Mathematical Software - ICMS 2006: Second International Congress on Mathematical Software, Castro Urdiales, Spain, September 1-3, 2006, Proceedings Book

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.