“Where do statistics get into it?” Iphwin asked.
“There’s a trivial argument that if you could look at all the possible propositions—a list that would include things like ‘Ice cream comprehends lions and dislikes beauty,’ ‘It always rains on vacuum-flavored machine tools,’ and ‘The king is polynomial’—most of them would be inapplicable to the real world, not testable by any means whatever, which is another way of saying we wouldn’t be able to know if they were true. Another large group is testable but not useful or interesting—’Monkeys wear red dresses to seduce geraniums.’ The number that would be interesting if true is a fairly small proportion—and of course the true ones are a small subset of that. It turns out that the important question is, what’s the shape of the population of possible ideas? And how many of those ideas are useful, which is shorthand for ‘capable of being true in some circumstance where it would matter to someone?’ And how is it possible for any finite mind to sample effectively from that population?
“As soon as you realize that the number of useless statements must be much, much greater than the number of useful ones, you have to see that people can’t possibly be generating propositions on a purely random basis, testing all of them, and keeping the ones that work. They must have a way to find a good-enough place to start, some way to come up with the subset of propositions worth examining, a process of some kind, because we don’t see people paralyzed about what to buy Uncle Ned for his birthday because first they have to think of all the possible statements involving buying, then all those involving Uncle Ned, and then all those involving birthdays.
“Well, I thought, the world has so few astronomers this century, they can’t possibly look for all the interesting things that might be happening in the sky—so how do they choose a proposition to test? With so few of us, could we really just rely on intuition? Or luck? But if you admit that there is some use in intuition, that it does something better than a random statement generator could, it must be a human capability of some kind, rooted in the real world, which means that very likely it can be developed and trained to make someone better at it—which might even be the same thing as making him lucky. And if you can invent a method for training intuition, you have to be able to describe what it does-—and in math a description is always at least halfway to a solution. So I started to think that maybe I could invent a way to imitate, computationally, what intuition does.
“From that initial idea, I developed some theories about sampling and about how to find the answer next to the answer next to the answer that’s the right answer, and so forth, and I’ve been publishing ever since. With, I might add, hardly any reaction worth talking about from any of my fellow astronomers, who are mostly just guys that like to photograph stars.”
Iphwin nodded. “The lack of reaction is profound, and more profoundly it is to be expected.” I wanted to ask him what he meant, but he went on before I could. “And yet, however large, the number of possible propositions must be finite, since it’s generated from a finite list of terms, and we know the list is finite because there’s only so many things in the universe, or at least only so many things that we can encounter between the beginning and the end of our species. Am I right?”
“I guess as far as it goes. But you know, there may be as many as half a million words in English, so that just the number of possible statements of some short length—maybe one hundred bytes and shorter—would have to be more propositions than could be thought of between the Big Bang and the end of time, even if the universe were made up of nothing but proposition-writing computers. No reason to be concerned about a number being finite when it’s infinite for every practical purpose— abduction from an infinite set is not materially different from abduction from an extremely large one.”
He sat back in one of the chairs, stretched, and put his hands behind his head. “So you have worked out the rudiments of a method for doing abduction mathematically, instead of just trusting whatever it is that human beings have and robots don’t.”
“Rudiments is the word,” I said. “I have little bits and pieces of a method and not the slightest idea whether the pieces could ever come together to form a coherent theory.”
“Have you solved the problems I asked you to solve?”
“I think so,” I said. “Let me pull out my computer and I’ll show you what I have.”
The problems had all been very peculiar—the first question was “Which English language poetic forms would be the best ones to study in order to understand the concept of triteness?” Another one was to explain why “meaningful” and “nonmeaningful” were or were not meaningful as categories applied to integers. Yet another problem was “How many published physical experiments would be required within a period of twenty years to cause all physicists worldwide to believe that there is a fifth fundamental force, and what is the likelihood that they would believe so correctly?”
Originally I had developed the abductive statistical methods because the number of possible hypotheses in astronomy, about things big and little, general and particular, and all, was so large relative to the number of astronomers actually working that it seemed unlikely to me that any astronomers at all, out of the whole population, were working on anything particularly important. The world only had one-tenth as many trained professional astronomers in 2050 as there had been in 1920, and yet the thousands of amateurs had flooded the databases with innumerable observations. I was looking for a way to choose the most productive paths of research—but since a path of research is a set of propositions about what hypothetical propositions should be tested by argumentation against a set of propositions about what did happen, that’s just another way of saying I needed a method of abduction, and the abductive problem in front of me was much bigger than the abductive abilities of the naive human brain.
The primary problem with all of this was that I saw absolutely no way in which any of this could be relevant to what ConTech did. The secondary problem that occurred to me then was that I also had no idea what ConTech did, except that I had a strong feeling that whatever it was, it wasn’t anything for which abduction was relevant.
Iphwin scanned the solutions for a moment, asked a couple of technical questions, then said, “Well, there you have it. These are all what we’d want you to have come up with. It looks to me like your abductive methods work, and that’s why I need you.”
“Excuse me, er, Iphwin, but that’s just what I don’t understand. Exactly why is it you need me?”
“Why, to solve a large number of abductive problems for ConTech in general and for me in particular, of course.”
“I guess I was really asking what kind of abductive problems you needed to have solved.”
“And I think I did a very neat job of evading the question.” Now he was standing at the window, looking south across the sea, toward Surabaya just over the horizon. “I’ve been extraordinarily impressed with your work, and more importantly, so have my engineers and research teams. Once you’re hired and have been on board for a while, perhaps we’ll all have a better picture of what you’ve been hired for. If you think about it, a company that needs problems in abduction solved is a company that isn’t coming up with the ideas that it needs.