# Randomness, Structure and Causality - Agenda

## Abstracts

To a Mathematical Theory of Evolution and Biological Creativity
Chaitin, Gregory (gjchaitin@gmail.com)
IBM Watson Research Center
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 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.

The Vocabulary of Grammar-Based Codes and the Logical Consistency of Texts

Debowski, Lukasz (ldebowsk@ipipan.waw.pl)
We will present a new explanation for the distribution of words in natural language which is grounded in information theory and inspired by recent research in excess entropy. Namely, we will demonstrate a theorem with the following informal statement: If a text of length ${\displaystyle n}$ describes ${\displaystyle n^{\beta }}$ independent facts in a repetitive way then the text contains at least ${\displaystyle n^{\beta }/\log n}$ different words.  In the formal statement, two modeling postulates are adopted. Firstly, the words are understood as nonterminal symbols of the shortest grammar-based encoding of the text. Secondly, the text is assumed to be emitted by a finite-energy strongly nonergodic source whereas the facts are binary IID variables predictable in a shift-invariant way. Besides the theorem, we will exhibit a few stochastic processes to which this and similar statements can be related.