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by Gregory J. Chaitin
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This essential companion volume to Chaitin's highly successful "The Limits of Mathematics", also published by Springer, gives a brilliant historical survey of the work of this century on the foundations of mathematics, in which the author was a major participant. The Unknowable is a very readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programming language used by Chaitin in both volumes. It will enable computer users to interact with the author's proofs and discover for themselves how they work. The software for The Unknowable can be downloaded from the author's Web site.
The author discusses his discovery of mathematical randomness as it is compared to Godel's discovery of incompleteness, and Turing's discovery of uncomputability. Explains the mathematical essence of these three different ways of exhibiting limits to mathematical reasoning. DLC: Machine theory.
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