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‘Over the next fifteen years a lot of good people came into computer science. Work on neural networks advanced by many hands, the hardware got faster and smaller and cheaper, and ideas were trading at a faster rate too. And it goes on. I remember being in Santa Barbara with Demis in 1965 to speak at a machine-learning conference. We had 7,000, most of them bright kids even younger than you. Chinese, Indians, Koreans, Vietnamese as well as westerners. The whole planet was there.’

I was aware of the history from the research for my book. I also knew something of Turing’s personal story. I wanted to let him know that I wasn’t completely ignorant.

I said, ‘A long road from Bletchley.’

He blinked this irrelevance away. ‘After various disappointments, we arrived at a new stage. We went beyond devising symbolic representations of all likely circumstances and inputting thousands of rules. We were approaching the gateway of intelligence as we understand it. The software now searched for patterns and drew inferences of its own. An important test came when our computer played a master at the game of go. In preparation, the software played against itself for months – it played and learned, and on the day – well, you know the story. Within a short while, we had stripped down our input to merely encoding the rules of the game and tasking the computer to win. At this point we passed through that gateway with so-called recurrent networks, from which there were spin-offs, especially in speech recognition. In the lab we went back to chess. The computer was freed from having to understand the game as humans played it. The long history of brilliant manoeuvres by the great masters were now irrelevant to the programming. Here are the rules, we said. Just win in your own sweet way. Immediately, the game was redefined and moved into areas beyond human comprehension. The machine made baffling mid-game moves, perverse sacrifices, or it eccentrically exiled its queen to a remote corner. The purpose might become clear only in a devastating endgame. All this after a few hours’ rehearsal. Between breakfast and lunch the computer quietly outclassed centuries of human chess. Exhilarating. For the first few days, after we realised what it had achieved without us, Demis and I couldn’t stop laughing. Excitement, amazement. We were impatient to present our results.

‘So. There’s more than one kind of intelligence. We’d learned that it was a mistake to attempt to slavishly imitate the human sort. We’d wasted a lot of time. Now we could set the machine free to draw its own conclusions and reach for its own solutions. But when we’d got well past that gateway, we found we had entered nothing more than a kindergarten. Not even that.’

The air conditioning was full on. I shivered as I reached for my jacket. He refilled our glasses. A rich red would have suited me better.

‘The point is, chess is not a representation of life. It’s a closed system. Its rules are unchallenged and prevail consistently across the board. Each piece has well-defined limitations and accepts its role, the history of a game is clear and incontestable at every stage, and the end, when it comes, is never in doubt. It’s a perfect information game. But life, where we apply our intelligence, is an open system. Messy, full of tricks and feints and ambiguities and false friends. So is language – not a problem to be solved or a device for solving problems. It’s more like a mirror, no, a billion mirrors in a cluster like a fly’s eye, reflecting, distorting and constructing our world at different focal lengths. Simple statements need external information to be understood because language is as open a system as life. I hunted the bear with my knife. I hunted the bear with my wife. Without thinking about it, you know that you can’t use your wife to kill a bear. The second sentence is easy to understand, even though it doesn’t contain all of the necessary information. A machine would struggle.