Saturday, February 09, 2013

A Literary Reference : A Mad Man Dreams Of Turing Machines

As they lean on the table above Alan, there is an exchange between Chris and one of the other boys. Alan wants to claw his way through the wood and nails and see if Chris is up for a game of chess. If only he could, Turing, covered in dirt and a very little bit of blood, would gladly clamber out of the floor without explaining the peculiar circumstances of his entrance, without resentment, and plead with Chris for a thoughtful game of chess.

During their last game Turing lost swiftly with an abysmal sequence of moves. He was searching for an algorithm to ensure board domination instead of adhering to the strategy of the moment. When Chris executed a move, deciding on the rook, Turing was flooded with a feeling of comfort - something like assurance because Chris chose. He exercised his free will and eliminated Turing's knight and Alan could see with his own eyes that he was free. The source of this will in the face of a scientific realism Turing knew to be true could only be the soul, could only be a manifestation of God. Where is God in 1+1=2? God is in our mind's recognition that 1+1=2.

But even as he felt the warmth of this revelation, something stuck in his head. Chris was following some instructions. He moved the rook forward four squares, respecting the pieces to the left and the right, respecting the rules of the game. He followed rules.


He writes to Chris in his diary, where he invents arguments about chemical models, or a blueprint for an automated machine, or a debate over K. Gödel's incompleteness theorems. He and Chris could have spent days together like this, talking all night, taking breaks with a game of chess. Alan is reassured by the memory of Chris shifting a rook back at Sherborne. Chris made a choice. He exercised free will. But still after all these years there remains a barb in Alan's head, a snare in his faith. Chris adhered to the rules. He executed a simple mechanical task. He applied some method. A computation.

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 eoncodes rules in the pattern 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 of night, 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.


There must be an algorithm for playing chess or for having an idea or for thinking itself. Press a button and a machine could execute the precise instruction and produce an answer or a move in a game of chess, or break a code. But then people all behave so differently. They respond so unexpectedly to the same input. Maybe somebody else would dig here and have an entirely different thought. Maybe someone else would think, Mud is filthy. Or, Tomatoes could be grown here. he thinks about predilections, tendencies, and desires - how these are determined. He thinks about he loathes boiled potatoes next to buttered rice. They are the same color but one comes in big lumps and the other horrid grains. The combination is enough to prompt Alan to fast. But his friend Joan loves her buttered rice topped with boiled potatoes. He and Joan execute different algorithms. They are different people with different tastes. Thinking about these thoughts he has another. There are many different algorithms that might produce some humanlike response. But surely there are many fewer right sequences than there are wrong sequences - sequences that could not produce a humanlike response. Maybe huge chunks of these wrong algorithms could be discarded somehow so that a smaller vein of correct sequences remain. But this is just like his original thought that precipitated his thought about thought. There is only one key to the encoded German transmission. It is nearly impossible to isolate. But huge possible combinations clearly lead nowhere: they are empty lumps of earth. If he could build a machine to run through possible combinations, a machine that stops when the combination goes wrong, then they could discard all of the bad keys, shovel them out of the way. They'd have a real chance of sifting through what's left, a far smaller number of possibilities. They shouldn't be trying to find the one right code; they should be trying to shovel away all the wrong ones.


Something is missing in his brain, a filter, an interpreter, a simple mechanism that explains the meaning of a smile or the current of feeling directing the hundreds of muscles in a face. Even the old woman who tends house at his residence in Bletchley Park seems a prophet on commonplace matters as she sweeps the walkway and makes wry comment as he comes and goes. "Your Miss Joan is looking for more than a chess game, Master Turing." Obvious, inane reflections of a meddling housekeeper but to Alan they are words of brilliance from a sage who knows things he cannot extract from life no matter how intently he focuses his attention. Exasperated with his genuine oblivion she says, "She wants to be your bride, Master Turing," and shakes her wiry shroud of hair as vigorously as she sweeps, with such punishing force it reminds Alan of how the Indian nannies used to scrub him red raw in the bath when his father was stationed on the subcontinent as a British civil servant.


It is the end of an eleven-hour shift, the end of too many months of turns in tactics and encryptions and machines. It is the middle of the night. Alan and Joan are still awake but just exhausted enough for a game of chess.

"You're a hero, Alan."

He doesn't look up from the game, but his head sort of bobs about nearly level with his shoulders. He is embarrassed.

"We're all heroes, Joan," he says to her white queen, leaning too far over the board; the lower pocket of his open navy jacket slides two pawns out of their squares as he looks over the moves. He likes to get a nearly aerial view of the checked board and the static war they enact.

"If anything, I'm a heroine, you know," she says in imitation of a petulant adolescent. She glares at him with narrowed eyes, a bit disappointed that her sentence landed on an accusation.

"To me you'll always be a hero," Alan sniggers through his nose, not fully realizing the twist in the pinch he just delivered.

Joan takes some satisfaction in knowing she is going to win this game. She can already see it will take only two more moves that Alan is not likely to obstruct. he is looking for a global pattern again, trying to invent a rule for generating the right strategy so that he misses this one reality, simple as it is. The board is hers, a worn cardboard pocket game not intended to weather the traffic of Alan's homemade pieces. It puckers upwards in the middle when the pieces are intiially aligned on opposing sides and then dips downwards in the middle as the game advances. Alan must have looked quite a sight wearing his gas mask, digging in an exposed clay pit near Bletchley, and then attempting to balance as he cycled home with fistfuls of clay hanging over the rim of the steering wheel. He molded the pieces in his room and baked them on his own hob. He made extras, though not enough that they can play with an entirely undamaged set. One-third are broken to some extent but their identity is still pretty easy to ascertain, although one of her knights could double as a pawn.

Alan makes a move. Who knows what he is thinking? It looks random after all that deliberation. He still hangs over the board so that she has to reach under the fringe of his hair for her bishop as she shifts the piece into place with neither deliberation nor hesitation.

Amazed by what he perceives as her lack of considered thought over her strategy, Alan shouts, "Joan!" and cranes his neck to look up at her, though not square in the eyes. His mouth hangs open with disbelief and he looks down at the game and up at her a few times before shouting again, "Joan!" and then he chuckles, bewildered.

"I know what I'm doing," she says, and she does.

They might win this war. She catches herself fretting anxiously over what will happen then. There's hope and relief but also fear that Alan's scheme for her will fail, that she will be alone. She wants Alan to fret with her. "When the war ends, we'll be free. We'll have played some part in that."

While she may have in mind the freedom to finally marry, this is not where he is led through the labyrinth of his mind. So many images occurring to a person at once. So many different thoughts and different levels of awareness. So hard to communicate or to witness. The word "freedom" emerges in his mind, the final output after a chain reaction of impulses and transformations until it is there, the one surviving thought. His expression darkens but he pretends to concentrate on his war tactics, fidgeting with the dry broken pieces he molded with his own hands. Are these very figurines proof of his free will? "We're never free, Joan".


"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.


He stops to chew on his fingers. "The machine must be allowed to have contact with human beings in order that it may adapt itself to their standards. The game of chess may perhaps be rather suitable for this purpose, as the moves of the opponent will automatically provide this contact."

"As your human opponent, Alan, I'm honored to be able to provide you with some proper standards." She loves him too when he is like this. She loves him, knotted hair, sticky complexion, filthy clothes, and all. Her own hair is not much better kept than Alan's at this late hour. It is frizzy and the curls have fallen loose but she knows he doesn't care any more than she does. "How could you write instructions that allow a machine to adapt? Maybe this won't be possible and it's exactly this ability of ours to adapt and change that makes us free."

"Yes, we change, but in a determined way. There is some input that is read by our internal configurations to produce an output that changes our internal configuration. So we change. This isn't freedom. We go from hating broccoli to liking broccoli. This isn't free will."

"What about creative leaps, leaps of intuition?"

"Neurons fire near other neurons, sending physical signals. The creative leap was inevitable, fixed in an internal configuration and the input received."

"What if someone could change your configuration? Give you a drug that changes how you feel."

"If my very construction were changed, then, yes, I would have different desires, would make different choices. But then it wouldn't be me. I would be dead and gone. You are configured to be Joan Clarke. The choices you make are really just the output of a complex series of internal rotors. You feel free, but you are not. And neither am I."

Angrily, she grabs her knight, shifts the piece into position, snapping the top off the figurine with the force of her disconnect as she gloats, "Checkmate."

He smears his forehead in amazement and his mouth drags open as he scans the board for all the lost moves he imagined. Grinning, actually delighted, he comes to grips with this outcome, still perched high up on his knees. Then he drops onto his heels and says, "My hero. Come, Joan, let's knit. You can show me how to finish the gloves I've made."

Work on the Manchester computer moves forward and I feel certain that these machines will be indispensable on day and that the machines will even think so themselves! At least you would find it more challenging to beat one at chess than it was to beat me.

Janna Levin, A Mad Man Dreams Of Turing Machines, Phoenix, 2008, p.32-3, p.102-3, p.150-1, p.158-9, p. 160-2, p. 164, p.167-8, p. 182-3. (Original date of publication 1975.)

[A Literary Reference index]
 [Thanks to Tom]


ejh said...

attempting to balance as he cycled home with fistfuls of clay hanging over the rim of the steering wheel

I have read only the chess-related sections that I was sent, not the whole book, so I'm not in a position to say whether the above is actually the nonsense that it seems.

Readers may also like to ask themselves (or indeed Levin, or their editor) whether the phrase "up for a game of chess" would have been in use in the Twenties, or whether the Englishman Turing would have said "gotten".

Anonymous said...

Two minor typos: "... pieces to the lift and right ..." (sounds like something the Allo Allo policeman would have said!) and "nexst".