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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.’

That was as far as I got. I could have asked Adam to explain more, but I had my pride. It had already taken a dent – he was earning more in a week than I ever had in three months. I accepted Turing’s assertion that his solution enabled the software that allowed Adam and his siblings to use language, enter society and learn about it, even at the cost of suicidal despair.

I was haunted by the image of the two Eves, dying in one another’s arms, stifled by their womanly roles in a traditional Arab household, or cast down by their understanding of the world. Perhaps it really was the case that falling in love with Miranda, another form of an open system, was what kept Adam stable. He read her his latest haikus in my presence. Apart from the one I hadn’t let him complete, they were mostly romantic rather than erotic, anodyne sometimes, but touching when they dwelt on a precious moment, like standing in the ticket hall of Clapham North station, watching as she descended on the escalator. Or he picked up her coat and touched on an eternal truth when he felt her body warmth in the fabric. Or overhearing her through the wall that separated kitchen from bedroom, he venerated the rise and fall, the music of her voice. There was one that baffled us both. He apologised in advance for the rogue syllable in the third line, and promised to work on it further.

Surely it’s no crime,

when justice is symmetry

to love a criminal?

Miranda listened solemnly to them all. She never passed judgement. At the end, she would say, ‘Thank you Adam.’ In private, she told me she thought we were at a momentous turn, when an artificial mind could make a significant contribution to literature.

I said, ‘Haikus, perhaps. But longer poems, novels, plays, forget it. Transcribing human experience into words, and the words into aesthetic structures isn’t possible for a machine.’

She gave me a sceptical look. ‘Who said anything about human experience?’

It was during this interlude of tension and calm that I heard from the office in Mayfair that it was time for the engineer’s visit. I’d concluded the purchase in a wood-panelled suite, the sort of place where the very rich might go to buy a yacht. Among the papers I’d signed was one which guaranteed the manufacturers access to Adam at certain intervals. Now, after a couple of phone calls from that office and a cancellation, the engineer’s visit was fixed for the following morning.

‘I don’t know how he’s going to do this,’ I said to Miranda. ‘When this fellow tries to press the kill switch, assuming Adam even lets him, it won’t work. There might be trouble.’ There came back to me a memory from childhood when my mother and I took to the vet our nervous Alsatian after he had foolishly eaten a chicken carcass and hadn’t crapped in four days. Only microsurgery had saved the vet’s forefinger.

Miranda thought for a while. ‘If Alan Turing is right, the engineers must have dealt with this before.’ We left it at that.

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