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A Madman Dreams of Turing Machines (2006)
Janna Levin

This novel about Alan Turing and Kurt Gödel contains much that has already been said many times before, and occasionally "tries too hard" artistically. Still I very much enjoyed reading it, and even felt that it was able to add a bit to my understanding and appreciation of these two mathematicians.

The many well known facts about the lives of Gödel (a friend of Einstein whose most famous result was a shocking demonstration that mathematics is not as powerful as many had believed) and Turing (most famous as a principle inventor of the digital electronic computer and a war hero for his work in breaking the German code during WWII, but also known for mathematical work including a version of Gödel's incompleteness theorem for computers -- the halting problem -- and early work on pattern formation with applications to biology) are intertwined into a story, with fictional details added liberally and the author added as a character to tie it all together.

From an artistic point of view, I was troubled by much that the author chose to do. Including the author as a character in the book is a technique that has been used successfully in the past, e.g. Cervantes appearing in Don Quixote and Kurt Vonnegut in Breakfast of Champions. However, I was not sure what it did here other than to distract from the two main characters. Presumably, adding the author -- who is herself a physicist -- makes the book about three scientists rather than two, a triangle, and she serves to tie them together. But, in fact, the characters of Gödel and Turing are so well contrasted in the story (with sufficient emphasis on both their many similarities and startling differences) that I did not feel this was necessary. Moreover, the frequent mention of apples and "Snow White" (foreshadowing Turing's suicide by poison apple) quickly became tiresome to me.

But, I don't want to dwell on this because I really did like the book and would like to recommend that people read it. What I found most interesting is what the book really seemed to be about! The previous reviews I have read and the blurbs on the jacket did not mention the importance of the questions of the existence of God and the existence of mathematics to the novel. Perhaps this is because these topics were to controversial to advertise, or perhaps it is because I am alone in thinking this...but I really think that what the book did was to contrast the viewpoints of these two mathematicians on these topics.

The book emphasizes (in my opinion, over-emphasizes) the similarities in the "quirkyness" of these two men. Rather than being an introverted man whose paranoid tendencies came into full bloom in his old age, Gödel is presented as being completely paranoid the entire time. And Turing, whose shyness I had always attributed to a reasonable fear of being recognized as a homosexual in a very intollerant society, is presented here as being a highly functional autistic. Certainly, there is no doubting that neither Kurt nor Alan was your typical "party animal", but the book takes this beyond what I think was the case. Reasonable artistic license? Perhaps. It certainly helps in setting up the similarities between the two...right down to the fact that both of their eventual deaths were tied to eating -- well, not eating in the case of Gödel.

But where the book really gets interesting is when it contrasts their world views. It was not just a matter of Turing's view being "mechanical", as the cover suggests. More importantly, it is about the nature of existence. As Goldstein argues in her wonderful (non-fictional) Incompleteness, Gödel interpreted his famous theorem as being proof that mathematics has an existence outside of the human mind...that it is some sort of alternate reality which we can partially perceive but had no role in creating. Similarly, Gödel had a belief in a deity that we could only partiallly perceive and did not create. In contrast, Turing's atheism is clearly (and very well) presented in the story. To him, God is something that humans created. Moreover, I think it is supposed to appear that Turing also believes that mathematics is something that lives in the human mind and not that it is some other universe with an independent existence. However, I am not as certain about this because this viewpoint seems to be less well represented.

Certainly, it is the case that some mathematicians are Platonists, believing that mathematics "exists" independently of human thought and others view it as being a human construction that is beautiful, interesting and extremely useful, but not "real" in the sense that the moon is real and existed before humanity. Often, discussions about this topic can become extremely emotional. (I love the scenes in Levin's novel where Turing and Wittgenstein argue about this in class.) Moreover, it is true and ironic that people with extreme views on this subject (in both directions) often point to Gödel's theorem as evidence that they are correct. (Apparently, this theorem does not help resolve the question after all.)

Janna Levin is a professor of physics at Columbia. Therefore it is not surprising that her knowledge and understanding of mathematics is excellent. I only object to one thing in the book from a mathematical point of view, but it is something that was repeated a few times and so I would like to mention it here. The book states that Gödel's theorem shows that there are true statements of arithmetic that cannot be proven mathematically. I would argue (though I admit some would debate me) that this is not quite accurate. What he actually showed is that it is either true that there are undecidable statements or that mathematics is inconsistent (i.e. that it contains actualy contradictions). That the latter alternative is ignored by some is evidence of their faith in the consistency of mathematics. Gödel had faith in mathematics just as he had faith in God, but such faith does not serve as proof to others.

Well, I've really got to stop writing because it is time for me to go teach a class. Let me just wrap up quickly by saying that I unquestionably recommend this book to anyone who does not already know the stories of these two "characters". But, more surprisingly, I would also recommend it to those who think they've already heard enough about Alan and Kurt. Even jaded readers like me may be able to find a few worthwhile insights in this well-written work of historical fiction.

Contributed by Robert S

First let me say I really value your site.

Regarding your comments on "A Madman Dreams of Turing Machines", I agree with you and disagree with you. I strongly disagree that the book tries too hard to be artistic. I think the poetic language is haunting and necessary to create a kind of hypereal atmoshpere. It is truly one of the most daring aspects of the book, at least in my opinion, since it challenges those interested in math to absorb the elegance of her writing and it also challenges fiction buffs to consider the elegance of mathematics. But I understand this is the most subjective aspect of the book and so people will respond in individual ways.

I also disagree that she over-emphasizes their "quirkiness". Godel was committed, perhaps unwillingly, on at least one occasion when he was only in his twenties. And Turing, according to his biographer Hodges, definitely showed signs of what we now call Asperger's Syndrome.

On the other hand, I really agree with you that their contrasted beliefes on the existence of God and the existence of mathematics is what this book is about. I thought this was a very insightful comment on your part. I wonder why they didn't make more of this on the cover as you pointed out. You would think that the publisher or the author would have drawn attention to such a profound theme. Too controversial?

I also agree that Godel proved that mathematics was either incomplete or inconsistent and that he believed it was consistent so concluded it must incomplete. In fact, Godel showed that the consistency of mathematics is an undecidable proposition. I really expect Levin knows this but chose not to go into that subtlety. Maybe one could argue that she should have, but I don't think one can argue she made a mathematical error.

A small thing, it would be phenomenal if many many people read this book and were touched by some feeling for mathematics. So for that reason I was surprised you opened your review with such a negative sentence when you then go on to say you liked it and would recommend it. I hope I'm not seeming too critical, just an observation to consider.

Thank you for your excellent blog and for an opportunity to respond. I was deeply moved by this book so wanted to share that with others with mathematical interests. Robert S.

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Works Similar to A Madman Dreams of Turing Machines
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Breaking the Code by Hugh Whitemore (playwright)
  2. Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis
  3. Continuums by Robert Carr
  4. A Certain Ambiguity: A Mathematical Novel by Gaurav Suri / Hartosh Singh Bal
  5. Oracle by Greg Egan
  6. Measuring the World by Daniel Kehlmann
  7. The Indian Clerk by David Leavitt
  8. The Three Body Problem by Catherine Shaw
  9. Eifelheim by Michael Flynn
  10. A Beautiful Mind by Sylvia Nasar / Akiva Goldsman
Ratings for A Madman Dreams of Turing Machines:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
2.67/5 (3 votes)
Literary Quality:
3.33/5 (3 votes)

GenreHistorical Fiction,
MotifGenius, Anti-social Mathematicians, Insanity, Academia, Real Mathematicians, Autism, Romance, Religion, Turing,
TopicComputers/Cryptography, Real Mathematics, Logic/Set Theory,

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