«Take a particular case. You know the two-body problem in astronomy? Given two bodies of known mass and distance from each other, and the laws of motion and gravitation, to find their position at any past or future time. Well, it’s mathematically simple. It was solved a long time ago, because there are only two interacting bodies. But the three-body problem is quite another story. Right away, with three interactions, it becomes so complex that as far as I know there’s never been any general solution, and only a few special ones. As for the n-body problem—!
«Now in the biological sciences, including psychology and sociology, you can’t simplify. You have to consider the whole. A living organism is an incredibly complex set of interactions, beginning, probably, on the subatomic level and going on up to the universal environment, from which the organism cannot be separated either, acting on and being acted on by that all the time. You can’t apply our single-track analysis methods to such a case. The result is, of course, that those sciences are almost purely empirical, sociology hardly deserving the name. If, to use an illustration that’s been used before, I want to tackle the three-body problem, I can and will start with the special case where one of them has zero mass. But suppose I were making an analysis of the influence of Pan-Asiatic policies on American domestic affairs before the war. I could certainly not ignore the converse case, or the existence of other countries, I’d have to consider them all at once—which no existing math can do. Any results I got would be qualitative, nonmathematical, inexact.»
«I think I see,» nodded Boyd. «Of course, people can think of two or more things at once.»
«That’s different,» said Karen. «That’s a case of divided attention, each branch of the mind following its single track. It’s normal enough, though carried to extremes it becomes schizophrenia.»
«You get what I’m driving at,» went on Wayne. «Our subhuman and human ancestors didn’t need to see the world as a whole. They were only concerned with their immediate surroundings and events. So we never evolved the ability to consider an entire entity. Alaric is a mutant—»
«Some different brain structure,» said Karen quietly. «The reversed internal organs may or may not be a linked characteristic. The X-rays showed no brain difference. They hardly would, as it’s probably a very subtle matter of cellular or colloidal integration.»
«Al didn’t have to think, in our ordinary sense of the word, of how to make a weapon,» added Wayne. «His extensive knowledge of scientific principles and data coordinated in his mind to show him that… well, if my guess is right, that the colloids of human bodies are resonant to a particular wave form. And at once he knew all the factors he’d need to generate that wave. It wasn’t reason, as we reason, though it was thought—to him, thought on a very elementary, almost intuitive level. Yet he wasn’t able to think of telling anybody.»
«I see,» answered Boyd. «Humans think in chains. He thinks in networks.»
«Yes, that’s about the size of it.»
«Do you think… we… can ever do that?»
«Hm-m-m—I don’t know. Since intelligence seems to depend on upbringing among normal humans, whereas genius and feeble-mindedness seem more independent of environment, and are hereditary, one might argue that they are both mutations, in the individual or an ancestor. Some people, such as Nikola Tesla, seem to have had a degree of network-thought ability, and the fact that Al is the son of a mathematician, who does deal with complexities, is suggestive. After all, no observed mutation has ever created a totally new characteristic. It would have to create a whole new set of genes for that. A mutation is a greater or less modification of an existing characteristic.
«The point I’m making is that humans naturally think in straight lines, but some sort of network, total-considering logic has been developed. The semanticists have their nonelementalistic principle. In math, we only add in special cases, the rest of the time we integrate, and we have our generalized calculi of vectors and tensors and the like. But—it doesn’t come naturally. It’s been worked out slowly and painfully, through many centuries. To Al, it’s the natural way to think; but, as like most mutations it involves a loss elsewhere, the simple straightforward logic of humans is unnatural to him and since he is just a kid, and probably not a genius anyway—merely an ordinary network thinker—he hasn’t seen the principles of that logic, any more than a human his age sees the principle of nonelementalism. I’d say, offhand, that both types of mind can learn the other type of thought, but not comprehend or apply it on its higher levels.»
«There’s another thing,» put in Karen. Her eyes held a light which hadn’t been there for a long time. «Rod just said it. Al should be able, with the proper training, to learn logic, at least enough to understand and communicate. His kind of thought is not adapted to the simple problems of life, but he can be taught to handle those, as we teach human children to think in terms of abstractions. Maybe… maybe, then, he can teach us something.»
Boyd nodded again. «It’s certainly worth the attempt,» he said. «We have psychiatrists and other specialists at the capital. If we’d known before that you’re a mathematician, Wayne, we’d have asked you there, to join the science center with which President Drummond hopes to rebuild our culture on a basis of genuine sanity. Consider yourself invited as of now. And if we and Alaric can come to understand each other—why, Wayne, you may even get your biological and sociological math. Then we may be able to pull ourselves out of this planetary mess.»
«I hope so.» murmured Wayne. «I certainly hope so, And thanks, Boyd.» He smiled tiredly, crookedly. «By the way, Karen, you have your superman there. The greatest genius, in his way, that the world ever saw—and if he hadn’t had some kind of protective civilization to grow up in and, now, to teach him the elements of thought, he’d never have lived. I’m afraid this particular kind of superman just isn’t a survivor type.»
«No,» whispered Karen, «nor human. But he’s our son.»
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«The work is, you understand, somewhat unusual,» said Mr. Gordon. «And confidential. I trust you can keep a secret?»
«Normally,» said Manse Everard. «Depends on what the secret is, of course.»
Mr. Gordon smiled. It was a curious smile, a closed curve of his lips which was not quite like any Everard had seen before. He spoke easy colloquial General American, and wore an undistinguished business suit, but there was a foreignness over him which was more than dark complexion, beardless cheeks, and the incongruity of Mongolian eyes above a thin Caucasian nose. It was hard to place.
«We’re not spies, if that’s what you’re thinking,» he said.
Everard grinned. «Sorry. Please don’t think I’ve gone as hysterical as the rest of the country. I’ve never had access to confidential data anyway. But your ad mentioned overseas operations, and the way things are—I’d like to keep my passport, you understand.»
He was a big man, with blocky shoulders and a slightly battered face under crew-cut brown hair. His papers lay before him: Army discharge, the record of work in several places as a mechanical engineer. Mr. Gordon had seemed barely to glance at them.
The office was ordinary, a desk and a couple of chairs, a filing cabinet, and a door leading off in the rear. A window opened on the banging traffic of New York, six stories down.