Adam B1: The Wrong Proof
Well — they had finally delivered him his proof. Not the one he wanted, but a proof.
And they had gone back to the Lebombo bone to do it. Forty thousand years to a notched length of bone, and up from there by degrees to the whole apparatus — as if to say, this is how far down the counting goes; this is the floor you were always standing on.
“Of all the knuckleheaded pranks —” He saw what they were doing. They were already inside his head again.
Yes. The cry had moved him; he had admitted it, said it out loud, and he would own besides that he had seen a face in every −1 for a good two months after. But a man cannot live on his emotions. Emotions are not facts. Emotions are not proof.
And here was the trick, starting up again, gentle as you please. Everybody has to accept some axioms, they said. Well — sure. True enough. You can’t count to five without Peano.
But that was the whole of the dodge. Grant us our two — the space, and the waking mind that knows it — the way you grant Peano his, and see what falls out. Hand over the keys the moment you confess you lock the door.
He knew the reply to that, and it was a good one. You grant Peano because Peano pays. Five follows four in every tongue that ever drew breath; nothing built on it has come back to bite the builder; the debt is paid every morning before breakfast and has never once bounced. That is not faith. That is a thing the world has settled in full, ten thousand times over.
The question — and he could feel them grinning up at him from the page, because it was their question, set down there on purpose for him to find — was whether this lot had paid the same debt. Whether what stood on their two small axioms held the way arithmetic holds, or whether he was being walked, very civilly and very patiently, exactly where he had sworn he would not go.
He couldn’t say. That was the devil in it. He could not honestly say yes, and he could not honestly say no, and they knew he couldn’t — they had built the thing so that the only road to the answer ran clean through the next page.
He had been outmanoeuvred by an envelope.
Three days later, and he was still thinking about it. They had gone all the way back to notches on a bone to show the lineage of the Gelfand triple.
And he had to admit it: he had never once asked Dirac’s delta function to prove itself. He had taken it, and used it, all his working life, and been glad of it.
He didn’t know what to make of that, and it unsettled him.
He was in that state of mind when the next letter plopped down on the mat.