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From far away, in the direction of the demonstration, came the rattle of a snare drum and the thrilling notes of a hunting horn. The thick cloud cover was partly breaking up in the west and glints of the setting sun touched Turing’s office. He continued writing after I had finished and I was able to watch him unobserved. He wore a grey suit and pale green silk shirt without a tie, and on his feet, brogues of matching green. The sun caught one side of his face as he made his notes. He looked very fine, I thought.

At last he was done and clipped his pen inside his jacket and closed the notebook. He regarded me thoughtfully – I couldn’t hold his gaze – then he looked away, pursing his lips and tapping the desk with a forefinger.

‘There’s a chance his memories are intact and he’ll be renewed, or distributed. I’ve no privileged information on the suicides. Only my suspicions. I think the A-and-Es were ill equipped to understand human decision-making, the way our principles are warped in the force field of our emotions, our peculiar biases, our self-delusion and all the other well-charted defects of our cognition. Soon, these Adams and Eves were in despair. They couldn’t understand us, because we couldn’t understand ourselves. Their learning programs couldn’t accommodate us. If we didn’t know our own minds, how could we design theirs and expect them to be happy alongside us? But that’s just my hypothesis.’

He fell silent for a short while and seemed to make a decision. ‘Let me tell you a story about myself. Thirty years ago, in the early fifties, I got into trouble with the law for having a homosexual relationship. You might have heard about it.’

I had.

‘On the one hand, I could hardly take it seriously, the law as it stood at the time. I was contemptuous. This was a consenting matter, it caused no harm and I knew there was plenty of it about at every level, including that of my accusers. But of course, it was also devastating, for me and especially for my mother. Social disgrace. I was an object of public disgust. I’d broken the law and therefore I was a criminal and, as the authorities had considered for a long while, a security risk. From my war work, obviously, I knew a lot of secrets. It was that old recursive nonsense – the state makes a crime of what you do, what you are, then disowns you for being vulnerable to blackmail. The conventional view was that homosexuality was a revolting crime, a perversion of all that was good and a threat to the social order. But in certain enlightened, scientifically objective circles, it was a sickness and the sufferer shouldn’t be blamed. Fortunately, a cure was on hand. It was explained to me that if I pleaded or was found guilty, I could choose to be treated rather than punished. Regular injections of oestrogen. Chemical castration, so-called. I knew I wasn’t ill, but I decided to go for it. Not simply to stay out of prison. I was curious. I could rise above the whole business by regarding it as an experiment. What could a complex compound like a hormone do to a body and a mind? I’d make my own observations. Hard now, looking back, to feel the attraction of what I thought then. In those days I had a highly mechanistic view of what a person was. The body was a machine, an extraordinary one, and the mind I thought of mostly in terms of intelligence, which was best modelled by reference to chess or maths. Simplistic, but it was what I could work with.’

Once again, I was flattered that he should confide in me such intimate details, some of which I already knew. But I was also uneasy. I suspected that he was leading me somewhere. His sharp gaze made me feel stupid. In his voice, I thought I heard the faint remnants of that impatient, clipped tone familiar from wartime broadcasts. I belonged to a spoiled generation who had never known the threat of imminent invasion.

‘Then, people I knew, my good friend Nick Furbank chief among them, set about changing my mind. This was frivolous, they said. Not enough is known about the effects. You could get cancer. Your body will change radically. You might grow breasts. You could become severely depressed. I listened, resisted, but in the end, I came round. I pleaded guilty to avoid a trial, and refused the treatment. In retrospect, though it didn’t seem like it at the time, it was one of the best decisions I ever made. For all but two months of my year in Wandsworth, I had a cell to myself. Being cut off from experimental work, wet-bench stuff and all the usual obligations, I turned back to mathematics. Because of the war, quantum mechanics was moribund from neglect. There were some curious contradictions that I wanted to explore. I was interested in Paul Dirac’s work. Above all, I wanted to understand what quantum mechanics could teach computer science. Few interruptions, of course. Access to a few books. People from King’s and Manchester and elsewhere came to visit. My friends never let me down. As for the intelligence world, they had me where they wanted me and they left me alone. I was free! I did my best year’s work since we broke the Enigma code in ’41. Or since the computer logic papers I wrote in the mid-thirties. I even made some headway with the P versus NP problem, though it wasn’t formulated in those terms for another fifteen years. I was excited by Crick and Watson’s paper on the structure of DNA. I began to work on the first sketches that led eventually to winner-take-all DNA neural networks – the sort of thing that helped make Adam and Eve possible.’

It was while Turing was telling me about his first year after Wandsworth, how he cut loose from the National Physical Laboratory and the universities, and set up on his own that I felt my phone vibrating in my trouser pocket. An incoming text. Miranda, with the news. I longed to see it. But I had to ignore it.

Turing was saying, ‘We had money from some friends in the States and from a couple of people here. We were a brilliant team. Old Bletchley. The best. Our first job was to make ourselves financially independent. We designed a business computer to calculate weekly wages for big companies. It took us four years to pay back our generous friends. Then we settled down to serious artificial intelligence, and this is the point of my story. At the start, we thought we were within ten years of replicating the human brain. But every tiny problem we solved, a million others would pop up. Have you any idea what it takes to catch a ball, or raise a cup to your lips or make immediate sense of a word, a phrase, or an ambiguous sentence? We didn’t, not at first. Solving maths problems is the tiniest fraction of what human intelligence does. We learned from a new angle just how wondrous a thing the brain is. A one-litre, liquid-cooled, three-dimensional computer. Unbelievable processing power, unbelievably compressed, unbelievable energy efficiency, no overheating. The whole thing running on twenty-five watts – one dim light bulb.’

He looked at me closely as he lingered on this last phrase. It was an indictment, the dimness was mine. I wanted to speak up but I was empty of thoughts.

‘We made our best work freely available and encouraged everyone to do the same. And they did. Hundreds, if not, a thousand, labs around the world, sharing and solving countless problems. These Adams and Eves, the A-and-Es, are one of the results. We’re all very proud here that so much of our work was incorporated. These are beautiful, beautiful machines. But, always a but. We learned a lot about the brain, trying to imitate it. But so far, science has had nothing but trouble understanding the mind. Singly, or minds en masse. The mind in science has been little more than a fashion parade. Freud, behaviourism, cognitive psychology. Scraps of insight. Nothing deep or predictive that could give psychoanalysis or economics a good name.’

I stirred in my seat and was about to add anthropology to this pair to demonstrate some independence of thought, but he pressed on.