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ate little, and his grave countenance (which, seldon thought, made him look older than his years) remained quiet and withdrawn.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 complexity does simulation cease to be possible? well, what i have shown, making use of a mathematical technique first invented in this past century and barely usable even if one employs a large and very fast computer, our galactic society falls short of that mark. it can be represented by a simulation simpler than itself. and i went on to show that this would result in the ability to predict future events in a statistical fashion--that is, by stating the probability for alternate sets of events, rather than flatly predicting that one set will take place."
"in that case," said hummin, "since you can profitably simulate galactic society, its only a matter of doing so. why is it impractical?"
"all i have proved is that it will not take an infinite time to understand galactic society, but if it takes a billion years it will still be impractical. that will be essentially the same as infinite time to us."
"is that how long it would take? a billion years?"
"i havent been able to work out how long it would take, but i strongly suspect that it will take at least a billion years, which is why i suggested that number."
"but you dont really know."
"ive been trying to work it out."
"without success?"
"without success."
"the university library does not help?" hummin cast a look at dors as he asked the question.
seldon shook his head slowly. "not at all."
"dors cant help?"
dors sighed. "i know nothing about the subject, chetter. i can only suggest ways of looking. if hari looks and doesnt find, i am helpless."
hummin rose to his feet. "in that case, there is no great use in staying here at the university and i must think of somewhere else to place you."
seldon reached out and touched his sleeve. "still, i have an idea."
hummin stared at him with a faint narrowing of eyes that might have belied surprise--or suspicion. "when did you get the idea? just now?"
"no. its been buzzing in my head for a few days before i went upperside. that little experience eclipsed it for a while, but asking about the library reminded me of it."
hummin seated himself again. "tell me your idea--if its not something thats totally marinated in mathematics."
"no mathematics at all. its just that reading history in the library reminded me that galactic society was less complicated in the past. twelve thousand years ago, when the empire was on the way to being established, the galaxy contained only about ten million inhabited worlds. twenty thousand years ago, the pre-imperial kingdoms included only about ten thousand worlds altogether. still deeper in the past, who knows how society shrinks down? perhaps even to a single world as in the legends you yourself once mentioned, hummin."
hummin said, "and you think you might be able to work out psychohistory if you dealt with a much simpler galactic society?"
"yes, it seems to me that i might be able to do so."
"then too," said dors with sudden enthusiasm, "suppose you work out psychohistory for a smaller society of the past and suppose you can make predictions from a study of the pre-imperial situation as to what might happen a thousand years after the formation of the empire--you could then check the actual situation at that time and see how near the mark you were."
hummin said coldly, "considering that you would know in advance the situation of the year 1,000 of the galactic era, it would scarcely be a fair test. you would be unconsciously swayed by your prior knowledge and you would be bound to choose values for your equation in such a way as to give you what you would know to be the solution."
"i dont think so," said dors. "we dont know the situation in 1,000 g.e. very well and we would have to dig. after all, that was eleven millennia ago."
seldons face turned into a picture of dismay. "what do you mean we dont know the situation in 1,000 g.e. very well? there were computers then, werent there, dors?"
"of course."
"and memory storage units and recordings of ear and eye? we should have all the records of 1,000 g.e. as we have of the present year of 12,020 g.e."
"in theory, yes, but in actual practice-- well, you know, hari, its what you keep saying. its possible to have full records of 1,000 g.e., but its not practical to expect to have it."
"yes, but what i keep saying, dors, refers to mathematical demonstrations. i dont see the applications to historical records."
dors said defensively, "records dont last forever, hari. memory banks can be destroyed or defaced as a result of conflict or can simply deteriorate with time. any memory bit, any record that is not referred to for a long time, eventually drowns in accumulated noise. they say that fully one third of the records in the imperial library are simply gibberish, but, of course, custom will not allow those records to be removed. other libraries are less tradition-bound. in the streeling university library, we discard worthless items every ten years.
"naturally, records frequently referred to and frequently duplicated on various worlds and in various libraries--governmental and private--remain clear enough for thousands of years, so that many of the essential points of galactic history remain known even if they took place in pre-imperial times. however, the farther back you go, the less there is preserved."
"i cant believe that," said seldon. "i should think that new copies would be made of any record in danger of withering. how could you let knowledge disappear?"
"undesired knowledge is useless knowledge," said dors. "can you imagine all the time, effort, and energy expended in a continual refurbishing of unused data? and that wastage would grow steadily more extreme with time."
"surely, you would have to allow for the fact that someone at some time might need the data being so carelessly disposed of."
"a particular item might be wanted once in a thousand years. to save it all just in case of such a need isnt cost-effective. even in science. you spoke of the primitive equations of gravitation and say it is primitive because its discovery is lost in the mists of antiquity. why should that be? didnt you mathematicians and scientists save all data, all information, back and back to the misty primeval time when those equations were discovered?"
seldon groaned and made no attempt to answer. he said, "well, hummin, so much for my idea. as we look back into the past and as society grows smaller, a useful psychohistory becomes more likely. but knowledge dwindles even more rapidly than size, so psychohistory becomes less likely--and the less outweighs the more."
"to be sure, there is the mycogen sector," said dors, musing.
hummin looked up quickly. "so there is and that would be the perfect place to put seldon. i should have thought of it myself."
"mycogen sector," repeated hari, looking from one to the other. "what and where is mycogen sector?"
"hari, please, ill tell you later. right now, i have preparations to make. youll leave tonight."
