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.*