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The Unkowable by Gregory Chaitin [Mar. 25th, 2006|06:07 pm]
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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 unself-serving, 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 self-elevation 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 self-billing :)
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