文档介绍：To a mathematical theory of evolution
and biological creativity
Gregory Chaitin∗
Draft September 29, 2010
Abstract
We present an information-theoretic analysis of Darwin’s theory of
evolution, modeled as a hill-climbing algorithm on a fitness landscape.
Our space of anisms consists puter programs, which
are subjected to random mutations. We study the random walk of in-
creasing fitness made by a single anism. In two different
models we are able to show that evolution will occur and to characterize
the rate of evolutionary progress, ., the rate of biological creativity.
Key words and phrases: metabiology, evolution of mutating software,
random walks in software space, algorithmic information theory
1 Introduction
For many years we have been disturbed by the fact that there is no fundamental
mathematical theory inspired by Darwin’s theory of evolution [1, 2, 3, 4, 5, 6,
7, 8, 9]. This is the fourth paper in a series [10, 11, 12] attempting to create
such a theory.
In a previous paper [10] we did not yet have a workable mathematical frame-
work: We were able to prove two not very impressive theorems, and then the
way forward was blocked. Now we have what appears to be a good mathemat-
ical framework, and have been able to prove a number of theorems. Things
are starting to work, things are starting to get interesting, and there are many
technical questions, many open problems, to work on.
So this is a working paper, a progress report, intended to promote interest
in the field and get others to participate in the research. There is much to be
done.
In order to present the ideas as clearly as possible and not get bogged down
in technical details, the material is presented more like a physics paper than a
math paper. Estimates are at times rather sloppy. We are trying to get an idea
of what is going on. The arguments concerning the basic math framework are
however very precise; that part is done more or less like a math paper.