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Gregory J. Chaitin eBooks

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Information, Randomness and Incompleteness

Papers on Algorithmic Information Theory
Information, Randomness and Incompleteness Image
2nd Edition
God not only plays dice in quantum mechanics, but even with the whole numbers! The discovery of randomness in arithmetic is presented in my book Algorithmic Information Theory published by Cambridge University Press. There I show that to decide if an algebraic equation in integers has finitely or infinitely many solutions is in some cases absolutely intractable. I exhibit an infinite series of such arithmetical assertions that are random arithmetical facts, and for which it is essentially the case that the only way to prove them is to assume them as axioms. This extreme form of Gdel incompleteness theorem shows that some arithmetical truths are totally...

Algorithmic Information Theory

Algorithmic Information Theory Image
Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gdel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation....


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