A Madman Dreams of Turing Machines
AI visionary Alan Turing set into motion our century of machine intelligence, yet his life was fraught with plot turns that outpaced fiction. Does his story matter? Will ours?
Who of us will be remembered? Are thoughts more valuable than the thinker? Which of life’s moments define the trajectory of genius? In the wake of last week’s event on AI, I found myself considering these questions, as I did while writing a book on Alan Turing. When contemplating our AI century, you may find his story evocative. This week, excerpts from the novel on the prime movers of thinking machines.
A MADMAN DREAMS OF TURING MACHINES
There is no beginning. I’ve tried to invent one but it was a lie and I don’t want to be a liar. This story will end where it began, in the middle. A triangle or a circle. A closed loop with three points.
At one apex is a paranoid lunatic, at another is a lonesome outcast: Kurt Gödel, the greatest logician of many centuries; and Alan Turing, the brilliant code breaker and mathematician. Their genius is a testament to our own worth, an antidote to insignificance; and their bounteous flaws are luckless but seemingly natural complements, as though greatness can be doled out only with an equal measure of weakness. These two people converge in history and diverge in belief. They act out lives that are only tangentially related and deaths that are written for each other, inverted reflections. They are both brilliantly original and outsiders. They are both loyal to reason and to truth. They are both besotted with mathematics.
But for all their devotion, mathematics is indifferent, unaltered by any of their dramas—Gödel’s psychotic delusions, Turing’s criminalized sexuality. One plus one will always be two. Their broken lives are mere anecdotes in the margins of their discoveries. But then their discoveries are evidence of our purpose, and their lives are parables on free will. Against indifference, I want to tell their stories.
Don’t our stories matter?
I shouldn’t even be here but some things you can only get to in the most awkward ways. Even if I tried to hide it, to lie, the truth is it’s still me telling this story. The unsorted catalogue of biographical facts provides nothing without stories with their dents and omissions and sometimes outright lies to create meaning that just won’t emerge from the debris of unassembled facts. Because some truths can never be proven by adhering to the rules. So this whole story about Truth is a Lie. The liar says, This is a lie.
I am that liar, the third and final point on the triangle, the weak link, the wobbling hinge, the misaligned vertex. I am meant to carry on from the previous point and give over to the next. But I don’t know where to begin. I am standing on a street, in a city. I’m going to catch a train. There are people streaming in all directions and one old woman strolling. Will any of us be remembered? Do any of us matter?
This story about truth and logic leads to atheism and mysticism. To despair and suicide. To the future, our past. To the present. So here’s a starting point as arbitrary as any because logic does not unfold in time. It exists forever into the past, dictating how the universe began; and forever into the future, our fate already written by the inescapable rules of logic. We can enforce chronology because the linearity of time helps; it gives us roles in the script, a place to start and to end. So here I start. In England. It is the year 1928. This place is as good a place, this time as good a time, as any.
D O R S E T, E N G L A N D. 1928
The scene is Sherborne boarding school for boys in Dorset. A sixteen-year-old boy lies in the grit and sawdust against the rough unfinished foundation below the floorboards of the dayroom at Westcott House. The boy under the floor is Alan Turing.
He isn’t there by choice. It has already been a while since the sudden shoving and scrabbling and it went dark. The wooden boards slotted into place. The clean ominous clink. The weighty, fitted lid of a makeshift coffin. Turing buried alive. It’s a transparent observation, but children always underestimate the menace of their weapons.
There is a window in time, no longer than it takes for a few wrought puffs of air to loosen dust clinging awkwardly to the underside of the floorboard, when the wood shifts a millimeter in response to his struggling. The force of several tangled arms pushing downward minus the force of one boy pushing upward. He isn’t entirely weak, Turing. He is wiry and strong, with a sinewy musculature. He strains and shoves until desperation bellows out of him in a deeper register than his voice can ordinarily reach. While the sound, a bit of a horror really, makes some of them anxious, no one of the boys has the authority to stop the others and so, with a small pit of dread planted deep in the lining at the tops of their stomachs, they collaborate to drag the heavy old oak table into place, two legs on the loose board, two well anchored on firmer slats.
Maybe this is an initiation ceremony. He grasps at the possibility optimistically. He means no irony. He does not mean a symbolic initiation of a boy into manhood. He neither uses nor understands metaphors. He means literally. There is a precedent for this miscomprehension. During his first week at Sherborne in 1925, there was an official ceremony that culminated in the older boys roughly collecting his arms and legs so that he was disconnected from the ground and folded up until he fit snugly into a barrel. He was then kicked down the hall. Although the blows were delivered indirectly, the humiliation was delivered rather more directly. Not knowing what else to do, he gave himself over to the incident. He bounced along—quite good-naturedly all in all—with eyes focused on a sliver of space between buckled wooden bands. But he thought it was stupid. He thought it was probably really stupid.
This is stupid too. He knows it is. He wants to shriek, to curse them, but the epithets catch in his throat, rough as sticklebacks. The boards brutally press his face to the right, mashing his cheek, his arms, and his thighs, so every arrested move is agony. The blackness an additional defeat.
He panics. He chokes on his own saliva. He twists. He knots his toes. He clamps his legs. He shrieks—a squeal that reaches up high in pitch as it mounts into a waterless sob. Struggling is making it worse. This is claustrophobia. This is delirium. Dementia. Even as he gags and spits vomit, he wants to yield. But he can’t relax, soften, surrender to the incident, be kicked down the hall in a wooden barrel. While he knows they are stupid, while he knows they are phonies, he also admits there are many things in the world he does not understand and, on occasion, it is better to confess this lack of knowledge of the world. On these occasions it is better to accept being trapped beneath the loose boards of Westcott House dayroom. But he can’t.
His knees grind. His toes kink. His back seizes and he recoils with a hyena’s laugh—not altogether uncharacteristic for Turing—such strange speech deserves a complementary laugh—but exaggerated, a high and serrated scream of a laugh. 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.
His overzealous volume and peculiar elocution sometimes come off as cheerful. This malfunction, along with the tendency to withdraw, leaves the masters of the school conflicted as to whether or not he is happy. When they correspond with Mrs. Turing, they try to structure their observations of her son into a poignant conclusion but bungle the job. Unable to temper their frustration they ultimately blurt, “Undeniably, he is not a normal boy.” This much she knew.
Above the floorboards, the room becomes a cavity trapping his shrieking laughter until it dies off ominously. The boys try to show off their callousness by ignoring the cackling vibrato slicing their ears. While they continue to play an anomalously quiet game, the pit of dread is jostled and falls deep into the fertile gastrointestinal soil where it begins its life cycle. Will it fester as an ulcer, or blossom into rancid abnormal cells? That depends on how each chooses to tend that messy garden.
Turing can’t see through the darkness. The blackness coats his open eyes, as do large salty dust grains so that his eyes burn and water but technically it doesn’t amount to crying. That comes later, when his ordeal is over. Or at least this one skirmish in his lifelong ordeal—a life of loneliness, persecution, and depression, lightly salted with childish bouts of happiness. But it won’t be a bad life all told and it will come to be laden with achievement and significance so great that even he never recognizes it.
This isn’t an initiation ceremony. It is punishment. Punishment for looking right through them, for looking right inside them.
There are bolts of luminescence in the world. Hard, brilliant candies that crackle like jewels, fanning pointed rays of gold through an otherwise gray landscape. Sometimes Alan can see these splendors unaided. He finds them in the woods or sees them in the sky. Sometimes he has to distill them from ordinary rock with clumsy chemical experiments he executes poorly in his room but pursues with the devotion of an alchemist until they yield gold, or just iodine, or some other element with a rightful place in the periodic table. Sometimes he discovers them with his mind like the inverse trigonometric function that he managed to express as an infinite series of simpler algebraic forms. These are the best, these dazzling gems of his brain’s relentless, systematic expeditions. The smells of his chemicals and their incendiary threat don’t deter him, but others are irritated by the mess and complain. His pure mathematical discoveries have the advantage of privacy—splinters of truth broken through the skin of confusion, framed by pools of crimson that only he can see.
To Alan, this is the world: luminous boulders, a string of precious stones. He jumps from one to the next just barely able to balance above the murky sea of fakes and phonies. Their world of facial signals and false strides, social norms. Their indirect, dull universe of dishonesty and contests and artifice.
He is baffled and lost in the tangled, witty exchanges the other boys are learning—mechanisms that evade candor with the flourish of the middle class. Through the swirl of debris of human behavior, he gropes for truth; and if he finds it, he stares at truth’s sparkle with a fidelity that offends the others. Annoyed, resentful, they kick the rocks up in his face, not knowing why he stares.
Seven years to the day that he is buried alive for nearly a full hour, Alan Turing lies in the grass of Grantchester Meadows. He came here by accident. He left his rooms in King’s College in search of an apple in the open-air market in Cambridge’s town center. The red apple skins in the first stall, usually his favorite, were papered with the withered remains of lettuce, evidence of an early morning transportation accident. After his initial revulsion, he considered buying the fruit and washing it clean but that option was dashed by the proximity of the red beets. The colors of the crops weren’t exactly the same but they were in the same family. And some of the beets were touching some of the apples, which in turn touched other apples, forming a chain of spilled crimson contaminating the box and spoiling his appetite. He considered settling for a yellow or green specimen until he spotted a young bloke displaying scarcely any other produce except a crate of red apples balanced on a barrel.
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.
Before the late hours, still on his back, growing cold in the dew, he sees how chess might be mechanized because he sees exactly how to mechanize 1+1. He invents a machine that can add. A machine with no mind, no spirit, no soul. His discovery shines in his thoughts. This jewel of his mind’s systematic expedition casts piercing rays of gold through the rotating dome above him.
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 are more sensitive to light. Maybe truth is just like that. You can see it, but only out of the corner of your eye.
Rising into the outright cold of the early night, he runs home, losing his apple, which falls from his pocket and gradually rots into the matter of the meadow.
These excerpts, drawn from the novel, A Madman Dreams of Turing Machines, were lightly edited for context.
It is wonderful; the way you play with the same self referential style of reasoning that I think is a core element of Godel's incompleteness theorem in literary terms through the transitional paragraph where the narrator (it reads like you are the narrator) riffs about being a liar.
I've not read the book, but I'm sure it elsewhere must address the fact that Godel's theorem and Turing's own proof about determining the runtime of a program are equivalent as well. Which deepens what that paragraph is suggesting further.
This is brilliant.