Charles Petzold

Kurt Gödel and Alan Turing never met. By the time Turing got to Princeton University in 1936, Gödel had left the Institute for Advanced Study to go back to Vienna, and by the time Gödel came back to the IAS, Turing had gone back to England, eventually to report for duty at Bletchley Park in September 1939. That was about the closest they ever came to an actual encounter, these two men whose early work tore down the two main pillars of the Hilbert Program — completeness and decidability.

Some novelists or playwrights (Thomas Pynchon and Tom Stoppard come to mind) might have prefered to reimagine history and find a way to let these two oddball mathematicians meet each other and entertain us with their conversation. Janna Levin, a professor of physics and astronomy at Barnard best known for her book How the Universe Got Its Spots, has something quite different in mind. In her novel A Madman Dreams of Turing Machines (Knopf, 2006), Gödel and Turing never actually meet, but their lives intertwine across space and time through the resonance of ideas and motifs.

Readers familiar with the lives of Gödel and Turing will recognize the stops along the way, but witness them anew. (Much of the biographical material is drawn from Andrew Hodges' biography of Turing and John Dawson's biography of Gödel, and several pages of footnotes gives sources for some of the quotations.) There is Gödel in a coffehouse in Vienna keeping mostly quiet as the rest of the Vienna Circle debate politics and Wittgenstein; here is Turing at the Sherborne boarding school being tortured by his schoolmates and developing a crush for Christopher Morcom. Yet, Dr. Levin provides more physical and psychological detail than a mere biographer would ever dare. Here is a description of Turing's speech, for example:

Alan's entire vocal instrumentation is unmanageable. It is a kind of aural deformity whose source is no doubt the extreme brain chemistry of the highly functioning autistic. His voice booms and bangs and halts and stalls. He modulates the pitch but never the rhythm or the tone. The language of intonation is missing. The cadence that makes a voice bearable and creates meaning is missing. His speech is the grating clatter of a child's spoon on a hard surface. (p. 15)

Keep in mind that although Turing's high-pitched voice is well documented, there are no known recordings of him speaking, let along a recording of the 16-year old Alan. And here is a wonderful description of Otto Neurath that I suspect comes entirely from the author's imagination:

Otto's first wife, Anna Shapire, died giving birth to their son. In his grief he would have consumed her if they had let him. He would have grabbed her by the handfuls and eather her raw — muscle, fat, and bone. He would have refused to expel a morsel of her flesh. He would have hung on to her corporeal self, storing her in fat and glands forever. As it was he was restrained by brute force; it took several men and women to coax him down. So instead he gobbled up her ideals — her feminism, her social criticism, her visions of political change. (p. 77)

The cover of the novel is decorated with a flowchart that tells us it is narrated by a physicist "obsessed with the lives" of its two protagonists (this is the "madman" of the title), but this narrator shows her face only rarely. Her presence seems to remind us that this is a novel (or at most, speculative biography) even as the narrative convinces us of its essential psychological truth, particularly in recounting the two protagonists' most humiliating moments and their eventual deaths.

The deaths of Gödel and Turing are both rather mysterious. Gödel's paranoia caused him to stop eating, while Turing ate an apple dipped in cyanide one (seeminly random) evening. Janna Levin's true skill in this novel is revealed when she takes the novelist's (or madman's?) prerogative and goes deep within their heads — for the first time making these two deaths seem not only reasonable but almost inevitable.

The flowchart on the cover also tells us that this is "a story completely imagined ... but entirely true," and you might have fun bouncing around ideas of truth in your head. You might recall the novelist's goal of telling the truth through lies, and relate that to the Liar's Paradox, and toy around with the implication of Gödel's Incompleteness Theorem of the differences between provability and truth. Or you might just relax and enjoy Dr. Levin's wonderful recreation of two of the twentieth century's most strange and interesting figures.