Meta Math!: The Quest for Omega (Peter N. Nevraumont Books)
Gregory Chaitin, one of the world’s foremost mathematicians, leads us on a spellbinding journey, illuminating the process by which he arrived at his groundbreaking theory.
Chaitin’s revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what we can ultimately know about the univer
At first glance, this seems just a technical tidbit with limited applicability, and of interest only to computer sciences practitioners. In reality the extraordinary features of such number, in conjunction with the important fin ...more
Chaitin takes every opportunity to remind ...more
Given the set of all possible computer programs you select one at random (p) and run it on a specific computer. Each time the computer requests the next bit of the program, you flip a fair coin to generate it. The computer then must decide by itself when to stop reading the program. You sum for each program that ...more
Chaitin tries to make a careful argument many times about his subject, but it's difficult because he wastes no words in constructing the bits of reasoning he lays out for us. He nearly takes an interdisciplinary approach in order to approach the same structure from more than one point of view -- and I find it to be successful. I ...more
L'autore fa diverse dimos ...more
But having said that, ...more
The text of the first part of the book was often tedious, but I was enthralled with the appendices. They described the fascinating philosophy of mathematics, enthusiasms my husband had oft ...more
Omega is the probability that a random program halts. No more than a finite number of bits of omega can be calculated by a formal system. And so most bits of omega are unprovable theorems. Omega is as close to random as math gets.
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