Exploring Randomness
by Gregory Chaitin,
Springer-Verlag, £24.50,
ISBN 1852334177
AT THE heart of pure mathematics, maintains Gregory Chaitin, is total unadulterated randomness. This has profound implications not only for mathematics, but for physics as well. So, who is Chaitin? Now an IBM mathematician, he invented algorithmic information theory as a teenager and discovered "Omega", a totally unknowable, totally random number. Not only can there never be a theory of everything in mathematics, he concludes, but because mathematics is the language of physics, there can never be a theory of everything in physics either.
This is revolutionary, explosive stuff. And if you've got the stomach for it, you can read all about it in Exploring Randomness, the sequel to Chaitin's equally mind-expanding The Unknowable (Springer-Verlag, 1999).
But be warned---this isn't an easy read: the book is filled with exercises to do. They range from the "mathematical equivalent of finger warm-ups for pianists" to substantial programming projects, from questions Chaitin can formulate precisely, but not answer, to questions he cannot even formulate.
Chaitin challenges readers to follow his lead and forge their own path into the black hole of randomness, the "darkness at the edge of mathematics". When Chaitin wrote "explore", he well and truly meant it.
An exhilarating, mind-blowing book from one of the great ideas men of mathematics and computer science.