The Unkowable by Gregory Chaitin 
[Mar. 25th, 200606:07 pm]

There is something about the endeavour we call science that has made us come to expect a fair degree of humility from its practitioners. As Carl Sagan says in The Demon Haunted World, The opening words of Albert Einstein's 1905 paper are characteristic of the scientific report. It is refreshingly unselfserving, circumspect, understated. Contrast its restrained tone with, say, the products of modern advertising, political speeches, authoritative theological pronouncements  or for that matter the blurb on the cover of this book So it is particularly jarring one sees a sentence like the following in the preface of a book: In a nutshell, Godel discovered incompleteness, Turing discovered uncomputability, and I discovered randomness. Really.
While such gratuitous selfelevation to immortal genius is difficult to swallow, the book in which that sentence appears, The Unknowable, is indeed a pretty good book. There are three chapters that the legendary 'interested intelligent layman' would find very stimulating. These chapters touch upon (a) Events in the field of mathematical logic at the turn of the 20th century, including Hilbert's famous formal system program and the lead up to the work of Godel and turing, (b) Turing's work on uncomputability and a 'proof' of the undecidability of the Halting Problem, and (c) Godel's work on incompleteness, including a 'proof'. There are other chapters that are support chapters on Lisp, and some others which are plugs to the authors own work on randomness. Overall worth a read, if you are into this kind of a thing. Just keep an open mind on the question of whether Gregory J. Chaitin, is really worth his selfbilling :) 

