Chapter 42 Chapter Thirty-Two

The two of them huddled together in Seldon's room until lunch was over.Seldon and Dors occasionally chatted softly about irrelevant topics, but Hummin was almost silent.He sat upright, ate little, and his serious expression (which made him look older than his age, Seldon thought) was always quiet and reserved. Seldon guessed he must be mentally scanning the vast geography of Trantor, trying to find an ideal corner.Undoubtedly, this is not an easy task. Seldon's homeland, Helicon, was one or two per cent larger than Trantor's, but the ocean was smaller, so Helicon's land surface was perhaps ten per cent larger than Trantor's.However, Helicon is sparsely populated, with only a few scattered cities on the surface, while Trantor as a whole is a single metropolis.Helicon was divided into twenty districts, and Trantor's more than eight hundred, each of which was subdivided into many complex units.

In the end, Seldon said with a bit of despair: "Perhaps the best way is to find someone who is closest to the good kind among those contenders who covet my so-called ability, and then hand me over to him and rely on him to protect me." I." Hummin raised his head and said in a very serious tone, "There's no need for that. I know which contender is closest to the good, and you're already in his hands." Seldon smiled slightly: "Do you consider yourself on the same level as District Chief Weiho and the emperor of the entire galaxy?" "As far as status goes, no. But when it comes to their desire to control you, I'm equal to them. Yet they—and everyone else I can think of—want you to increase their own wealth and influence; but I have no ambitions, only the welfare of the entire galaxy."

"I suppose," said Seldon, calmly, "that each of your rivals - if asked - would insist that he thinks only of the good of the Galaxy." "I'm sure they'll answer that," said Hummin, "but so far—to use your title—among my competitors, the only one you've seen is the Emperor. He's interested in you, I want you to come up with a fictitious prediction that will help stabilize his dynasty. I'm not asking you to do anything like that, just to develop the technique of psychohistory to the point where you can make a mathematically based prediction, even if it's It's just statistical in nature."

"Honestly, at least so far." Seldon said with a half-smile. "So maybe I should ask: How are you doing with this work? Any progress?" Seldon didn't know whether to laugh or rage.After pausing for a while, he just tried to say in a calm tone: "Progress? In less than two months? Hummin, this kind of thing is likely to take my whole life, and I will lose more than a dozen generations." successor to the 1980s—and the result may still be nothing.” "I'm not asking if you've derived the right answer, or even if you've made a breakthrough. You've said categorically many times that practical psychohistory is possible but not feasible. What I'm asking is. Any hope of it becoming feasible?"

"Frankly, no." Dors said, "Sorry, I'm not a mathematician, so I hope I'm not asking too stupid a question. How do you know if something is both possible and not possible? I've heard you say that, theoretically, you might To be able to personally visit everyone in the Empire. Say hello to everyone, but it’s not practical, because you can’t live that long. But, how do you know that psychohistory also falls into this category?” Seldon looked at Dors with some disbelief. "You want me to 'explain' this?" "Yes." She nodded vigorously, shaking her curly hair.

"Actually," said Hummin, "I would, too." "No mathematics?" Seldon said with a slight smile. "Please," Hummin said. "Okay—" He was silent for a while, thinking about an appropriate expression.Then he said: "If you want to understand a certain level of the universe, it will be of great help if you can simplify it as much as possible to include only the properties and characteristics that are closely related to that level. If you want to decide a How objects fall. You don't have to care whether it's new or old, red or green, or has a certain smell. By ignoring these properties, you avoid unnecessary complexity. You can call this simplification a model or a simulation , which can be physically displayed on a computer screen, or described mathematically. If you consider the original non-relativistic theory of gravity—”

Dors protested immediately: "You promise not to mention mathematics. Don't try to sneak it in with the title 'primitive.'" "No, no. By 'primitive' I mean something that has existed since time immemorial, whose discovery is lost in the mists of antiquity, like the invention of the wheel or fire. At any rate, the equations of this theory of gravity imply The motion of planetary systems and binary stars, the phenomena of tides, and many other things. Using this equation, we can build a graphical simulation that shows a planet orbiting a star, or two stars orbiting each other on a two-dimensional screen; Even more complex systems can be built in three-dimensional holograms. This simplified simulation makes our grasp of phenomena much easier than if we had to study the phenomena themselves. In fact, without the equations of gravity, our knowledge of planetary motion would be As well as the general knowledge of celestial mechanics, will become poor and superficial.

"When you want to learn more about a phenomenon, or when a phenomenon becomes more complex, you need more elaborate equations, and more detailed computer programs. In the end, you will get a more and more Computerized simulations that are difficult to master." "Can't you build a simulation of a simulation?" Hummin asked, "so you're simplifying one level more." "Then you have to ignore certain features of the phenomenon that you want to cover, and your simulation becomes useless. So-called 'minimum simulations'—that is, feasible The most simplified simulation of , its complexity increases faster than the simulated object, and finally the simulation will keep pace with the phenomenon itself. Therefore, as early as thousands of years ago, it was proved that the complexity of the universe as a whole, including the whole , which cannot be represented by any analog smaller than that.

"In other words, you can't get any picture of the universe as a whole unless you study the universe as a whole. It has also been shown that if you try to replace one small part of the universe with a simulation, and then another small part with another simulation, the rest will follow. By analogy, if you intend to put these simulations together to form an overall picture of the universe, you will find that there are infinitely many such partial simulations. Therefore, it will take an infinitely long time to understand the entire universe, which is another reason why it is impossible to obtain complete knowledge of the universe. A way of saying."

"So far. I understand," Dors said, a little surprised in her voice. "Okay, besides, we know that some fairly simple things are easy to simulate, and as things get more and more complex, it becomes harder and harder to simulate them, until eventually it becomes impossible. But how complex at a temperature where simulations are no longer possible? Well, I used a mathematical technique invented in the last century--which is almost useless even with large, high-speed computers--to prove that our galactic society is On the tipping point side, it can indeed be represented by a simpler simulation than itself. I have further demonstrated that this leads to an ability to predict the future. It is statistical, that is, computes the odds, not which set will happen."

"So," said Hummin, "since you can indeed simulate galactic society effectively, it's just a question of how to go about it. Why isn't it practical?" "All I've shown is that it doesn't take an infinite amount of time to understand galactic society, but if it takes a billion years, it's still not feasible. To us, it's effectively the same as infinite time." "Does it really take that long? A billion years!" "I haven't been able to work out how long it will take, but I have a strong feeling it will be at least a billion years, so that's why I'm coming up with that number." "But you don't really know." "I'm trying to figure it out." "did not succeed?" "did not succeed." "Isn't the university library helping?" Hummin asked, casting a glance at Dors. Seldon shook his head slowly: "Not at all." "Can't Dors help?" Dors sighed. "I don't know anything about the subject, Chet. I can only suggest where to look. If Harry tries and finds nothing, there's nothing I can do." Hummin stood up: "In this case, staying in this university is useless. I have to find another place to accommodate you." Seldon reached out and grabbed Hummin's sleeve: "I have another idea." Hummin narrowed his eyes slightly and stared at him, as if surprised, but also suspicious. "When did you think of it? Just now?" "No, it's been on my mind for days, long before I went up to the dome. That little accident put it down for a while, but I remembered it when you asked about the library." Hummin sat down again. "Tell me what you think—if it's not a product of mathematics from beginning to end." "No math at all. Just when I was studying history in the library, it occurred to me that galactic society used to be not that complex. Twelve thousand years ago, when the Empire was being established, the galaxy contained only about ten million inhabitants Worlds. Twenty thousand years ago, there were only about ten thousand worlds in the thousand kingdoms of the pre-imperial era. And before much earlier, who knows what society shrunk down to? There might even be only one world, as you mentioned yourself That's what the legend says, Hummin." Hummin said, "And you think it's possible to develop psychohistory if you study a much simpler galactic society?" "Yes, I think it should be possible." "So," said Dors in a tone of sudden eagerness, "suppose you develop the psychohistory of a smaller society in the past; — you can go back and check the actual situation at the time and see how far you were from the right target.” Hummin said indifferently: "Since you can know the situation in the year 1000 of the Galactic Era in advance, this is not an objective test. You will be unconsciously swayed by the knowledge you have, and you will do your best for your own. The parameters chosen for the equation must be those values ​​that will give you the correct answer." "I don't think so," said Dors. "We don't know very well about the millennium. We'll have to dig deeper. After all, that was eleven thousand years ago." A bewildered expression appeared on Seldon's face: "What do you mean we don't know much about the situation in the year 1000? There were already computers back then, weren't there, Dors?" "certainly." "And memory storage units and audio-visual records? We should have all the records for Silver Year 1000, just as we have all records for this year—Silver Year 12020." "That's right in theory, but in practice—well, you know, huh, that's what you're always talking about. It's possible to keep all the records for a millennium, and it's expected. But unrealistic." "Yes, but I meant the mathematical argument, Dors. I didn't know it could apply to the historical record." Dors said in a defensive tone, "Records don't last forever, Harry. Memory banks can be destroyed or damaged by war, or decay over time. Any bit of memory, any record, if it goes unreferenced for a long time , will eventually be drowned in the accumulated noise. It is said that in the Imperial Library, a full third of the records are unintelligible, although, of course, those records are not allowed to be removed as a rule. Other libraries do not have so many Legacy baggage, at Trantor University Libraries we purge worthless data every ten years. "Naturally, the oft-quoted and oft-replicated records in every world, in every government or private library, remain legible thousands of years later. Thus many major events in galactic history are still well known to households today, even though they occurred earlier Age of Empires. But the further you go back in time, the less material is preserved." "I can't believe it," said Seldon. "I thought that when any record was destroyed, a copy was made in real time. How can you allow knowledge to disappear?" “Knowledge that no one wants is knowledge that no one wants,” Dors said. “Can you imagine the time, effort, and energy that people need to spend maintaining data that no one uses? It's getting worse." "You always have to take into account the fact that at some point, somebody might need something that's been thrown away." "The need for a particular item may only come once in a thousand years. It is never cost-effective to preserve it just in case of such a need. Even in the field of science, you just mentioned the primordial nature of gravity. Equation, say it is called primordial because its discovery was lost in the fog of ancient times. Why is that? Don't you mathematicians and scientists keep all your data going back to the foggy primordial times when those equations were discovered ?” Seldon snorted and made no attempt to answer the question. "Well, Hummin, that's pretty much what I think. As we go back in time, and as societies get smaller, practical psychohistory becomes more and more possible. But at the same time, knowledge dwindles Even faster than the shrinking of the size of society, psychohistory becomes less and less possible—and the effect of the latter outweighs the former.” "Yeah, there's a wheatgrass area," said Dors thoughtfully. Hummin raised his head quickly: "That's right, that's the ideal place to place Seldon, I should have thought of it myself." "Maiqusheng District?" Seldon repeated, looking at the other two in turn. "Where is the Maiqusheng area? What kind of place is it?" "Harry, please, I'll tell you later. Now I need to make some preparations, and you leave tonight."