One of the post is about Ockham Razor and genetic algoritms for machine learning (Ockham versus Darwin). Eventually, I was writing something about the implications of darwinian evolution and the mathemathical simplicity of the world, that makes the Ockham razor so sucessful: Among two theories that explain the same phenomena, choose the simplest one
Why? Why the word has such bias? I think that I have an answer:
I´m interested both in machine learning trough genetic algoritms and in the reason why the reality appears to adopt the most simple mathematical law among the ones compatible whith the dat facts.
My conjecture link both aspects : By the anthropic principle and the multiverse hypotesis, It appears that the universe in which we live is the most simple possible because for biological organism to "learn" instictivelely trough variation and selectión (and , thus, to learn the world trough genetic algoritms), it is a requisite that the fitness landscape, the world, must obey simple, lineal and, smoth laws at the macroscopic scale most of the time for most of the environments.
A more complex universe may need much more time for life to evolve, and this time could be more that the life span of the entire universe.
Chaotic and non lineal phenomena must be marginal effects of underliying microscopic lineal laws that also describe the rest of the world. (for example a local turbulence of the water obey the same simple hidrodinamic laws that a laminar flow)
This conjecture simply says that, among the universes complex enough, the simplest ones are more probable to harbor complex life.
A more rigurous explanation in mathematical and phisical terms need to introduce the concept of fitness landscape
A fitness landscape (FL) is a N-dimensional surface, each coordinate contains one parameter that defines an living being. One parameter could be le length of the legs, another could be the mean intake of food of this animal and so on. The vertical axis is the fitness of this combination of parameters. Along the surface, certaing combinations of parameters produce more fitness that others.
The FL uses to be represented as a two dimensional surface, but the real FL includes all the relevant paramenters. Don´t get overhemled by the complexity of this. Just let´s mentally take two of the N paramenters (a projection on two axis). For every two arbitrary parameters, there must be a two dimensional surface like the one in the figure.
Natural selection by definition, try to find more optimal design starting from less optimal ones. By definition, the combination of animal parameters will describe, trough evolution time, generation to generation, a line in the fitness landscape that goes from less to more values of fitness.
The worst case is a random fitness landscape where peaks and valleys are close together. There is no defined direction of evolution in this case. Selection can not work.
Moreover, as I said before, selection operates better with simple laws because non complex curves with a lot of local maximums impede a rapid progress towards higuer maximums. If , for example, laws of circular momentum were non lineal perhaps for legs of 25, 50 and 60 cm would have had local maximums. This would impede a rapid progress towards the global maximum of 1,30 m for example. Fractal or chaotic relationships betweeen phisical parameters would make evolution impossible, because the fitness landscape would be random. No life could evolve in such universe.
-In some cases, linear laws produce linear environments (with smooth fitness landscapes) where life can evolve.
it follows that we must live in a certain universe where macroscopic phenomena must obey smooth, continuous, and parsimonious laws for the fitness landscape to be that way; that is, to permit life.
It is our universe, the thing that has been selected for life, just because it is simple. Therefore we, living beings, succeed when we try to explain real phenomena through smooth, simple, continuous, and parsimonious laws with little assumptions (some of them, that does not work always). Our universe has the bias (at least withing the limits of sizes, energies and so on withing which life evolve). It is not by chance. Other universes have not such bias, but they are empty of observers. The so called kolmogorov complexity of the everyday world is a minimum.
it seems like our ordinary environment is an oasis of simplicity for which the more complicated laws of the very small and the very big conspirates to produce indeed.