]] since energy recuperation inefficiencies
* in force applying mechanosynthesis and
* "covalent welding" block assembly
likely dominates.

But let's confirm that: 
The proposed [[nanofactory]] convergent assembly system architecture (Nanosystems Table 14.1.)
lists (as reasonable) a few times 10^17 units at the lowest [[assembly levels]].
Nanosystems provides no info about how many bearings per unit to assume.
But Let's assume 100 bearings per unit. This kinda seems like a reasonable
(that is pessimistic and on the safe side) assumption. (applied [[Exploratory engineering]])
This gives:
* P = TODO
* P = TODO

Note that this is (on purpose) a rather pessimistic ("conservative") estimation.

Also the assumed 1019 bearings give ''a total internal bearing sliding surface area of about: 
S = 200m^2''' -- Which intuitively feels like quite a lot but not overly excessive.

=== Side-notes regarding the Numbers given above ===

In [[Nanosystems]] 10.4.6. some examples are calculated for 1m/s sliding speed (it gives about 80MHz for the r=2nm l=2nm bearing).
It's worth to note that a sliding speed of 1m/s is already quite fast.
The actually proposed speeds are more on the order of about 1mm/s (1000 times slower).
This makes power losses no less than one million times lower (since the two dominant drag mechanisms scales quadratically with speed).

According to [[Nanosystems]] 10.4.6.f. the two dominating effects of for friction in [[crystolecule]] bearings (at speeds of interest ) are:
* band-stiffness scallering and
* shear-reflection drag
Other drag mechanisms (acoustic radiation, band-flutter scattering, thermoelastic damping)
all give negligible contributions (at least for the speeds of interest).

= Numbers from papers -- less safe (since more optimistic) =

For much more optimistic but less absolutely certainly on the safe side numbers there is work on coaxial carbon nanotubes:
Also in contrast to crystolecule bearings nanotube bearings are already somewhat accessible to experiments.

The following is from the paper: 
"Evaluating the Friction of Rotary Joints in Molecular Machines"

'''Assumed:'''
* A nanotube bearing with 0.6nm radius and 5nm length
* Bearing operating temperature: Roomtemperature 300K
* Simulation was done at the rather high speed of 30m/s ~ 8GHz

* P = 2.9(+-1.5)*10^-33 W/(rad/s)^2
Or converted into the same units as used in Nanosystems :
* P = 7.25*10^-12 W/(m/s)^2

For the above assumed 10^19 bearings this gives:
* P = TODO

= '''TODO''' update chapters below =

=== Flawless surfaces drop friction significantly ===

In contrast to etched micro-systems where the relative manufacturing error gets bigger with shrinking size.
Atomically precise machinery has no error
allow [[superlubrication]] which drops friction at least three orders of magnitude

== Evolved molecular biology is not a proof that diffusion transport is the ideal solution with minimal losses ==

With those aforementioned effects cog-and-gear nanomachinery could potential feature smaller losses than diffusion driven natural systems (more on that comparison further down). To quantify that more in depth investigations are needed.

=== The issue ===

Nature is often (probably mostly out of psychological reasons) seen as unsurpassable.
But actually it is completely unknowable whether nature as a whole will be "surpassed" by artificial technology in the far future ([[nature vs technology|get side-tracked]]).
Regardless of that, specific aspects of nature definitively can (and have been) surpassed by artificial technologies
(there are [[technology exceeding nature in performance|countless examples]]).

Evolution ended up with diffusion transport and not cog-and-gear-machinery.
Taken the former in to consideration that does by no means imply that this is the best or only solution.
Actually evolution is facing severe [[Evolution#Limits_of_natural_evolution|limitations]] (lock-in-effect, incrementalism, ...).

(This is only one of the many cases where [[misconceptions|bio-analogies]] can have a problematic effect on perception.)

=== Why cog-and-gear transport may be more efficient ===

While diffusion transport features no friction during the transport process itself
diffusion transport is not at all lossless.
At intermediate passing stations some energy always needs to be converted to heat (tech term: dissipated).
Otherwise the chemical reactions would not have a preferred direction to go and all the molecular "machinery" would cease to do anything.

Of course cog-and gear nanomachinery has exactly the same requirement.
The big difference is that in biological systems energy often comes in discrete disconnected chunks.
If ther's more than needed the excess is dissipated without being used for some desired effect.
In a crude analogy it's like being unable to accept the change money.

In cog-and-gear nanomachinery everything is linked together in one big [[machine phase]]
There energy can be drawn in a continuous rather than discrete fashion.
The dissipation necessary for forward moving operation (arrow of time) can be
balanced and minimized further down to the absolutely unconditionally required minimum.
See main article: "[[Low speed efficiency limit]]"

== Proposed machine speeds are WAY below speeds of thermal motion ==

In gemstone based nanomachinery one usually wants the operation frequencies to be well below the thermal motion frequencies. Otherwise the mechanical motions couple too strongly into thermal motions and things will get very hot very quickly. The frequencies of thermal motions can be seen in oscillation infrared spectra. Typical covalent bonds are located in the wavelength range of 3µm-30µm. This corresponds to 10THz-0.1PHz.

Related: [[Stroboscopic illusion in animations of diamondoid molecular machine elements]]

== Typical operation frequencies ==

This is strongly depending on the method of bearing ([[superlubrication]] / single sp3 bonds as bearings / some for m of levitation / ... ) and efficiency of operations.

* For mechanosynthetic mills in a [[nanofactory]] where larger forces are present and potentially slightly inefficient mechanosynthesis is performed the low MHz range is a good target.
* For low friction bearings (like in [[nanomechanical computing]]) one can go up into the high MHz to low GHz range. This still leaves a gap of three orders of magnitude to the oszillative thermal motion DOFs.

== Less soft nanomachinery => less drag ==

Unlike compliant bio-molecules in water [[stiffness|stiff structures]] like carbon nanotubes (or bearings out of gemstone) in dry vacuum do not provide low energy low frequency rotative degrees of freedom (DOFs) to couple into. Those DOFs could (if they where present like in water) go down all the way to the microwave range: ~ 3cm & 10GHz. So overlap of mechanical motion with rotative thermal motion isn't so much of a problem
even at higher operation frequencies.

Note that existing simulations of [[crystolecule]]s can show a
a '''stroboscopic effect'''. That can lead one to believe
machine motion and thermal motion lie very close together and that consequently friction would be horrendous.
This is not the case. It's just an artifact of the simulation.

== Related ==

* '''[[Friction]]'''
* The myth that [[diffusion transport]] does not need to dissipate energy or is fundamentally more efficient.
* [[Superlubricity]]
* [[Levitation]]
* [[Crystolecule]]s
* [[How friction diminishes at the nanoscale]]
* [[Atomically precise bearings]] – especially [[Atomically precise slide bearing]]s
* '''[[Mesoscale friction]]'''

[[Nanosystems]] – Chapter 7 – Energy Dissipation – (page 161 to 190)
----
* [[Losses from mechanochemical reactions]]
----
* '''[[Wear]]'''

== External links ==

* {{todo|Add ref's to relevant chapters in "Nanosystems"}}
----
* Paper: [https://www.mse.ncsu.edu/CompMatSci/papers/TTN4_p9700_1.pdf Molecular-dynamics simulations of atomic-scale friction of diamond surfaces]
----
* Wikipedia: [https://en.wikipedia.org/wiki/Rotational_spectroscopy Rotational spectroscopy]
* Wikipedia: [https://en.wikipedia.org/wiki/Rotational%E2%80%93vibrational_spectroscopy Rotational–vibrational spectroscopy]
* Wikipedia: [https://en.wikipedia.org/wiki/Infrared_spectroscopy Infrared spectroscopy] & [https://en.wikipedia.org/wiki/Thermal_infrared_spectroscopy Thermal infrared spectroscopy]
----
* https://sci-nanotech.com/index.php?thread/43-a-closer-look-at-friction-in-cog-gear-style-stiff-nanomachinery/
----
* [https://pubs.rsc.org/en/content/articlehtml/2017/me/c7me00021a 2017 Evaluating the Friction of Rotary Joints in Molecular Machines] [https://arxiv.org/abs/1701.08202 (arxiv)]

[[Category:Surprising facts]]

= References =

<references/>

Friction in gemstone metamaterial technology

2026-09-29T08:37:13Z

Apm: To the doubly logarithmic friction chart

{{wikitodo|This page needs major cleanup - several parts need to be merged and completed and factored out}} 
[[File:Superlubricity scaling chart.png|800px|thumb|right|Double logarithmic chart of several estimations for [[superlubricity|superlubric friction]] and its quadratic scaling. Note that at moderate speeds like 1m/s it is actually quite high but it quickly drops off going to lower (proposed) speeds around ~1mm/s. The black line (way higher up than all the others) is not superlubric friction but dynamic friction in fluids for comparison. '''This does not cover [[reciprocative dissipation mechanism]]s modes''' which can be significant and can't be co-plotted without a number of (at this point in 2025 still too difficult to pin down) assumptions.]]
Up: [[Friction]]

'''[[Macroscale style machinery at the nanoscale]]''' has in the past received some seriously bad reputation
because it comes with a bunch of [[common misconceptions|mental trapdoors]] that led a a number of very smart reputational and vocal people to bad conclusions.
One of these bad conclusions is that macroscale style machinery at the nanoscale would lead to exorbitant amounts of friction. A very wrong conclusion, as I will try to show below.
(There are other misled criticisms to the idea beside the false conclusion of exorbitant friction. For a discussion of those you may want to check out the main page about [[macroscale style machinery at the nanoscale]].)

= To the doubly logarithmic friction chart =

The chat is meant as …
* a common comparing ground for a broad set different results.
* a starting point to be improved on.

In particular:
* (A) Eventually adding more lines from more suitable data sources eventually.
* (B) Finding the high speed and low speed limits where the quadratic scaling breaks down and gives way to other scaling laws (or destructive end) eventually.

For now in the chart beside results only the book [[Nanosystems]] a source 
there is also one second independent source at least. This one is also theoretical though. {{Wikitodo|Check if fully true.}} 

A big problem with current day (2026) experimental results is that 
experimental limitations introduce uncontrollable side effects that overshadow 
what one would get with atomically precise surfaces sliding in an advanced much cleaner not yet preparable setup. 
{{Wikitodo|Elaborate on that eventually. This may deserve a dedicated page. Add papers and explain associated concrete issues with them.}} 

= Dodge the trapdoors =

* '''Yes, It is true that physics changes when the size-scale changes.''' But who says it changes for the worse when it comes to [[macroscale style machinery at the nanoscale]]?
* '''Yes, It is true that [[rising surface area|surface area grows with shrinking structure sizes]], and that this contributes to friction.''' But there are other effects that overcompensate growing surface area and these are very often overlooked.
* '''Yes, It is true that unlike diffusion transport there is friction all the time along the whole way.''' But it's often overlooked that diffusion must devaluate chunks of energy at its "pit-stops" to prevent transport from running backwards and that the "change money" energy that gets left over at these "pit-stops" cannot be kept for later usage. Whereas in [[machine phase system]]s keeping and reuseing the energetic change money may be possible.
* '''Yes, It is true that there is no natural example of macro style machinery at the nanoscale (similar to the one proposed).''' But concluding from that that it's not possible or a worse solution is a fallacy. There are plenty of human invented things that exceed capabilities of nature by orders of magnitude. To give just a few examples: Bicycles, combustion engines (spaceships), copper wires (superconductors), wheels and streets, ...
* '''Yes, It is true that MEMS (microelectromechanical systems) have high friction (and bad wear from "stiction").''' But in case of MEMS this is due to MEMS not having atomically precise [[superlubricity|suberbublicating]] bearings but instead having a really bad signal to noise ratio in their geometry due to them being manufactured top-down.

= Main sources of friction and countermeasures =

Friction in [[gem-gum-tec|gemstone based nanomachinery]] is mainly caused by:
* (1) band-stiffness scattering drag and
* (2) shear-reflection drag
Source: [[Nanosystems]] 10.4.6. Mechanisms of Energy dissipation f. Summary 
{{todo|find and add an intuitively comprehensible explanation for these two [[phonon interaction based dissipation mechanisms]]}}

Furthermore there are energy dissipation mechanisms that are specific to reciprocative motion. 
'''See page: [[Reciprocative friction in gem-gum technology]]'''

== Tuning for superlubricity against band-stiffness scattering drag ==

Only (1) can be reduced by tuning for [[superlubricity]] till (2) gets dominant. 
'''Maybe about x100 lower friction possible tuned vs untuned?'''

== Cranking up "compenslow" to reduce friction overall ==

Both (1) and (2) can be reduced cranking up the "[[compenslow]]" design parameter. 
Higher "compenslow" means an increased amount of nanomachinery that all runs at a slower absolute speed. 
"Compenslow" is a portemonteau for "by more machinery compensated slowdown"

'''When doubling the compenslow:'''
* The total throughput per chip area (areal throughput density) stays unchanged!
* Friction losses are cut in half.
* The thickness of the nanomachinery layer doubles. (this is not an issue)
* the internal bearing area per chip area doubles and speeds are cut in half.

'''Increasing compenslow can reduce losses from friction by many orders of magnitude.''' 

=== Limits to optimization by increase of "compenslow" ===

At some point friction from fast transport motions becomes relevant. 
Only the assembly motions are slowed down but assembly motions make up most of the distance the robotics travels. 
Once transport motions get similar in length to the assembly motions. Increasing compenslow is no longer a viable optimization option.

Also:
* the more parts are assembled per [[assembly cycle]] across an [[assembly level]]
* the more there is potential for reduction of friction by increase of compenslow across that assembly level

== Don't over-optimize friction way below mechanochemical losses ==

For systems that perform [[piezochemical mechanosynthesis]] and or [[chemomechanical conversion]] 
it's only sensible to tune friction down so far that [[losses from mechanochemical reactions]] become clearly dominant. 
Note that the increased amount of nanomachinery that results from for standard parts specialized subsystems 
already leads to some minimal compenslow.

For systems that do not perform any mechanochemical conversions like e.g. [[microcomponent recomposer]]s 
losses from friction may become the remaining dominant factor. Relevant in the context of [[recycling]]. 
So here going all out on minimizing friction may really pay off.

= Employing scaling laws against friction =

'''Overcompensating increased friction from increased bearing area''' 
'''See main page: [[How friction diminishes at the nanoscale]]'''

=== The two core physical facts that provide the lion-share of lowering friction ===

[[File:NongrowingAreaInConvergentAssembly.png|thumb|400px|In simple [[convergent assembly]] all layers feature the same total bearing area. So the bottommost nanomachinery has no more bearing surface area than the topmost macromachinery (despite [[higher bearing surface area of smaller machinery]]). Furthermore for practical jumps of scale (x32?) there are only a few layers of convergent assembly.]]

* [[higher throughput of smaller machinery]] Halving the size of the robotics has doubles the throughput per volume when robotic keeping speeds (NOT frequencies) constant. This means that in a naive first approximation the total bearing area of nanomchinery in a [[gem-gum factory]] is no bigger than the bearing area of macromachinery. It's desirable to deviate quite a bit from that first approximation, but as it turns out that only drops friction even further despite increasing bearing area.
* [[power losses from friction scale quadratic with speed]] that is: 1/2 the speed of the machinery => 1/4th friction power losses

=== The two main tricks that apply and combine these physical facts to great avail ===

[[File:ReducingFrictionByDeliberateSlowdown.png|thumb|left|400px|'''The first trick:''' Friction can be reduced by a lot by slowing down the speed of operation of (bottom-most) nanomachinery. In order to not loose throughput capacity [[Multilayer assembly layers|just add more nanomachinery compensating the slowdown]]. This still remains an imperceptibly thin layer on the [[gem-gum factory]] chip due to the [[higher throughput of smaller machinery|high throughput density of nanomachinery]]. '''Total friction losses falls despite rising bearing area!!''']]

[[File:Infinitesimal-bearing-sketch.png|thumb|right|250px|speed distributions from conventional to infinitesimal bearing|frame|'''The second trick:''' [[Infinitesimal bearings]]: 2x the number of layers => 1/2x the friction. This is because the drop in friction from reduced speed (x1/4) overcompensates the rise in friction from increased bearing area (x2). This is only applicable at the higher assembly levels with larger scale machinery.]]

* Distribute productive activity over a lot more layers of nanomachinery (there is more than sufficient space to do so. See [[multilayer assembly layers]])
* [[Infinitesimal bearings|Distribute speed differences over multiple coplanar surfaces]] (there is ore than sufficient space to do so)
----
* In both cases there is more then sufficient space available to do so.
* In both cases speed falls linearly with the number of bearing layers. This gives simultaneously a linear increase (more bearing area) and a quadratic fall (less bearing speed) of friction losses. That is: overall a linear fall of friction losses.
----
* The first case is relevant for the bottom-most layer of [[convergent assembly]] in [[gemstone metamaterial on-chip factories]]
* The second case is relevant for higher up layers of [[convergent assembly]] where larger scale bearings are possible.

== Smaller contributions ==

* Bearing can be tuned for good [[superlubricity]]
* minimization of travel-distance needed per chemical synthesis operation dissipation falls linearly with the path traveled

Minimization of travel-distance leads towards the nanofactory design and away from the molecular assembler design. 
{{wikitodo|elaborate on that}}

= Quantitatively (Math and Numbers) =

== Dynamic drag in superlubricating gemstone bearings - vs - viscous drag in liquids ==

'''There is at least 2,000.0 to 100,000.0 times less friction in gemstone bearings compared to movement at the same speed in water.''' 

So when it comes to peak performance parameters 
soft nanotechnologies and artificial [[synthetic biology]] derived from molecular biology, 
is fundamentally massively inferior to [[gemstone metamaterial technology]]

Yes, this much lower friction is still more than the zero friction that is as present in diffusion transport. 
But this misses a crucial point. 
For diffusion transport to happen it still needs to "expend" energy (still needs to devaluate free energy). 
It is just that the free energy expense need to be payed up at the pitstops (when crossing cell- and vesticle-membranes) rather than during the transport motion. (see external links)

So: 
'''Diffusion transport driven by concentration gradients does NOT make biological nanosystems fundamentally more efficient than conveyorbelt style transport in stiff dry artificial nanosystems in a vacuum.'''

=== Associated math ===

Source: <ref name="phononvsviscousdrag"> '''Eric Drexlers former homepage (webarchive):''' [https://web.archive.org/web/20160305212101/http://e-drexler.com/p/04/03/0322drags.html Phonon drag in sleeve bearings can be orders of magnitude smaller than viscous drag in liquids]</ref>

'''Rotating sphere in Water:''' (Source: <ref name="viscdrag"> '''Viscous torque on a sphere:''' Landau, L, and Lifshitz, E (1987) Fluid Mechanics, 2nd ed. Pergamon Press p.91.</ref>)
* <math> \omega = v/R </math>
* Drag-torque: <math> M_{flow} = -8 \pi \eta R^3 \omega </math>
* Dissipation: <math> P_{flow} = M_{flow} \omega = 8 \pi \eta R v^2 </math>
With: <math> \eta \approx 10 \times 10^{-3} Pa \cdot s </math> and <math> R = 2nm </math>
* Dissipation: <math> P_{flow} \approx 5 \times 10^{-11} v^2 W = 5 \times 10^{-11} W/(m/s)^2</math>

----
'''Gemstone sleeve nearing:''' (Source: <ref name="pdrag"> '''Drag mechanisms in symmetrical sleeve bearings:''' Drexler, K. E. (1992) ''[[Nanosystems]]: Molecular Machinery, Manufacturing, and Computation.'' Wiley/Interscience, pp.290–293.</ref>)
* <math> P_{drag} = 5.8 \times 10^{-16} W/(m/s)² -- \Delta k_a / k_a = 0.003</math>
* <math> P_{drag} = 2.7 \times 10^{-14} W/(m/s)² -- \Delta k_a / k_a = 0.4 </math>
----
'''Ratio:'''
* <math> P_{flow} / P_{drag} \approx 2000 … 100000</math>

== Despite superlubricity dynamic drag can be significant ==

{{wikitodo|add doublelog gnulot plot of examples}}

While static friction in superlubricity falls to nigh zero, 
'''Dynamic (speed dependent) friction can be quite significant for higher speeds.'''

For higher speeds and bearings that do not resort to:
* [[levitation|some mean of levitation]] ( only possible for low loads ) or
* [[infinitesimal bearings|bearing stratification]] ( only possible for bigger nearings )
... the friction per area can actually get quite high for higher speeds.

{| class="wikitable left" style="margin-left: auto; margin-left: 0px;"
|-
| v=100µm/s
| '''v=1mm/s''' (proposed speed)
| '''v=10mm/s''' (proposed speed)
| v=100mm/s
| v=1m/s
| v=10m/s
|-
| 230nW/m² to 10µW/m²
| 23µW/m² to 1mW/m²
| 2.3mW/m² to 100mW/m²
| 230mW/m² to 10W/m²
| 23W/m² to 1kW/m²
| 2.3kW/m² to 100kW/m²
|}
* <math> P_{drag} = 23 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.003</math>
* <math> P_{drag} = 1080 W/(m²(m/s)²) -- \Delta k_a / k_a = 0.4 </math>
Source: [[Nanosystems]] Equation (10.27) <ref name="pdrag"/> --
But here calculated backwards to friction per area from friction per bearing. 
'''Note:''' These are highly conservative estimates. Real values should be quite a bit lower.

Halving the linear speed (in units of m/s) quaters the friction losses. 
And going down from 1m/s to 1mm/s the friction losses fall by a factor of a million (1,000,000). 
More technically: Dynamic friction for crystolecules scales quadratically with speed. 

=== Why significant dynamic drag at higher speeds is this is not a problem ===

 Note: This section is redundant but provides a different formulation.
Skip ahead if the everything so far was clear.

==== Worry #1: Looking at the table friction per area for small speeds like 1m/s is quite high. ====

Friction can be ''massively'' massively reduced by reducing the linear speed of motions (speed in units m/s NOT Hz!). 
And '''we can totally afford to reduce the linear speed of motion in [[advanced productive nanosystem]]s because all the machinery that is needed for practical levels of throughput fits in a super thin layer at the very bottom of the [[convergent assembly]] of a [[gem-gum factory]] chip.''' 
(Reason: [[Higher throughput of smaller machinery]] - things scale favorably here)

We just need to make the bottom layer [[gem-gum factory]] chip a bit thicker 
to compensate for the loss of speed and we are back at the original throughput. 
(We want to do that anyway because many different specialized assembly lines need space.)

One totally can afford to slow down so much in advanced productive nanosystems like [[gem-gum factories]] 
because there is plenty of space to compensate by just adding more nanomachinery.

'''Q:''' '''But what about the additional bearing area?''' 
'''A:''' Yes, the total bearing area increases. 
But while 10x the amount of nanomachinery gives 10x the bearing area 
the friction per area falls by 100x due to 1/10th the speed. 
So overall friction falls by 10x.

PS: Also note that the table above gives conservative (pessimistic) estimates on levels of friction.

==== Worry #2: Nanotech has a lot of surface area per volume. Won't that cause friction to become excessive? ====

'''Q:''' Shouldn't there be massive amounts of bearing surface area? 
It's nanomachinery after all, and and for nanotechnology the surface to volume ratio gets extremely high? 
'''A:''' Surface per volume is indeed high. BUT: '''We barely need any volume to achieve practical levels of throughput.''' 
(Reason: [[Higher throughput of smaller machinery]] - things scale favorably here)

Looking at [[convergent assembly]] in a first naive approximation every layer has exactly the same bearing area. 
So the bottom-most nanomachinery layer has exactly the same bearing area as the topmost macroscale assembly chamber. 
In practice one would want to deviate form naive [[convergent assembly]] by making the bottom layer thicker, 
which, as described above, only improves the situation with friction losses from dynamic drag.

As for the bearing area of the convergent assembly layers higher up:
* (1) There are only a few convergent assembly layers present (take 32nm chambers times 32 four times and you are at 32mm).
* (2) Bigger bearings can [[nest many layers|infinitesimal bearings]]. Again. Same trick. Area x10 & speed x1/10 => overall friction x1/10.

== Highly conservative form Nanosystems {{wikitodo|check and merge this section}} ==

'''Assumed:'''
* A [[crystolecule]] bearing with 2nm radius and 2nm length
* Bearing stiffness k = 1000N/m
* Bearing bumpiness [[superlubricity|incommensurability]]: R = abs(m/(m-n)) = 10
* Bearing operating temperature: Roomtemperature 300K

The dominant power loss contributions (Nanosystems 10.4.6.f.) give: 
* P = 2.7*10⁻14 W / (m/s)^2 -- (for Δka/ka = 0.4) or
* P = 5.8*10⁻16 W / (m/s)^2 -- (for Δka/ka = 0.003)

So how much waste heat would one get for a reasonable desktop [[gemstone metamaterial on-chip factory]]? 
It is not calculated in [[Nanosystems]] since energy recuperation inefficiencies
* in force applying mechanosynthesis and
* "covalent welding" block assembly
likely dominates.

But let's confirm that: 
The proposed [[nanofactory]] convergent assembly system architecture (Nanosystems Table 14.1.)
lists (as reasonable) a few times 10^17 units at the lowest [[assembly levels]].
Nanosystems provides no info about how many bearings per unit to assume.
But Let's assume 100 bearings per unit. This kinda seems like a reasonable
(that is pessimistic and on the safe side) assumption. (applied [[Exploratory engineering]])
This gives:
* P = TODO
* P = TODO

Note that this is (on purpose) a rather pessimistic ("conservative") estimation.

Also the assumed 1019 bearings give ''a total internal bearing sliding surface area of about: 
S = 200m^2''' -- Which intuitively feels like quite a lot but not overly excessive.

=== Side-notes regarding the Numbers given above ===

In [[Nanosystems]] 10.4.6. some examples are calculated for 1m/s sliding speed (it gives about 80MHz for the r=2nm l=2nm bearing).
It's worth to note that a sliding speed of 1m/s is already quite fast.
The actually proposed speeds are more on the order of about 1mm/s (1000 times slower).
This makes power losses no less than one million times lower (since the two dominant drag mechanisms scales quadratically with speed).

According to [[Nanosystems]] 10.4.6.f. the two dominating effects of for friction in [[crystolecule]] bearings (at speeds of interest ) are:
* band-stiffness scallering and
* shear-reflection drag
Other drag mechanisms (acoustic radiation, band-flutter scattering, thermoelastic damping)
all give negligible contributions (at least for the speeds of interest).

= Numbers from papers -- less safe (since more optimistic) =

For much more optimistic but less absolutely certainly on the safe side numbers there is work on coaxial carbon nanotubes:
Also in contrast to crystolecule bearings nanotube bearings are already somewhat accessible to experiments.

The following is from the paper: 
"Evaluating the Friction of Rotary Joints in Molecular Machines"

'''Assumed:'''
* A nanotube bearing with 0.6nm radius and 5nm length
* Bearing operating temperature: Roomtemperature 300K
* Simulation was done at the rather high speed of 30m/s ~ 8GHz

* P = 2.9(+-1.5)*10^-33 W/(rad/s)^2
Or converted into the same units as used in Nanosystems :
* P = 7.25*10^-12 W/(m/s)^2

For the above assumed 10^19 bearings this gives:
* P = TODO

= '''TODO''' update chapters below =

=== Flawless surfaces drop friction significantly ===

In contrast to etched micro-systems where the relative manufacturing error gets bigger with shrinking size.
Atomically precise machinery has no error
allow [[superlubrication]] which drops friction at least three orders of magnitude

== Evolved molecular biology is not a proof that diffusion transport is the ideal solution with minimal losses ==

With those aforementioned effects cog-and-gear nanomachinery could potential feature smaller losses than diffusion driven natural systems (more on that comparison further down). To quantify that more in depth investigations are needed.

=== The issue ===

Nature is often (probably mostly out of psychological reasons) seen as unsurpassable.
But actually it is completely unknowable whether nature as a whole will be "surpassed" by artificial technology in the far future ([[nature vs technology|get side-tracked]]).
Regardless of that, specific aspects of nature definitively can (and have been) surpassed by artificial technologies
(there are [[technology exceeding nature in performance|countless examples]]).

Evolution ended up with diffusion transport and not cog-and-gear-machinery.
Taken the former in to consideration that does by no means imply that this is the best or only solution.
Actually evolution is facing severe [[Evolution#Limits_of_natural_evolution|limitations]] (lock-in-effect, incrementalism, ...).

(This is only one of the many cases where [[misconceptions|bio-analogies]] can have a problematic effect on perception.)

=== Why cog-and-gear transport may be more efficient ===

While diffusion transport features no friction during the transport process itself
diffusion transport is not at all lossless.
At intermediate passing stations some energy always needs to be converted to heat (tech term: dissipated).
Otherwise the chemical reactions would not have a preferred direction to go and all the molecular "machinery" would cease to do anything.

Of course cog-and gear nanomachinery has exactly the same requirement.
The big difference is that in biological systems energy often comes in discrete disconnected chunks.
If ther's more than needed the excess is dissipated without being used for some desired effect.
In a crude analogy it's like being unable to accept the change money.

In cog-and-gear nanomachinery everything is linked together in one big [[machine phase]]
There energy can be drawn in a continuous rather than discrete fashion.
The dissipation necessary for forward moving operation (arrow of time) can be
balanced and minimized further down to the absolutely unconditionally required minimum.
See main article: "[[Low speed efficiency limit]]"

== Proposed machine speeds are WAY below speeds of thermal motion ==

In gemstone based nanomachinery one usually wants the operation frequencies to be well below the thermal motion frequencies. Otherwise the mechanical motions couple too strongly into thermal motions and things will get very hot very quickly. The frequencies of thermal motions can be seen in oscillation infrared spectra. Typical covalent bonds are located in the wavelength range of 3µm-30µm. This corresponds to 10THz-0.1PHz.

Related: [[Stroboscopic illusion in animations of diamondoid molecular machine elements]]

== Typical operation frequencies ==

This is strongly depending on the method of bearing ([[superlubrication]] / single sp3 bonds as bearings / some for m of levitation / ... ) and efficiency of operations.

* For mechanosynthetic mills in a [[nanofactory]] where larger forces are present and potentially slightly inefficient mechanosynthesis is performed the low MHz range is a good target.
* For low friction bearings (like in [[nanomechanical computing]]) one can go up into the high MHz to low GHz range. This still leaves a gap of three orders of magnitude to the oszillative thermal motion DOFs.

== Less soft nanomachinery => less drag ==

Unlike compliant bio-molecules in water [[stiffness|stiff structures]] like carbon nanotubes (or bearings out of gemstone) in dry vacuum do not provide low energy low frequency rotative degrees of freedom (DOFs) to couple into. Those DOFs could (if they where present like in water) go down all the way to the microwave range: ~ 3cm & 10GHz. So overlap of mechanical motion with rotative thermal motion isn't so much of a problem
even at higher operation frequencies.

Note that existing simulations of [[crystolecule]]s can show a
a '''stroboscopic effect'''. That can lead one to believe
machine motion and thermal motion lie very close together and that consequently friction would be horrendous.
This is not the case. It's just an artifact of the simulation.

== Related ==

* '''[[Friction]]'''
* The myth that [[diffusion transport]] does not need to dissipate energy or is fundamentally more efficient.
* [[Superlubricity]]
* [[Levitation]]
* [[Crystolecule]]s
* [[How friction diminishes at the nanoscale]]
* [[Atomically precise bearings]] – especially [[Atomically precise slide bearing]]s
* '''[[Mesoscale friction]]'''

[[Nanosystems]] – Chapter 7 – Energy Dissipation – (page 161 to 190)
----
* [[Losses from mechanochemical reactions]]
----
* '''[[Wear]]'''

== External links ==

* {{todo|Add ref's to relevant chapters in "Nanosystems"}}
----
* Paper: [https://www.mse.ncsu.edu/CompMatSci/papers/TTN4_p9700_1.pdf Molecular-dynamics simulations of atomic-scale friction of diamond surfaces]
----
* Wikipedia: [https://en.wikipedia.org/wiki/Rotational_spectroscopy Rotational spectroscopy]
* Wikipedia: [https://en.wikipedia.org/wiki/Rotational%E2%80%93vibrational_spectroscopy Rotational–vibrational spectroscopy]
* Wikipedia: [https://en.wikipedia.org/wiki/Infrared_spectroscopy Infrared spectroscopy] & [https://en.wikipedia.org/wiki/Thermal_infrared_spectroscopy Thermal infrared spectroscopy]
----
* https://sci-nanotech.com/index.php?thread/43-a-closer-look-at-friction-in-cog-gear-style-stiff-nanomachinery/
----
* [https://pubs.rsc.org/en/content/articlehtml/2017/me/c7me00021a 2017 Evaluating the Friction of Rotary Joints in Molecular Machines] [https://arxiv.org/abs/1701.08202 (arxiv)]

[[Category:Surprising facts]]

= References =

<references/>

Same absolute speeds for smaller machinery

2026-09-29T07:42:12Z

Apm: /* Related */

[[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|400px|thumb|right|In this screencap of an animation the base assumption is "[[same absolute speeds for smaller machinery]]" (leading to linearly higher frequency of smaller machinery) this is only good as a first crude approximation. In an actual system one will want to slow down at the smallest scales, thus this geometry does not correspond to an actually proposed system, at least not at the smallest scales. More infos to this grapic on the page: [[Higher throughput of smaller machinery]].]]

'''Constancy as the natural scaling option for speed of operations of machinery'''

What are the motivating factors to keep speed of machinery motions constant across scales (as a first approximation)?
* Keeping relative scale deflections from machine motions constant across scales (see: [[Same relative deflections across scales]])
* Keeping friction losses constant across scales
As it turns out both imply constant speeds across scales. 
There's a caveat for the latter motivating some deviation from constancy. 
A "tiny" bit of intentional slowdown. ("Tiny" meaning less than linear.)

'''Potential trapdoor to comprehension:''' Here "absolute speeds" refers to motion in terms of m/s (using SI units) 
It does not refer to frequencies (in Hertz or 1/s). For frequencies see: [[Scale natural frequency]]. 
⚠️ '''One may colloquially say "smaller machinery moves faster" but in that case one is actually referinng to operation frequencies!'''

== Keeping relative scale deflections from machine motions constant across scales ==

Keeping absolute speeds constant across scales 
(or in other words keeping the same absolute speeds for smaller machinery) 
can be considered as a natural choice when the main motivating factor is: 
[[Same relative deflections across scales]]

== Keeping friction losses constant across scales ==

While one might expect losses to go up due to 
'''the well known scaling law of [[twice the surface area of half the volume]]''' applied to bearing area, 
there is also the compensating factor of 
'''the poorly known scaling law of [[Higher throughput of smaller machinery]]'''.

Both of these [[scaling laws]] are linear. 
Thus for machinery of scale invariant [[throughput density]] and scale invariant operation speeds
they exactly compensate.

{{wikitodo|Maybe bring this into a more formalized math form to make the point more clear.}}

=== Important caveats – Leading to scaling of speeds that differ from constancy ===

'''Alternate natural scaling options for speed of operations of machinery.'''

Since dynamic friction scales quadratically with speed ([[Hundredfold smaller frictionlosses from tenfold slowdown]]) and 
Productive nanomachinery takes up very little volume ([[Higher throughput of smaller machinery]]) 
it is possible to cheat by trading decreased speeds for increased volume of nanomachinery.
See:
* [[Deliberate slowdown at the lower assembly levels]]
* [[Increasing bearing area to decrease friction]]
* [[Optimal sublayernumber for minimal friction]]

----

Also: Optimal bearing technologies across scales likely change. 
This makes deviating a bit from constant speeds across scales desirable. 
See: [[Mesoscale friction]]

=== Dispelling eventual concerns regarding convergent assembly ===

Adding [[convergent assembly levels]] atop that are exponentially growing in size 
only adds at best logarithmic amounts of additional friction. 
Thus it for the most part can be ignored.

=== Discussion of an perhaps counterintuitive aspect of constant speeds across scales ===

When conceptually for visualization scaling up just space but not scaling time, 
then the assumption of constant speeds across scales leads to magnified models featuring magnified speeds. 
One might intuitively expect increased wear and such, but this is misled. 
High encounter frequencies are just natural at small scales ([[Scale natural frequency]]). 
One should remember that even today's macroscale roller bearing in the end feature nanoscale surface-on-surface contacts. 
The only change when going to bearings that as a hole are at the nanoscale is 
that they necessarily need to be atomically precise because 
the wear of imprecisions of the scale of today's macroscale bearings would annihilate nanoscale bearings instantly. 
Or rather imprecisions of the scale of today's macroscale bearing can be bigger than whole nanoscale bearings.

Related: [[Intuitive feel]]

== Impractical extreme ends and the golden middle as a start for optimizations ==

{| class="wikitable" style="text-align:center; width:100%;"
|-
| [[File:NanosystemsNotAProposedDesignConvergentAssembly.jpg|200px|thumb|center|'''NOT A PROPOSED SYSTEM''' – The other extreme end. '''[[Same frequencies for smaller machinery]]''' leading to '''linearly falling absolute speeds for smaller machinery.'''}}]]
| [[File:productive-nanosystems-video-snapshot.png|thumb|center|200px|'''THIS(!) IS A PROPOSED SYSTEM''' – Real systems will be an intermediate between the two leaning to the latter as baseline but skewing a bit over to the former for the bottom-most layer. Motivations being: (A) Reducing speeds to reduce friction. See: [[Increasing bearing area to decrease friction]] and (B) Specialized part assembly line machanosynthesis to get a nicely high spacial density of operating reaction sites.]]
| [[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|200px|thumb|center|'''NOT A PROPOSED SYSTEM''' – The other extreme end of '''same absolute speeds for smaller machinery''' leading to '''linearly rising frequencies form smaller machiners''' this is better more natural starting point that rising frequencies but still just a bad starting point very far away from even crudely optimized systems.]]
|}

== Related ==

* [[Scale natural frequency]] (Twice the frequency of half sized machinery)
* Complement page: [[Same frequencies for smaller machinery]] (not scale natural)
----
* [[Scaling law]]
----
* '''[[Same relative deflections across scales]]'''
* '''[[Higher throughput of smaller machinery]]'''

[[Category:Scaling law]]
[[Category:Surprising facts]]

Same absolute speeds for smaller machinery

2026-09-29T07:40:33Z

Apm: /* Related */

[[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|400px|thumb|right|In this screencap of an animation the base assumption is "[[same absolute speeds for smaller machinery]]" (leading to linearly higher frequency of smaller machinery) this is only good as a first crude approximation. In an actual system one will want to slow down at the smallest scales, thus this geometry does not correspond to an actually proposed system, at least not at the smallest scales. More infos to this grapic on the page: [[Higher throughput of smaller machinery]].]]

'''Constancy as the natural scaling option for speed of operations of machinery'''

What are the motivating factors to keep speed of machinery motions constant across scales (as a first approximation)?
* Keeping relative scale deflections from machine motions constant across scales (see: [[Same relative deflections across scales]])
* Keeping friction losses constant across scales
As it turns out both imply constant speeds across scales. 
There's a caveat for the latter motivating some deviation from constancy. 
A "tiny" bit of intentional slowdown. ("Tiny" meaning less than linear.)

'''Potential trapdoor to comprehension:''' Here "absolute speeds" refers to motion in terms of m/s (using SI units) 
It does not refer to frequencies (in Hertz or 1/s). For frequencies see: [[Scale natural frequency]]. 
⚠️ '''One may colloquially say "smaller machinery moves faster" but in that case one is actually referinng to operation frequencies!'''

== Keeping relative scale deflections from machine motions constant across scales ==

Keeping absolute speeds constant across scales 
(or in other words keeping the same absolute speeds for smaller machinery) 
can be considered as a natural choice when the main motivating factor is: 
[[Same relative deflections across scales]]

== Keeping friction losses constant across scales ==

While one might expect losses to go up due to 
'''the well known scaling law of [[twice the surface area of half the volume]]''' applied to bearing area, 
there is also the compensating factor of 
'''the poorly known scaling law of [[Higher throughput of smaller machinery]]'''.

Both of these [[scaling laws]] are linear. 
Thus for machinery of scale invariant [[throughput density]] and scale invariant operation speeds
they exactly compensate.

{{wikitodo|Maybe bring this into a more formalized math form to make the point more clear.}}

=== Important caveats – Leading to scaling of speeds that differ from constancy ===

'''Alternate natural scaling options for speed of operations of machinery.'''

Since dynamic friction scales quadratically with speed ([[Hundredfold smaller frictionlosses from tenfold slowdown]]) and 
Productive nanomachinery takes up very little volume ([[Higher throughput of smaller machinery]]) 
it is possible to cheat by trading decreased speeds for increased volume of nanomachinery.
See:
* [[Deliberate slowdown at the lower assembly levels]]
* [[Increasing bearing area to decrease friction]]
* [[Optimal sublayernumber for minimal friction]]

----

Also: Optimal bearing technologies across scales likely change. 
This makes deviating a bit from constant speeds across scales desirable. 
See: [[Mesoscale friction]]

=== Dispelling eventual concerns regarding convergent assembly ===

Adding [[convergent assembly levels]] atop that are exponentially growing in size 
only adds at best logarithmic amounts of additional friction. 
Thus it for the most part can be ignored.

=== Discussion of an perhaps counterintuitive aspect of constant speeds across scales ===

When conceptually for visualization scaling up just space but not scaling time, 
then the assumption of constant speeds across scales leads to magnified models featuring magnified speeds. 
One might intuitively expect increased wear and such, but this is misled. 
High encounter frequencies are just natural at small scales ([[Scale natural frequency]]). 
One should remember that even today's macroscale roller bearing in the end feature nanoscale surface-on-surface contacts. 
The only change when going to bearings that as a hole are at the nanoscale is 
that they necessarily need to be atomically precise because 
the wear of imprecisions of the scale of today's macroscale bearings would annihilate nanoscale bearings instantly. 
Or rather imprecisions of the scale of today's macroscale bearing can be bigger than whole nanoscale bearings.

Related: [[Intuitive feel]]

== Impractical extreme ends and the golden middle as a start for optimizations ==

{| class="wikitable" style="text-align:center; width:100%;"
|-
| [[File:NanosystemsNotAProposedDesignConvergentAssembly.jpg|200px|thumb|center|'''NOT A PROPOSED SYSTEM''' – The other extreme end. '''[[Same frequencies for smaller machinery]]''' leading to '''linearly falling absolute speeds for smaller machinery.'''}}]]
| [[File:productive-nanosystems-video-snapshot.png|thumb|center|200px|'''THIS(!) IS A PROPOSED SYSTEM''' – Real systems will be an intermediate between the two leaning to the latter as baseline but skewing a bit over to the former for the bottom-most layer. Motivations being: (A) Reducing speeds to reduce friction. See: [[Increasing bearing area to decrease friction]] and (B) Specialized part assembly line machanosynthesis to get a nicely high spacial density of operating reaction sites.]]
| [[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|200px|thumb|center|'''NOT A PROPOSED SYSTEM''' – The other extreme end of '''same absolute speeds for smaller machinery''' leading to '''linearly rising frequencies form smaller machiners''' this is better more natural starting point that rising frequencies but still just a bad starting point very far away from even crudely optimized systems.]]
|}

== Related ==

* [[Scale natural frequency]] (Twice the frequency of half sized machinery)
----
* [[Scaling law]]
----
* '''[[Same relative deflections across scales]]'''
* '''[[Higher throughput of smaller machinery]]'''

[[Category:Scaling law]]
[[Category:Surprising facts]]

Twice the frequency of half sized machinery

2026-09-29T07:39:11Z

Apm: /* Related */ added Same frequencies for smaller machinery

{{stub}}

Keeping operation speeds (in terms of length per time) constant over all size scales. 
As is natural in two senses (See: [[Same absolute speeds for smaller machinery]]) 
makes operation frequencies rise linearly with linearly falling size. 
This leads to massively [[higher throughput of smaller machinery]]. 

For a specific reference speed there are different scale natural frequencies for different sizes. 
'''Halve size double frequency.''' 
These scale natural frequencies keep the deflections from accelerations of inertial masses constant over all scales. 
See: [[Same relative deflections across scales]].

This is a crude and bad approximation for what one would actually want to do in a [[gemstone metamaterial factory]]. 
See: [[Deliberate slowdown at the lowest assembly level]]. 
Desirable is to go up a little less with the operation frequencies that the linear scaling law implies.

== Deviation from scale natural frequencies in proposed nanosystems ==

A reasonable macroscale reference speed is between 10mm/s and 100mm/s (seen in todays fused filament fabbrication 3D printers) 
(And 1m/s to 10m/s for fast delta style pick and place robots.) 
Proposed speeds for [[macroscale style machinery at the nanoscale]] in [[Nanosystems]] are about one to two orders of decimal magnitude lower than for macroscale 3D printers. 
~4mm/s? (to check!)

That is: The proposed [[macroscale style machinery at the nanoscale]] operates well below "scale natural frequencies" in the sense that 
the speeds are not limited by overswinging vibrations and resonances from inertial mass. (Assuming no very high Q factor structures are built). 
The limit for the speeds is rather set by an attempt to minimize energy dissipation from [[friction]].

== Related ==

* [[Unsupported rotating ring speed limit]] – this follows scale natural frequencies at the upper physical limit
* '''[[Same absolute speeds for smaller machinery]]''' & [[Same frequencies for smaller machinery]]
* [[Scaling law]]
* [[Scaling laws by degree of knownness]]

[[Category:Scaling law]]

Same frequencies for smaller machinery

2026-09-29T07:38:17Z

Apm: * Scale natural frequency

{{stub}}
With frequencies kept constant for smaller machinery, speeds fall linearly for smaller machinery. 
This is leading to a bad unter-utilization of nanoscale machinery capabilities. 

Random example taking taking FFF 3D printing as a macroscale baseline for frequency.
* 100mm/s like average 3D printer speeds at 10cm=100mm scale (1Hz)
* => 1mm/s at 1mm scale => 1um/s at 1um scale
* => 10nm/s at 10nm scale

That is even slower than diffusion based transport in bilogical nanosystems. 
Proposed speeds for advanced [[diamondoid]]/[[gemstone]]-based nanosystems.
In the book [[Nanosystems]] proposed where around 4mm/s at the smallest scales (~10nm). 
And natural would be to (non-gradually) move back up to at least 100mm/s when moving back up to the the macroscale (10cm=100mm). 

[[Same absolute speeds for smaller machinery]] seems to be a better baseline but also a bad one. 
Still giving a design space point far away from even the beginning of any halfway decent optimization. 

== Related pages ==

* Complement page to: [[Same absolute speeds for smaller machinery]]
* [[Convergent assembly]]
----
Resonance frequencies for smaller mechanical resonators going up. 
Insect wing frequencies going up for smaller insects. And such. 
See: '''[[Scale natural frequency]]'''

Same frequencies for smaller machinery

2026-09-29T07:34:59Z

Apm: basic page

Same absolute speeds for smaller machinery

2026-09-29T07:13:09Z

Apm: /* Impractical extreme ends and the golden middle as a start for optimizations */ reordered, put the "golden middle" in the middle

[[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|400px|thumb|right|In this screencap of an animation the base assumption is "[[same absolute speeds for smaller machinery]]" (leading to linearly higher frequency of smaller machinery) this is only good as a first crude approximation. In an actual system one will want to slow down at the smallest scales, thus this geometry does not correspond to an actually proposed system, at least not at the smallest scales. More infos to this grapic on the page: [[Higher throughput of smaller machinery]].]]

'''Constancy as the natural scaling option for speed of operations of machinery'''

What are the motivating factors to keep speed of machinery motions constant across scales (as a first approximation)?
* Keeping relative scale deflections from machine motions constant across scales (see: [[Same relative deflections across scales]])
* Keeping friction losses constant across scales
As it turns out both imply constant speeds across scales. 
There's a caveat for the latter motivating some deviation from constancy. 
A "tiny" bit of intentional slowdown. ("Tiny" meaning less than linear.)

'''Potential trapdoor to comprehension:''' Here "absolute speeds" refers to motion in terms of m/s (using SI units) 
It does not refer to frequencies (in Hertz or 1/s). For frequencies see: [[Scale natural frequency]]. 
⚠️ '''One may colloquially say "smaller machinery moves faster" but in that case one is actually referinng to operation frequencies!'''

== Keeping relative scale deflections from machine motions constant across scales ==

Keeping absolute speeds constant across scales 
(or in other words keeping the same absolute speeds for smaller machinery) 
can be considered as a natural choice when the main motivating factor is: 
[[Same relative deflections across scales]]

== Keeping friction losses constant across scales ==

While one might expect losses to go up due to 
'''the well known scaling law of [[twice the surface area of half the volume]]''' applied to bearing area, 
there is also the compensating factor of 
'''the poorly known scaling law of [[Higher throughput of smaller machinery]]'''.

Both of these [[scaling laws]] are linear. 
Thus for machinery of scale invariant [[throughput density]] and scale invariant operation speeds
they exactly compensate.

{{wikitodo|Maybe bring this into a more formalized math form to make the point more clear.}}

=== Important caveats – Leading to scaling of speeds that differ from constancy ===

'''Alternate natural scaling options for speed of operations of machinery.'''

Since dynamic friction scales quadratically with speed ([[Hundredfold smaller frictionlosses from tenfold slowdown]]) and 
Productive nanomachinery takes up very little volume ([[Higher throughput of smaller machinery]]) 
it is possible to cheat by trading decreased speeds for increased volume of nanomachinery.
See:
* [[Deliberate slowdown at the lower assembly levels]]
* [[Increasing bearing area to decrease friction]]
* [[Optimal sublayernumber for minimal friction]]

----

Also: Optimal bearing technologies across scales likely change. 
This makes deviating a bit from constant speeds across scales desirable. 
See: [[Mesoscale friction]]

=== Dispelling eventual concerns regarding convergent assembly ===

Adding [[convergent assembly levels]] atop that are exponentially growing in size 
only adds at best logarithmic amounts of additional friction. 
Thus it for the most part can be ignored.

=== Discussion of an perhaps counterintuitive aspect of constant speeds across scales ===

When conceptually for visualization scaling up just space but not scaling time, 
then the assumption of constant speeds across scales leads to magnified models featuring magnified speeds. 
One might intuitively expect increased wear and such, but this is misled. 
High encounter frequencies are just natural at small scales ([[Scale natural frequency]]). 
One should remember that even today's macroscale roller bearing in the end feature nanoscale surface-on-surface contacts. 
The only change when going to bearings that as a hole are at the nanoscale is 
that they necessarily need to be atomically precise because 
the wear of imprecisions of the scale of today's macroscale bearings would annihilate nanoscale bearings instantly. 
Or rather imprecisions of the scale of today's macroscale bearing can be bigger than whole nanoscale bearings.

Related: [[Intuitive feel]]

== Impractical extreme ends and the golden middle as a start for optimizations ==

{| class="wikitable" style="text-align:center; width:100%;"
|-
| [[File:NanosystemsNotAProposedDesignConvergentAssembly.jpg|200px|thumb|center|'''NOT A PROPOSED SYSTEM''' – The other extreme end. '''[[Same frequencies for smaller machinery]]''' leading to '''linearly falling absolute speeds for smaller machinery.'''}}]]
| [[File:productive-nanosystems-video-snapshot.png|thumb|center|200px|'''THIS(!) IS A PROPOSED SYSTEM''' – Real systems will be an intermediate between the two leaning to the latter as baseline but skewing a bit over to the former for the bottom-most layer. Motivations being: (A) Reducing speeds to reduce friction. See: [[Increasing bearing area to decrease friction]] and (B) Specialized part assembly line machanosynthesis to get a nicely high spacial density of operating reaction sites.]]
| [[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|200px|thumb|center|'''NOT A PROPOSED SYSTEM''' – The other extreme end of '''same absolute speeds for smaller machinery''' leading to '''linearly rising frequencies form smaller machiners''' this is better more natural starting point that rising frequencies but still just a bad starting point very far away from even crudely optimized systems.]]
|}

== Related ==

* [[Scale natural frequency]]
----
* [[Scaling law]]
----
* '''[[Same relative deflections across scales]]'''
* '''[[Higher throughput of smaller machinery]]'''

[[Category:Scaling law]]
[[Category:Surprising facts]]

Same absolute speeds for smaller machinery

2026-09-29T07:10:09Z

Apm: new section == Impractical extreme ends and the golden middle as a start for optimizations ==

[[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|400px|thumb|right|In this screencap of an animation the base assumption is "[[same absolute speeds for smaller machinery]]" (leading to linearly higher frequency of smaller machinery) this is only good as a first crude approximation. In an actual system one will want to slow down at the smallest scales, thus this geometry does not correspond to an actually proposed system, at least not at the smallest scales. More infos to this grapic on the page: [[Higher throughput of smaller machinery]].]]

'''Constancy as the natural scaling option for speed of operations of machinery'''

What are the motivating factors to keep speed of machinery motions constant across scales (as a first approximation)?
* Keeping relative scale deflections from machine motions constant across scales (see: [[Same relative deflections across scales]])
* Keeping friction losses constant across scales
As it turns out both imply constant speeds across scales. 
There's a caveat for the latter motivating some deviation from constancy. 
A "tiny" bit of intentional slowdown. ("Tiny" meaning less than linear.)

'''Potential trapdoor to comprehension:''' Here "absolute speeds" refers to motion in terms of m/s (using SI units) 
It does not refer to frequencies (in Hertz or 1/s). For frequencies see: [[Scale natural frequency]]. 
⚠️ '''One may colloquially say "smaller machinery moves faster" but in that case one is actually referinng to operation frequencies!'''

== Keeping relative scale deflections from machine motions constant across scales ==

Keeping absolute speeds constant across scales 
(or in other words keeping the same absolute speeds for smaller machinery) 
can be considered as a natural choice when the main motivating factor is: 
[[Same relative deflections across scales]]

== Keeping friction losses constant across scales ==

While one might expect losses to go up due to 
'''the well known scaling law of [[twice the surface area of half the volume]]''' applied to bearing area, 
there is also the compensating factor of 
'''the poorly known scaling law of [[Higher throughput of smaller machinery]]'''.

Both of these [[scaling laws]] are linear. 
Thus for machinery of scale invariant [[throughput density]] and scale invariant operation speeds
they exactly compensate.

{{wikitodo|Maybe bring this into a more formalized math form to make the point more clear.}}

=== Important caveats – Leading to scaling of speeds that differ from constancy ===

'''Alternate natural scaling options for speed of operations of machinery.'''

Since dynamic friction scales quadratically with speed ([[Hundredfold smaller frictionlosses from tenfold slowdown]]) and 
Productive nanomachinery takes up very little volume ([[Higher throughput of smaller machinery]]) 
it is possible to cheat by trading decreased speeds for increased volume of nanomachinery.
See:
* [[Deliberate slowdown at the lower assembly levels]]
* [[Increasing bearing area to decrease friction]]
* [[Optimal sublayernumber for minimal friction]]

----

Also: Optimal bearing technologies across scales likely change. 
This makes deviating a bit from constant speeds across scales desirable. 
See: [[Mesoscale friction]]

=== Dispelling eventual concerns regarding convergent assembly ===

Adding [[convergent assembly levels]] atop that are exponentially growing in size 
only adds at best logarithmic amounts of additional friction. 
Thus it for the most part can be ignored.

=== Discussion of an perhaps counterintuitive aspect of constant speeds across scales ===

When conceptually for visualization scaling up just space but not scaling time, 
then the assumption of constant speeds across scales leads to magnified models featuring magnified speeds. 
One might intuitively expect increased wear and such, but this is misled. 
High encounter frequencies are just natural at small scales ([[Scale natural frequency]]). 
One should remember that even today's macroscale roller bearing in the end feature nanoscale surface-on-surface contacts. 
The only change when going to bearings that as a hole are at the nanoscale is 
that they necessarily need to be atomically precise because 
the wear of imprecisions of the scale of today's macroscale bearings would annihilate nanoscale bearings instantly. 
Or rather imprecisions of the scale of today's macroscale bearing can be bigger than whole nanoscale bearings.

Related: [[Intuitive feel]]

== Impractical extreme ends and the golden middle as a start for optimizations ==

{| class="wikitable" style="text-align:center; width:100%;"
|-
| [[File:NanosystemsNotAProposedDesignConvergentAssembly.jpg|200px|thumb|center|'''NOT A PROPOSED SYSTEM''' – The other extreme end. '''[[Same frequencies for smaller machinery]]''' leading to '''linearly falling absolute speeds for smaller machinery.'''}}]]
| [[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|200px|thumb|center|'''NOT A PROPOSED SYSTEM''' – The other extreme end of '''same absolute speeds for smaller machinery''' leading to '''linearly rising frequencies form smaller machiners''' this is better more natural starting point but still just a bad starting point very far away from even crudely optimized systems.]]
| [[File:productive-nanosystems-video-snapshot.png|thumb|center|200px|'''THIS(!) IS A PROPOSED SYSTEM''' – Real systems will be an intermediate between the two leaning to the latter as baseline but skewing a bit over to the former for the bottom-most layer. Motivations being: (A) Reducing speeds to reduce friction. See: [[Increasing bearing area to decrease friction]] and (B) Specialized part assembly line machanosynthesis to get a nicely high spacial density of operating reaction sites.]]
|}

== Related ==

* [[Scale natural frequency]]
----
* [[Scaling law]]
----
* '''[[Same relative deflections across scales]]'''
* '''[[Higher throughput of smaller machinery]]'''

[[Category:Scaling law]]
[[Category:Surprising facts]]

Higher throughput of smaller machinery

2026-09-29T06:45:03Z

Apm: /* Related */

[[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|600px|thumb|right|Convergent assembly illustrating the scaling law '''"Higher throughput of smaller machinery"'''. '''The bottommost microscopically thin layer has the exact same throughput as the topmost macroscopic one. Thus filling the whole volume with nanomachinery would lead to exorbitant throughput and exorbitant waste heat. This is neither necessary nor desirable.''' All layers are [[Same absolute speeds for smaller machinery|operating at the exact same speed]] (not same frequency). Chosen here is a [[branching factor]] of four for illustrative purposes only. – While this is related to [[convergent assembly]] in the form of [[assembly layers]]. This specific topology and geometry does not match any concretely proposed designs. Actually (via [[exploratory engineering]]) proposed designs have significant deviations from this.]]

[[File:productive-nanosystems-video-snapshot.png|thumb|400px|'''This here is an actually proposed design''' for convergent [[assembly level]]s in the form of convergent [[assembly layer]]s. Note that the most part of the stack are the bottom nanoscale [[sub-layer]]s all of same size. Further convergent assembly in the naive form (shown in the first image on the page here) is optional (replacing product assemblers) at the top and not present here at all. – Image taken from [[Productive Nanosystems From molecules to superproducts]] video.]]

[[File:NanosystemsNotAProposedDesignConvergentAssembly.jpg|400px|thumb|right|Even more so than the naive layered stack: '''THIS IS NOT A PROPOSED DESIGN (so explicitly stated in [[Nanosystems]])'''. Just an example of a non-planar [[convergent assembly]] topology and geometry (or morphology as in biology). '''More or less planar [[assembly layers]] likely match natural scaling laws applied to the problem domain much better. But only as a baseline.''' {{wikitodo|Add Josh Halls analytic math comparison to scaling laws in bio-systems too. Plus his picture.}}]]

Video: '''[https://www.youtube.com/watch?v=kJ_K2aYaNCM "The Surprising Productivity of Nano-Machinery"]''' 
Short preview version: [https://www.youtube.com/watch?v=_O4uoxEt47c "Convergent Assembly and its effect on friction in Cog-and-Gear-style Nanomachinery"] 

When production machines are made smaller 
(but are still operated at the [[Same absolute speeds for smaller machinery|same unchanged speed]]) 
then they can produce more product per time.

* Halve sized machinery has double the throughput per volume of machinery.
* Ten times smaller machinery has ten times the throughput per volume of machinery.
* '''A million times smaller machinery has a million times the throughput per volume of machinery.''' At that point other effects become mixed in though.
In short: It is a linear [[scaling law]].

For the math behind why this scaling law applies see: 
[[Math of convergent assembly]]

== Limits ==

'''Important fact:''' 
This scaling law does not take under consideration
* the necessary ingress of resource supply and
* the necessary removal of the product

And this is ok as long as these contribute only a tiny fraction of the total friction losses 
But once transport motions become dominant in contribution of friction losses the scaling law breaks down. 
'''The bigger the [[branching factor]] B, the more there can be gained form this scaling law.'''

Concretely: '''The optimal [[sub-layer]] number where total frictionloss is mimimal is B³.''' 
Beyond that friction goes up again (eventually linearly). The scaling law breaks down. 

This happens to also be the point where assembly friction losses and transport friction losses are equal. 
For derivation of these results see page: [[Optimal sublayernumber for minimal friction]]

{{wikitodo|Make a infographic here in analogy to the one the page [[Level throughput balancing]]}}

== Some basic intuition ==

How the heck can throughput rise when the very first assumption was 
that speed of robotic manipulation will be kept constants over all size scales?!

The answer:
* [[In place assembly]] is assumed here.
* Removal of the assembled product from the manufacturing structure (the scaffold) is not included.
* This looks at assembly motions only. The necessary transport motions that emerge when nanomachinery is stacked beyond the [[macroscale slowness bottleneck]] are for now ignored. See: [[Multilayer assembly layers]] for how these motions relate to each other.

No, part removal for densely packed nanomachinery is not a problem 
in the case of basic [[gem-gum factories]] where: 
* (1) there is no densely packed nanomachinery instead a stack of one monolayer of each assembly level is the baseline design which: – makes throughput constant over all size scales (see math section below) and – makes removal of the assembled product from the manufacturing structure correspond to pusing products up in the next assembly level (where streaming further up continues)
* (2) the bottom assembly level is a thicker stack (a multilayer slab) that has much lower assembly speeds than transport speeds.

{{speculativity warning}} 
Higher degrees of filling space with nanomachinery than just thin monolayers may not be completely impossible. 
It would certainly be way beyond everyday practical. 
Transport speeds for product removal would "just" need to be faster than what is robotically possible. 
Imaginable would e.g. be a [[ultra high throughput microcomponent recomposer unit]] that is a block full of nanomachinery that has lots of straight coaxial high speed product shootout channels with [[stratified shear bearings]]. It would also need significant active cooling.

Related: [[Producer product pushapart]]

=== Visualizing the assembly speed difference by animation ===

Imagine unassembled block-fragments (color coded red) on the bottom of an robotic assembly cell 
being assembled by the robotic mechanism inside of the cell 
to one product block (color coded green) at the top of the cell.

Taking just one big macroscopic cell this process takes a while since all the parts need to travel the macroscopic distance from the bottom of the big assembly cell to the the top to turn from red to green.

When instead taking many small robotic cells (that have with their robotics inside moving with the same speed)
the distance from red to green is much shorter and thus everything turns from red (unassembled) to green (assembled) much much faster.

'''Advanced Q&A:'''

Why is the transition from red unassembled to green assembled 
in a 2D monolayer of robotic assembly cells faster than in one big cell of same 2D cross section? 
Isn't it supposed to finish in the same time if it's just a single monolayer? 

You're looking a a cross section! 
The red to green transition in a single monolayer is indeed way faster. 
But that single monolayer needs to repeat that transition many times over in order to 
make up for all the other the other layers that would be needed to completely fill up the volume of the big cell. 
In the simple model this exactly cancels out.

{{wikitodo|make (that is program) that animation – via OpenSCAD or Blender}}

== Basic math ==

(1) Take a cube with some [[macroscale style machinery at the nanoscale|robotic cog and gear assembly machinery]] of unspecified nature inside. 
(2) Replace the contents of the cube with several scaled down copies of the original cube. A whole numbered cuberoot is advantageous. 
(3) How does the throughput change in terms of how much volume can be assembled per unit of time?

Used constants:
* n = 1 ... one robotic unit in one robotic cell – this is just here to not mix it up with other dimensionless numbers
* s ... sidelength of the product blocks that the robotic unit assembles s^3 ... volume rho*s^3 ... mass
* f ... frequency of operation that is how often per unit of time a block assembly gets finished
* v ... constant speed for robotics on all size scales (crude approximation)
* Q ... throughput in terms of assembled volume per time

=== Full volume filled with robotics of original size ===

Throughput of one robotic cell: 
'''Q = (n * s^3 * f)''' 

=== Full volume filled with robotics of halve size ===

Throughput of eight robotic cells that
* are two times smaller each
* fill the same volume
* operate at the same speed:
(same speed means same magnitude of velocity not same frequency) 
'''Q° = (n' * s'^3 * f') where n' = 2^3 n and s' = s/2 and f' = 2f''' 
'''Q° = (2^3 n) * (s/2)^3 * (2f)''' 
'''Q° = 2 * (n * s^3 * f)''' 
'''Q° = 2Q'''

The ring ° could be interpreted as: 
The whole volume gets filled with smaller machinery.

=== Full volume filled with robotics of 1/10th size ===

Throughput of a thousand robotic cells that
* are ten times smaller each
* fill the same volume
* operate at the same speed:
'''Q°° = (10^3 n) * (s/10)^3 * (10f)''' 
'''Q°° = 10 * (n * s^3 * f)''' 
'''Q°° = 10Q'''

Generalization to arbitrary size steps was avoided here because 
it reduces comprehensibility.

=== One monolayer filled with robotics of 1/32th size ===

An actual practical nanofactory would (in first approximation) fill just one single monolayer.
* That means the smaller machinery matches the bigger machinery in throughput (Q' = Q).
* That is indeed done in order to match the throughput of the differently sized machiners such that they can be matchingly stacked.

Throughput of a hundred robotic cells that:
* are ten times smaller each
* fill 1/10th of same volume
* operate at the same speed:
'''Q' = (32^2 n) * (s/32)^3 * (32f)''' 
'''Q' = (n * s^3 * f)''' 
'''Q' = Q'''

The dash ' could be interpreted as: 
Only a 2D monolayer gets filled with smaller robotic cell machinery.

The size step of 32 here makes for somewhat more realistic numbers.
* This way two convergent assembly steps make a nice size step of a 1000.
* This way four convergent assembly steps make a factor of a million which bridges big nano (~32nm) to small macro (~32mm)

=== Supplemental: Scaling of frequency ===

The unexplained scaling of frequency is rather intuitive. 
Going back and forth halve the distance with the speed you get double the frequency. 
If you really want it formally then here you go: 
f = v/(constant*s) ~ v/s 
f' ~ v/s' ~ v/(s/2) ~ 2f

== From the perspective of diving down into a prospective nanofactory ==

=== Simplified nanofactory model ===

Let's for simplicity assume that the [[convergent assembly]] architecture in an advanced [[gem-gum factory]] is organized
* in simple coplanarly stacked assembly layers.
* that are each only one assembly cell in height, monolayers so to say
* that all operate at the same speed

=== Here ignored model deviations ===

There are good reasons to significantly deviate from that simple-most model. 
Especially for the lowest assembly levels. E.g.
* high energy turnover in [[mechanosynthesis]] and
* fast [[recycling]] of pre-produced [[microcomponents]] and
* high bearing area
But the focus here is on conveying a baseline understanding. 
And for assembly layers above the lowermost one(s) the simple-model above might hold quite well.

=== Same throughput of successively thinner layers ===

When going down the convergent [[assembly level]] layer stack …
* from a higher layer with bigger robotic assembly cells down
* to a the next lower layer with (much) smaller robotic assembly cells
… then one finds that the throughput capacity of both of these layers needs to be equal.
* If maximal throughput capacity would rise when going down the stack then the upper layers would form a bottleneck.
* If maximal throughput capacity would fall when going down the stack then the upper layers would be underutilized.
See main article: [[Level throughput balancing]]

The important thing to recognize here is that 
while all the mono-layers have the same maximal product throughput 
the thickness of these mono-layers becomes thinner and thinner. 
More generally the volume of these layers becomes smaller and smaller. 
'''So the throughput per volume shoots through the roof.'''

That is a very pleasant surprise! 
In a first approximation halving the size of manufacturing robotics doubles throughput capacity per volume. 
That means going down from one meter to one micrometer (a factor of a million) 
the throughput capacity per volume equally explodes a whopping millionfold. 
This is because it's a is a linear [[scaling law]].

As mentioned this can't be extended arbitrarily though. 
Below the micrometer level several effects (mentioned above) make 
full exploitation of that rise in productivity per volume impossible.

== Getting silly – questionable and unnecessary productivity levels ==

Now what if one would take a super thin microscale (possibly non-flat) assembly mono-"layer" that one finds pretty far down the convergent assembly stack and fills a whole macroscopic volume with many copies of it?

The answer is (in case of general purpose [[Nanofactory|gem-gum factories]]) that the product couldn't be removed/expulsed fast enough.
One hits [[Unsupported rotating ring speed limit|fundamental acceleration limits]] (even for the strongest available [[diamondoid metamaterial]]s) and long before that severe problems with mechanical resonances are likely to occur.

Note that the old and obsolete idea of packing a volume full with diamondoid [[molecular assembler]]s wouldn't tap into that potential because these devices
are below the microscale level in the nanoscale where the useful behavior of physics of raising throughput density with falling size of assembly machinery is hampered by other effects.

More on silly levels of throughput here: 
* [[Macroscale slowness bottleneck]]
* [[Hyper high throughput microcomponent recomposition]]

== Relation to Convergent assembly ==

[[File:Throughput_of_convergent_assembly_-_annotated.svg|200px|thumb|right|Q...throughput s...side-length f...frequency {{wikitodo|Resolve the issue with the text in this illustration!}}]]

Instead of filling the whole volume with nanomachinery which would provide waay more productivity than in allmost all conceivable circumstances needed nanofactories would use only monolayers (or thin stacks).

In a first approximation successively stacked monolayers of consecutive [[assembly levels]] (and thus vastly different sizes) match in their maximal throughput. See: [[Level throughput balancing]]

And that despite the thickness of the layers with smaller machinery being insignificant compared to the thickness of the layers above.
With the major exception of the bottommost assembly layers where things diverge notably from the first approximation.

=== Antagonistic effects/laws – sub microscale ===

The problem that emerges at the nanoscale is twofold.
* falling size => rising bearing area per volume => rising friction => to compensate: lower operation speed (and frequency) – summary: lower assembly event density in time
* falling size => rising machinery size to part size (atoms in the extreme case) – summary: lower assembly site density in space

Due to the nature of [[superlubrication|superlubricating]] friction:
* it scales with the square of speed (halving speed quaters friction losses)
* it scales linear with surface area (doubling area doubles friction)
It makes sense to slow down a bit and compensate by stacking layers for [[level throughput balancing]].
A combination of halving speed and doubling the number of stacked equal mono-"layers" halves friction while keeping throughput constant.

== Lessening the macroscale throughput bottleneck ==

There are also effects/laws (located in the macroscale) that can help increase throughput density above the first approximation.
Details on that can be found (for now) on the "[[Level throughput balancing]]" page.

== Alternate names for this scaling law as a concept ==

* Higher throughput-density of smaller machinery (more precise & more cumbersome naming)
* Higher productivity of smaller machinery (well not all stuff made may be a desirable products, pessimistic view)
* Productivity explosion (too over-hyping & unspecific)

The thing is higher throughput does not necessarily means higher productivity in the sense of generation of useful products. 
Thus the rename to the current page name "Higher throughput of smaller machinery".

== Related ==

'''[[Higher bearing area of smaller machinery]]''': 
The concern that this leads to excessive sliding friction losses 
is mended by the here discussed "[[higher throughput of smaller machinery]]" 
as it implies that only a very small overall volume of nanomachinery is needed 
for practical [[advanced productive nanosystem]]s. 
----
* '''[[Friction in gem-gum-tec]]''' & [[Friction]]
----
* '''[[Math of convergent assembly]]'''
* [[Convergent assembly]]
* [[Deliberate slowdown at the lowest assembly level]] & [[Increasing bearing area to decrease friction]]
* '''[[Optimal sublayernumber for minimal friction]]'''
* [[Level throughput balancing]]
* [[Macroscale slowness bottleneck]]
* [[Low speed efficiency limit]]
* [[Atom placement frequency]] (MHz TeraCore systems as desktop devices)
----
* [[Pages with math]]
* [[Scaling law]] -- [[Scaling law#Speedup]]
----
* Harvesting the benefits of the scaling law: [[Hyper high throughput microcomponent recomposition]]
* [[High performance of gem-gum technology]]
----
* Another very important as of 2022 barely known scaling law: '''[[Same relative deflections across scales]]'''
* '''[[How macroscale style machinery at the nanoscale outperforms its native scale]]'''
* Slightly violated baseline scaling law: '''[[Same absolute speeds for smaller machinery]]'''
----
Another seemingly massively overpowered performance parameter is: 
'''Higher [[power density]] of smaller machinery.''' 
This is less of a scaling law and more of a property of [[gem-gum]] systems though {{todo|to check}}.

[[Category:Pages with math]]

== External links ==

* Video: '''[https://www.youtube.com/watch?v=kJ_K2aYaNCM&t=1555s The Surprising Productivity of Nano-Machinery]'''
* Video: [https://www.youtube.com/watch?v=_O4uoxEt47c Convergent Assembly and its effect on friction in Cog-and-Gear-style Nanomachinery – a sneak preview]

[[category:Pages with math]]
[[Category:Scaling law]]
[[Category:Surprising facts]]

Higher throughput of smaller machinery

2026-09-29T06:43:45Z

Apm: /* Related */ reformulation

[[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|600px|thumb|right|Convergent assembly illustrating the scaling law '''"Higher throughput of smaller machinery"'''. '''The bottommost microscopically thin layer has the exact same throughput as the topmost macroscopic one. Thus filling the whole volume with nanomachinery would lead to exorbitant throughput and exorbitant waste heat. This is neither necessary nor desirable.''' All layers are [[Same absolute speeds for smaller machinery|operating at the exact same speed]] (not same frequency). Chosen here is a [[branching factor]] of four for illustrative purposes only. – While this is related to [[convergent assembly]] in the form of [[assembly layers]]. This specific topology and geometry does not match any concretely proposed designs. Actually (via [[exploratory engineering]]) proposed designs have significant deviations from this.]]

[[File:productive-nanosystems-video-snapshot.png|thumb|400px|'''This here is an actually proposed design''' for convergent [[assembly level]]s in the form of convergent [[assembly layer]]s. Note that the most part of the stack are the bottom nanoscale [[sub-layer]]s all of same size. Further convergent assembly in the naive form (shown in the first image on the page here) is optional (replacing product assemblers) at the top and not present here at all. – Image taken from [[Productive Nanosystems From molecules to superproducts]] video.]]

[[File:NanosystemsNotAProposedDesignConvergentAssembly.jpg|400px|thumb|right|Even more so than the naive layered stack: '''THIS IS NOT A PROPOSED DESIGN (so explicitly stated in [[Nanosystems]])'''. Just an example of a non-planar [[convergent assembly]] topology and geometry (or morphology as in biology). '''More or less planar [[assembly layers]] likely match natural scaling laws applied to the problem domain much better. But only as a baseline.''' {{wikitodo|Add Josh Halls analytic math comparison to scaling laws in bio-systems too. Plus his picture.}}]]

Video: '''[https://www.youtube.com/watch?v=kJ_K2aYaNCM "The Surprising Productivity of Nano-Machinery"]''' 
Short preview version: [https://www.youtube.com/watch?v=_O4uoxEt47c "Convergent Assembly and its effect on friction in Cog-and-Gear-style Nanomachinery"] 

When production machines are made smaller 
(but are still operated at the [[Same absolute speeds for smaller machinery|same unchanged speed]]) 
then they can produce more product per time.

* Halve sized machinery has double the throughput per volume of machinery.
* Ten times smaller machinery has ten times the throughput per volume of machinery.
* '''A million times smaller machinery has a million times the throughput per volume of machinery.''' At that point other effects become mixed in though.
In short: It is a linear [[scaling law]].

For the math behind why this scaling law applies see: 
[[Math of convergent assembly]]

== Limits ==

'''Important fact:''' 
This scaling law does not take under consideration
* the necessary ingress of resource supply and
* the necessary removal of the product

And this is ok as long as these contribute only a tiny fraction of the total friction losses 
But once transport motions become dominant in contribution of friction losses the scaling law breaks down. 
'''The bigger the [[branching factor]] B, the more there can be gained form this scaling law.'''

Concretely: '''The optimal [[sub-layer]] number where total frictionloss is mimimal is B³.''' 
Beyond that friction goes up again (eventually linearly). The scaling law breaks down. 

This happens to also be the point where assembly friction losses and transport friction losses are equal. 
For derivation of these results see page: [[Optimal sublayernumber for minimal friction]]

{{wikitodo|Make a infographic here in analogy to the one the page [[Level throughput balancing]]}}

== Some basic intuition ==

How the heck can throughput rise when the very first assumption was 
that speed of robotic manipulation will be kept constants over all size scales?!

The answer:
* [[In place assembly]] is assumed here.
* Removal of the assembled product from the manufacturing structure (the scaffold) is not included.
* This looks at assembly motions only. The necessary transport motions that emerge when nanomachinery is stacked beyond the [[macroscale slowness bottleneck]] are for now ignored. See: [[Multilayer assembly layers]] for how these motions relate to each other.

No, part removal for densely packed nanomachinery is not a problem 
in the case of basic [[gem-gum factories]] where: 
* (1) there is no densely packed nanomachinery instead a stack of one monolayer of each assembly level is the baseline design which: – makes throughput constant over all size scales (see math section below) and – makes removal of the assembled product from the manufacturing structure correspond to pusing products up in the next assembly level (where streaming further up continues)
* (2) the bottom assembly level is a thicker stack (a multilayer slab) that has much lower assembly speeds than transport speeds.

{{speculativity warning}} 
Higher degrees of filling space with nanomachinery than just thin monolayers may not be completely impossible. 
It would certainly be way beyond everyday practical. 
Transport speeds for product removal would "just" need to be faster than what is robotically possible. 
Imaginable would e.g. be a [[ultra high throughput microcomponent recomposer unit]] that is a block full of nanomachinery that has lots of straight coaxial high speed product shootout channels with [[stratified shear bearings]]. It would also need significant active cooling.

Related: [[Producer product pushapart]]

=== Visualizing the assembly speed difference by animation ===

Imagine unassembled block-fragments (color coded red) on the bottom of an robotic assembly cell 
being assembled by the robotic mechanism inside of the cell 
to one product block (color coded green) at the top of the cell.

Taking just one big macroscopic cell this process takes a while since all the parts need to travel the macroscopic distance from the bottom of the big assembly cell to the the top to turn from red to green.

When instead taking many small robotic cells (that have with their robotics inside moving with the same speed)
the distance from red to green is much shorter and thus everything turns from red (unassembled) to green (assembled) much much faster.

'''Advanced Q&A:'''

Why is the transition from red unassembled to green assembled 
in a 2D monolayer of robotic assembly cells faster than in one big cell of same 2D cross section? 
Isn't it supposed to finish in the same time if it's just a single monolayer? 

You're looking a a cross section! 
The red to green transition in a single monolayer is indeed way faster. 
But that single monolayer needs to repeat that transition many times over in order to 
make up for all the other the other layers that would be needed to completely fill up the volume of the big cell. 
In the simple model this exactly cancels out.

{{wikitodo|make (that is program) that animation – via OpenSCAD or Blender}}

== Basic math ==

(1) Take a cube with some [[macroscale style machinery at the nanoscale|robotic cog and gear assembly machinery]] of unspecified nature inside. 
(2) Replace the contents of the cube with several scaled down copies of the original cube. A whole numbered cuberoot is advantageous. 
(3) How does the throughput change in terms of how much volume can be assembled per unit of time?

Used constants:
* n = 1 ... one robotic unit in one robotic cell – this is just here to not mix it up with other dimensionless numbers
* s ... sidelength of the product blocks that the robotic unit assembles s^3 ... volume rho*s^3 ... mass
* f ... frequency of operation that is how often per unit of time a block assembly gets finished
* v ... constant speed for robotics on all size scales (crude approximation)
* Q ... throughput in terms of assembled volume per time

=== Full volume filled with robotics of original size ===

Throughput of one robotic cell: 
'''Q = (n * s^3 * f)''' 

=== Full volume filled with robotics of halve size ===

Throughput of eight robotic cells that
* are two times smaller each
* fill the same volume
* operate at the same speed:
(same speed means same magnitude of velocity not same frequency) 
'''Q° = (n' * s'^3 * f') where n' = 2^3 n and s' = s/2 and f' = 2f''' 
'''Q° = (2^3 n) * (s/2)^3 * (2f)''' 
'''Q° = 2 * (n * s^3 * f)''' 
'''Q° = 2Q'''

The ring ° could be interpreted as: 
The whole volume gets filled with smaller machinery.

=== Full volume filled with robotics of 1/10th size ===

Throughput of a thousand robotic cells that
* are ten times smaller each
* fill the same volume
* operate at the same speed:
'''Q°° = (10^3 n) * (s/10)^3 * (10f)''' 
'''Q°° = 10 * (n * s^3 * f)''' 
'''Q°° = 10Q'''

Generalization to arbitrary size steps was avoided here because 
it reduces comprehensibility.

=== One monolayer filled with robotics of 1/32th size ===

An actual practical nanofactory would (in first approximation) fill just one single monolayer.
* That means the smaller machinery matches the bigger machinery in throughput (Q' = Q).
* That is indeed done in order to match the throughput of the differently sized machiners such that they can be matchingly stacked.

Throughput of a hundred robotic cells that:
* are ten times smaller each
* fill 1/10th of same volume
* operate at the same speed:
'''Q' = (32^2 n) * (s/32)^3 * (32f)''' 
'''Q' = (n * s^3 * f)''' 
'''Q' = Q'''

The dash ' could be interpreted as: 
Only a 2D monolayer gets filled with smaller robotic cell machinery.

The size step of 32 here makes for somewhat more realistic numbers.
* This way two convergent assembly steps make a nice size step of a 1000.
* This way four convergent assembly steps make a factor of a million which bridges big nano (~32nm) to small macro (~32mm)

=== Supplemental: Scaling of frequency ===

The unexplained scaling of frequency is rather intuitive. 
Going back and forth halve the distance with the speed you get double the frequency. 
If you really want it formally then here you go: 
f = v/(constant*s) ~ v/s 
f' ~ v/s' ~ v/(s/2) ~ 2f

== From the perspective of diving down into a prospective nanofactory ==

=== Simplified nanofactory model ===

Let's for simplicity assume that the [[convergent assembly]] architecture in an advanced [[gem-gum factory]] is organized
* in simple coplanarly stacked assembly layers.
* that are each only one assembly cell in height, monolayers so to say
* that all operate at the same speed

=== Here ignored model deviations ===

There are good reasons to significantly deviate from that simple-most model. 
Especially for the lowest assembly levels. E.g.
* high energy turnover in [[mechanosynthesis]] and
* fast [[recycling]] of pre-produced [[microcomponents]] and
* high bearing area
But the focus here is on conveying a baseline understanding. 
And for assembly layers above the lowermost one(s) the simple-model above might hold quite well.

=== Same throughput of successively thinner layers ===

When going down the convergent [[assembly level]] layer stack …
* from a higher layer with bigger robotic assembly cells down
* to a the next lower layer with (much) smaller robotic assembly cells
… then one finds that the throughput capacity of both of these layers needs to be equal.
* If maximal throughput capacity would rise when going down the stack then the upper layers would form a bottleneck.
* If maximal throughput capacity would fall when going down the stack then the upper layers would be underutilized.
See main article: [[Level throughput balancing]]

The important thing to recognize here is that 
while all the mono-layers have the same maximal product throughput 
the thickness of these mono-layers becomes thinner and thinner. 
More generally the volume of these layers becomes smaller and smaller. 
'''So the throughput per volume shoots through the roof.'''

That is a very pleasant surprise! 
In a first approximation halving the size of manufacturing robotics doubles throughput capacity per volume. 
That means going down from one meter to one micrometer (a factor of a million) 
the throughput capacity per volume equally explodes a whopping millionfold. 
This is because it's a is a linear [[scaling law]].

As mentioned this can't be extended arbitrarily though. 
Below the micrometer level several effects (mentioned above) make 
full exploitation of that rise in productivity per volume impossible.

== Getting silly – questionable and unnecessary productivity levels ==

Now what if one would take a super thin microscale (possibly non-flat) assembly mono-"layer" that one finds pretty far down the convergent assembly stack and fills a whole macroscopic volume with many copies of it?

The answer is (in case of general purpose [[Nanofactory|gem-gum factories]]) that the product couldn't be removed/expulsed fast enough.
One hits [[Unsupported rotating ring speed limit|fundamental acceleration limits]] (even for the strongest available [[diamondoid metamaterial]]s) and long before that severe problems with mechanical resonances are likely to occur.

Note that the old and obsolete idea of packing a volume full with diamondoid [[molecular assembler]]s wouldn't tap into that potential because these devices
are below the microscale level in the nanoscale where the useful behavior of physics of raising throughput density with falling size of assembly machinery is hampered by other effects.

More on silly levels of throughput here: 
* [[Macroscale slowness bottleneck]]
* [[Hyper high throughput microcomponent recomposition]]

== Relation to Convergent assembly ==

[[File:Throughput_of_convergent_assembly_-_annotated.svg|200px|thumb|right|Q...throughput s...side-length f...frequency {{wikitodo|Resolve the issue with the text in this illustration!}}]]

Instead of filling the whole volume with nanomachinery which would provide waay more productivity than in allmost all conceivable circumstances needed nanofactories would use only monolayers (or thin stacks).

In a first approximation successively stacked monolayers of consecutive [[assembly levels]] (and thus vastly different sizes) match in their maximal throughput. See: [[Level throughput balancing]]

And that despite the thickness of the layers with smaller machinery being insignificant compared to the thickness of the layers above.
With the major exception of the bottommost assembly layers where things diverge notably from the first approximation.

=== Antagonistic effects/laws – sub microscale ===

The problem that emerges at the nanoscale is twofold.
* falling size => rising bearing area per volume => rising friction => to compensate: lower operation speed (and frequency) – summary: lower assembly event density in time
* falling size => rising machinery size to part size (atoms in the extreme case) – summary: lower assembly site density in space

Due to the nature of [[superlubrication|superlubricating]] friction:
* it scales with the square of speed (halving speed quaters friction losses)
* it scales linear with surface area (doubling area doubles friction)
It makes sense to slow down a bit and compensate by stacking layers for [[level throughput balancing]].
A combination of halving speed and doubling the number of stacked equal mono-"layers" halves friction while keeping throughput constant.

== Lessening the macroscale throughput bottleneck ==

There are also effects/laws (located in the macroscale) that can help increase throughput density above the first approximation.
Details on that can be found (for now) on the "[[Level throughput balancing]]" page.

== Alternate names for this scaling law as a concept ==

* Higher throughput-density of smaller machinery (more precise & more cumbersome naming)
* Higher productivity of smaller machinery (well not all stuff made may be a desirable products, pessimistic view)
* Productivity explosion (too over-hyping & unspecific)

The thing is higher throughput does not necessarily means higher productivity in the sense of generation of useful products. 
Thus the rename to the current page name "Higher throughput of smaller machinery".

== Related ==

'''[[Higher bearing area of smaller machinery]]''': 
The concern that this leads to excessive sliding friction losses 
is mended by the here discussed "[[higher throughput of smaller machinery]]" 
as it implies that only a small very volume of nanomachinery is needed. 
----
* '''[[Friction in gem-gum-tec]]''' & [[Friction]]
----
* '''[[Math of convergent assembly]]'''
* [[Convergent assembly]]
* [[Deliberate slowdown at the lowest assembly level]] & [[Increasing bearing area to decrease friction]]
* '''[[Optimal sublayernumber for minimal friction]]'''
* [[Level throughput balancing]]
* [[Macroscale slowness bottleneck]]
* [[Low speed efficiency limit]]
* [[Atom placement frequency]] (MHz TeraCore systems as desktop devices)
----
* [[Pages with math]]
* [[Scaling law]] -- [[Scaling law#Speedup]]
----
* Harvesting the benefits of the scaling law: [[Hyper high throughput microcomponent recomposition]]
* [[High performance of gem-gum technology]]
----
* Another very important as of 2022 barely known scaling law: '''[[Same relative deflections across scales]]'''
* '''[[How macroscale style machinery at the nanoscale outperforms its native scale]]'''
* Slightly violated baseline scaling law: '''[[Same absolute speeds for smaller machinery]]'''
----
Another seemingly massively overpowered performance parameter is: 
'''Higher [[power density]] of smaller machinery.''' 
This is less of a scaling law and more of a property of [[gem-gum]] systems though {{todo|to check}}.

[[Category:Pages with math]]

== External links ==

* Video: '''[https://www.youtube.com/watch?v=kJ_K2aYaNCM&t=1555s The Surprising Productivity of Nano-Machinery]'''
* Video: [https://www.youtube.com/watch?v=_O4uoxEt47c Convergent Assembly and its effect on friction in Cog-and-Gear-style Nanomachinery – a sneak preview]

[[category:Pages with math]]
[[Category:Scaling law]]
[[Category:Surprising facts]]

Higher throughput of smaller machinery

2026-09-29T06:43:01Z

Apm: /* Related */

[[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|600px|thumb|right|Convergent assembly illustrating the scaling law '''"Higher throughput of smaller machinery"'''. '''The bottommost microscopically thin layer has the exact same throughput as the topmost macroscopic one. Thus filling the whole volume with nanomachinery would lead to exorbitant throughput and exorbitant waste heat. This is neither necessary nor desirable.''' All layers are [[Same absolute speeds for smaller machinery|operating at the exact same speed]] (not same frequency). Chosen here is a [[branching factor]] of four for illustrative purposes only. – While this is related to [[convergent assembly]] in the form of [[assembly layers]]. This specific topology and geometry does not match any concretely proposed designs. Actually (via [[exploratory engineering]]) proposed designs have significant deviations from this.]]

[[File:productive-nanosystems-video-snapshot.png|thumb|400px|'''This here is an actually proposed design''' for convergent [[assembly level]]s in the form of convergent [[assembly layer]]s. Note that the most part of the stack are the bottom nanoscale [[sub-layer]]s all of same size. Further convergent assembly in the naive form (shown in the first image on the page here) is optional (replacing product assemblers) at the top and not present here at all. – Image taken from [[Productive Nanosystems From molecules to superproducts]] video.]]

[[File:NanosystemsNotAProposedDesignConvergentAssembly.jpg|400px|thumb|right|Even more so than the naive layered stack: '''THIS IS NOT A PROPOSED DESIGN (so explicitly stated in [[Nanosystems]])'''. Just an example of a non-planar [[convergent assembly]] topology and geometry (or morphology as in biology). '''More or less planar [[assembly layers]] likely match natural scaling laws applied to the problem domain much better. But only as a baseline.''' {{wikitodo|Add Josh Halls analytic math comparison to scaling laws in bio-systems too. Plus his picture.}}]]

Video: '''[https://www.youtube.com/watch?v=kJ_K2aYaNCM "The Surprising Productivity of Nano-Machinery"]''' 
Short preview version: [https://www.youtube.com/watch?v=_O4uoxEt47c "Convergent Assembly and its effect on friction in Cog-and-Gear-style Nanomachinery"] 

When production machines are made smaller 
(but are still operated at the [[Same absolute speeds for smaller machinery|same unchanged speed]]) 
then they can produce more product per time.

* Halve sized machinery has double the throughput per volume of machinery.
* Ten times smaller machinery has ten times the throughput per volume of machinery.
* '''A million times smaller machinery has a million times the throughput per volume of machinery.''' At that point other effects become mixed in though.
In short: It is a linear [[scaling law]].

For the math behind why this scaling law applies see: 
[[Math of convergent assembly]]

== Limits ==

'''Important fact:''' 
This scaling law does not take under consideration
* the necessary ingress of resource supply and
* the necessary removal of the product

And this is ok as long as these contribute only a tiny fraction of the total friction losses 
But once transport motions become dominant in contribution of friction losses the scaling law breaks down. 
'''The bigger the [[branching factor]] B, the more there can be gained form this scaling law.'''

Concretely: '''The optimal [[sub-layer]] number where total frictionloss is mimimal is B³.''' 
Beyond that friction goes up again (eventually linearly). The scaling law breaks down. 

This happens to also be the point where assembly friction losses and transport friction losses are equal. 
For derivation of these results see page: [[Optimal sublayernumber for minimal friction]]

{{wikitodo|Make a infographic here in analogy to the one the page [[Level throughput balancing]]}}

== Some basic intuition ==

How the heck can throughput rise when the very first assumption was 
that speed of robotic manipulation will be kept constants over all size scales?!

The answer:
* [[In place assembly]] is assumed here.
* Removal of the assembled product from the manufacturing structure (the scaffold) is not included.
* This looks at assembly motions only. The necessary transport motions that emerge when nanomachinery is stacked beyond the [[macroscale slowness bottleneck]] are for now ignored. See: [[Multilayer assembly layers]] for how these motions relate to each other.

No, part removal for densely packed nanomachinery is not a problem 
in the case of basic [[gem-gum factories]] where: 
* (1) there is no densely packed nanomachinery instead a stack of one monolayer of each assembly level is the baseline design which: – makes throughput constant over all size scales (see math section below) and – makes removal of the assembled product from the manufacturing structure correspond to pusing products up in the next assembly level (where streaming further up continues)
* (2) the bottom assembly level is a thicker stack (a multilayer slab) that has much lower assembly speeds than transport speeds.

{{speculativity warning}} 
Higher degrees of filling space with nanomachinery than just thin monolayers may not be completely impossible. 
It would certainly be way beyond everyday practical. 
Transport speeds for product removal would "just" need to be faster than what is robotically possible. 
Imaginable would e.g. be a [[ultra high throughput microcomponent recomposer unit]] that is a block full of nanomachinery that has lots of straight coaxial high speed product shootout channels with [[stratified shear bearings]]. It would also need significant active cooling.

Related: [[Producer product pushapart]]

=== Visualizing the assembly speed difference by animation ===

Imagine unassembled block-fragments (color coded red) on the bottom of an robotic assembly cell 
being assembled by the robotic mechanism inside of the cell 
to one product block (color coded green) at the top of the cell.

Taking just one big macroscopic cell this process takes a while since all the parts need to travel the macroscopic distance from the bottom of the big assembly cell to the the top to turn from red to green.

When instead taking many small robotic cells (that have with their robotics inside moving with the same speed)
the distance from red to green is much shorter and thus everything turns from red (unassembled) to green (assembled) much much faster.

'''Advanced Q&A:'''

Why is the transition from red unassembled to green assembled 
in a 2D monolayer of robotic assembly cells faster than in one big cell of same 2D cross section? 
Isn't it supposed to finish in the same time if it's just a single monolayer? 

You're looking a a cross section! 
The red to green transition in a single monolayer is indeed way faster. 
But that single monolayer needs to repeat that transition many times over in order to 
make up for all the other the other layers that would be needed to completely fill up the volume of the big cell. 
In the simple model this exactly cancels out.

{{wikitodo|make (that is program) that animation – via OpenSCAD or Blender}}

== Basic math ==

(1) Take a cube with some [[macroscale style machinery at the nanoscale|robotic cog and gear assembly machinery]] of unspecified nature inside. 
(2) Replace the contents of the cube with several scaled down copies of the original cube. A whole numbered cuberoot is advantageous. 
(3) How does the throughput change in terms of how much volume can be assembled per unit of time?

Used constants:
* n = 1 ... one robotic unit in one robotic cell – this is just here to not mix it up with other dimensionless numbers
* s ... sidelength of the product blocks that the robotic unit assembles s^3 ... volume rho*s^3 ... mass
* f ... frequency of operation that is how often per unit of time a block assembly gets finished
* v ... constant speed for robotics on all size scales (crude approximation)
* Q ... throughput in terms of assembled volume per time

=== Full volume filled with robotics of original size ===

Throughput of one robotic cell: 
'''Q = (n * s^3 * f)''' 

=== Full volume filled with robotics of halve size ===

Throughput of eight robotic cells that
* are two times smaller each
* fill the same volume
* operate at the same speed:
(same speed means same magnitude of velocity not same frequency) 
'''Q° = (n' * s'^3 * f') where n' = 2^3 n and s' = s/2 and f' = 2f''' 
'''Q° = (2^3 n) * (s/2)^3 * (2f)''' 
'''Q° = 2 * (n * s^3 * f)''' 
'''Q° = 2Q'''

The ring ° could be interpreted as: 
The whole volume gets filled with smaller machinery.

=== Full volume filled with robotics of 1/10th size ===

Throughput of a thousand robotic cells that
* are ten times smaller each
* fill the same volume
* operate at the same speed:
'''Q°° = (10^3 n) * (s/10)^3 * (10f)''' 
'''Q°° = 10 * (n * s^3 * f)''' 
'''Q°° = 10Q'''

Generalization to arbitrary size steps was avoided here because 
it reduces comprehensibility.

=== One monolayer filled with robotics of 1/32th size ===

An actual practical nanofactory would (in first approximation) fill just one single monolayer.
* That means the smaller machinery matches the bigger machinery in throughput (Q' = Q).
* That is indeed done in order to match the throughput of the differently sized machiners such that they can be matchingly stacked.

Throughput of a hundred robotic cells that:
* are ten times smaller each
* fill 1/10th of same volume
* operate at the same speed:
'''Q' = (32^2 n) * (s/32)^3 * (32f)''' 
'''Q' = (n * s^3 * f)''' 
'''Q' = Q'''

The dash ' could be interpreted as: 
Only a 2D monolayer gets filled with smaller robotic cell machinery.

The size step of 32 here makes for somewhat more realistic numbers.
* This way two convergent assembly steps make a nice size step of a 1000.
* This way four convergent assembly steps make a factor of a million which bridges big nano (~32nm) to small macro (~32mm)

=== Supplemental: Scaling of frequency ===

The unexplained scaling of frequency is rather intuitive. 
Going back and forth halve the distance with the speed you get double the frequency. 
If you really want it formally then here you go: 
f = v/(constant*s) ~ v/s 
f' ~ v/s' ~ v/(s/2) ~ 2f

== From the perspective of diving down into a prospective nanofactory ==

=== Simplified nanofactory model ===

Let's for simplicity assume that the [[convergent assembly]] architecture in an advanced [[gem-gum factory]] is organized
* in simple coplanarly stacked assembly layers.
* that are each only one assembly cell in height, monolayers so to say
* that all operate at the same speed

=== Here ignored model deviations ===

There are good reasons to significantly deviate from that simple-most model. 
Especially for the lowest assembly levels. E.g.
* high energy turnover in [[mechanosynthesis]] and
* fast [[recycling]] of pre-produced [[microcomponents]] and
* high bearing area
But the focus here is on conveying a baseline understanding. 
And for assembly layers above the lowermost one(s) the simple-model above might hold quite well.

=== Same throughput of successively thinner layers ===

When going down the convergent [[assembly level]] layer stack …
* from a higher layer with bigger robotic assembly cells down
* to a the next lower layer with (much) smaller robotic assembly cells
… then one finds that the throughput capacity of both of these layers needs to be equal.
* If maximal throughput capacity would rise when going down the stack then the upper layers would form a bottleneck.
* If maximal throughput capacity would fall when going down the stack then the upper layers would be underutilized.
See main article: [[Level throughput balancing]]

The important thing to recognize here is that 
while all the mono-layers have the same maximal product throughput 
the thickness of these mono-layers becomes thinner and thinner. 
More generally the volume of these layers becomes smaller and smaller. 
'''So the throughput per volume shoots through the roof.'''

That is a very pleasant surprise! 
In a first approximation halving the size of manufacturing robotics doubles throughput capacity per volume. 
That means going down from one meter to one micrometer (a factor of a million) 
the throughput capacity per volume equally explodes a whopping millionfold. 
This is because it's a is a linear [[scaling law]].

As mentioned this can't be extended arbitrarily though. 
Below the micrometer level several effects (mentioned above) make 
full exploitation of that rise in productivity per volume impossible.

== Getting silly – questionable and unnecessary productivity levels ==

Now what if one would take a super thin microscale (possibly non-flat) assembly mono-"layer" that one finds pretty far down the convergent assembly stack and fills a whole macroscopic volume with many copies of it?

The answer is (in case of general purpose [[Nanofactory|gem-gum factories]]) that the product couldn't be removed/expulsed fast enough.
One hits [[Unsupported rotating ring speed limit|fundamental acceleration limits]] (even for the strongest available [[diamondoid metamaterial]]s) and long before that severe problems with mechanical resonances are likely to occur.

Note that the old and obsolete idea of packing a volume full with diamondoid [[molecular assembler]]s wouldn't tap into that potential because these devices
are below the microscale level in the nanoscale where the useful behavior of physics of raising throughput density with falling size of assembly machinery is hampered by other effects.

More on silly levels of throughput here: 
* [[Macroscale slowness bottleneck]]
* [[Hyper high throughput microcomponent recomposition]]

== Relation to Convergent assembly ==

[[File:Throughput_of_convergent_assembly_-_annotated.svg|200px|thumb|right|Q...throughput s...side-length f...frequency {{wikitodo|Resolve the issue with the text in this illustration!}}]]

Instead of filling the whole volume with nanomachinery which would provide waay more productivity than in allmost all conceivable circumstances needed nanofactories would use only monolayers (or thin stacks).

In a first approximation successively stacked monolayers of consecutive [[assembly levels]] (and thus vastly different sizes) match in their maximal throughput. See: [[Level throughput balancing]]

And that despite the thickness of the layers with smaller machinery being insignificant compared to the thickness of the layers above.
With the major exception of the bottommost assembly layers where things diverge notably from the first approximation.

=== Antagonistic effects/laws – sub microscale ===

The problem that emerges at the nanoscale is twofold.
* falling size => rising bearing area per volume => rising friction => to compensate: lower operation speed (and frequency) – summary: lower assembly event density in time
* falling size => rising machinery size to part size (atoms in the extreme case) – summary: lower assembly site density in space

Due to the nature of [[superlubrication|superlubricating]] friction:
* it scales with the square of speed (halving speed quaters friction losses)
* it scales linear with surface area (doubling area doubles friction)
It makes sense to slow down a bit and compensate by stacking layers for [[level throughput balancing]].
A combination of halving speed and doubling the number of stacked equal mono-"layers" halves friction while keeping throughput constant.

== Lessening the macroscale throughput bottleneck ==

There are also effects/laws (located in the macroscale) that can help increase throughput density above the first approximation.
Details on that can be found (for now) on the "[[Level throughput balancing]]" page.

== Alternate names for this scaling law as a concept ==

* Higher throughput-density of smaller machinery (more precise & more cumbersome naming)
* Higher productivity of smaller machinery (well not all stuff made may be a desirable products, pessimistic view)
* Productivity explosion (too over-hyping & unspecific)

The thing is higher throughput does not necessarily means higher productivity in the sense of generation of useful products. 
Thus the rename to the current page name "Higher throughput of smaller machinery".

== Related ==

'''[[Higher bearing area of smaller machinery]]''': 
The concern that this leads to excessive sliding friction losses 
is mended by "[[higher throughput of smaller machinery]]" implies that 
only a small very volume of nanomachinery is needed. 
----
* '''[[Friction in gem-gum-tec]]''' & [[Friction]]
----
* '''[[Math of convergent assembly]]'''
* [[Convergent assembly]]
* [[Deliberate slowdown at the lowest assembly level]] & [[Increasing bearing area to decrease friction]]
* '''[[Optimal sublayernumber for minimal friction]]'''
* [[Level throughput balancing]]
* [[Macroscale slowness bottleneck]]
* [[Low speed efficiency limit]]
* [[Atom placement frequency]] (MHz TeraCore systems as desktop devices)
----
* [[Pages with math]]
* [[Scaling law]] -- [[Scaling law#Speedup]]
----
* Harvesting the benefits of the scaling law: [[Hyper high throughput microcomponent recomposition]]
* [[High performance of gem-gum technology]]
----
* Another very important as of 2022 barely known scaling law: '''[[Same relative deflections across scales]]'''
* '''[[How macroscale style machinery at the nanoscale outperforms its native scale]]'''
* Slightly violated baseline scaling law: '''[[Same absolute speeds for smaller machinery]]'''
----
Another seemingly massively overpowered performance parameter is: 
'''Higher [[power density]] of smaller machinery.''' 
This is less of a scaling law and more of a property of [[gem-gum]] systems though {{todo|to check}}.

[[Category:Pages with math]]

== External links ==

* Video: '''[https://www.youtube.com/watch?v=kJ_K2aYaNCM&t=1555s The Surprising Productivity of Nano-Machinery]'''
* Video: [https://www.youtube.com/watch?v=_O4uoxEt47c Convergent Assembly and its effect on friction in Cog-and-Gear-style Nanomachinery – a sneak preview]

[[category:Pages with math]]
[[Category:Scaling law]]
[[Category:Surprising facts]]

Higher throughput of smaller machinery

2026-09-29T06:42:13Z

Apm: /* Related */ some reordering of links

[[File:ConvergentAssemblyThroughputScalingLaw-compressed.jpg|600px|thumb|right|Convergent assembly illustrating the scaling law '''"Higher throughput of smaller machinery"'''. '''The bottommost microscopically thin layer has the exact same throughput as the topmost macroscopic one. Thus filling the whole volume with nanomachinery would lead to exorbitant throughput and exorbitant waste heat. This is neither necessary nor desirable.''' All layers are [[Same absolute speeds for smaller machinery|operating at the exact same speed]] (not same frequency). Chosen here is a [[branching factor]] of four for illustrative purposes only. – While this is related to [[convergent assembly]] in the form of [[assembly layers]]. This specific topology and geometry does not match any concretely proposed designs. Actually (via [[exploratory engineering]]) proposed designs have significant deviations from this.]]

[[File:productive-nanosystems-video-snapshot.png|thumb|400px|'''This here is an actually proposed design''' for convergent [[assembly level]]s in the form of convergent [[assembly layer]]s. Note that the most part of the stack are the bottom nanoscale [[sub-layer]]s all of same size. Further convergent assembly in the naive form (shown in the first image on the page here) is optional (replacing product assemblers) at the top and not present here at all. – Image taken from [[Productive Nanosystems From molecules to superproducts]] video.]]

[[File:NanosystemsNotAProposedDesignConvergentAssembly.jpg|400px|thumb|right|Even more so than the naive layered stack: '''THIS IS NOT A PROPOSED DESIGN (so explicitly stated in [[Nanosystems]])'''. Just an example of a non-planar [[convergent assembly]] topology and geometry (or morphology as in biology). '''More or less planar [[assembly layers]] likely match natural scaling laws applied to the problem domain much better. But only as a baseline.''' {{wikitodo|Add Josh Halls analytic math comparison to scaling laws in bio-systems too. Plus his picture.}}]]

Video: '''[https://www.youtube.com/watch?v=kJ_K2aYaNCM "The Surprising Productivity of Nano-Machinery"]''' 
Short preview version: [https://www.youtube.com/watch?v=_O4uoxEt47c "Convergent Assembly and its effect on friction in Cog-and-Gear-style Nanomachinery"] 

When production machines are made smaller 
(but are still operated at the [[Same absolute speeds for smaller machinery|same unchanged speed]]) 
then they can produce more product per time.

* Halve sized machinery has double the throughput per volume of machinery.
* Ten times smaller machinery has ten times the throughput per volume of machinery.
* '''A million times smaller machinery has a million times the throughput per volume of machinery.''' At that point other effects become mixed in though.
In short: It is a linear [[scaling law]].

For the math behind why this scaling law applies see: 
[[Math of convergent assembly]]

== Limits ==

'''Important fact:''' 
This scaling law does not take under consideration
* the necessary ingress of resource supply and
* the necessary removal of the product

And this is ok as long as these contribute only a tiny fraction of the total friction losses 
But once transport motions become dominant in contribution of friction losses the scaling law breaks down. 
'''The bigger the [[branching factor]] B, the more there can be gained form this scaling law.'''

Concretely: '''The optimal [[sub-layer]] number where total frictionloss is mimimal is B³.''' 
Beyond that friction goes up again (eventually linearly). The scaling law breaks down. 

This happens to also be the point where assembly friction losses and transport friction losses are equal. 
For derivation of these results see page: [[Optimal sublayernumber for minimal friction]]

{{wikitodo|Make a infographic here in analogy to the one the page [[Level throughput balancing]]}}

== Some basic intuition ==

How the heck can throughput rise when the very first assumption was 
that speed of robotic manipulation will be kept constants over all size scales?!

The answer:
* [[In place assembly]] is assumed here.
* Removal of the assembled product from the manufacturing structure (the scaffold) is not included.
* This looks at assembly motions only. The necessary transport motions that emerge when nanomachinery is stacked beyond the [[macroscale slowness bottleneck]] are for now ignored. See: [[Multilayer assembly layers]] for how these motions relate to each other.

No, part removal for densely packed nanomachinery is not a problem 
in the case of basic [[gem-gum factories]] where: 
* (1) there is no densely packed nanomachinery instead a stack of one monolayer of each assembly level is the baseline design which: – makes throughput constant over all size scales (see math section below) and – makes removal of the assembled product from the manufacturing structure correspond to pusing products up in the next assembly level (where streaming further up continues)
* (2) the bottom assembly level is a thicker stack (a multilayer slab) that has much lower assembly speeds than transport speeds.

{{speculativity warning}} 
Higher degrees of filling space with nanomachinery than just thin monolayers may not be completely impossible. 
It would certainly be way beyond everyday practical. 
Transport speeds for product removal would "just" need to be faster than what is robotically possible. 
Imaginable would e.g. be a [[ultra high throughput microcomponent recomposer unit]] that is a block full of nanomachinery that has lots of straight coaxial high speed product shootout channels with [[stratified shear bearings]]. It would also need significant active cooling.

Related: [[Producer product pushapart]]

=== Visualizing the assembly speed difference by animation ===

Imagine unassembled block-fragments (color coded red) on the bottom of an robotic assembly cell 
being assembled by the robotic mechanism inside of the cell 
to one product block (color coded green) at the top of the cell.

Taking just one big macroscopic cell this process takes a while since all the parts need to travel the macroscopic distance from the bottom of the big assembly cell to the the top to turn from red to green.

When instead taking many small robotic cells (that have with their robotics inside moving with the same speed)
the distance from red to green is much shorter and thus everything turns from red (unassembled) to green (assembled) much much faster.

'''Advanced Q&A:'''

Why is the transition from red unassembled to green assembled 
in a 2D monolayer of robotic assembly cells faster than in one big cell of same 2D cross section? 
Isn't it supposed to finish in the same time if it's just a single monolayer? 

You're looking a a cross section! 
The red to green transition in a single monolayer is indeed way faster. 
But that single monolayer needs to repeat that transition many times over in order to 
make up for all the other the other layers that would be needed to completely fill up the volume of the big cell. 
In the simple model this exactly cancels out.

{{wikitodo|make (that is program) that animation – via OpenSCAD or Blender}}

== Basic math ==

(1) Take a cube with some [[macroscale style machinery at the nanoscale|robotic cog and gear assembly machinery]] of unspecified nature inside. 
(2) Replace the contents of the cube with several scaled down copies of the original cube. A whole numbered cuberoot is advantageous. 
(3) How does the throughput change in terms of how much volume can be assembled per unit of time?

Used constants:
* n = 1 ... one robotic unit in one robotic cell – this is just here to not mix it up with other dimensionless numbers
* s ... sidelength of the product blocks that the robotic unit assembles s^3 ... volume rho*s^3 ... mass
* f ... frequency of operation that is how often per unit of time a block assembly gets finished
* v ... constant speed for robotics on all size scales (crude approximation)
* Q ... throughput in terms of assembled volume per time

=== Full volume filled with robotics of original size ===

Throughput of one robotic cell: 
'''Q = (n * s^3 * f)''' 

=== Full volume filled with robotics of halve size ===

Throughput of eight robotic cells that
* are two times smaller each
* fill the same volume
* operate at the same speed:
(same speed means same magnitude of velocity not same frequency) 
'''Q° = (n' * s'^3 * f') where n' = 2^3 n and s' = s/2 and f' = 2f''' 
'''Q° = (2^3 n) * (s/2)^3 * (2f)''' 
'''Q° = 2 * (n * s^3 * f)''' 
'''Q° = 2Q'''

The ring ° could be interpreted as: 
The whole volume gets filled with smaller machinery.

=== Full volume filled with robotics of 1/10th size ===

Throughput of a thousand robotic cells that
* are ten times smaller each
* fill the same volume
* operate at the same speed:
'''Q°° = (10^3 n) * (s/10)^3 * (10f)''' 
'''Q°° = 10 * (n * s^3 * f)''' 
'''Q°° = 10Q'''

Generalization to arbitrary size steps was avoided here because 
it reduces comprehensibility.

=== One monolayer filled with robotics of 1/32th size ===

An actual practical nanofactory would (in first approximation) fill just one single monolayer.
* That means the smaller machinery matches the bigger machinery in throughput (Q' = Q).
* That is indeed done in order to match the throughput of the differently sized machiners such that they can be matchingly stacked.

Throughput of a hundred robotic cells that:
* are ten times smaller each
* fill 1/10th of same volume
* operate at the same speed:
'''Q' = (32^2 n) * (s/32)^3 * (32f)''' 
'''Q' = (n * s^3 * f)''' 
'''Q' = Q'''

The dash ' could be interpreted as: 
Only a 2D monolayer gets filled with smaller robotic cell machinery.

The size step of 32 here makes for somewhat more realistic numbers.
* This way two convergent assembly steps make a nice size step of a 1000.
* This way four convergent assembly steps make a factor of a million which bridges big nano (~32nm) to small macro (~32mm)

=== Supplemental: Scaling of frequency ===

The unexplained scaling of frequency is rather intuitive. 
Going back and forth halve the distance with the speed you get double the frequency. 
If you really want it formally then here you go: 
f = v/(constant*s) ~ v/s 
f' ~ v/s' ~ v/(s/2) ~ 2f

== From the perspective of diving down into a prospective nanofactory ==

=== Simplified nanofactory model ===

Let's for simplicity assume that the [[convergent assembly]] architecture in an advanced [[gem-gum factory]] is organized
* in simple coplanarly stacked assembly layers.
* that are each only one assembly cell in height, monolayers so to say
* that all operate at the same speed

=== Here ignored model deviations ===

There are good reasons to significantly deviate from that simple-most model. 
Especially for the lowest assembly levels. E.g.
* high energy turnover in [[mechanosynthesis]] and
* fast [[recycling]] of pre-produced [[microcomponents]] and
* high bearing area
But the focus here is on conveying a baseline understanding. 
And for assembly layers above the lowermost one(s) the simple-model above might hold quite well.

=== Same throughput of successively thinner layers ===

When going down the convergent [[assembly level]] layer stack …
* from a higher layer with bigger robotic assembly cells down
* to a the next lower layer with (much) smaller robotic assembly cells
… then one finds that the throughput capacity of both of these layers needs to be equal.
* If maximal throughput capacity would rise when going down the stack then the upper layers would form a bottleneck.
* If maximal throughput capacity would fall when going down the stack then the upper layers would be underutilized.
See main article: [[Level throughput balancing]]

The important thing to recognize here is that 
while all the mono-layers have the same maximal product throughput 
the thickness of these mono-layers becomes thinner and thinner. 
More generally the volume of these layers becomes smaller and smaller. 
'''So the throughput per volume shoots through the roof.'''

That is a very pleasant surprise! 
In a first approximation halving the size of manufacturing robotics doubles throughput capacity per volume. 
That means going down from one meter to one micrometer (a factor of a million) 
the throughput capacity per volume equally explodes a whopping millionfold. 
This is because it's a is a linear [[scaling law]].

As mentioned this can't be extended arbitrarily though. 
Below the micrometer level several effects (mentioned above) make 
full exploitation of that rise in productivity per volume impossible.

== Getting silly – questionable and unnecessary productivity levels ==

Now what if one would take a super thin microscale (possibly non-flat) assembly mono-"layer" that one finds pretty far down the convergent assembly stack and fills a whole macroscopic volume with many copies of it?

The answer is (in case of general purpose [[Nanofactory|gem-gum factories]]) that the product couldn't be removed/expulsed fast enough.
One hits [[Unsupported rotating ring speed limit|fundamental acceleration limits]] (even for the strongest available [[diamondoid metamaterial]]s) and long before that severe problems with mechanical resonances are likely to occur.

Note that the old and obsolete idea of packing a volume full with diamondoid [[molecular assembler]]s wouldn't tap into that potential because these devices
are below the microscale level in the nanoscale where the useful behavior of physics of raising throughput density with falling size of assembly machinery is hampered by other effects.

More on silly levels of throughput here: 
* [[Macroscale slowness bottleneck]]
* [[Hyper high throughput microcomponent recomposition]]

== Relation to Convergent assembly ==

[[File:Throughput_of_convergent_assembly_-_annotated.svg|200px|thumb|right|Q...throughput s...side-length f...frequency {{wikitodo|Resolve the issue with the text in this illustration!}}]]

Instead of filling the whole volume with nanomachinery which would provide waay more productivity than in allmost all conceivable circumstances needed nanofactories would use only monolayers (or thin stacks).

In a first approximation successively stacked monolayers of consecutive [[assembly levels]] (and thus vastly different sizes) match in their maximal throughput. See: [[Level throughput balancing]]

And that despite the thickness of the layers with smaller machinery being insignificant compared to the thickness of the layers above.
With the major exception of the bottommost assembly layers where things diverge notably from the first approximation.

=== Antagonistic effects/laws – sub microscale ===

The problem that emerges at the nanoscale is twofold.
* falling size => rising bearing area per volume => rising friction => to compensate: lower operation speed (and frequency) – summary: lower assembly event density in time
* falling size => rising machinery size to part size (atoms in the extreme case) – summary: lower assembly site density in space

Due to the nature of [[superlubrication|superlubricating]] friction:
* it scales with the square of speed (halving speed quaters friction losses)
* it scales linear with surface area (doubling area doubles friction)
It makes sense to slow down a bit and compensate by stacking layers for [[level throughput balancing]].
A combination of halving speed and doubling the number of stacked equal mono-"layers" halves friction while keeping throughput constant.

== Lessening the macroscale throughput bottleneck ==

There are also effects/laws (located in the macroscale) that can help increase throughput density above the first approximation.
Details on that can be found (for now) on the "[[Level throughput balancing]]" page.

== Alternate names for this scaling law as a concept ==

* Higher throughput-density of smaller machinery (more precise & more cumbersome naming)
* Higher productivity of smaller machinery (well not all stuff made may be a desirable products, pessimistic view)
* Productivity explosion (too over-hyping & unspecific)

The thing is higher throughput does not necessarily means higher productivity in the sense of generation of useful products. 
Thus the rename to the current page name "Higher throughput of smaller machinery".

== Related ==

[[Higher bearing area of smaller machinery]]: 
The concern that this leads to excessive sliding friction losses 
is mended by "[[higher throughput of smaller machinery]]" implies that 
only a small very volume of nanomachinery is needed. 
----
* '''[[Friction in gem-gum-tec]]''' & [[Friction]]
----
* '''[[Math of convergent assembly]]'''
* [[Convergent assembly]]
* [[Deliberate slowdown at the lowest assembly level]] & [[Increasing bearing area to decrease friction]]
* '''[[Optimal sublayernumber for minimal friction]]'''
* [[Level throughput balancing]]
* [[Macroscale slowness bottleneck]]
* [[Low speed efficiency limit]]
* [[Atom placement frequency]] (MHz TeraCore systems as desktop devices)
----
* [[Pages with math]]
* [[Scaling law]] -- [[Scaling law#Speedup]]
----
* Harvesting the benefits of the scaling law: [[Hyper high throughput microcomponent recomposition]]
* [[High performance of gem-gum technology]]
----
* Another very important as of 2022 barely known scaling law: '''[[Same relative deflections across scales]]'''
* '''[[How macroscale style machinery at the nanoscale outperforms its native scale]]'''
* Slightly violated baseline scaling law: '''[[Same absolute speeds for smaller machinery]]'''
----
Another seemingly massively overpowered performance parameter is: 
'''Higher [[power density]] of smaller machinery.''' 
This is less of a scaling law and more of a property of [[gem-gum]] systems though {{todo|to check}}.

[[Category:Pages with math]]

== External links ==

* Video: '''[https://www.youtube.com/watch?v=kJ_K2aYaNCM&t=1555s The Surprising Productivity of Nano-Machinery]'''
* Video: [https://www.youtube.com/watch?v=_O4uoxEt47c Convergent Assembly and its effect on friction in Cog-and-Gear-style Nanomachinery – a sneak preview]

[[category:Pages with math]]
[[Category:Scaling law]]
[[Category:Surprising facts]]