THE LIMITS OF MATHEMATICS. : A course on information theory and the limits of formal reasoning [Anglais] [Relié]

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.

The book is composed of a small set of speeches given at various occasions to maths students.
Each speech share the same topic and is build almost according to the same plan, and merely
introduces the research area of G. Chaitin from a very high standpoint, without giving any details.

So this can hardly be considered as a course.

The book is very frustrating because at several places the author jump over many expected details because he says he lacks time, yet in the following speech he again skip over details because he still lacks time. One would rather have an actual course that's diging from chapter to chapter into the core of the matter, instead of having to repeatedly read an introduction.