Customer Reviews

Gödel: A Life of Logic

5 star:		(4)
4 star:		(5)
3 star:		(2)
2 star:		(4)
1 star:		(0)

 

 

This book seems to be put forth as a biography of Godel--at least, that's what I thought I would be getting. As a physics and mathematics teacher, I am very interested in this man who revolutionized 20th century thought. However, only a portion of this already very slight book, is biographical material about Godel. So, if you are looking for a real biography, look elsewhere.

Instead, this book briefly covers Godel's life, briefly covers his work, and briefly covers a few of the effects Godel has had on current thought. In that sense, it is not bad. A person who understands very little about modern mathematical thought but has an interest might find this book digestable and learn a bit. Others are not going to enjoy this book. People with strong backgrounds in mathematics are going to find it too weak and people with weak backgrounds in mathematics are going to find most of it indecipherable.

It's depressing to compare this book with "Logical Dilemmas: The Life and Work of Kurt Goedel" by Dawson. Dawson's book is illuminating, well researched and well written. It is universally considered to be the definitive biography of Goedel, and I'm not sure why someone would want to write another without some new idea or approach. The book by Casti and De Pauli unfortunately has nothing new to contribute. It's a more superficial account than Dawson's. Dawson's book is based on the premise that the reader has no specialized background but is curious and wants to think; Casti and De Pauli's book seems to be based on the premise that the reader wants a flashy but ultimately unsatisfying overview.

A few of Casti's interests (e.g., Chaitin's work) play a prominent role towards the end of the book, despite being only tenuously connected to Goedel. Sure, they're a late 20th century continuation of Goedel's work, but they represent only a very narrow direction among such continuations, and are not nearly as highly regarded by most logicians as by Casti. They may give readers an unrepresentative view of where Goedel's work has led.

This is not a bad book, and if you want to read a biography of Goedel, it is certainly better than nothing. However, I strongly recommend reading Dawson's book instead.

Godel was an interesting man who thought up some interesting things. Contrary to the opinions of previous reviewers, I think the authors got the "interesting life/intersting things" ratio of content just about right. The biographical section, which is only really a couple of chapters, certainly expanded my knowledge of his life(all I knew previously was that he was Austrian and neurotic). But his work and it's philosophical implications are far more enthraling than what appears to be years of drinking tea at Princeton( after it had been screened by his wife of course) .Fair enough, much of the book was spent introducing Godel's work but this should have been anticipated and the task was done with some merit.Also, the critisism that the authors diverge from the work of Godel himself is valid, but I do not feel this detracts from the book in any way.By including the work of Turing and Chaittin much later on, we get an idea of the implications his discoveries have had and continue to have. Often we read that the work of any particular famous scientist still has a strong influence today but are not given any concrete examples. This leads ultra-sceptics like me to the belief that writers include commments like this to make their chosen subject appear more relevant and topical.The extensive discussion of Chaittin and his work indicated that Godel really does influence much of todays work in certain fields.The account also happened to be fascinating,well explained and as yet unmentioned in any other books on this subject I have encountered.So what if it was not directly attributibal to Godel, it was welcome bonus material.Perhaps, the only fault is in the title, which may have misled some into thinking the book was more biographical, but the pages inbetween provide a clear and conscise account of Godel and his legacy.

I would agree with other reviewers who point out that Casti and DePauli's book really doesn't work as a biography. While there are some interesting biographical factoids, they are offered in such a disjoint manner that it is hard to see this book as a good biography of Kurt Godel.

However, as a book that gives an accessible overview of Godel's work, it is very effective. The best parts of the book deal with Godel's Theorem and Turing's Halting Problem. While there are other books out there that do a good job of making both those topics accessible to a wide audience, Casti and DePauli's treatment is worth a read because they also offer some unique insights not (easily) found elsewhere.

But the best part of this book is the second to the last chapter that gives an accessible account of Algorithmic Information Theory (aka 'Kolmogorov Complexity') ... especially Gregory Chaitin's work on the randomness of natural numbers. While Chaitin has also written some accessible works on this topic, Casti and DePauli does a great job of explaining this topic to a wider audience as well as showing the connections between AIT and Godel/Turing. This chapter alone is worth the price of the book.

A very interesting and insightful thing that Casti and DePauli did was to periodically re-define Godel's Theorem in terms of Turing's Halting Problem, Chaitin's work, and from other interesting angles.

The book is not without fault. Besides the rather haphazard biographical details, the chapters dealing with some of Godel's other projects (physics, mysticism, etc.) were rather poorly written. Also, Casti and DePauli did a very bad job with citations/suggestions for further reading. E.g., they often cite to other works, or suggest readers consult other sources for further details, and then do NOT provide those sources in the bibliography. There are some other examples of sloppy editing and writing that would be hard to point out to those who haven't actually read the book.

Having said all of that, the book deserves 5 stars because of the material on the incompleteness of mathematics, solvability/computability, random nature of mathematics, and some of the biographical trivia (to the extent that they are offered). My recommendation is that people buy the paperback if they are interested in AIT, mathematical logic, and theoretical computer science, and want those topics dealt with in an accessible and interesting manner without sacrificing on insights.

Although I may be biased (having just read Ray Monk's excellent biography of Wittgenstein 'The Duty of Genius'), I really don't see that this is a biography of Kurt Gödel. Rather, it seems to be an introduction to his ideas and theorems, and their relations to other areas in mathematics and computation. While this is certainly interesting, it is disappointing to someone who is already familiar with these ideas and is looking for more information about Gödel as a person.

However, it is a fairly quick book to read, and the authors do a good job of elucidating what can be fairly difficult material. The last few chapters, for example, provide a compact exposition of just how the Incompleteness Theorem relates to other areas. It is nice to see this in such a brief format.

If you are looking for a good biography, look elsewhere; and if you're looking for a complete exposition of Gödel's ideas, again look elsewhere. But if you just want a nice, brief introduction to Gödel and his ideas, this is a good place to start.

Author shows a great skill in Chapter Two and Three to explain a crux of famous theorem in a very succinct language without using mathematical terms. Also a short biography of Godel's strange life explains: why he died of paranoia; why he hated Austria; why he was suffering a guilt of not producing enough academic result in Princeton.
As the author acknowledges, many metaphors used in this book overlaps with the Douglas Hofstadter's Pulitzer-winning book. However, as many other books for past twenty years, the author presents a theorem in a way that is easily misinterpreted. In p11, he says "Essentially, what Godel showed is that no kind of mathematics is ever going to be comprehensive enough to express fully the everyday notion of truth." And then, the author spends a great deal of pages on AI and computer.
As far as I know, Godel's theorem mentions nothing about "truth in daily life" or computer. Godel's theorem applies only in a strictly circumscribed sphere, i.e., first-order logic. For example, Euclidean geometry is not imcomplete, and the higher-order logic doesn't produce Russel-type paradox. So, what we cannot speak of we must pass over in silence.
Also, author asserts in p71 that Wittgenstein's shift to "sociocultural position" later in his life, but he failed to mention that Wittgenstein did describe his thought about Godel's theorem in his "Remarks on the Foundations of Mathematics".

I am a mathematician and know Goedel's work fairly well. I bought this book to learn more about Goedel as a person, and I was disappointed. Although any biography necessarily presents an incomplete picture of its subject, this book offers little more than a sketch of the man. I had hoped for something more thorough. The book may be of more interest to those who do not already know Goedel's work, but my impression was that it covers that material less well than other popular texts on the subject.

The main result of Godel's Completeness Theorem is that in arithmetic, there are true statements that can never be proven to be true in the system of arithmetic. Using this as a base system, this means that in any system equal to or greater than arithmetic in complexity, there will be true statements that cannot be proven to be true in the system. This result has been used by many people to argue for or against many things.
I have seen it used to argue for the existence of God.

"According to Godel's theorem, there are things that are true that cannot be proven to be true within the system of human thought. God is one such thing, therefore God exists."

I have seen it used to argue against the possibility of artificial intelligence (AI).

"According to Godel's theorem, there are things that are true that cannot be proven to be true within the system of programmable human thought. Humans take advantage of these unprovable truths, which makes intelligence. Since this advantage can never be programmed, AI is impossible."

I have suggested on more than one occasion that the people making these arguments need to spend more time studying both logic and what Gödel really concluded. For example, they could read this book.
It presents a brief biography of Kurt Gödel. In his later years he was quite eccentric and reclusive, however in his early years he apparently was quite a ladies man. Certainly Gödel was a genius; Albert Einstein himself openly expressed his admiration for Godel's intelligence. I was pleased to see the authors spend as much time as they did describing Gödel in his earlier years. So many other commentators spend so much time on his social difficulties that his achievements become overshadowed.
A complete explanation of his main results is also expressed in terminology that almost everyone can understand. There are few formulas; simple algebra is all that is needed to understand all of the mathematical symbolism used in the book. If I was teaching a course in popular mathematics, it would have to include Godel's Completeness Theorem and this is the book I would select for that section.

Sorry, but this book was somewhat a disappointment for me. The authors for the most part keep personal life and work of Gödel separated, instead of seeing them as a unity. A biography has to be the best of both worlds in my opinion. That's what makes the work of a biographical writer a difficult task. Maybe one of the two authors did the biographical part, the other one the mathematical ? And of course, everything about Gödel is great, brillant and alltogether grand. I am missing a critical view on his lifestyle and his view on music e.g.. Appearently the author of the biographical part was so in awe of Gödel, that he didn't dare to critisize anything about Gödel. Ironic, since Gödel stands for the idea, that you are allowed and even have the obligation to question everything to get to the bottom of the truth of things.
I am still waiting for the real biography of Kurt Gödel.

I am a mathematician and know Goedel's work fairly well. I bought this book to learn more about Goedel as a person, and I was disappointed. Although any biography necessarily presents an incomplete picture of its subject, this book offers little more than a sketch of the man. I had hoped for something more thorough. The book may be of more interest to those who do not already know Goedel's work, but my impression was that it covers that material less well than other popular texts on the subject.