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Exploring RANDOMNESS (Discrete Mathematics and Theoretical Computer Science) ハードカバー – 2001/1/25
購入オプションとあわせ買い
- 本の長さ174ページ
- 言語英語
- 出版社Springer
- 発売日2001/1/25
- 寸法15.88 x 1.91 x 22.86 cm
- ISBN-101852334177
- ISBN-13978-1852334178
商品の説明
レビュー
From the reviews:
"In this book on algorithmic information theory, the author compares his concept of randomness (for recursive functions) which is based on the complexity (length) of the generating algorithm (program) with other concepts (by Martin-Löw, Solovay) and discusses its relation to incompleteness and the halting problem. Algorithms (needed for proof) are described in a (small) dialect of LISP. The style mostly is that of a lecture, lively and readable." (P. Schmitt, Monatshefte für Mathematik, Vol. 141 (1), 2004)
"Chaitin is the main architect of a new branch of mathematics called algorithmic information theory, or ‘AIT’. … in Exploring Randomness, he develops algorithmic theory, further revealing its technical core. This is important work, with implications that go far beyond the arcane arguments of one branch of mathematics. … As one gets to the substance … it is difficult to resist Chaitin’s enthusiastic style and obvious intelligence. Beyond the technicalities of the argument, the reader is quickly drawn into a fundamental new landscape of ideas." (Jacques F. Vallee, Journal of Scientific Exploration, Vol. 16 (4), 2002)
"Chaitin’s latest three books form a nice triangular base to support and explore the concepts underlying algorithmic information theory (AIT) – a clever blend of Gödel, Turing, and Shannon that Chaitin developed in his late teens … . this set of three volumes packages the material in a nice, quite digestible fashion … . Chaitin’s results demonstrate that not only there is no structure to foundation of mathematics, the foundation is in fact random." (The Mathematica Journal, April, 2002)
"The book is devoted to a Lisp formalism for exploring the basic ideas, concepts and results on program-size complexity and random sequences. The book contains a wealth of exercises, ranging from the ‘mathematical equivalent of finger warm-ups for pianists’ to substantial programmingprojects, from open questions to questions the author cannot even formulate. Highly recommended to anyone interested in understanding algorithmic information theory through programming." (Cristian S. Calude, Zentralblatt MATH, Vol. 963, 2002)
"This book uses LISP to explore the theory of randomness, called algorithmic information theory (AIT). This is the third of Chaitin’s book … . The common theme of the books is the study of H(x), the size in bits of the smallest program for calculating x … . Each book has a different emphasis. This book gives a detailed discussion of the metamathematical implications of these ideas and presents the technical core of Chaitin’s algorithmic theory." (Book News on the Internet, October, 2001)
"This is revolutionary, explosive stuff. … Chaitin challenges readers to follow his lead and forge their own path into the black hole of randomness, the ‘darkness at the edge of mathematics’. When Chaitin wrote ‘explore’, he well and truly meant it. An exhilarating, mind-blowing book from one of the great ideas men of mathematics and computer science." (Marcus Chown, New Scientist, January, 2002)
登録情報
- 出版社 : Springer; 第2001版 (2001/1/25)
- 発売日 : 2001/1/25
- 言語 : 英語
- ハードカバー : 174ページ
- ISBN-10 : 1852334177
- ISBN-13 : 978-1852334178
- 寸法 : 15.88 x 1.91 x 22.86 cm
- カスタマーレビュー:
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That leads me to a final observation: this work benefits tremendously from Dr. Chaitin's unabashed passion, which he goes so far as to liken to demonic possession (carefully pointing out you should hope to be possessed by a GOOD demon). It's another quality Dr. Jaynes shared, and that is sorely lacking in most rigorous mathematical writing, with the inevitable stultifying effect.
This book belongs on the shelf of everyone who has ever wondered why mathematics is as it is, who has wondered what "random" really means, who has thought about what learning (especially machine learning!) could possibly mean, and who has an experimental bent to go with their theorizing. Grab both it and Jaynes, pour yourself that glass of wine, and dig in!
But it is deplorable the propagation of his inacceptable
mesure of the complexity of a sequence as the size in bits
of the minimum program that reproduces it.
According to that, the complexity of the sequence of a
polynomial of 10th degree is greater than the complexity
of the sequence of prime numbers.
The list of the coeficients of the polynomial needs more bits
that the whole program for prime numbers.
Ludovicus