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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

Chaitin e-book online

Meta Math! The Quest for Omega

http://www.cs.umaine.edu/~chaitin/omega.html

Abstract - Gregory Chaitin has devoted his life to the attempt to understand what mathematics can and cannot achieve, and is a member of the digital philosophy/digital physics movement. Its members believe that the world is built out of digital information, out of 0 and 1 bits, and they view the universe as a giant information-processing machine, a giant digital computer. In this book on the history of ideas, Chaitin traces digital philosophy back to the nearly-forgotten 17th century genius Leibniz. He also tells us how he discovered the celebrated Omega number, which marks the current boundary of what mathematics can achieve. This book is an opportunity to get inside the head of a creative mathematician and see what makes him tick, and opens a window for its readers onto a glittering world of high-altitude thought that few intellectual mountain climbers can ever glimpse.

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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

My review - This is a fun book about standard Chaitin subjects
dealing with higher cardinals and complexity. While it continues to have some of the limits of his previous algorithmic complexity theory, he is taking some pains to adjust his arguments to NKS. He does not pretend to fully understand NKS or what it is driving at. What he does do is provide a kind of indirect support for a version of Church's thesis, in a paradoxical way. He thinks constructables and computables are a tiny special subset of reals, but that the infinite sea of reals beyond them is largely a mathematical fiction of our own and must always remain so. He drives at this with theorems like "almost all reals are unnamable".
He wants to make the idea of any physical reality for continuum infinity reals daunting. It is definitely relevant to NKS subjects although it contains no NKS work proper. It does contain references to NKS, not fully digested it in my opinion, but aware of its arguments and convinced of its importance.

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