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.

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.