The Unknowable (Discrete Mathematics and Theoretical Computer Science) [Hardcover]

Gregory J. Chaitin (Author)

Book Description

Publication Date: August 5, 1999 | ISBN-10: 9814021725 | ISBN-13: 978-9814021722 | Edition: 1

This essential companion to Chaitins highly successful The Limits of Mathematics, gives a brilliant historical survey of important work on the foundations of mathematics. The Unknowable is a very readable introduction to Chaitins ideas, and includes software (on the authors website) that will enable users to interact with the authors proofs. "Chaitins new book, The Unknowable, is a welcome addition to his oeuvre. In it he manages to bring his amazingly seminal insights to the attention of a much larger audience His work has deserved such treatment for a long time." JOHN ALLEN PAULOS, AUTHOR OF ONCE UPON A NUMBER

Product Details

• Hardcover: 132 pages
• Publisher: Springer; 1 edition (August 5, 1999)
• Language: English
• ISBN-10: 9814021725
• ISBN-13: 978-9814021722
• Product Dimensions: 9.2 x 6.2 x 0.6 inches
• Shipping Weight: 12.8 ounces (View shipping rates and policies)
• Average Customer Review: 3.2 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #1,729,242 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

22 of 22 people found the following review helpful:

2.0 out of 5 stars More annoying than amusing, January 20, 2004

By 

Sander - See all my reviews

This review is from: The Unknowable (Discrete Mathematics and Theoretical Computer Science) (Hardcover)

First the good part about this book. Chaitins first chapter is quite good. Here he outlines the results of Godel, Turing and his own. It is very readable. Without going into the real mathematics he can really make you feel you understand these deep ideas. The later chapters go more deeply in to the ideas presented there and illustrate them with lisp computer programs. Especially the search for lisp programs that evaluate to themselves is amusing.

But let's now focus on the parts of the books that I did not like. His exposition is mixed with an account of how he first learned these result. I am charmed the first time when he explains how he read so many books as a kid. But soon I do not want to hear again what he felt as 12 year old. Also he keeps comparing his own work to that of other scientist. We really need to now that he is just as good as Godel and as Turing.
For example he takes pages to explain that Kolmogorov ripped of his ideas. What I also find funny as well is both chapter 1 and chapter 6 give an identical link to "my first major paper".

Sigh. He's the best, we get it, ok?, now please move on.

Then one more thing. The computer programs that he uses are in lisp. That is fine by me, lisp is a beautiful language. But do you think he uses any of the available dialects? No, of course not, he introduces he own strange version. The programs given do not run in clisp for example.

So to sum it up. I learned his own result on incompleness (that one cannot produce the shortes program for a particular function) and that is a nice result. Reading the rest of the book is more annoying than amusing.

23 of 24 people found the following review helpful:

5.0 out of 5 stars Not a modest man but why should he be?, May 16, 2000

By 

P MARTIN (Hertfordshire, UK) - See all my reviews

This review is from: The Unknowable (Discrete Mathematics and Theoretical Computer Science) (Hardcover)

...reasons that I rated this a 5 star read.

Firstly I agree that Chaitin is not a modest man. I don't think that really matters, because he has made a major contribution to my understanding of this whole area which previously I had found almost impenetrable. The only other criticism I had is the excessive use of the exclamation mark!

In all other respects this is a superb book. I found the chapter introducing LISP a little dense (much like me) but I read a book called "The Little Lisper" which is a great book in itself and that helped me.

The real beauty of this book for me was working through the various LISP exercises and beginning to understand, to feel almost, the logic and concepts behind the work of people such as Godel and Turing.

In other words I felt able to walk for a while in the footsteps of geniuses - and I would count Chaitin among that number. END

9 of 10 people found the following review helpful:

5.0 out of 5 stars Modesty not a strong suit - but then why should it be..., March 16, 2000

By 

P MARTIN (Hertfordshire, UK) - See all my reviews

This review is from: The Unknowable (Discrete Mathematics and Theoretical Computer Science) (Hardcover)

Chaitin is not a modest writer, but then given his personal contribution to the field he discusses here, there's no reason why he should be. This book is not an easy read for the layperson (I know, I am one) but does reward perseverance. The beauty of "The Unknowable" is that it allows the reader to understand the points Chaitin makes by working through the important proofs by famous thinkers such as Godel and Turing (and ,of course, Chaitin). It's a great feeling to walk in the footsteps of giants such as these - and to understand the conlusions rather than accept them as received wisdom. My only reservation is that the chapter introducing the reader to LISP is fairly dense and tough to follow. However I found that reading the first couple of chapters of Friedman and Felleisen's "Little LISPer" made it more comprehensible - and LL is a great book anyway. I'd thoroughly recommend this book to readers with an interest in the Philosophy of Mathematics who do not necessarily have an in-depth mathematical background.