Exploring Randomness

by Gregory Chaitin

This essential companion to Chaitin's successful books The Unknowable and The Limits of Mathematics, presents the technical core of his theory of program-size complexity. The two previous volumes are more concerned with applications to meta-mathematics. LISP is used to present the key algorithms and to enable computer users to interact with the authors proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter. "No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. This book tells you everything hes seen. Don miss it." John Casti, Santa Fe Institute, Author of Goedel: A Life of Logic.'

Genres: Mathematics

174 pages, Hardcover

First published January 25, 2001

About the author

Gregory Chaitin is widely known for his work on metamathematics and for his discovery of the celebrated Omega number, which proved the fundamental unknowability of math. He is the author of many books on mathematics, including Meta Math! The Quest for Omega. Proving Darwin is his first book on biology. Chaitin was for many years at the IBM Watson Research Center in New York. The research described in this book was carried out at the Federal University of Rio de Janeiro in Brazil, where Chaitin is now a professor. An Argentine-American, he is an honorary professor at the University of Buenos Aires and has an honorary doctorate from the National University of Cordoba, the oldest university in Argentina.

Reviews

[Mark · Rating 4 out of 5]

This was ok. A bit too much transcribed talks pasted together. Chaitin suffers from not being able to explain himself very well. I am hoping that Calude's book does a better job.

[David · Rating 4 out of 5]

I normally don’t do this, but I’m going to copy/paste this review across three separate books: Chaitin’s “The Unknowable”, “The Limits of Mathematics”, and “Exploring Randomness”.

All three are all thin, overpriced, but very approachable books on Algorithmic Information Theory. Themes include:

- Undecidability, as the basis of formulating a new kind of randomness measure for numbers that have already been generated (not just restricting randomness measures to the processes that generate numbers).

- Chaitin’s Omega constant, which is the probability that universal Turning machine will halt on random input. This constant is “maximally unknowable”, but that doesn’t stop one from performing math with it.

- Philosophy surrounding these topics.

One might underestimate Kolmogorov’s contributions, given how ridiculously self-promoting Chaitin has been with this AIT. However, the topics are interesting enough that he’s easy to forgive. And he uses many code demonstrations (LISP) to make concrete examples out of the math.