Solve for X

Trelawny sat at the small kitchen table. He took out a small pack of Lucky Strikes and lit one up, exhaling smoke that wreathed the bare 20 watt bulb hanging from the ceiling. He looked at the detective sitting across the table from him.

'When did I first notice something was wrong? Is that even the right question? There was always something off kilter about him, the flywheels of his mind always spun a little faster than most. You got the feeling that he angled away from reality in a direction you couldn't quite follow.' Trelawny took another draw from his Lucky Strike. 'Of course there were rumours of what he got up to even back then, although nothing was ever concrete. But if there was one moment when I noticed that his direction to the rest of us had changed, it would have been the game of chess we had in his lecture hall before the war.

We had played fairly regularly together as undergrads at Kings, but it was never anything too serious. On my part at least. He was mad about Capablanca and would play though his games constantly, especially after new games would come in after a tournament. It was the math of course, that was driving him. Quite before anything Turing was doing with it, he felt every game was a puzzle to be unlocked. That there was one true game of chess locked away inside the pieces. Fiendishly difficult yet devatatingly simple. He won our games more often than not, but after I went to the States to teach we fell out of touch and hadn't played each other in years until I came back home for a short visit. I recieved a telegram from him, quite short, abrupt really, in his usual style, simply asking me to come around to his school for a game that Saturday.

Well of course I went, but as soon as I arrived he ushered me from his office to an empty classroom. The whole place was deserted being the weekend and all, but he closed and locked the door behind us. Said something about not wanting to be disturbed. On the student desk on the front row a chess board had already been set up. As we sat down he told me that he would not be playing me, but that he had worked out a formula that would be playing me instead. I asked what he meant and he just smiled and moved his first piece out. Pawn to king four I think it was. I moved out my piece and then he did something quite peculiar. He dragged up a second desk with some papers on it and began writing on them. As he worked he explained he had created an algorithm that would assess the value of each piece, it's position, and give him an answer on the next move.

So we sat there, heads bent over the desk towards each other like two young students gossiping in the front of study hall. With him just working away furiously at his calculations. Each move took around half and hour for him to compute. I asked him if it would not just be easier for him to make the move, but he shook his head. 'No' he said. 'Only math can find the true move to make.' That phrase has always stuck in my head ever since. 'Only math can find the true move.'

Well we continued on for most of the afternoon until he made a horrible blunder, left a rook en prise I think it was. He looked quite shaken when he made the move, he knew it would lose him the game, but the math had told him what to do so he did it anyway. He looked back over his notes and shook his head. Got up quickly smiling, shook my hand, said he hoped I had a good trip, and then walked out of the theatre. I didn't see him again for five years.'

Trelawny butted out another cigaratte and stood up. He walked to the small window that looked out into the snow. A train whistle sounded in the distance.

'The next time I heard from him was by telegram. Again, it was simply a short message. 'Have completed the machine stop come at once stop'. Well, I didn't have the foggiest what he meant, but I was heading home anyway and it was a simple enough thing to drop by. But when I got to the school I was told he had been fired twelve months earlier. What for they would not tell me, but I had never heard of it so it must have been scandalous for them to hush it up. I feared some of the old rumours might have been true so I rushed over here.

Gods, he looked like he had aged twenty years in the time I had seen him. Well, you know what he looks like I guess don't you? Just horrible. I had come in and barely removed my coat when he started without any preamble into a long rambling monologue about algorithms and this abstract pure mathematical argument. Never my strong suit you know, application of math was always my field. But from what I could follow it seemed quite advanced from what is being bandied about in the literature. Suddenly he stopped and simply said 'I built it.'

'Built what?' I said.

'A Turing machine.' he replied.

Well, I can tell you I didn't know what to say. You may not know this detective, but a Turing machine is not something you build, it is an intellectual exercise, like Schrodinger's Cat. No one ever put a cat in a box with some decaying radioactive material. Just as no one has 'built' a Turing machine. It is merely a way to think of a procedure of ascertaining the truth or falsity of an assertion in a finite number of steps. For heaven's sake, one of the core components it needs is an infinite amount of tape to run through it. You could never 'build' one.

I told him that and all he said was 'you don't need an infinite tape if the correct algorithm is given at the start. The right algorithm will tell you the truth of any question.'

'You mean any mathematical question' I asked.

He looked away and asked me to come by again tomorrow. He would have it ready to demonstrate to me then.


When I came back, I found the place as you see it now. It is like it was last night, except for his body on the couch with the back of his head blown out and the smashed pile of gears, rotors and tapes lying on the table.

Trelawney tapped the last cigarette out of its packet. He crumpled the pack in his hand, dropping it onto the table.

'I can see him now, detective, entering into that infernal machine the one question he needed so desperately to know the answer to. Then, with the cold implacable logic of the universe, the machine spitting back out the one, ultimate answer. Math showed him the only true move he could make.'