Difference between revisions of "The limits and guesses in math"

From apm
Jump to: navigation, search
(→‎Related: added some related points - move some to other topics?)
m (minor edit as math not necessarily counts as science)
 
(6 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
{{stub}}
 
{{stub}}
 
{{speculative}}
 
{{speculative}}
−
  math is not an exact science
+
  Even math is not achieving absolute truth.
−
  the necessity of faith in Axioms outside the proof system
+
  There is no way around faith in at least a few axioms outside the proof system.
  
−
Does a number which is not representable by the means that our universe provide ([[big bang as spontaneous demixing event|amount of demixing in the big bang]]) us even exist?
+
Disclamer #1:
−
Ridiculously large numbers can easily be represented by simple compression methods e.g. the ackermann function but between those numbers there are gaping holes of unrepresentability.
+
* Math is the best and most formal system we have and (as it very much looks) the best and most formal system we will ever have
−
While we don't know  which of the ridiculously big numbers we can represent in a smaller compressed form we can be certain that there are unaccountably many more which certainly can't be represent within the limits of our universe.
+
* This page is not meant to undermine the faith in math and science.
 +
Disclaimer #2:
 +
* All "certainties" in this article (and anywhere else in this universe) are in the very end only certainties to the degree of practicability from experience.
  
−
Disclaimer: All "certainties" in this article (and anywhere else in this universe) are only certainties to the degree of practicability from experience.
+
== About realizing the unprovability of fundamental axioms ==
 +
 
 +
Here's a way how one could maybe question one of the most fundamental axioms of math:  
 +
That every natural number has an successor.
 +
 
 +
Does a number which is not representable by the means that our universe provide ([[big bang as spontaneous demixing event|amount of demixing in the big bang]]) even exist?
 +
Ridiculously large numbers can easily be represented by simple compression methods (e.g. the Ackermann-function) but between those numbers there are gaping holes of unrepresentability.
 +
While we don't know  which of the ridiculously big numbers we can represent in a smaller compressed form we can be certain that there are many more which certainly can't be represent within the limits of our universe.
  
 
== Related ==
 
== Related ==
Line 20: Line 29:
 
* beauty as scale variant inhomogeneous anisotropic structures on all scales
 
* beauty as scale variant inhomogeneous anisotropic structures on all scales
 
* Helmholz free energy {{WikipediaLink|https://en.wikipedia.org/wiki/Helmholtz_free_energy}}
 
* Helmholz free energy {{WikipediaLink|https://en.wikipedia.org/wiki/Helmholtz_free_energy}}
 +
* [[A true but useless theory of everything]]
 +
* [[Foundations of mathematics]]
 +
* [[Philosophical topics]]
  
 
[[Category:Philosophical]]
 
[[Category:Philosophical]]
 +
 +
== External links ==
 +
 +
* Youtube: [https://www.youtube.com/watch?v=HeQX2HjkcNo This is Math's Fatal Flaw] – by Veritasium – 2021-05-22

Latest revision as of 19:23, 11 February 2024

This article is a stub. It needs to be expanded.
This article is speculative. It covers topics that are not straightforwardly derivable from current knowledge. Take it with a grain of salt. See: "exploratory engineering" for what can be predicted and what not. 
Even math is not achieving absolute truth.
There is no way around faith in at least a few axioms outside the proof system.

Disclamer #1:

  • Math is the best and most formal system we have and (as it very much looks) the best and most formal system we will ever have
  • This page is not meant to undermine the faith in math and science.

Disclaimer #2:

  • All "certainties" in this article (and anywhere else in this universe) are in the very end only certainties to the degree of practicability from experience.

About realizing the unprovability of fundamental axioms

Here's a way how one could maybe question one of the most fundamental axioms of math: That every natural number has an successor.

Does a number which is not representable by the means that our universe provide (amount of demixing in the big bang) even exist? Ridiculously large numbers can easily be represented by simple compression methods (e.g. the Ackermann-function) but between those numbers there are gaping holes of unrepresentability. While we don't know which of the ridiculously big numbers we can represent in a smaller compressed form we can be certain that there are many more which certainly can't be represent within the limits of our universe.

Related

External links

Retrieved from "http://apm.bplaced.net/w/index.php?title=The_limits_and_guesses_in_math&oldid=16068"