Daily Archives: Monday, June 12, 2017

Is there a mathematical theory of evolution?

Introduction to Evolutionary InformaticsAn article about a book titled Introduction to Evolutionary Informatics starts out like this:

Five years ago, Gregory Chaitin, a co-founder of the fascinating and mind-bending field of algorithmic information theory, offered a challenge:

The honor of mathematics requires us to come up with a mathematical theory of evolution and either prove that Darwin was wrong or right!

In Introduction to Evolutionary Informatics, co-authored by William A. Dembski, Winston Ewert, and myself, we answer Chaitin’s challenge in the negative: There exists no model successfully describing undirected Darwinian evolution. Period. By “model,” we mean definitive simulations or foundational mathematics required of a hard science.

The article is very interesting in its own right, but I am also looking forward to reading the book. I am sure the whole book is worth a read, but my interest got piqued in particular by a some statements in the article about the measurement of meaning in information:

8. Information theory cannot measure meaning.

Poppycock.

The manner in which information theory can be used to measure meaning is addressed in Introduction to Evolutionary Informatics. We explain, for example, why a picture of Mount Rushmore containing images of four United States presidents has more meaning to you than a picture of Mount Fuji even though both pictures might require the same number of bits when stored on your hard drive. The degree of meaning can be measured using a metric called algorithmic specified complexity.

Rather than summarize algorithmic specified complexity derived and applied in Introduction to Evolutionary Informatics, we refer instead to a quote from a paper from one of the world’s leading experts in algorithmic information theory, Paul Vitányi. The quote is from a paper he wrote over 15 years ago, titled “Meaningful Information.”22

One can divide…[KCS] information into two parts: the information accounting for the useful regularity [meaningful information] present in the object and the information accounting for the remaining accidental [meaningless] information.23

In Introduction to Evolutionary Informatics, we use information theory to measure meaningful information and show there exists no model successfully describing undirected Darwinian evolution.