Meta Math! The Quest for Omega.META MATH! The Quest for Verb 1. quest for - go in search of or hunt for; "pursue a hobby" quest after, go after, pursue look for, search, seek - try to locate or discover, or try to establish the existence of; "The police are searching for clues"; "They are searching for the Omega GREGORY CHAITIN Gregory John Chaitin (born 1947) is an Argentine-American mathematician and computer scientist. Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a new incompleteness theorem similar in spirit to Mathematics is often deemed the infallible in·fal·li·ble adj. 1. Incapable of erring: an infallible guide; an infallible source of information. 2. foundation of the hard sciences. Yet, surprisingly to many people, mathematics itself is full of randomness. Chaitin, a mathematician at IBM's Watson Research Center, explains with infectious enthusiasm how mathematics doesn't equal certainty. He begins with Godel's theorem theorem, in mathematics and logic, statement in words or symbols that can be established by means of deductive logic; it differs from an axiom in that a proof is required for its acceptance. , which asserts that any finite system of mathematical axioms This is a list of axioms as that term is understood in mathematics, by Wikipedia page. In epistemology, the word axiom is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system. is incomplete. He then describes how computers have revolutionized mathematical thought, focusing on Alan Turing's halting theorem, which states that there's no algorithm for deciding whether a self-contained computer program will finish or run forever. His discussion culminates in a detailed explanation of omega, the number he famously described 30 years ago to demonstrate Turing's halting theorem. This book is a clearly written and witty look at a difficult subject. It will appeal especially to people interested in the philosophy and creative process behind mathematics. Pantheon, 2005, 240 p., hardcover, $26.00. |
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