Evolution of Regularites?

How do mathematical patterns evolve in nature? Is it anything like animal evolution — the result of chance varieties coalescing until some “species” become more prominent? Why are certain shapes and ratios taken repeatedly, over others?

For example:

"…many networks are found to contain a small but significant number of "hubs" — vertices with an unusually high degree."
- from Networks: An Introduction

It seems obvious and “natural” in that it makes sense to us, but why should it be the case?




{ camerxn }:

This question stumped me, but I’ll give it a try :) Perhaps the evolution of mathematical patterns happens alongside the evolution of other systems in nature. Our recognition of mathematical patterns may be evidence of where that system currently is in its evolution.

A question I have is would it be possible to determine levels of fitness from mathematical patterns of a given system?

OS re: camerxn :

The two statements that I set in bold are essentially the questions I’m asking as well, although yours are perhaps more clearly stated.

For the second, I would think it would be, right? “Fitness” would likely be determined in terms of the physics of our universe — the laws set forth during the initial conditions of this place, if it happened that way. (Although, those laws themselves can be counted as emergent patterns, also.) Everything else follows according to what works best with those laws, and things that don’t work so well don’t “survive” — I’d imagine they end up “breaking down”, or being unable to complete formation in the first place due to some physical/mathematical disagreements.

Actually this reminds me of the { Rule 30 }, wherein you have an initial condition and a set of rules determined by a system (the programmer) which result in something that appears random (but is actually pseudorandom due to the deterministic programming in the beginning) and contains repeating similarities.

{ memeengine } said:

I suspect some number of hubs might minimize distance between two random nodes… both neural networks, and human-designed networks are subject to survival of the fittest. Hmmmm

OS re: memeengine :

Yes, likely. That idea about the hubs is something that makes sense for us. But I’m wondering how things got to a place where that is a sensible thing to happen. A loaded question obviously :/ , maybe won’t be truly answerable for some time. But definitely, a beginning lies in the evolution of systems…

I wonder if you could share some knowledge/examples of survival in neural and human networks? Message, or post — I’ll reblog or add it here?