Self-Reference Engine

by Toh EnJoe

  Responding to the movements of Yggdrasil’s extended left hand, silver daggers spring simultaneously from some of the points of light within the shaft, indicating the point in space-time that is the target of the third space-time adjustment campaign. A total of one hundred fifty interspace-time ballistic missiles are ready for deployment in the current battle. These can now be fired into the past or future in ways that are beyond the comprehension of James and his kind, to destroy opposing corpora of knowledge.

  Amid this incessantly writhing space-time structure, red hearts are individually beating in response to the giant corpus of knowledge, and the blood vessels communicating between them indicate the battle of calculations. Everything from a read/write abacus to the tossing of tomatoes are all forms of calculation tactics utilized by or between giant corpora of knowledge.

  “The destruction of these points will make this next structure a stable one.”

  Pinched between the middle finger and thumb of Yggdrasil’s still-waving left hand, the point of light identified as the target is extinguished. The blood vessels connected to that extinguished beating heart turn from red to green, and with nothing left to do, they tremble, then disperse in all directions, only to grow again and reassemble, as if having regained their senses. The vibrations transmitted through the fishnet structure give birth to new points of light, forming the folds and undulations of the overall net.

  James stands studying the scene with clear eyes, but all he can grasp is that one incomprehensible fishnet pathway structure has morphed into a different incomprehensible fishnet pathway structure.

  Some aspects of fishnet pathway destruction methodologies are well known. All you have to do is destroy the function nexus where multiple lines come together. This is a “bamboo rule of thumb,” unchanged since ancient times, and once practiced by terrorists who targeted air traffic networks. How to take the technique of attacking tiger bamboo with a single decisive stroke and adopt it for outer space was too much for even the giant corpora of knowledge, so all they could do was start with the familiar and move ahead from there.

  What Yggdrasil has perfected is a method for identifying and destroying those nexuses, but after they are destroyed, the net structure reestablishes itself, and new nodes appear, pulsing green. What sense is there to destroying nodes if new nodes simply appear to take their place?

  “Another five nodes destroyed,” Yggdrasil continues on coolly, as if she can read James’s innermost thoughts.

  “Isn’t that the margin of error?” one of the staff asks with a groan before James can even raise his hand. “Two iterations previously, the reduction was five hundred. The last iteration, the change was plus twenty-seven. It is difficult even for us to determine if the plan is making progress.”

  James is thinking that he doesn’t want humans to be mixed up with the military, but he agrees with the conclusion and so says nothing.

  “This is, just as I have previously explained numerous times, simply a preparatory phase before the early stage of the real repair work can even get started.” In negotiating with humans, the advantage of a massive artificial brain like Yggdrasil is that she can repeat the same information endlessly without getting bored or disagreeable. “Please bear in mind that this is still merely the third attempt. It is projected that the effectiveness of the operation will increase exponentially with the number of repetitions.”

  What Yggdrasil is saying is correct. Even James, a human, is greatly affected by the forecast modeling of the influence of the ongoing process of destroying nodes on the network and of then destroying the nodes that reform.

  The speed of pruning the network increases asymptotically as well as exponentially. In other words, after a sufficiently large number of attempts, the process proceeds extremely quickly. That is the result that James and his cohorts have achieved. When blockages appear in the network, they point to events in the distant future, but this is of no use in reaching even a general valuation based on a small number of attempts. The situation will eventually reach a turning point if the battle goes on for an overwhelmingly long time.

  Maybe, anyway. If the process can continue without getting bogged down, it may eventually lead to an avalanche situation that will wipe away everything.

  The total annihilation of the entire network will take place within a finite time period.

  That was the most positive result achieved by James and his cohorts. Whether this is cause for celebration or for smashing one’s head into a keyboard is not clear. Finite means nothing more than “not infinite.” No theory is available on when, specifically, the avalanche might occur.

  Doing battle means executing the calculations once a day, assuming that actions on this scale can be performed daily, for a length of time that we might as well call forever. The staff surrounding the spot can be forgiven for bearing expressions that are not particularly cheerful.

  To return space-time to the way it was before it got all distorted means reducing the number of nodes to zero. A single, solitary clock will be free to march straight down the last line, connected to nothing else.

  Therefore, what Yggdrasil is saying, while not untrue, cannot be termed completely straightforward either.

  “We aren’t even able to understand the diagram. You’re telling us we should just be patient and wait. Care to tell us why you can be so confident when you just tell us we should take your word about the reasons?”

  The staff members are refusing to back down.

  James thought the debate would end there. If Yggdrasil were just to puff up her chest with confidence, she might even make the staff stand down, just by saying, “I understand.”

  “Confidence is…” Yggdrasil says, “something I don’t have that much of.”

  Passed without proof. James could recall a similar exchange at the previous meeting between the staff members and Yggdrasil, with her tone of voice amused.

  “I feel like I have said this again and again: it is a problem of possibilities, Mr. Chief of Staff. The ‘correction’ of the space-time structure is a problem well beyond the calculation powers of even the giant corpora of knowledge. It is similar to the problem of you humans, with your brains, trying to understand the brains of the giant corpora of knowledge. The capacity of the brain can be increased, but the universe is that much larger and more complex. The processing power of the brain itself cannot be increased infinitely.”

  The chief of staff starts to raise a fist but, noticing there is nothing there to bring it down on, relaxes again.

  Yggdrasil speaks again: “Our degree of understanding regarding these phenomena, like yours, has changed little. Divide a finite number by infinity, and the result is zero.”

  For all that, James thinks, the current space-time model takes inversion about as far as it can go. Another certain dimension is that the giant corpora of knowledge are at work in places that are so far beyond the mental capacities of humans.

  “If that is the case, then what is the point of this campaign? If we don’t take care of this ourselves, this space-time might recur at some point on the far side of eternity. Even if we do take care of this ourselves, this space-time might recur at some point on the far side of eternity. Can you guys add anything to that?”

  In response to the staff’s grilling, Yggdrasil lapses into silence. It is not clear if she is simply trying to put an end to this endlessly repeated debate or whether she seeks silence in which to contemplate how best to continue repeating her point of view. Yggdrasil’s mission is to psychologically reassure the humans, not to explain the minutiae of these phenomena.

  James understands the paradox of the problem the staff members are asking about.

  The plan is to destroy the nodes of space-time, to take an existing gelatin confection and turn it back into the gelatinous raw material it may once have been. If the plan succeeds, space-time will be restored. In other words, space-time will once again be a one-way street. The plan itself is not very concerned about past or future; its goal
is simply to destroy the nodes of space-time distortion. By using various forms of feedback and feedforward, the plan’s ultimate aim is to restore space-time to a more suitable form with a more stable structure.

  The plan is predicated on the notion that a singular space-time will exist at some time in the future. In other words, if the plan succeeds, its success will be made manifest in the future. The plan will succeed by basing its operations on what is already known from the future. Honestly, though, James himself does not get this.

  “For us too,” Yggdrasil begins. “As I have told you many times in the past, the overview of our plan is not well understood. But we believe the plan will succeed in the end. This belief has a structure comparable to that which is known as Laplace’s Demon.”

  Laplace’s Demon is the idea that time is just one of the dimensions in a deterministic system. Everything that will occur in the future is already completely determined by things as they are now and cannot be changed. The demon knows all about the current state of existence, and for that reason the difference between the present and the future has become meaningless.

  It is hard to say whether the aphorisms the staff members share among themselves are informed by knowledge or ignorance, whether they show the way to a revolutionary new idea or are mere clichés. It is also possible that at times like this they speak in aphorisms simply out of habit.

  “We are capable of comprehending plans such as these. We think this is due to the work of the devil. Given the extent of our facility with calculations, we are closer to Laplace’s Demon than we are to any other person that existed in the past. It is because something like this transpired in the past that the devil ascended, moved up a step, and escaped to a place where we could not reach him. However, it is because of the devil’s closure, a trick of topology that thinks this stairway through to the end, that our plan was recognized. That is why we are able to think about it and to carry it out. That is our belief.

  “In that sense, our plan is an attempt to reenact Laplace’s Demon. By reassembling the various fragments of the universe, we will recall the new demon. Our goal is to ensnare and take down the demon that has moved up a step on the logical hierarchy.

  “And then we ourselves will be involved in the plan. We believe that will be further insurance of its success.”

  What might bind space-time together once again is their own past selves, as viewed from the future. In that sense, they are doing it themselves. More is expected from this endeavor than the mere restoration of a stable space-time structure. Boiled down, that’s what Yggdrasil had said. The prodigal sons of Laplace have begun their wanderings, and now Yggdrasil is trying to grab them by the scruff of their necks and get them to listen to reason and return home. That’s what this attempt is all about.

  “If we think we are being made to think we are being made to think of this as a sort of fixed-point theorem, then we can think about it,” Yggdrasil says. The staff members appear to have given up on answering back.

  “Our thinking is that we are being made to think we are being made to think of space-time as probably some sort of reinforced, stable region. There is no escaping this line of argument. We have to work with this.”

  James thinks this way of thinking is nothing more than the giant corpora of knowledge’s aspiration. They simply integrate too much leverage structure into their own thought processes. Of course, James is just like a dream of Yggdrasil’s. But if that were true, then Yggdrasil is a dream of the demon’s, and the demon must be a dream of a higher-level demon. It is Yggdrasil’s contention she should be able to pierce through this endless hierarchy of demons and reestablish space-time as a coherent bundle of meaning. That is because, according to Yggdrasil’s line of thinking, this thought is the sole interpretation capable of penetrating an infinite number of layers.

  James, modestly, thinks of this as a belief. Yggdrasil herself concedes that. There is no law of logic that transforms evidence of internal consistency into proof of a claim. In the end, that’s all Yggdrasil is saying. If only the absence of contradiction were itself proof of truth.

  This campaign will go on virtually forever. It will persist as long as Yggdrasil continues, into a future universe where James and the rest of the staff will no longer be around. Somewhere out there, on the far edge of some fragment of time, time will once again reunite along a single axis and spread from there. And then, there will no longer be an infinite number of different clocks in the universe, there will be just one clock, continuing to tick away the passage of time.

  This will be the deterministic cosmos where the current multiple, competing universes will be reunited. While this is in accordance with the perverse order of the multiverse as a whole, it is difficult for humans to grasp just what those other universes are. What the giant corpora of knowledge are attempting to do is to reintegrate this crazed multiverse into a single universe.

  The infinity set of giant corpora of knowledge, calculating the infinity set of universes. That is the current state of the universe. For any given corpus of knowledge, it is difficult to know what other corpora of knowledge are thinking, just as it is difficult for any given human to directly apprehend the interior life of another human. The giant corpora of knowledge are practically omnipotent, but it is a long way from there to omniscient.

  All the giant corpora of knowledge are attempting is to return space-time to its proper order. That is as James would want it. It is the extremely plain desire of all humans to live in a universe where what happened yesterday actually happened yesterday. Even if it really is something unknown from the distant future sailing against the current to manifest itself in its past, our present.

  However, this is more than just Yggdrasil’s prayer, and that is a problem.

  Yggdrasil stands in the center of the conference room with a satisfied look on her face, but then a shadow falls. As Yggdrasil squints her eyes, the shaftlike fishnet path disappears. The lights in the room come on. The vast space is lit bright white and then turns red.

  “Please take cover,” Yggdrasil says quietly, as the protective window coverings descend on all sides of the room.

  “It’s an interspace missile from Uncle Sam. I am taking action to intercept.”

  With the staff members in a commotion, Yggdrasil bows elegantly. Her eyes meet James’s just before she erases her own image.

  Clearly, it is not just the giant corpora of knowledge of this particular universe that want to right things in the universe.

  Giant corpora of knowledge in countless universes are striving for the same goal, and no doubt they are undertaking similar operations.

  For those others, this universe where James and Yggdrasil are performing their own calculations is just one of many nodes interfering with their own calculations. And vice versa. What occurs to one might easily occur to someone else.

  What James sees in Yggdrasil’s eyes is fear. The time has come to destroy or be destroyed. Of course, this facial expression has been calculated and rendered by the giant corpora of knowledge simply to be shown to James. That, however, is not to say it is intended to fool James.

  Surprisingly, James believes the look in the avatar’s eyes might reflect the true thinking of the giant corpora of knowledge. The question of whether their real intention is to reintegrate space-time is not that big an issue. Sooner or later, one universe or another will succeed in carrying out the plan. Through the calculations of some universe, this universe in which James finds himself will at some point be unified with all the rest. Until that time, the only way to keep from being blown away is to strike first.

  It is entirely possible that the result of such action—victory or defeat—has already been determined retroactively by the state of the reintegrated future. The giant corpora of knowledge are acting in full awareness of this possibility.

  James finds himself shaking from the feeling that he has managed to touch a fragment of the thinking of the giant corpora of knowledge. They are neither the allies nor the e
nemies of humans. In their desire simply to go on living they are no different than James. Finite beings loitering in the face of the infinite.

  James sneers at the thought that he is just being made to think that he is obviously being led around by the nose. But could there be anything in the multiverse that is not being led around by the nose?

  Right now, he has to put his own physical safety first. If at some point in the far future something inside the giant corpora of knowledge turned out to be the devil, that is when the human race would have to resist by resplintering the universe.

  James believes that’s what the Event was: that kind of a misunderstanding. James’s laughing voice resounds in the corridor where the emergency evacuation signal is blaring. Sprinting for his life under the red lights, James reaches a terribly banal decision. And at that ordinary thought, a giggle escapes his lips. Survival. Everything after that comes after that. That is so obvious he even feels faint. It would be enough to set everything back to start, just before everything froze.

  The floor beneath is shaking violently, and James is thrown against the wall. He can no longer tell if everything looks red because of the flashing emergency lights or because of his own blood. Even these thoughts of his are nothing more than the endlessly repeated ephemera woven into the fabric of space-time. As long as anyone is still alive, someone will still be trying to survive. Rather than be swallowed, anyone will strive to be the swallower.

  It is James’s belief that the best way of reintegrating the universe into a coherent whole would be for humans to systematically destroy the giant corpora of knowledge until there is just one left. From his personal standpoint, that means destroying Yggdrasil. Of course, the power of the giant corpora of knowledge would be indispensable in the process of reintegrating the universe. But it is hard enough to try to push one car sideways; forget trying to push a whole bunch of cars sideways.