Chaitin Proving Darwin
Posted by jgrant, 2011-06-16 15:26:56
White paper : To a mathematical theory of evolution and biological creativity
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 in-creasing fitness made by a single mutating organism. In two different 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
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 attempting to create such a theory.
In a previous paper 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 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.
