Exploring Randomness (Discrete Mathematics and Theoretical Computer Science)
| Author | : | |
| Rating | : | 4.40 (708 Votes) |
| Asin | : | 1852334177 |
| Format Type | : | paperback |
| Number of Pages | : | 164 Pages |
| Publish Date | : | 2014-09-04 |
| Language | : | English |
DESCRIPTION:
… 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’. 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. 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 … . Calude, Zentralblatt MATH, Vol. Schmitt, Monatshefte für Mathematik, Vol. Beyond the technicalities of the argument, the reader is quickly drawn into a fundamental new landscape of ideas." (Jacques
A message from the author Hello, I'm Gregory Chaitin and I'm the author ofExploring RANDOMNESS, which is my attempt to explainthe technical heart of my theory of algorithmicinformation as understandably as possible. To makemy theory more concrete, I've converted it into atheory of the size in bits of real computer programs,programs that you can actually run. See also mynew book, "Conversations with a Mathematician: Math,Art, Science and the Limits of Reason", which is acollection of my most wide-ranging and non-technicallectures and interv. Paul Snively said A golden spike unifying much more than can easily be summarized, simultaneously exuberant and subtle. This admirably slender volume deserves to be much more widely appreciated by computer scientists than it appears to be. Dr. Chaitin explains the program in a single sentence in his preface—algorithmic information theory is constructive measure theory—then proves his point in a dialect of Lisp he designed for the purpose in the rest of the book. I disagree with Dr. Chaitin's belief that Dr. Kolmogorov erred in thinking their results applied primarily to probability, but that's really neither here nor th. Just for LISP and randomness The treatment of LISP and randomness is interesting.But it is deplorable the propagation of his inacceptablemesure of the complexity of a sequence as the size in bitsof the minimum program that reproduces it.According to that, the complexity of the sequence of apolynomial of 10th degree is greater than the complexityof the sequence of prime numbers.The list of the coeficients of the polynomial needs more bitsthat the whole program for prime numbers.Ludovicus
"No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter. The two previous volumes are more concerned with applications to meta-mathematics. LISP is used to present the key algorithms and to enable computer users to interact with the authors proofs and discover for themselves how they work. This book tells you everything hes seen. This essential companion to Chaitin's successful books The Unknowable and The Limits of Mathematics, presents the technical core of his theory of program-size complexity. Don miss it." John Casti, Santa Fe Institute, Author of Goedel: A Life of Logic.'