[[[Former Title: Mathematics and Biology]]]

Mathematics, Biology and Metabiology

G. J. Chaitin, IBM Research
[gjchaitin_at_gmail.com]

In Memoriam Jacob T. "Jack" Schwartz (1930-2009)

[Lecture given at the Facultad de Ciencias Exactas of the University of Buenos Aires, 14 May 2009,
at the IBM T. J. Watson Research Center, Yorktown Heights, 5 June 2009,
and at the Frege Centre for Structural Sciences of the University of Jena, 20 June 2009.
The author thanks Veronica Becher, Pablo Jacovkis, Gustavo Stolovitzky, Olaf Dreyer, Robert Berwick,
David B. Searls, and other members of the Buenos Aires, IBM and Jena audiences for their helpful comments.]

Abstract

It would be nice to have a mathematical understanding of basic biological concepts
and to be able to prove that life must evolve in very general circumstances.
At present we are far from being able to do this.
But I'll discuss some partial steps in this direction
plus what I regard as a possible future line of attack.

Introduction: Goals of Our Theory

The Nature of Biological Information

The Halting Probability Ω has infinite irreducible complexity
and is the DNA of pure math, and shows that pure math is infinitely complex
and is therefore closer to biology than to theoretical physics.

DNA as Digital Software (Jack!), Software Organisms

When I visited Jack at the Cold Spring Harbor Laboratory where he was working on molecular biology,
he emphasized to me that I should just think of DNA as digital software.

Let's take this idea and run with it: How about modeling organisms as digital software?
How about studying random walks in software space?

Two important places where thinking of organisms as digital software is helpful:

A Toy Model of Evolution:
Evolution of Mutating Software

What Next? The Following Analogy U is to V as X is to Y:

Summary: What Does this Analogy Buy Us?

Conclusion

Note

[Our random walk model was inspired by the stimulating critique of Darwinian evolution in
D. Berlinski, The Devil's Delusion, Crown Forum, New York, 2008. See especially pp. 192-195.
In a nutshell, model = Jack (digital software) + Berlinski (random walk) + Busy Beaver Problem.
Our model is an attempt to answer Berlinski's criticisms.]

 

[19 July 2009]