The Limits of Mathematics: A course on information theory and the limits of formal reasoning (Springer Series in Discrete Mathematics and Theoretical Computer Science) (Hardcover)

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Review

"...a very personal and idiosyncratic account of Greg Chaitins entire career in developing algorithmic information theory. The combination of the edited transcripts of his three introductory lectures maintains all the energy and content of the oral presentations, while the material on AIT itself gives a full explanation of how to implement Gregs ideas on real computers ..." John Casti, Santa Fe Institute

"…the edited transcripts of his three introductory lectures maintains all the energy and content of the oral presentations..." -- THE SANTA FE INSTITUTE

Product Description

This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. It discusses Einstein and Goedel's views on the nature of mathematics in the light of information theory, and sustains the thesis that mathematics is quasi-empirical. There is a foreword by Cris Calude of the University of Auckland, and supplementary material is available at the author's web site. The special feature of this book is that it presents a new "hands on" didatic approach using LISP and Mathematica software. The reader will be able to derive an understanding of the close relationship between mathematics and physics. "The Limits of Mathematics is a very personal and idiosyncratic account of Greg Chaitin's entire career in developing algorithmic information theory. The combination of the edited transcripts of his three introductory lectures maintains all the energy and content of the oral presentations, while the material on AIT itself gives a full explanation of how to implement Greg's ideas on real computers for those who want to try their hand at furthering the theory."

Product Details

• Hardcover: 147 pages
• Publisher: Springer; 1 edition (November 14, 1997)
• Language: English
• ISBN-10: 981308359X
• ISBN-13: 978-9813083592
• Product Dimensions: 9.6 x 6.5 x 0.6 inches
• Shipping Weight: 15.7 ounces
• Average Customer Review: 2.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #2,035,932 in Books (See Bestsellers in Books)

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19 of 20 people found the following review helpful:

2.0 out of 5 stars A subjective estimation, March 3, 2007

By	Gary L. Herstein (Prescott, AZ USA) - See all my reviews

This review is from: The Limits of Mathematics: A Course on Information Theory and the Limits of Formal Reasoning (Discrete Mathematics and Theoretical Computer Science) (Hardcover)

I wish that I could give this book a higher rating than I have, for the subject matter is one that I find of enormous intrinsic interest. Moreover, Dr. Chaitin is one of the most important contributors to this field of the last 30+ years.

My reasons for being disappointed in this book may well be the reasons others enthusiastically endorse it. Dr. Chaitin himself, in his preface, places this volume as the one thing he would most wish to save were a disaster to wipe out the rest of his oeuvre.

The sub-title of the book is "A Course on Information Theory and the Limits of Formal Reasoning." This sub-heading I find to be quite misleading. The book is not a "course" on any thing -- rather, it is a collection of a very small number of informal papers that Dr. Chaitin has given in recent years, and a very large number of pages devoted to LISP programs that can be used to demonstrate aspects of his extensions to the results of Turing and Goedel. The collection of articles seem largely redundant to me; any one of the articles by itself would be sufficient to summarize the rest of the book's contents. As for the programming, that should either have been provided in the form of a CD-ROM (as only someone of a genuinely "special" nature would actually sit down and manually type in all those instructions) or a functioning URL (such URL's as do appear in the book do not seem to be working as of this writing, Mar. 2007).

I was hoping to get something more comprehenive, and that could function as a stand-alone text. This book seems to be neither. The technical details are all to be found elsewhere, and the functional aspects that might translate into an actual course of study are simply not to be found at all. Dr. Chaitin notes that the original technical work of his, published in the 60's, had a formal error that has since been corrected. Quite frankly, I would rather have that work plus a footnote regarding the later developments, than this volume which (sadly) I find of no real help. (I have since ordered and received a used, 1987 imprint of his "Algorithmic Information Theory" as printed by Cambridge.)

Alternatively, and perhaps more importantly, I would very much liked to have seen this "course" developed as a *COURSE*, rather than as three more or less popular, and largely independent, lectures. These lectures seem, at best, only to minimally build upon one another. A more integrated and coherent work that developed its subject in a step-wise manner, rather than repeating itself with only slightly different glosses, is something that I would have liked much more.

My background in logic and computer science, while not trivial, remains that of a studious and committed autodidact. It is possible that someone with less of a background in topics of formal reasoning than myself would find this book of enormous value. For me, however, it lacked both the technical details to make it a worthy struggle, and the pedagogical depth to make it of significant value.