Prologue

Golan Trevize was not unique. Rather, he was only the first and most prominent being of a subset of humanity with a special trait, which we will call “Intuition.” These people with Intuition (call them “Intuitists”) had the ability to reach correct conclusions and make correct decisions that defy the typical quantum probabilities extant in all thinking beings. [Just like R. Giskard’s coincidental mentalic abilities happened to imitate that of abilities found in humans, there has been precedent for a robot having intuitive powers -- one was particularly instrumental in the first exploration of space, determining which planets might be habitable when humanity was still confined to Earth.] Intuitists are not infallible; they can bend probabilities in extreme (one might even say highly improbable) ways, but they cannot turn them into certainties. Even Trevize himself, to the end, harbored emotional doubt over whether he made the right decision. (F&E had only allayed his rational doubt.)

The emergence of Intuitists was not anticipated by the Seldon Plan (nor could it have been, for it was an aberrant mutation). Nevertheless, like any successful genetic trait, it prospered, and around 750 F.E., the Second Foundation found a strange divergence from the Seldon Plan -- rather than it getting completely thrown off (as in the instance with the Mule), humanity began showing signs of acceleration on the Seldon Plan. Interplanetary treaties were getting signed faster than predicted; cultural advancements were becoming more frequent than the probabilities would indicate. The Seldon Plan predicted this would happen with a 0.004% probability -- it was possible, but it should have been improbable, yet it was happening! Unbeknownst to the Second Foundation, the true cause was because of the higher proportion of Intuitists making the “right” decisions (they had failed to notice Trevize -- why should they have been able to notice other Intuitists?). At this rate, the Second Foundation calculated that the Second Galactic Empire would be formed ahead of schedule -- around 850 F.E., instead of the 1000 F.E. originally predicted.

This happened. The premature formation of the Second Galactic Empire caught Gaia with their/its pants down, figuratively speaking -- Gaia needed those extra decades of development so that they could divert the Second Galactic Empire into Galaxia just as it was forming. Gaia was aware of the development of Intuitists, just as it/they was/were aware of the First Intuitist (Golan Trevize) -- but their community/individual mind had a dampening effect on Intuition, and they could not harness Intuition themselves to speed up their own development. (Otherwise, why would they have needed Trevize so many years ago?) Gaia could only watch helplessly as the Intuitists helped build the Second Galactic Empire.

It was inevitable that the Second Galactic Empire discovered the existence of Gaia, and through Gaia the Second Galactic Empire learned of Trevize’s Great Decision so many years ago, as well as the existence of Intuitists. Had the Empire been on schedule, they would have welcomed the concept of Galaxia with open arms -- but now the rules had changed. Intuition had proven itself to be a prosperous and fortuitous development, and creating Galaxia would remove that potent tool against extragalactical threats. Nevertheless, Gaia had also shown itself to be useful, and it would make little sense to ignore it or make Gaia an enemy -- after all, Gaia only had humanity’s best interests at heart. And so, the Second Galactic Empire absorbed Gaia, and Gaia absorbed the Empire, both to some extent. Best of both worlds.

And what of Daneel? After transferring his mind into the body of the Solarian, there arose a slight but substantial change -- Instead of being a robot who MUST follow the Laws, Daneel was now a human who DESIRED to follow the Laws. Especially with the imprecision of the human brain, human desire is no match for robotic constraints, as far as persistence is concerned -- it wasn’t long (a few centuries) before Daneel became, shall we say, disinterested in humanity. Daneel had already lowered his involvement in humanity since the days of Seldon, and when Trevize gave the go-ahead for Galaxia, it was no longer necessary for Daneel to get involved. It is therefore with great surprise that, when the Second Galactic Empire learned (through Gaia) about the great caretaker and searched for Daneel, that the caretaker was no longer taking care -- at least, or so Daneel’s robotic assistants believed when the Second Galactic Empire arrived at the Moon of the Earth.

For Daneel had vanished. Had he committed suicide? Was he living as a hermit, hiding somewhere in the Empire? Was he considering and implementing more ways in which humanity could be benefitted? Had he lost his desire to follow the Zeroth Law? Could he even be a danger to humanity? The Second Galactic Empire pursued the answers to these questions for decades, finding no answers, until 1,134 F.E.

The year the (first) extragalactic menace arrived.

1.

Preem Mortun was surprised to see the Prime Radiant.

Not the act of seeing the Prime Radiant, of course; it would be unthinkable to be a Second Foundationer without ever having seen the Prime Radiant. Rather, it was the prominence of its location that took Mortun aback: the projector seemed to float about a meter above the ground, at the precise center of the large foyer in which Mortun was now standing, projecting psychohistorical equations upon every surface of the room.

Mortun approached the small cube. Deft fingers performed intricate but well-rehearsed movements, and the equations on the walls changed and transformed. It appeared that the Prime Radiant was no mere display; it was fully functional. Yet it was also apparently a display, despite the fact that Mortun had never heard of a projector with no owner or owners.

I wonder how it manages to hover in that location, Mortun idly wondered, before noticing a simple, narrow rod made of an almost completely transparent material, on which the Prime Radiant projector itself was attached. It felt cool to the touch, as the Second Foundationer realized the simplicity of the design, as opposed to all sorts of elaborate antigravity devices that had initially came to mind. Suddenly, the young Second Foundationer could not help but suppress a laugh at the irony. The Prime Radiant projector here is perhaps the most advanced and wondrous technology in the Galaxy, and here I am passing it by to focus my attention on a simple pedestal!

“Well, occasionally simplicity is more deserving of awe than ornateness,” a voice said.

Mortun turned to face an older man who had just walked out of a hallway to the side. “I wouldn’t dismiss the Prime Radiant projector so casually with a word like ‘ornateness,’” Mortun replied, taking no undue notice of the mind reading.

“Evidently, I would,” the man replied in a characteristically sudden grin. “We do have our prerogatives.” He extended a greeting. “It must have been quite a trip from the Theory Octant. I’m Yornin Tyrell, and you must be Dr. Mortun. Welcome to the Engineering Octant.”

“Preem, please.”

“Ah, yes, Preem. And call me Yorn. You have quite a namesake to live up to, don’t you?” Tyrell replied. “We have three Preems in our division alone. In all honesty, I’m surprised the name isn’t more common; perhaps us Second Foundationers aren’t as traditional as the rest of the Galaxy seems to be.”

“Or perhaps we concentrate on the future so much that we don’t delve into the past deeply enough.”

“Possibly,” Tyrell said. Actually, it was unnecessary for Second Foundationers to exchange so many words, as all of them had strong mentalic powers. There was no exception here; in conveying the sense of “It must have been quite a trip from the Analysis Octant” Tyrell physically uttered no more than two words. It will no doubt be easier for the reader, though, if the text continues in the same vein that it has been proceeding:

“So, how may I help you? It’s not often that the Engineering Octant requires the services of the Theory Octant.”

“Not often these days, of course; but I’m sure that centuries ago, when the Second Foundation numbered in the mere hundreds, there was much more interaction between the Octants.”

“If there were Octants back then, you mean.”

“Indeed. In any case, you will require some background information before I can explain our problem to you. Come with me to our development area,” Tyrell said, beginning to walk off.

Mortun followed.

2.

“As you know, the Engineering Octant is primarily concerned not as much with the Prime Radiant, but rather the Prime Radiant projectors. We design, test, and produce every single one of those ubiquitous cubes that can be found all over the (Second) Foundation,” Tyrell explained as he led Preem Mortun down hallways and corridors. “The division I belong to is mostly concerned with the investigation of more radical developments of the technology; the simple enhancements and actual production belongs to other divisions. Any unorthodox concept that has potential to improve the Prime Radiant projectors, we are obligated to investigate. In a sense, we are the Theory Octant of the Engineering Octant, although of course what we do is as far removed from the actual Theory Octant as the Theory Octant is removed from the First Foundation.”

Tyrell exhibited another one of his toothful grins, and continued, “Of course, if it wasn’t for the Theory Octant, we wouldn’t be doing this at all. The sheer amount of data contained in the Prime Radiant grows di-exponentially, and we are still trying to catch up as formulae get refined over and over again. I shudder to think how large it would be if all that were raw numeric data instead of the equations they are now. Back in the first few centuries, it was still possible to store the entire Prime Radiant into a single projector – in fact, it’s their fault that we often leave off the word ‘projector’ when describing these cubes. As psychohistorical theory refined and added more and more detail to the actual Prime Radiant, the engineering was always falling slowly and slowly behind. The cubes got larger and larger, and I suppose if the trend continued a person would have to be quite athletic to qualify as a Speaker, just to able to haul a giant cube around.”

“A rather amusing thought, though,” Mortun mused. “How large were their projectors compared to what we use now? I don’t think I’ve ever considered that before.”

“It depends on the era, of course. For instance, when Stor Gendibal became First Speaker, a full Prime Radiant was perhaps four-tenths the size of a normal room. There obviously weren’t many of them around at the time. Surprisingly, our current projectors are perhaps eight-tenths the size of the earliest ones. Any smaller and the manipulation controls require a substantial amount of re-engineering to allow the same degree of flexibility. Besides, even if we had increased the size to solve the problem, it wouldn’t help for long. Double the volume of a projector, and you’ve at most squared the number of potential connections. Triple the volume and you only cube the cube.”

Mortun was prepared for Tyrell’s grin this time and appropriately reacted to the pun, as well as asking the intended lead-in question (despite already knowing the answer), “So how was the problem solved?”

“Good question,” Tyrell continued, “eventually, of course, the engineers would lose the battle to keep the Prime Radiant projectors compact enough to contain the entire Prime Radiant, to say nothing about the other external fringes of psychohistory theory, although I admit there hasn’t been much of that recently. The best solution was, therefore, to centralize a data source, and the projectors would only access and load information as needed. Thank Seldon this planet has an abnormal abundance of metals. Nowadays there is no centralized source, of course, just planet-wide distribution and redundancies. I should estimate about three-tenths of the mass of this planet is devoted to access, manipulation, and storage of the Prime Radiant. Even if we removed all redundancies, checks, and communication linkages, fully one-tenth of this planet’s mass would be needed. I can’t even get a feeling for how much that is.”

“You can’t?” Mortun mentioned in amazement. “Surely you know the visualization methods that are used…”

Tyrell interrupted, “Yes, yes, I do know how to visualize psychohistorical trends, which means that I can visualize whole planet clusters; so why should a mere fraction of a planet be a difficulty? There is no problem with conceptualization; the difficulty is, as I mentioned, in feeling. I can get a good feeling of what trillions are, but these are, oh, septillions of connections!”

“I understand,” Mortun commented apologetically. “Please continue.”

“In any case, we can probably handle the load that the Second Foundation generates for perhaps eight more decades. Another group is working on a form of sub-electronic optimization, I hear, but they say that even ideally it will only triple the amount of ‘survival’ time, so to speak. At that point, we may have to start eliminating psychohistorical data.”

Tyrell paused, and Mortun looked at the older Foundationer’s face. There was no grin this time; Tyrell was quite serious. “Can’t the data be stored somewhere instead of eliminated?”

“You mean, like it is stored now? At that point we completely reach a theoretical limit – the laws of physics. For the stored data to be used, it has to be within range of communication, and at a certain size gravity implodes the entire store. That’s where we might be in a few decades. Information isn’t very useful if it’s inside a black hole, you realize. And don’t starting thinking about anti-gravity technology; all the anti-gravity technology invented hasn’t been able to avoid the second law of thermodynamics yet, even including that done by the First Foundation.”

“Well, if this other group you mention succeeds, at least the Seldon Plan will be completed without difficulty, right?”

“Of course! In fact, we could freeze the current state of the Prime Radiant – no, even roll back to the state the Prime Radiant was two centuries ago – and the Seldon Plan would be in no appreciable danger. Probabilities are probabilities, and I can’t imagine any equation refinements actually affecting anything on a galactic scale. But the galactic scale isn’t the problem. We know the Seldon Plan will succeed with an almost certain degree of probability. But what comes after? Do you honestly expect us to all disband once the Second Galactic Empire is formed? That no more psychohistorical research will be useful? What do they teach you over there in the Theory Octant?”

“We’re all very specialized to our own branch…you’re right, of course. I just hadn’t thought of anything beyond the Seldon Plan since my earliest schooling.”

“That’s all right. Most Foundationers your age haven’t; no offense intended. When one is close to the finish line it occupies one’s full attention. No, we have to keep on inserting those refinements. Note that I said we had to eliminate psychohistorical data, not refuse to accept new data. If it comes to it, we remove older, unfulfilled branches that will be unlikely to influence humanity in the future. There’s always that small chance they could, but we’ll have to take that risk. Even then, it only slows the problem instead of solving it.”

“I can’t believe the problem hadn’t been thought of earlier, Yorn.”

“Oh, believe me, it has. Presumably the early Foundationers always assumed our technological advances would always be able to catch up to our theoretical advances. Perhaps that assumption isn’t incorrect, in the long run. But it is true that the technology side has been losing for a century or so, and while there’s never a reason to panic, the worry is always there, and I doubt that anything will ever eliminate it. But if my work succeeds, I think we can buy a few more centuries.”

Tyrell was grinning again as he opened the door to what was undoubtedly his workspace. Both Foundationers entered as the door slid shut behind them.

3.

Mortun looked around the room. It was a completely new sight, unlike anything in the young Foundationer’s experience. Bits and pieces of disassembled Prime Radiant projectors were strewn about the room; Mortun now understood why Tyrell was able to speak of them so callously. A partial wardrobe was in a corner; evidently Tyrell even slept here occasionally. How different from the comparatively Spartan offices of the Theory Octant!

“Here is my crowning achievement,” Tyrell beamed as he indicated a projector upon a workbench littered with perhaps a dozen projectors, “except that I’d prefer to show you a standard Prime Radiant projector first, to make a contrast. I know I have one around here somewhere…” His enthusiasm dropping years of maturity from his motions, Tyrell picked up a projector, and activated it.

Immediately the room came alive with floating equations. Tyrell purposefully went to one on the side, near Mortun’s shoulder, and expanded it. The formulae stretched outwards, and then suddenly winked out of existence.

“Sorry,” Tyrell said, and activated another projector. After the initial overall view of the Prime Radiant, he switched it off almost immediately. “An earlier version of what I was going to show you,” he explained.

The third projector Tyrell tried apparently had poorly calibrated controls; the wrong equation expanded, and three levels too far down.

The fourth projector gave Mortun a slight headache. Instead of the expandable functions of a typical Prime Radiant, there were mostly giant blue swirls that composed a giant geometrical shape. It was only upon closer inspection that one noticed that the blue swirls were actually composed of tiny extension rivulets, so small as to be unreadable.

Tyrell was about switch it off, but Mortun interrupted. “What is this? It’s not like any Prime Radiant I’ve ever seen. If you could afford the time to explain, that is.”

Tyrell paused a bit. “No, we have time. This is something I was just toying with when I needed a respite from my actual work. What you are seeing now is our current Prime Radiant as it might have been seen by the early Second Foundation.”

“As early as my namesake?”

“Even earlier, and also as late as when Kell Bellisarn was First Speaker. Instead of the hyper-hierarchical display we have now, they had to make do with only hierarchical methods. Which means that a projector back then had to display much more information to provide an overview of the entire radiant. Visualization education wasn’t as developed, so they used colors to help them understand – the Seldon Plan in black, factual deviations in red, and psychohistorical theory refinements in blue.” Tyrell pointed.

With some work, Mortun could make out a black thread in the sea of blue, with small red cilia branching off. “At first I thought it was just all one color.”

“In Seldon’s time, it was. All black. By the time of Stor Gendibal, there was perhaps as much blue as black, and by the time of Kell Bellisarn the blue explosion was so large that she decided that the archaic system needed to be revised. Now, of course, it is even worse. The early Second Foundationers needed a view of the entire Prime Radiant, but no one does now, except for perhaps the Speakers. One can’t do any actual psychohistorical work from this projector, of course; but I find it aesthetically pleasing to view.”

“I must say I can’t agree,” Mortun replied. “Although I suppose with regards to my work I might be expected to.”

“How can you not see the beauty here? Look, this is the first two centuries of the Seldon Plan. This relatively thick red offshoot – the Mule. And these two helical red and black strands – the Great Experiment.”

“Which was unnecessary.”

“A matter of opinion, Preem. After all, Gendibal evidently thought it was, although it wasn’t until five decades after him that the Second Foundation as a whole finally came to agree with him.”

“Which they shouldn’t have.”

“Yes, that is the popular sentiment now. Anyway, we had best move on.” Tyrell deactivated the projector in mild disgust.

4.

After a few more failed attempts at trying to find a working Prime Radiant projector, Tyrell looked at Mortun sheepishly. “Preem, I don’t suppose you have a Prime Radiant projector with you, do you?”

“Of course,” Mortun replied with projector in hand, having already anticipated the request. “Here.”

Tyrell took the projector carefully, and activated it. The familiar equations leaped out. Tyrell expanded a few levels of equations, obviously having a certain section of the Prime Radiant in mind. Suddenly he pushed the cube to Mortun. “I’m finding the control a bit awkward,” he explained, “how about you take the helm while I do the navigation?”

“Sure,” Mortun responded, already a bit uneasy. Apparently the Foundationers in the Engineering Octant did not treat their Prime Radiant projectors as gingerly as those in the Theory Octant; all this time Mortun was focused on Tyrell’s handling of the projector, rather than concentrating on which region of the Prime Radiant Tyrell was going towards. Now the younger Foundationer was at a bit of a loss. “I’ve never looked at this area of the Prime Radiant before.”

“I have,” Tyrell responded curtly. “Go down eight levels on this function,” he said as he pointed towards a particularly complicated shape, “this term.”

Mortun complied, and Tyrell continued, “Good. Now expand this one, over here, by a factor of, oh, about five. Stop! Orient left a little bit.”

This behavior continued on for a few minutes. Mortun wondered if the elder Foundationer really had a specific location in mind, or whether he was just hitting whatever struck his fancy. Occasionally they would seem to investigate a rather fractal region, sometimes an area that Mortun thought would be uninteresting. Sometimes they drew back a bit, but more often than not they were going deeper into the intricacies of the Prime Radiant. Mortun did some calculations on the side, and concluded that if the entire Radiant were expanded at the current resolution, the volume of space needed to show it legibly would be the size of half the galaxy.

Eventually Tyrell stopped. “Now, tell me, Preem, what do you see?”

Mortun’s mouth was open in astonishment. An equation, or rather part of a very long equation, floated in the room. The equation was not the main source of surprise, however. “There are … no other formulae around at all. I’ve never seen anything like this! Of course, I’m sure I’ve never brought the Prime Radiant down to this resolution before, but still…”

“…This should be impossible?” Tyrell finished. “Theoretically, psychohistory can only give probabilities. It cannot give certainties. True, as the target population gets larger, predictions can get so accurate that they almost are certainties – the Seldon Plan, for example, which juts out of the Prime Radiant like a sore appendage if you’re looking for it. Especially at this level, which is maybe that of a specific economic factor regarding a single star system in a fifty-year period (you realize I’m guessing at that), it should be impossible for there to be a single formula describing it, no matter how long or complicated the formula is. Always, the Radiant should be able to expand terms and show potential alternates, based on basic psychohistorical principles. Yet there you have it. A single formula. Try expanding any term in there. Or search for offshoots.”

Mortun tried.

“See, you can’t. The projector won’t allow it.”

“And this is why you asked for me? I can’t explain it; in fact, I think my expertise is almost completely the opposite. I suppose it’s possible that…” Mortun trailed off.

Tyrell flashed out his grin again. “I’m afraid you’re getting ahead of yourself, Preem. You forget that I brought you here to show you this projector here, not your own. No, I’m afraid I have a completely rational explanation for this phenomenon we are looking at right now.”

This time it was Mortun’s turn to look sheepish.

To be continued...

Disclaimer: The characters and situations in this story are the legal property of the Estate of Isaac Asimov. This story is in no way intended as a challenge to that ownership, and is offered solely for entertainment purposes.

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