The three remained huddled in Seldons quarters till past lunch. During that time, Hari and Dors spoke occasionally and quietly on indifferent subjects, but Hummin maintained an almost complete silence. He sat upright, ate little, and his grave countenance (which, Seldon thought, made him look older than his years) remained quiet and withdrawn.
Seldon imagined him to be reviewing the immense geography of Trantor in his mind, searching for a corner that would be ideal. Surely, it couldnt be easy. Seldons own Helicon was somewhat larger by a percent or two than Trantor was and had a smaller ocean. The Heliconian land surface was perhaps 10 percent larger than the Trantorian. But Helicon was sparsely populated, its surface only sprinkled with scattered cities; Trantor was all city. Where Helicon was divided into twenty administrative sectors; Trantor had over eight hundred and every one of those hundreds was itself a complex of subdivisions.
Finally Seldon said in some despair, "Perhaps it might be best, Hummin, to choose which candidate for my supposed abilities is most nearly benign, hand me over to that one, and count on him to defend me against the rest."
Hummin looked up and said in utmost seriousness, "That is not necessary. I know the candidate who is most nearly benign and he already has you."
Seldon smiled. "Do you place yourself on the same level with the Mayor of Wye and the Emperor of all the Galaxy?"
"In point of view of position, no. But as far as the desire to control you is concerned, I rival them. They, however, and anyone else I can think of want you in order to strengthen their own wealth and power, while I have no ambitions at all, except for the good of the Galaxy."
"I suspect," said Seldon dryly, "that each of your competitors--if asked--would insist that he too was thinking only of the good of the Galaxy."
"I am sure they would," said Hummin, "but so far, the only one of my competitors, as you call them, whom you have met is the Emperor and he was interested in having you advance fictionalized predictions that might stabilize his dynasty. I do not ask you for anything like that. I ask only that you perfect your psychohistorical technique so that mathematically valid predictions, even if only statistical in nature, can be made."
"True. So far, at least," said Seldon with a half-smile.
"Therefore, I might as well ask: How are you coming along with that task? Any progress?"
Seldon was uncertain whether to laugh or cage. After a pause, he did neither, but managed to speak calmly. "Progress? In less than two months? Hummin, this is something that might easily take me my whole life and the lives of the next dozen who follow me.--And even then end in failure."
"Im not talking about anything as final as a solution or even as hopeful as the beginning of a solution. Youve said flatly a number of times that a useful psychohistory is possible but impractical. All I am asking is whether there now seems any hope that it can be made practical."
"Frankly, no."
Dors said, "Please excuse me. I am not a mathematician, so I hope this is not a foolish question. How can you know something is both possible and impractical? Ive heard you say that, in theory, you might personally meet and greet all the people in the Empire, but that it is not a practical feat because you couldnt live long enough to do it. But how can you tell that psychohistory is something of this sort?"
Seldon looked at Dors with some incredulity. "Do you want that explained."
"Yes," she said, nodding her head vigorously so that her curled hair vibrated.
"As a matter of fact," said Hummin, "so would I."
"Without mathematics?" said Seldon with just a trace of a smile.
"Please," said Hummin.
"Well--" He retired into himself to choose a method of presentation. Then he said, "--If you want to understand some aspect of the Universe, it helps if you simplify it as much as possible and include only those properties and characteristics that are essential to understanding. If you want to determine how an object drops, you dont concern yourself with whether it is new or old, is red or green, or has an odor or not. You eliminate those things and thus do not needlessly complicate matters. The simplification you can call a model or a simulation and you can present it either as an actual representation on a computer screen or as a mathematical relationship. If you consider the primitive theory of nonrelativistic gravitation--"
Dors said at once, "You promised there would be no mathematics. Dont try to slip it in by calling it primitive. "
"No, no. I mean primitive only in that it has been known as long as our records go back, that its discovery is shrouded in the mists of antiquity as is that of fire or the wheel. In any case, the equations for such gravitational theory contain within themselves a description of the motions of a planetary system, of a double star, of tides, and of many other things. Making use of such equations, we can even set up a pictorial simulation and have a planet circling a star or two stars circling each other on a two-dimensional screen or set up more complicated systems in a three-dimensional holograph. Such simplified simulations make it far easier to grasp a phenomenon than it would be if we had to study the phenomenon itself. In fact, without the gravitational equations, our knowledge of planetary motions and of celestial mechanics generally would be sparse indeed.
"Now, as you wish to know more and more about any phenomenon or as a phenomenon becomes more complex, you need more and more elaborate equations, more and more detailed programming, and you end with a computerized simulation that is harder and harder to grasp."
"Cant you form a simulation of the simulation?" asked Hummin. "You would go down another degree."
"In that case, you would have to eliminate some characteristic of the phenomenon which you want to include and your simulation becomes useless. The LPS--that is, the least possible simulation gains in complexity faster than the object being simulated does and eventually the simulation catches up with the phenomenon. Thus, it was established thousands of years ago that the Universe as a whole, in its full complexity, cannot be represented by any simulation smaller than itself.
"In other words, you cant get any picture of the Universe as a whole except by studying the entire Universe. It has been shown also that if one attempts to substitute simulations of a small part of the Universe, then another small part, then another small part, and so on, intending to put them all together to form a total picture of the Universe, one would find that there are an infinite number of such part simulations. It would therefore take an infinite time to understand the Universe in full and that is just another way of saying that it is impossible to gain all the knowledge there is."
"I understand you so far," said Dors, sounding a little surprised.
"Well then, we know that some comparatively simple things are easy to simulate and as things grow more and more complex they become harder to simulate until finally they become impossible to simulate. But at what level of............