The Unknowable

by Gregory Chaitin

This essential companion volume to Chaitin's highly successful "The Limits of Mathematics", also published by Springer, gives a brilliant historical survey of the work of this century on the foundations of mathematics, in which the author was a major participant. The Unknowable is a very readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programming language used by Chaitin in both volumes...

• Format: Hardcover
• Language: English
• ISBN: 9814021725
• ISBN13: 9789814021722
• Release Date: July 1999
• Publisher: Springer
• Length: 124 Pages
• Weight: 0.90 lbs.
• Dimensions: 0.7" x 6.4" x 9.6"

Customer Reviews

Not a modest man but why should he be?

...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

Future Classic - Beautiful Ideas

In the 21st century mathematicians will debate the meaning of Chaitin's theorems just as we now debate the meaning of Godel's and Cantor's theorems. We have a rare opportunity here to read the author's interpretation. This book is wonderful. It is, by far, the most polished and most readable of Chaitin's publications. Much of the value of this book comes from the terse LISP proofs, which can be appreciated for their beauty and craftiness. The reader must not only read the proofs but also run the proofs. This can be accomplished by downloading the author's LISP interpreter applet.If you like Hofstadter's GEB you'll love this book but you'll come out of it with a much more optimistic outlook. Hofstadter believes that man is just a machine. I don't think Chaitin shares that view. I know that Godel didn't share that view. Nevertheless, parts of mathematics are beyond our understanding. We have gotten use to the idea that there are true propositions that can't be proved. Chaitin defines numbers, like omega, that can't be known. But this means that there is no end to mathematics. It is optimistic because it means that theorems that have been proved and numbers that are known are all the more interesting. If something is unknowable well then it's just unknowable, but if you can know that it's unknowable then that's really remarkable.

Modesty not a strong suit - but then why should it be...

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.