lunes, junio 23, 2008

Why an universe with life needs the Ockham Razor

Yesterday I found a very interesting weblog Apperceptual, about philosophy of science, evolution, algoritmic complexity and so on.

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.
This is a cross-cut, in the fitness landscape around a local maximum; To this maximum converges different lines of evolution trough natural selection, because more appropiate combinations of parameters gives more fitness, more offspring that continues the tendency to climb to te maximum. We see two of such lines in this crosscut.

It can be demonstrated that every small change in the parameter values towards tha optimum value must correspond with an increase of fitness for the evolution to progress towards the maximum. That is , the first derivative of the curve must be positive when ascending from the left side. There can be relatively big or small changes in fitness for a small change, but the fitness change must grow towards the maximum. otherwise, the evolution will stop at every local maximum it encounters (for example, A). Suboptimal mutations can move down from a local maximum A to the bottom of the valley so that the offspring of the apparently less adapted living being can start to climb towards a higuer maximum B than A. However, a landscape plagued with similar local maximums will make evolution towards higuer maximums very difficult.

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.

The shape of the fitness landscape is closely related with the laws of phisics. For example, there is la lineal, non chaotic relationship between the lengt of the leg of anthelope and the maximum speed that he can achive with other parameters staying constant. This is because the laws of forces, both for lineal and circular movements are constants. The relation between force and acceleration, the relation bettween angular momentum and angular acceleration are expressed in simple lineal functions that are analitically continuous. Because this lineality, the muscular and nervous system must not be complex in order to control for more or less velocity. Simple systems are more easily "discoverable" by natural selection.

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.

To sumarize:

-Complicated laws produce complicated phenomena

-In some cases, linear laws produce linear environments (with smooth fitness landscapes) where life can evolve.

These are the strong points in my argumentation.

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.

My arguments advocate for continuity and simplicity applied to the phisical laws relevant for the living beings. This is not the case of the extreme small and the extreme big.(In this case the Ockham razor should not apply for these strange cases, according with my congecture).

For example if a world like ours to exist, it is necessary the quantization of energy, plus fermionic particles. Without these ingredients, atoms would inmediatelly collapse if the classical macroscopic laws were also valid for the subatomic scales. The only kind of matter existent would have been black holes!.
A quantization of energy in the microscopic world is necessary for the existence of the atoms, chemistry, organic chemistry and life.

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.

4 comentarios:

fersonio dijo...

congratulations for the page!!!

Kevembuangga dijo...

I found a very interesting weblog Apperceptual

The topics are interesting, the author is not, you will find out after a while.
I stopped commenting on this blog, too much pedantic nitpicking and the nasty habit of editing the comments for silly details like line breaks and commas (!)

Turney's response to your last comment which is supposed to dismiss "continuity":
Space is divided into Planck lengths and time is divided into chronons.
Is typical of his kind of misunderstandings and "rigid thinking", space is not "divided into Planck lengths" the very idea of atoms or "grains" of anything is elusive and a projection of our perceptions in a macroscopic world.
On the very contrary quantum mechanics explains the emergence of discontinuity from the continuous, this is very well elucidated in paper by Christoph Schiller which formerly appeared in a French book but is now at arXiv: Does matter differ from vacuum?.

Memetic Warrior dijo...

Yes he misunderstand the quantum concept.

In fact I answered his last reply lately yesterday. I´m waiting for my last answer to appear.

I basically said that a quantization of energy in the macroscopic world is necessary for the existence of the atoms, chemistry, organic chemistry and life. I also said that my arguments advocate for continuity and simplicity applied to the phisical laws relevant for the living beings. This is not the case of the extreme small and the extreme big.(In this case the Ockham razor does not apply fot these cases)

Ministro Iñigo dijo...

Parece interesante, lastima que mi ingles no sea lo suficientemente bueno como para entenderlo como es debido.