The Unknowable (Discrete Mathematics and Theoretical Computer Science) 1999th Edition by Gregory J. Chaitin (PDF)

Description

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

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Book about fundamental mathematics in IT age

⭐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.

⭐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.

⭐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.

⭐This Book is horrible. The only point of the Unknowable is to prove that Chaitin is as smart as Godel and Turing. The entire book can also be retrived off his homepage. If you want to have a good overview of this topic buy Limits of Mathematics by Chaitin.

⭐I checked out this book from the library with high hope. It turned out to be a complete waste of time. The only purpose of this book is to claim that the author is as great as Godel and Turing. The reason? Unknowable.

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