{"product_id":"a-madman-dreams-of-turing-machines-isbn-9781400032402","title":"A Madman Dreams of Turing Machines","description":"\u003cp\u003eKurt 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.\u003c\/p\u003e“Intelligent . . . compelling. . . . As Levin alternates between the lives of Turing and G?del, she delivers a convincing, palpably human portrait of solitary genius.” —\u003ci\u003eThe Philadelphia Inquirer\u003c\/i\u003e“A simple work of genius.”—\u003ci\u003eToronto Globe \u0026amp; Mail\u003c\/i\u003e“Her characters and their century come brilliantly . . . alive.” —\u003ci\u003eThe Los Angeles Times Book Review\u003c\/i\u003e“Like a lyrical mash-up, Levin interweaves the personal narrative style of her first book with taut prose evocative of Alan Lightman's \u003ci\u003eEinstein's Dreams\u003c\/i\u003e.” —\u003ci\u003eSeed Magazine\u003c\/i\u003e\u003cp\u003eBorn in Texas and raised in Chicago, \u003cb\u003eJanna Levin\u003c\/b\u003e 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 \u003ci\u003eHow the Universe Got Its Spots\u003c\/i\u003e, published in 2003 by Anchor.\u003c\/p\u003eVienna, Austria. 1931The 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 \u003ci\u003ehate\u003c\/i\u003e mysticism and metaphysics, religion and  faith. They \u003ci\u003eloathe\u003c\/i\u003e 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 \u003ci\u003eknow\u003c\/i\u003e it.  They didn’t prove it.Gödel didn’t \u003ci\u003ebelieve\u003c\/i\u003e that truth would elude us. He \u003ci\u003eproved\u003c\/i\u003e 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 \u003ci\u003ecan\u003c\/i\u003e 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.","brand":"Anchor","offers":[{"title":"Default Title","offer_id":46302328193253,"sku":"NP9781400032402","price":17.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781400032402.jpg?v=1767720623","url":"https:\/\/k12savings.com\/products\/a-madman-dreams-of-turing-machines-isbn-9781400032402","provider":"K12savings","version":"1.0","type":"link"}