Her studies were more intense and she was out of the house for longer stretches. She had delivered her paper on the Corn Laws. Now she was writing a short essay, to be read aloud in a summer-course seminar, that argued against empathy as a means of historical exploration. Then all of her group was to write a commentary on a quotation from Raymond Williams: ‘There are… no masses, only ways of seeing people as masses.’ She often came home at the end of the day not exhausted but energised, even elated, with a new interest in housework, in tight order, in rearranging the furniture. She wanted the windows cleaned and the bathtub and surround-tiles scrubbed. She cleaned up her own place as well, with Adam’s help. She wanted yellow flowers on the kitchen table to set off the blue tablecloth she had brought from upstairs. When I asked her if she was keeping something from me, and was she by any chance pregnant, she told me forcefully that she was not. We were living on top of one another and we needed to be tidy. But my question pleased her. We were certainly closer now. Her long absences during the day gave our evenings an air of celebration, despite the vague sense of threat that came as night fell.
There was another simple reason for our happiness under duress – we had more money. A lot more. Since my visit to Camden, I was seeing Adam in different terms. I watched him closely for signs of existential misery. As Turing’s lone horseman, he roamed the digital landscapes at night. He must have already encountered some part of man’s cruelty to man, but I saw no signs of despair. I didn’t want to initiate the kind of conversation that would lead him too soon to the gates of Auschwitz. Instead, in a self-interested way, I decided to keep him busy. Time to earn his keep. I gave him my seat at the grubby screen in my bedroom, put £20 into the account and left him alone. To my amazement, by close of business, he had only £2 left. He apologised for his ‘giddy risk-taking’ which caused him to ignore all he knew of probability. He had also failed to recognise the sheep-like nature of markets: when one or two well-regarded characters took fright, the flock was liable to panic. He promised me that he would do everything to make up for my broken wrist.
The next morning, I gave him another £10 and told him that this could be his last day on the job. By six that evening his £12 was £57. Four days later, the account was at £350. I took £200 of it and gave half to Miranda. I considered moving the computer into the kitchen so that Adam could work into the night on the Asian markets while we slept.
Later in the week, I peeked at the history of his transactions. In a single day, his third, there were 6,000. He bought and sold within fractions of a second. There were a few twenty-minute gaps when he did nothing. I assumed he watched and waited and made his calculations. He dealt in minute currency fluctuations, mere tremors in the exchange rate, and advanced his gains by minuscule amounts. From the doorway I watched him at work. His fingers flew across the ancient keyboard, making the sound of pebbles poured onto slate. His head and arms were rigid. For once, he looked like the machine he was. He designed a graph whose horizontal axis represented the passing days, the vertical, his, or rather, my, accumulated profit. I bought a suit, my first since leaving the legal profession. Miranda came home in a silk dress and bearing a soft leather shoulder bag for her books. We replaced the fridge for one that dispensed crushed ice, then the old cooker was carried out on the day we acquired many thick-bottomed saucepans of expensive Italian make. Within ten days, Adam’s £30 stake had generated the first £1,000.
Better groceries, better wine, new shirts for me, exotic underwear for her – these were the foothills rising towards a mountain range of wealth opening before us. I began to dream again about a house across the river. I spent an afternoon alone, wandering among the stuccoed, pastel-coloured mansions of Notting Hill and Ladbroke Grove. I made enquiries. In the early eighties, £130,000 could situate you rather grandly. On the bus home, I made my projections: if Adam continued at his present rate, if the curve on his graph kept to its steady steepening… well, within months… and no need for a mortgage. But was it moral, Miranda wondered, to get money like this for nothing? I felt it wasn’t somehow, but couldn’t explain who or what it was we were stealing from. Not the poor surely. At whose expense were we flourishing? Distant banks? We decided that it was like winning daily at roulette. In which case, Miranda told me one night in bed, there would come a time when we must lose. She was right, probability demanded it and I had no answer. I took £800 out of the account and gave her half. Adam pushed on with his work.
There are people who see the word ‘equation’ and their thoughts rear up like angry geese. That’s not quite me, but I sympathise. I owed it to Turing’s hospitality to attempt to understand his solution to the P versus NP problem. I didn’t even understand the question. I tried his original paper, but it lay well beyond me – too many different forms of bracket, and symbols that encapsulated histories of other proofs or entire systems of mathematics. There was an intriguing ‘iff’ – not a misspelling. It meant ‘if and only if’. I read the responses to the solution, made to the press in layman’s terms by fellow mathematicians. ‘A revolutionary genius’, ‘breathtaking shortcuts’, ‘a feat of orthogonal deduction’ and, best of all, by a winner of the Fields Medal, ‘He leaves many doors behind him that are barely ajar and his colleagues must do their best to squeeze through one and try to follow him through the next.’
I turned back and tried to understand the problem. I learned that P stood for polynomial time and N stood for non-deterministic. That took me nowhere. My first meaningful discovery was that if the equation was shown not to be true, that would be extremely helpful, for then everyone could stop thinking about it. But if there was a positive proof, that P really did equate to NP, it would have, in the words of the mathematician Stephen Cook, who formulated the problem in these terms in 1971, ‘potentially stunning practical consequences’. But what was the problem? I came across an example, an apparently famous one, that helped only a little. A travelling salesman has a hundred cities on his patch. He knows all the distances between every pair of cities. He needs to visit each city once and end up at his starting point. What’s his shortest route?
I came to understand the following: the number of possible routes is vast, far greater than the number of atoms in the observable universe. In a thousand years a powerful computer wouldn’t have time to measure out each route one by one. If P equals NP, there’s a discoverable right answer. But if someone gave the salesman the quickest route, it could be quickly verified mathematically as the correct answer. But only in retrospect. Without a positive solution, or without being handed the key to the shortest route, the travelling salesman remains in the dark. Turing’s proof had profound consequences for other kinds of problems – for factory logistics, DNA sequencing, computer security, protein folding and, crucially, machine learning. I read that there was fury among Turing’s old colleagues in cryptography because the solution, which he eventually put into the public domain, blew apart the foundations of the code-maker’s art. It should have become, one commentator wrote, ‘a treasured secret in the government’s exclusive possession. We would have had an immeasurable advantage over our enemies as we quietly read their encrypted messages.’