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A Madman Dreams of Turing Machines

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Overview

Kurt Gödel’s Incompleteness Theorems sent shivers through Vienna’s intellectual circles and directly challenged Ludwig Wittgenstein’s dominant philosophy. Alan Turing’s mathematical genius helped him break the Nazi Enigma Code during WWII. Though they never met, their lives strangely mirrored one another—both were brilliant, and both met with tragic ends. Here, a mysterious narrator intertwines these parallel lives into a double helix of genius and anguish, wonderfully capturing not only two radiant, fragile ...
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Overview

Kurt Gödel’s Incompleteness Theorems sent shivers through Vienna’s intellectual circles and directly challenged Ludwig Wittgenstein’s dominant philosophy. Alan Turing’s mathematical genius helped him break the Nazi Enigma Code during WWII. Though they never met, their lives strangely mirrored one another—both were brilliant, and both met with tragic ends. Here, a mysterious narrator intertwines these parallel lives into a double helix of genius and anguish, wonderfully capturing not only two radiant, fragile minds but also the zeitgeist of the era.
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Editorial Reviews

From the Publisher
“Intelligent . . . compelling. . . . As Levin alternates between the lives of Turing and G?del, she delivers a convincing, palpably human portrait of solitary genius.” —The Philadelphia Inquirer“A simple work of genius.”—Toronto Globe & Mail“Her characters and their century come brilliantly . . . alive.” —The Los Angeles Times Book Review“Like a lyrical mash-up, Levin interweaves the personal narrative style of her first book with taut prose evocative of Alan Lightman's Einstein's Dreams.” —Seed Magazine
Publishers Weekly
The lives of Kurt Godel (1906-1978) and Alan Turing (1912- 1954) never crossed physically, but did intellectually: Godel's incompleteness theorem implies a sort of Platonism, and Turing's mechanical decision theory implies, conversely, hard-nosed materialism. Levin, a mathematician, juxtaposes both lives in her debut novel. She begins with Godel as a young man in Vienna, his incompleteness theorem destroying the line of inquiry (arguably spearheaded by Wittgenstein, who cameos)that argued math was complete in itself; his courtship with a nightclub dancer, Adele; his misunderstanding of the Nazi takeover of Austria. Alan Turing's not very charmed life is skewed not only by what looks like autism but by being hounded for his homosexuality in Britain-after breaking the German Enigma code during WWII. Turing is an innocent in many ways, while Godel, a greater thinker, is a monster of selfishness; both, however, have a passion for the invisible that is hard to dramatize. Godel becomes a paranoid old man, living with Adele (who comes alive through Levin's shrewd novelistic guesswork) in solitude in Princeton, and eventually starving himself to death. Levin is sympathetic to all concerned, but doesn't quite make a larger point, dramatic or otherwise. (Aug. 25) Copyright 2006 Reed Business Information.
Library Journal
Levin (physics & astronomy, Barnard; How the Universe Got Its Spots) has written an illuminating, highly personalized account of the intellectual confrontation of two of the last century's most brilliant thinkers-logician Kurt Godel and mathematician Alan Turing. Turing, who broke the Nazis' Enigma Code for the British in World War II, argues that "mathematics is not a human invention [but] the purest form of natural law." Godel is determined to refute Turing's thesis that "mental procedures cannot go beyond mechanical procedures." Yet for all that brilliance, Levin searingly portrays the inability of either man to manage his own life, with one starving himself to death and the other committing suicide. The author enters unobtrusively into her story and wonders, along with her characters, whether we can ever know the truth. The one thing we do know is real are library budgets, and libraries that can spring for this book will richly reward patrons who enjoy a novel of ideas.-Edward Cone, New York Copyright 2006 Reed Business Information.
Kirkus Reviews
In her first novel, Levin, using two mathematical geniuses, showcases the life of the mind. The Austrian Kurt Godel (1906-78) and the British Alan Turing (1912-54) never met, but they were intensely aware of each other's work. Levin, a mathematics professor, cuts between their life stories. We meet Godel in 1931 at a cafe gathering of the Vienna Circle founded by philosophy professor Moritz Schlick (later murdered by a Nazi student). Its members, in Wittgenstein's shadow, oppose religion and mysticism. Godel's incompleteness theorems cause him to break reluctantly with Moritz, another tribulation for a paranoid individual fearful of food poisoning. Despite being mothered by his guardian angel Adele, a nightclub dancer, he must spend time in a sanatorium before leaving for the U.S. and Princeton with Adele. Years later, he will die there from self-starvation, bitter at inadequate professional recognition, unlike Turing. The Englishman now has the higher profile, thanks to the successful play Breaking the Code. His difficulties begin in boarding school, where some boys bury him beneath floorboards. He's rescued from this traumatic ordeal by his friend Chris, the (unrequited) love of Turing's life. At Cambridge, Turing rejects God, embraces materialism, debates Wittgenstein and dreams of thinking machines. As a Government cryptographer during the war, he breaks the Germans' Enigma Code, an important contribution to the Allied victory. But Turing's homosexuality catches up with him, dooming his engagement to a fellow cryptographer. After the war, involved with a thief, he guilelessly incriminates himself and is sentenced to castration. A broken man, he kills himself by eating a poisonedapple. Levin highlights intriguing details (apples, blue liquids, visits to psychics) that unite these tormented men, whose intellectual journeys may give readers a frisson. It's a fair bet, however, that the lurid material will resonate more, and that their achievements as trailblazers will be overshadowed by, their plight as victims. Levin writes with elegant precision, but ultimately her account, hewing closely to the record, adds little to what's already available. First printing of 40,000
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Product Details

  • ISBN-13: 9781400032402
  • Publisher: Knopf Doubleday Publishing Group
  • Publication date: 9/18/2007
  • Edition description: Reprint
  • Pages: 240
  • Sales rank: 251,514
  • Product dimensions: 5.16 (w) x 7.97 (h) x 0.74 (d)

Meet the Author

Born in Texas and raised in Chicago, Janna Levin is currently a professor of mathematics and physics at Barnard and Columbia universities. She holds a Ph.D. from the Massachusetts Institute of Technology and has been Scientist-in-Residence at the Ruskin School of Drawing and Fine Art at the University of Oxford and an Advanced Fellow in the Department of Applied Mathematics and Theoretical Physics at Cambridge University. Levin is the author of How the Universe Got Its Spots, published in 2003 by Anchor.
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Read an Excerpt

Vienna, Austria. 1931

The scene is a coffeehouse. The Café Josephinum is a smell first, a stinging smell of roasted Turkish beans too heavy to waft on air and so waiting instead for the more powerful current of steam blown off the surface of boiling saucers fomenting to coffee. By merely snorting the vapors out of the air, patrons become overstimulated. The café appears in the brain as this delicious, muddy scent first, awaking a memory of the shifting room of mirrors second—the memory nearly as energetic as the actual sight of the room, which appears in the mind only third. The coffee is a fuel to power ideas. A fuel for the anxious hope that the harvest of art and words and logic will be the richest ever because only the most fecund season will see them through the siege of this terrible winter and the siege of that terrible war. Names are made and forgotten. Famous lines are penned, along with not so famous lines. Artists pay their debt with work that colors some walls while other walls fall into an appealing decrepitude. Outside, Vienna deteriorates and rejuvenates in swatches, a motley, poorly tended garden. From out here, the windows of the coffeehouse seem to protect the crowd inside from the elements and the tedium of any given day. Inside, they laugh and smoke and shout and argue and stare and whistle as the milky brew hardens to lace along the lip of their cups.

A group of scientists from the university begin to meet and throw their ideas into the mix with those of artists and novelists and visionaries who rebounded with mania from the depression that follows a nation’s defeat. The few grow in number through invitation only. Slowly their members accumulate and concepts clump from the soup of ideas and take shape until the soup deserves a name, so they are called around Europe, and even as far as the United States, the Vienna Circle.

At the center of the Circle is a circle: a clean, round, white marble tabletop. They select the Café Josephinum precisely for this table. A pen is passed counterclockwise. The first mark is made, an equation applied directly to the tabletop, a slash of black ink across the marble, a mathematical sentence amid the splatters. They all read the equation, homing in on the meaning amid the disordered drops. Mathematics is visual not auditory. They argue with their voices but more pointedly with their pens. They stain the marble with rays of symbolic logic in juicy black pigment that very nearly washes away.

They collect here every Thursday evening to distill their ideas—to distinguish science from superstition. At stake is Everything. Reality. Meaning. Their lives. They have lost any tolerance for ineffectual and embroidered attitudes, for mysticism or metaphysics. That is putting it too dispassionately. They hate mysticism and metaphysics, religion and faith. They loathe them. They want to separate out truth. They feel, I imagine, the near hysteria of sensing it just there, just beyond the nub of their fingers at the end of arms stretched to their limits.

I’m standing there, looking three hundred and sixty degrees around the table. Some of them stand out brighter than the others. They press forward and announce themselves. The mathematician Olga Hahn-Neurath is here. She has a small but valuable part to play in this script as does her husband, Otto Neurath, the over- sized socialist. Most important, Moritz Schlick is here to form the acme and source of the Circle. Olga, whose blindness descended with the conclusion of an infection, smokes her cigar while Otto drinks lethal doses of caffeine and Moritz settles himself with a brush of his lapels. The participation of the others present today is less imperative. A circle can be approximated by a handful of discrete points and the others will not be counted. There are perhaps more significant members of the Circle over the years, but these are the people who glow in color against my grainy black-and-white image of history. A grainy, worn, poorly resolved, monochromatic picture of a still scene. I can make out details if I look the shot over carefully. Outside, a wind frozen in time burns the blurred faces of incidental pedestrians. Men pin their hats to their heads with hands gloved by wind-worn skin. Inside a grand mirror traps the window’s images, a chunk of animated glass.

In a plain, dark wooden chair near the wall, almost hidden behind the floral arm of an upholstered booth, caught in the energy and enthusiasm of that hopeful time as though caught in a sandstorm, is Kurt Gödel.

In 1931 he is a young man of twenty-five, his sharpest edges still hidden beneath the soft pulp of youth. He has just discovered his theorems. With pride and anxiety he brings with him this discovery. His almost, not-quite paradox, his twisted loop of reason, will be his assurance of immortality. An immortality of his soul or just his name? This question will be the subject of his madness. Can I assert that suprahuman longevity will apply only to his name? And barely even that. Even now that we live under the shadow of his discovery, his name is hardly known. His appellation denotes a theorem; he’s an initial, not a man. Only here he is, a man in defense of his soul, in defense of truth, ready to alter the view of reality his friends have formulated on this marble table. He joins the Circle to tell the members that they are wrong, and he can prove it.

Gödel is taciturn, alone even in a crowd, back against the wall, looking out as though in the dark at the cinema. He is reticent but not unlikable. The attention with which his smooth hair, brushed back over his head away from his face, is creamed and tended hints at his strongest interest next to mathematics, namely women. His efforts often come to fruition, only adding to his mystery for a great many of the mathematicians around him. And while he has been known to show off a girlfriend or two, he keeps his real love a secret. His bruised apple, his sweet Adele.

There is something sweet about his face too, hidden as it is behind thick-rimmed goggle glasses, inverted binoculars, so that those who are drawn into a discussion of mathematics with him feel as though they are peering into a blurry distant horizon. The completely round black frames with a thick nosepiece have the effect of accentuating his eyes or replacing them with cartoon orbs—a physical manifestation of great metaphorical vision. They leave the suggestion, with anyone looking in, that all emphasis should be placed there on those sad windows or, more important, on the vast intellectual world that lies just beyond the focus of the binocular lenses.

He speaks only when spoken to and then only about mathematics. But his responses are stark and beautiful and the very few able to connect with him feel they have discovered an invaluable treasure. His sparse counsel is sought after and esteemed. This is a youth of impressive talent and intimidating strength. This is also a youth of impressive strangeness and intimidating weakness. Maybe he has no more weaknesses than the rest of us harbor, but his all seem so extreme—hypochondria, paranoia, schizophrenia. They are even more pronounced when laid alongside his incredible mental strengths. They appear as huge black voids, chunks taken out of an intensely shining star.

He is still all potential. The potential to be great, the potential to be mad. He will achieve both magnificently.

Everyone gathered on this Thursday, the rotating numbers accounting for some three dozen, believe in their very hearts that mathematics is unassailable. Gödel has come tonight to shatter their belief until all that is left are convincing pieces that when assembled erect a powerful monument to mathematics, but not an unassailable one—or at least not a complete one. Gödel will prove that some truths live outside of logic and that we can’t get there from here. Some people—people who probably distrust mathematics—are quick to claim that they knew all along that some truths are beyond mathematics. But they just didn’t. They didn’t know it. They didn’t prove it.

Gödel didn’t believe that truth would elude us. He proved that it would. He didn’t invent a myth to conform to his prejudice of the world—at least not when it came to mathematics. He discovered his theorem as surely as if it was a rock he had dug up from the ground. He could pass it around the table and it would be as real as that rock. If anyone cared to, they could dig it up where he buried it and find it just the same. Look for it and you’ll find it where he said it is, just off center from where you’re staring. There are faint stars in the night sky that you can see, but only if you look to the side of where they shine. They burn too weakly or are too far away to be seen directly, even if you stare. But you can see them out of the corner of your eye because the cells on the periphery of your retina are more sensitive to light. Maybe truth is just like that. You can see it, but only out of the corner of your eye.

From the Hardcover edition.

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Customer Reviews

Average Rating 2.5
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Sort by: Showing 1 – 5 of 4 Customer Reviews
  • Anonymous

    Posted September 17, 2006

    The wrong half of the story

    Godel and Turing are two of the greatest and most influential minds of the 20th century. They were also seriously disturbed individuals. Ms. Levin fails to provide a glimpse into the mind of genius and gives only a superficial rendering of the stereotypical socially dysfunctional genius.

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  • Anonymous

    Posted September 5, 2006

    Written in a prose lacking elegance, clarity and precision, and riddled with grammatical errors

    ¿Proper words in proper places,¿ wrote the great Irish writer Jonathan Swift, ¿make the true definition of style.¿ I have always believed that if you wish to consider a novel as good, it must be written well, with clarity and precision. And, of course, adhering to the rules of grammar always helps. I had read a good review of this novel in The New York Times, and so I decided to read this book, hoping to experience the joy of reading a book that many critics have admired. So, imagine my surprise as I read the first two pages. The prose lacked elegance and clarity, the words lacked precision and, to make the matter worse, riddled with grammatical errors. I checked who published this book, and I was quite astonished, because Knopf Publishing Group publishes V. S. Naipaul¿s books also. (Without a doubt, Naipaul, winner of the Nobel Prize in literature, is the greatest master of English prose among living writers.) These five sentences are from the first chapter of the novel: ¿The Cafe Josephinum is a smell first, a stinging smell of roasted Turkish beans too heavy to waft on air and so waiting instead for the more powerful current of steam blown off the surface of boiling saucers fomenting to coffee. By merely snorting the vapors out of the air, patrons become overstimulated. The cafe appears in the brain as this delicious, muddy scent first, awaking a memory of the shifting room of mirrors second--the memory nearly as energetic as the actual sight of the room, which appears in the mind only third. The coffee is a fuel to power ideas. A fuel for the anxious hope that the harvest of art and words and logic will be the richest ever because only the most fecund season will see them through the siege of this terrible winter and the siege of that terrible war.¿ After reading these sentences three times, I still didn¿t understand what the author was trying to inform the reader. It felt like gobbledygook to me. I know that one can snort snuff, cocaine, or a drug in powder form, but how does one snort vapors? Since vapors just hang in the air, you simply breathe in the vapor, as you breathe air. No violent force is needed to breathe the vapors in. I have never heard of anyone snorting vapors. Also, read what the author says about Olga: ¿Olga, whose blindness descended with the conclusion of an infection,¿..¿. What does the author mean? Does she simply mean to inform the reader that Olga¿s blindness was caused by an infection? ¿Everyone gathered on this Thursday, the rotating numbers accounting for some three dozen, believe in their very hearts that mathematics is unassailable.¿ Every one gathered on this Thursday believe in their very hearts? Did an editor at Knopf Publishing Group ever read this book? I can go on and on, but what¿s the point? Well, you get the drift. Give this book to an English grammarian and watch him pass out after reading ten pages. Among the people involved in the publication of this book, however, the person who has impressed me the most is the author¿s agent. I admire her ability to persuade and to sell. Considering the fact that she sold this horror of the English language to the venerable Knopf Publishing Group, I have no doubt that she is a great asset to her agency.

    0 out of 2 people found this review helpful.

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    Posted January 15, 2010

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    Posted October 26, 2010

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    Posted December 14, 2008

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