The Unknowable

by Gregory Chaitin

This essential companion volume to Chaitin's highly successful "The Limits of Mathematics", also published by Springer, gives a brilliant historical survey of the work of this century on the foundations of mathematics, in which the author was a major participant. The Unknowable is a very readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programming language used by Chaitin in both volumes. It will enable computer users to interact with the author's proofs and discover for themselves how they work. The software for The Unknowable can be downloaded from the author's Web site.

Genres: Mathematics

133 pages, Hardcover

First published August 5, 1999

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

[M. W. · Rating 5 out of 5]

I will be reading this book for the rest of my life......or until the theory explained becomes a practical reality. If you're a Computer Science nut....add this to your library. Do it now!

[Aritra Sarkar · Rating 4 out of 5]

Overall a much lighter introduction to meta-mathematics. The LISP expressions really drive home the ideas (at least for me, as a computer scientist). It does not require much background and is self-contained. The only thing I dislike is the author's tone when it comes to comparing his work with his contemporaries.

[Mark · Rating 4 out of 5]

Enjoyable, though a bit vague. A little bit too much talk about himself.

[Gavin · Rating 4 out of 5]

Incredibly clear and deep but marred by his constant self-promotion. It's like a cheap ad, but written by god

[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.

[Nick Black]

Amazon, third party, 2009-05-23. Got it at an absolutely reasonable price, perhaps a result of rather vicious customer reviews? Chaitin's a Top 10 badass for sure and I look forward to reading this one.