Het verhaal start in het Wenen van 1931

We zijn in een koffiehuis waar kunstenaars en wetenschappelijk onderzoekers vaak komen en elkaar op allerlei manieren inspireren. Zoals hier en nu de Wiener Kreis met de Neurath's, Moritz Schlick. En Kurt Gödel.

"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." [mijn nadruk] (6)

"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."(11)

Dan over naar Dorset, England

Waar Turing - iemand die 'anders is' en zich sociaal gezien onhandig gedraagt - in 1928 door zijn klasgenoten gepest wordt.

"Either he doesn't understand how to clean or he doesn't care or, most flattering of all interpretations, he is too preoccupied with deep and complex distractions, the sanctity and purity of mathematics, the profound truth so completely immune to human stains that even his clumsy approach can't tarnish its luster. Probably he just does not understand what it means to be clean, both for personal hygiene and for social success."(18)

En zo blijft het heen en weer gaan tussen Wenen en Dorset.

Terug naar Gödel.

"It's Moritz Schlick's circle. Drawn together by his invitation and kept together by his soothing tones. They come here to orbit around truth, to throw off centuries of misguided faith, the shackles of religion, the hypnotism of metaphysics."(55)

"It is no surprise that in his [Schlicks] review of the trajectory that brought him here, there are many images of Wittgenstein. The man mesmerizes anyone who comes near him, and he mesmerized Moritz. Wittgenstein is a philosopher, a great philosopher, and progeny of one of the most extravagantly wealthy and cultured families in Vienna, in fact, in all of Europe. Some people say he is the greatest philosopher of the twentieth century. He certainly thinks so. Members of the Circle obsess over his only book, the Tractatus Logico-Philosophicus, a series of logical proclamations, a polemic, each phrase exuded without explanation or defense ..."(63)

[Wat een waardeoordeel is dat toch. Een boeiende uitstraling - er wordt hier nogal overdreven werk gemaakt van Wittgensteins charisma, alsof niemand er weerstand aan kon bieden - maakt iemand nog niet 'de beste filosoof van de 20ste eeuw'. Zo'n bewering zou niet eens passen in Wittgensteins filosofie van die periode, trouwens.]

"A man with a rare and intoxicating personality, he rules them from afar and with near complete disinterest. He never comes to the Café Josephinum, perhaps only heightening their obsession with him, the intense desire fed on unrequited love. Moritz is the only one Wittgenstein actually agrees to see in person."(63)

"In the commotion of the café, with his Circle to bear witness, Moritz, animated by an aberrant sarcasm and contempt, tore off the yoke of German metaphysics, ripping down notions like “The Absolute,” “Spirit,” and “God” and watched them vaporize before hitting the ground. Faith, Mysticism — it's not that these ideas are false. They are meaningless. Meaningless statements vying for the status of Truth. Pathetic contaminants fouling people's minds."(65)

Terug naar Dorset, het jaar 1930

Dat is het jaar waarin Turings jeugdvriend Chris overlijdt.

En weer terug naar Wenen

Daar probeert Gödel zijn diepste inzicht naar voren te brengen - dat binnen de wiskunde niet alles compleet bewijsbaar is - , ook al brengt hem dat in aanvaring met Moritz:

"Playing the part of the good big sister, Olga pitched forward in her seat, her eyes looking up as though waiting to receive a salve. She tried to catch up to Kurt's argument, keeping pace better than the others, still not quite there. “And then you prove the relation is true?” “No, I prove that the truth or falsity of the relation cannot be decided by adhering to the rules of arithmetic.”
“And so it has no mathematical proof.”
“Exactly. But this is precisely what the relation asserts: This statement is unprovable.”
“So it is true?”
“Yes, it is true. We can recognize its truth plainly, not through mathematical rules, but from outside of mathematics. The truth of this statement does not follow from the inflexible chain of logical relations, the links that cleave one mathematical fact to another. It comes instead from a glance.”"(98)

"“Are you saying Moritz is wrong?”
“Yes.”
Otto drew a deep breath, making room for his belly to expand and then, like a Bavarian accordion, wheezed laughter into the parlor, slapping his stomach as he rose to order a cake from the bar. Otto was wholly entertained, elevated by adrenaline. The possibility gave him a start, an instinctive jolt. But Moritz took the news less well. Crossing his legs and arms as if to bar the very idea, coming as close to anger as Moritz ever gets, he tucked in his chin to point his words toward Kurt, the tone meant to highlight the ridiculous. “Is Wittgenstein wrong?”
Gödel's hands sprung out from within his overcoat, whittled down spikes ruefully warding off his own reply. “Yes.”
There is nearly a roar from the students, but Otto applauded merrily. “What if Kurt is right? What is so bad?”
Moritz shook his finger vigorously. “It is cause for the greatest despair. Reason. Must. Prevail. And for that, mathematics must be perfect — and complete. It must be logically possible to answer all meaningful questions. It must be possible.”
To which Kurt replied, “Mathematics is perfect. But it is not complete. To see some truths you must stand outside and look in.”
“No,” Moritz nearly bellowed. He followed with a backhanded swat at the air, holding his upper arm as though waving a flag. “No.”"(100)

"His whole thin strand of a body pleaded, “Moritz,” leaning in over the marble table and the liquid lines on its surface. His words were elongated into a lament, “We cannot prove it is true, but we can recognize that it is true. Our minds can see truth. See it even when mathematics cannot. Our minds are bigger than that. Our minds are bigger."(102)

[Moritz kan geen kritiek hebben op zijn opvattingen: alles moet compleet bewijsbaar zijn vanuit de wiskunde. En er mag geen kritiek geleverd worden op Wittgenstein die hij totaal kritiekloos idealiseert. Waarna Moritz doet wat zo veel mensen uit de hogere burgerij van die tijd zo goed konden: iemand doodzwijgen. Hij verandert bruusk van onderwerp en schuift de opvattingen van Gödel onder de tafel. Diep beledigd gaat Gödel er vandoor.]

Nu schakelen we over naar New York City. Naar de auteur zelf. En dan weer naar Cambridge, Engeland, in het jaar 1935.

"Although Alan is agitated by his own faith — a faith that has never crystallized as well as he had hoped — he does not allow his spiritual leniency to corrupt his pure view of mathematics. As a tribute to Morcom, Turing analyzed sulfur dioxide and iodic acid in explicit mathematical detail. Beneath the differential equations and the chemical compositions he found a sharp result. Lucid and true. He recorded it in black ink on white paper. His proof did not glow in blue or throb with the thrill of the moment the beaker trapped Chris's radiance. But it was honest and right. His homage to Chris."(113)

"Lying on his back in the lush grass with a view of gray sky, Alan thinks about choice. He thinks about rules. About method. About mechanization. He wonders if thought itself can be mechanized. The brain modeled by a mechanical process — by a machine. He wonders if a machine could think. He draws the squares of a chessboard in a small, slightly damp notebook he keeps in his back pocket. Then he redraws the board as a strip, unfolding the blocks into a tape — the beginning of an infinite tape of squares. He draws 0s and 1s into the squares, crossing them out and starting again with small corrections. He encodes rules in the patterns of numbers. Then he draws a machine that reads the tape. He is not a fine draftsman so the machine is rubbed out several times and replaced with a simple illustration of a box. The finite states of his machine will respond to the pattern of 0s and 1s, will do as they instruct."(114)

"The human mind can also be reduced to a machine. This idea drives all the others as he runs on grass, past trees, over bridges, through cattle. States of the mind can be replaced by states of the machine. Human thought can be broken down into simple rules, instructions a machine can follow. Thought can be mechanized. The connection isn't perfectly clear, but it is there, the catalyst of a great crystal. It is not just that thought can be mechanized. It is mechanized. The brain is a machine. A biological machine."(118)

[Maar waarom zou je de menselijke geest willen reduceren tot iets wat alleen maar mechanisch regels en instructies volgt als een machine? Waarom is dat zo belangrijk?]

"Over the coming days and weeks and on into months, he feels the last of his spiritualism evaporate like the cooling remains of a fever. He is left without remorse and wonders how he ever clung to his awkward faith with such emotion. We're just machines. At the age of twenty-three and for the rest of his life he embraces, without reservation, a mathematics that exists independently of us — although we, by contrast, do not live independently of it. We are biological machines. Nothing more. We have no souls, no spirit. But we are bound to mathematics and mathematics is flawless. This has to be true. Where is God in 1 + 1 = 2? There is no God."(119)

Naar Wenen in het jaar 1936

Gödel; is zwaar teleurgesteld en belandt uiteindelijk in een psychiatrische inrichting. De wegh ernaartoe was hobbelig. Hij verbleef bijvoorbeeld een tijdje in Princeton, USA.

"On his first day at the institute in Princeton he was greeted by at least one familiar face, the economist Oskar Morgenstern, whom Moritz had introduced to the Vienna Circle several years earlier. Oskar sought refuge in America after his brisk dismissal as the director of the Austrian Institute for Economic Research owing to what the Nazis characterized as his despicable politics. He established himself as an accomplished scholar at the Institute for Advanced Study and though grateful for the shelter provided by the New World, he often ached for the disease-rotted soul of his own country." [mijn nadruk] (125)

"His initial optimism on arriving in the New World only served to increase the height of his fall as isolation disoriented him. He was nothing, nobody, insignificant. A temporary scholar in America on a year-by-year stipend. No permanent position on offer. Not in Europe, not in Princeton."(128)

Hij keert depressief terug naar Wenen, maar als Schlick daar - door een stalker met Nazisympathieën - wordt vermoord wordt is het gedaan met Gödel en moet hij opgenomen worden.

"While Wittgenstein's frustration with Moritz and indeed the entire world often flared wildly, Moritz endured the rages and the fickle turns with characteristic patience. (...) Moritz saw that Wittgenstein was not a madman, nor a bully. He was tormented, fragile even, sometimes crumpling like an eggshell. And so Moritz managed not to feel hurt by the increasingly frequent bites."(134)

"Moritz is dead. He is lost but for fragments in the minds of those who have moved around the globe since his death. The Vienna Circle died with him as the headlines condemned Moritz Schlick as a Jew sympathizer who got what he deserved at the top of the stairs in the University of Vienna at the hands of a pan-Germanic hero who rightly killed this Jew philosopher." [mijn nadruk] (139)

Dan Wenen in 1938

"In a month's time, Kurt leaves Europe forever, traveling to the United States by boat, sailing around the globe, past Japan, past glorious California, to return to green and handsome Princeton, New Jersey. Something else is remarkable about that trip. This time he isn't traveling to America alone. This time he brings his defense — his new wife, Adele."(146)

En weer naar Cambridge, nu in 1939

Turing gaat voor de regering werken om de gecodeerde berichten van de Duitsers te kraken. Hij volgt op dat moment eenn achttal colleges bij Wittgenstein, "Cambridge's most noted recent émigré and current professor of philosophy."(150).

"Turing has become the focus of the philosopher's campaign to shake the idolatry for science out of people's eyes, so his course on mathematics has become a live debate between them. Alan is unaccustomed to philosophical methods of argumentation. The course that Alan teaches happens to have the same title but by contrast is a forceful lesson in mathematical methods, an impressive demonstration of logical manipulations of symbols, and nearly opposite Wittgenstein's in every way."(151)

Meer over Wittgenstein. Turing heeft na het achtste college geen contact meer met Wittgenstein en werkt verder aan het kraken van codes.

"Several of the local residents of Buckinghamshire already suspect something is going on at Bletchley Park, the mansion on the hill — something for His Majesty's Service or MI5."(164)

Turing werkt er in Barak 8. Zijn verloofde Joan werkt er ook, is ook goed in wiskunde. Een gesprek tussen hen:

"“We're not free. None of us. There's no such thing as free will. I don't know. I don't think so. If a machine can mechanically add a list of numbers, it is entirely determined and not at all exercising free will.”
“But that's just a rote process; it shows no evidence of thought.”
“Just because it's simple? Enigma is a machine; the outcome of an encryption is completely determined by the configuration, more elaborate, but no more free.” “It's still not thought, Alan, not human, independent, free thought and action. Enigma is just a typewriter. I strike a key and it is entirely fixed which letter that key transforms into.”
“Yes, it is entirely determined.”
“Enigma is a machine, not a living, breathing person,” like me, she is getting near to crying. Like me.
“We are machines too, Joan. Far more elaborate but that's all. One day there will be machines, like human computers, only electrical ones. A mechanical-electrical computer. I'm going to build one after the war, maybe taking something of our machines but I have a more general design in mind. It will add or divide or compute any number of tasks. It will be universal, like the universal machine that answers mathematical questions. Only this one will be real, not just a logical possibility.” And grinning as if to himself he says simply, “I'm going to build a brain.”"(186)

[Ik vind zo'n kijk op mensen-als-machines zoals Turing die heeft zorgwekkend. En waarom zou je die opvatting serieus nemen? De man ziet zijn eigen perspectief niet.]

"“But we are machines. Machines just beat other machines. One day the computers, they'll think just as we do. Will they be free? Or are they just determined machines carrying out the elaborate processes they are configured to execute? Are we free? Or are we just determined machines, bound to carry out the elaborate processes that each of us is configured to execute?” As if in illustration, he finally moves his pawn. He thinks he is just three moves from implementing his game plan. His weakness in this game, and in life, is that he is never prepared for how others will act. They are predetermined but too complex to solve or predict, and there are rules that he is just no good at applying.
“But none of our machines think. They don't make any actual decisions.”" [mijn nadruk] (187)

"“What do you mean 'think'? How can it think? How would you even know if a machine was thinking?”
“Ask it.”
“Ask it?”
“Yes, if it can imitate conscious thinking, then who are we to say it is not doing so.”
There is a pause as Joan internally tests her own atheism. “And if we are just executing programs, who did the programming?”"(189)

"“Alan, when you explained Gödel's incompleteness theorems to me, you said that there were true statements that could never be proven. Isn't that right? So Gödel proved that we can recognize true statements even if they can't be logically proven?”
“Yes.”
“So if a machine is programmed to be perfectly logical, if it can only follow one logical step after another, how could it ever recognize one of these true but unprovable statements? And if it can't see a truth as plainly as you or I can because it blindly follows a series of instructions, then how can we call it intelligent? I guess I'm trying to ask if Gödel's theorems, and indeed your own, imply that machines can never think?”"(190)

""If a machine is expected to be infallible, it cannot also be intelligent. Gödel's theorem implies almost exactly this. When we program a machine, we only want to get it started. What we really want, I suppose, is to build a machine that can adapt so that it is like any living thing that starts from a simple program and evolves a complex intelligence. Then we will have them — machines that are as alive as we are. As free or as not free as us.”"(190)

Dan naar Wilmslow, England. 1952

"Hollymeade is a semi-detached Victorian house in the middle-class town of Wilmslow, located a comfortable ten miles south of Manchester, where Alan Turing continues his postwar life with an appointment to oversee design of a massive computer at the University of Manchester."(193)

Turings arrestatie vanwege zijn homoseksuele gedrag.

Dan naar Princeton, USA. Het jaar is 1977.

Gödel aan het woord tegen Oskar Morgenstern

"“If I die, you must promise to publish my article refuting Alan Turing's thesis on the limits of the mind. A Turing machine is a concept, equivalent to a mechanical procedure or algorithm. Turing was able to completely replace reasoning by mechanical operations on formulas — by Turing machines. Good, agreed? However, are we supposed to equate the human soul with a Turing machine? No. There is a philosophical error in Turing's work. Turing in his 1937 paper, page 250, gives an argument which is supposed to show that mental procedures cannot go beyond mechanical procedures. However this argument is inconclusive. What Turing disregards completely is the fact that mind, in its use, is not static, but constantly developing. They murdered him, you realize?”" [mijn nadruk] (213)

En hij sterft omdat hij niet voor zichzelf kan zorgen als Adele dat vanwwege haar eigen fysieke problemen niet kan.

Terug naar Engeland, naar Wilmslow. Het jaar is 1954

Turing werd veroordeeld tot gevangenistraf of chemische castratie. Hij koos het laatste. Hij voelt zich vernederd en pleegt zelfmoord.

Nog eens naar New York City, naar de auteur zelf.