To a mathematical theory of evolution and biological creativity
Gregory Chaitin
Draft August 18, 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 possible organisms consists of computer programs, which are subjected to random mutations. We study the random walk of increasing fi tness made by a single mutating organism. In two dif erent models we are able to show that evolution will occur and to characterize the rate of evolutionary progress, i.e., the rate of biological creativity.
Key words and phrases: metabiology, evolution of mutating software, random walks in software space, algorithmic information theory
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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. This is the fourth paper in a series [1, 2, 3] attempting to create such a theory.
In a previous paper [1] we did not yet have a workable mathematical framework: 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 mathematical 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
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Chaitin is emeritus researcher at the IBM Watson Research Center, an honorary professor at the University of Buenos Aires, and a member of the Acad emie Internationale de Philosophie
des Sciences. His email address is gjchaitin@gmail.com
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NOTA DESTE BLOGGER:
Na seção 5 Chaitin aborda o design inteligente através de um teorema: Model A (Naming Integers) Intelligent Design.
Não sei não, mas logo a Nomenklatura científica vai cair de pau em cima do Chaitin. Esses matemáticos não tem jeito, não é mesmo Marcel-Paul Schutzenberger?
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