that we’ve all ended up with this mysterious ability to know that Godel’s statement is true?
Where does this advantage, this great insight, come from? From our souls? From some immaterial entity that no machine could ever possess? Is that the only possible source, the only conceivable explanation?
Or might it come from something a little less ethereal? “As Professor Hamilton explained, we believe Godel’s statement is true because we trust the rules of arithmetic not to lead us into contradictions and falsehoods. But where does that trust come from? How does it arise?”
Robert turned the blackboard back to Hamilton’s side, and pointed to the cancellation rule. “If x plus z equals y plus z, then x equals y. Why is this soreasonable? We might not learn to put it quite like this until we’re in our teens, but if you showed a young child two boxes-without revealing their contents-added an equal number of shells, or stones, or pieces of fruit to both, and then let the child look inside to see that each box now contained the same number of items, it wouldn’t take any formal education for the child to understand that the two boxes must have held the same number of things to begin with.
“The child knows, we all know, how a certain kind of object behaves. Our lives are steeped in direct experience of whole numbers: whole numbers of coins, stamps, pebbles, birds, cats, sheep, buses. If I tried to persuade a six- year-old that I could put three stones in a box, remove one of them, and be left with four…he’d simply laugh at me. Why? It’s not merely that he’s sure to have taken one thing away from three to get two, on many prior occasions. Even a child understands that some things that appear reliable will eventually fail: a toy that works perfectly, day after day, for a month or a year, can still break.
But not arithmetic, not taking one from three. He can’t even picturethat failing. Once you’ve lived in the world, once you’ve seen how it works, the failure of arithmetic becomes unimaginable.
“Professor Hamilton suggests that this is down to our souls. But what would he say about a child reared in a world of water and mist, never in the company of more than one person at a time, never taught to count on his fingers and toes. I doubt that such a child would possess the same certainty that you and I have, as to the impossibility of arithmetic ever leading him astray. To banish whole numbers entirely from his world would require very strange surroundings, and a level of deprivation amounting to cruelty, but would that be enough to rob a child of hissoul? “A computer, programmed to pursue arithmetic as Professor Hamilton has described, is subject to far more deprivation than that child. If I’d been raised with my hands and feet tied, my head in a sack, and someone shouting orders at me, I doubt that I’d have much grasp of reality-and I’d still be better prepared for the task than such a computer. It’s a great mercy that a machine treated that way wouldn’t be able to think: if it could, the shackles we’d placed upon it would be criminally oppressive! “But that’s hardly the fault of the computer, or a revelation of some irreparable flaw in its nature. If we want to judge the potential of our machines with any degree of honesty, we have to play fair with them, not saddle them with restrictions that we’d never dream of imposing on ourselves. There really is no point comparing an eagle with a spanner, or a gazelle with a washing machine: it’s our jets that fly and our cars that run, albeit in quite different ways than any animal.
“Thoughtis sure to be far harder to achieve than those other skills, and to do so we might need to mimic the natural world far more closely. But I believe that once a machine is endowed with facilities resembling the inborn tools for learning that we all have as our birthright, and is set free to learn the way a child learns, through experience, observation, trial and error, hunches and failures-instead of being handed a list of instructions that it has no choice but to obey-we will finally be in a position to compare like with like.
“When that happens, and we can meet and talk and argue with these machines-about arithmetic, or any other topic-there’ll be no need to take the word of Professor Godel, or Professor Hamilton, or myself, for anything. We’ll invite them down to the local pub, and interrogate them in person. And if we play fair with them, we’ll use the same experience and judgment we use with any friend, or guest, or stranger, to decide for ourselves whether or not they can think.”
The BBC put on a lavish assortment of wine and cheese in a small room off the studio. Robert ended up in a heated argument with Polanyi, who revealed himself to be firmly on the negative side, while Helen flirted shamelessly with Hamilton’s young friend, who turned out to have a Ph.D. in algebraic geometry from Cambridge; he must have completed the degree just before Robert had come back from Manchester. After exchanging some polite formalities with Hamilton, Robert kept his distance, sensing that any further contact would not be welcome.
An hour later, though, after getting lost in the maze of corridors on his way back from the toilets, Robert came across Hamilton sitting alone in the studio, weeping.
He almost backed away in silence, but Hamilton looked up and saw him. With their eyes locked, it was impossible to retreat.
Robert said, “It’s your wife?” He’d heard that she’d been seriously ill, but the gossip had included a miraculous recovery. Some friend of the family had lain hands on her a year ago, and she’d gone into remission.
Hamilton said, “She’s dying.”
Robert approached and sat beside him. “From what?”
“Breast cancer. It’s spread throughout her body. Into her bones, into her lungs, into her liver.” He sobbed again, a helpless spasm, then caught himself angrily. “Suffering is the chisel God uses to shape us.What kind of idiot comes up with a line like that?”
Robert said, “I’ll talk to a friend of mine, an oncologist at Guy’s Hospital. He’s doing a trial of a new genetic treatment.”
Hamilton stared at him. “One of yourmiracle cures? ”
“No, no. I mean, only very indirectly.”
Hamilton said angrily, “She won’t take your poison.”
Robert almost snapped back:She won’t? Or you won’t let her? But it was an unfair question. In some marriages, the lines blurred. It was not for him to judge the way the two of them faced this together.
“They go away in order to be with us in a new way, even closer than before.” Hamilton spoke the words like a defiant incantation, a declaration of faith that would ward off temptation, whether or not he entirely believed it.
Robert was silent for a while, then he said, “I lost someone close to me, when I was a boy. And I thought the same thing. I thought he was still with me, for a long time afterward. Guiding me. Encouraging me.” It was hard to get the words out; he hadn’t spoken about this to anyone for almost thirty years. “I dreamed up a whole theory to explain it, in which ‘souls’ used quantum uncertainty to control the body during life, and communicate with the living after death, without breaking any laws of physics. The kind of thing every science-minded seventeen-year-old probably stumbles on, and takes seriously for a couple of weeks, before realizing how nonsensical it is. But I had a good reason not to see the flaws, so I clung to it for almost two years. Because I missed him so much, it took me that long to understand what I was doing, how I was deceiving myself.”
Hamilton said pointedly, “If you’d not tried to explain it, you might never have lost him. He might still be with you now.”
Robert thought about this. “I’m glad he’s not, though. It wouldn’t be fair to either of us.”
Hamilton shuddered. “Then you can’t have loved him very much, can you?” He put his head in his arms.
“Just fuck off, now, will you?”
Robert said, “What exactly would it take, to prove to you that I’m not in league with the devil?”
Hamilton turned red eyes on him and announced triumphantly, “Nothing will do that! I saw what happened to Quint’s gun!”
Robert sighed. “That was a conjuring trick. Stage magic, not black magic.”
“Oh yes? Show me how it’s done, then. Teach me how to do it, so I can impress my friends.”
“It’s rather technical. It would take all night.”
Hamilton laughed humorlessly. “You can’t deceive me. I saw through you from the start.”
“Do you think X rays are Satanic? Penicillin?”
“Don’t treat me like a fool. There’s no comparison.”
“Why not?Everything I’ve helped develop is part of the same continuum. I’ve read some of your writing on medieval culture, and you’re always berating modern commentators for presenting it as unsophisticated. No one really thought the Earth was flat. No one really treated every novelty as witchcraft. So why view any of my work any differently than a fourteenth-century man would view twentieth-century medicine?”
Hamilton replied, “If a fourteenth-century man was suddenly faced with twentieth-century medicine, don’t you think he’d be entitled to wonder how it had been revealed to his contemporaries?”
