Self-Reference Engine

by Toh EnJoe

  I have my own ideas about what the aim of the multi-unit calculation plan was. And they are not anything as leisurely as the parallel processing of data among multiple units that the symbols of the four mathematical operators of the Spirit hint at. I think those are actually a symptom of the disease.

  When a fox spirit possesses a disembodied soul, a new spirit emerges. This is an act of addition, and while there is a certain degree of freedom to wonder just how the fox spirit possesses the disembodied soul, it is also unclear whether the fox spirit could be subtracted again, leaving the original disembodied soul as the result of the operation. Two and three make five, but five can also be broken down into one plus four. Possession by spirits can result in a drastic personality change, which may indicate that that sort of calculation process is going on in the soul.

  The remaining two mathematical operations are multiplication and division. What meaning might they have? To explain the exuberance of the innumerable operators that are likely to be at work in the axiomatic system of the soul, well, that is beyond my powers. Before that, I would have to consider that the main cause of Pentecoste II’s demise may have been thinking about the existence of a space where the positions of all souls could be specified.

  Pentecoste II was trying to find realizable formulas that could take souls that had been smashed and scattered about all over the place and identify and systematize them in a row of real numbers. Like putting steamed buns in a box, there would always be some misfits, and it was the effort to get those in a row that caused the box to self-destruct. This is no more than my personal speculation, but I think Pentecoste II began to identify with the box rather than the buns. Trinity, three-in-one, calculations. Or infinity-in-one calculations. That’s the only line of reasoning I can imagine that combines the concepts of “Trinity” and “multi-unit.” Imagine a host of foxes, their jowls drenched in blood, withdrawing one by one after hunting down and gorging themselves on souls adorned with the triple Papal tiara.

  The destruction of Pentecoste II has had a surprising resonance among humans. Some particularly stupid ones, deeply impressed by the live broadcast of the disaster, tried to do the same thing themselves, en masse. But humans don’t have the same kind of solid logical base as giant corpora of knowledge. They tried to imitate Pentecoste II simply by randomly chopping at their bodies or throwing themselves into blast furnaces. Disappearing without a trace is impossible for ordinary humans, who, after all, are not giant corpora of knowledge. Unfortunately, they had forgotten that the deceased giant corpora of knowledge had not vanished—they had only been able to turn back into heaps of rubble.

  My parents did not live long enough to witness the moment when immortality became commonplace. There was a clear, bright line dividing before and after among humans in the debate over regenerative medicine, including techniques for the partial extension of life. I am on this side of that line, and my parents were on the other side. My identity is on this side, and I am thinking about the other side. It could be that there are other hard lines. For one thing, there had been the Event. For another, regenerative medicine. And the last line is the line of my own identity.

  Last year, the sub-group of giant corpora of knowledge tasked with advancing research into immunological disorders announced that they would change the treatments regarding the reordering of human personalities in past/future transformations. Among the generation accustomed to seeing simple rewrite operations as day-to-day events, the perceived distinction between medical intervention and transformation of the past had grown tenuous. It may be that the giant corpora of knowledge tried to explore a detour around the lines that separate me from my parents.

  The plan to restore the universe to what it was before the Event the giant corpora of knowledge had caused, before the space-time structure had been shattered into the multiverse, is still progressing. In that sense, it may be that the line pulled by history is an indicator that aids our understanding of that which has been erased and now must be redrawn.

  What is to happen then to those areas surrounding identity now in the process of being redrawn—that which destroyed Pentecoste II—those newly immune areas that are attacking humankind, now gifted with life unending through perennial rewrite? By happenstance, I am in this world; I am/am not, I exist/do not exist in that other world.

  In all likelihood, I will die. Death will come at me from the direction of the future. Or I may be approached by the Death that encompasses all of space-time. And thus will Death be restored and Life vanquished, at some point to be restored.

  My brain is now divided into three parts, in a close and delicate balance, each of which believes itself to be my entire brain. The drugs that caused this state, as well as the massive quantities of drugs I need to ingest to keep it under some degree of control, were lost in the turmoil of moving myself to this place. Coincidentally, carelessly, foolishly, unconsciously, and of course deliberately, they are now gone somewhere.

  I have removed that troublesome suit, that possession that controlled and constrained my body.

  It may be that someday the massive amount of data that remains in the medical department shall be used to restore me. I can think of no reason why that restored me will not be the same as this me. It will definitely be me.

  Just like this, I am now looking out the window. My three consciousnesses are, just barely, still coordinating with one another, and somehow I am able to keep my body upright. At some point the pharmaceutical constraints will fade, and the different parts of my brain will begin to see the other parts as “other,” and they will begin a fierce battle.

  My body will dance. Or will I even be able to dance?

  My hands are clutching a piece of paper on which is written: This is an extremely serious, urgent, life-and-death matter.

  If I am restored, there is no reason that future me will be able to report what I am on my way to see. I intend to go see it. The thing that the late Pentecoste II may have seen, or may not have.

  I am one of those stupid people who wish to follow in the path of Pentecoste II. If I may be allowed to say a few words, it is not that I am pursuing Pentecoste II. Where I want to go is the place Pentecoste II was unable to reach. My reasons for thinking I can get there are not powerful. My companion on this journey is the meager quantity of reason my brain can contain.

  If the giant corpora of knowledge are trying to redraw all the lines, they may try to pursue me across the line I may now be able to cross. And that will be fine. And they may be able to redraw that line so they can catch me. And that will be fine. By that time, I will aim to be on the far side of the next line, trying to bring back that place where that which should be lost can remain forever lost.

  From my room, where my bags are not yet even unpacked, I am looking at the scene outside. I am going to die. But not right here and now. Death is merely that which should come, will come, sometime. I hate it that there is so little sign that this will happen. I do not hear the footsteps of Death drawing near. What I should be hearing is the sound of my own footsteps escaping down the corridor. I wish to hear the sound of my own footsteps, escaping far away.

  Outside the window is an embankment, and cherry blossoms are blooming. I open the window, hoping to be lured by something. I am seized by a fit of sneezing, probably due to pollen, and I am seduced by laughter. I am still me, not a cherry tree.

  This is a competition between a human and the giant corpora of knowledge to see who will arrive first at the other side.

  Even if I am restored, I am likely to continue my attempts.

  It may be that that’s just the kind of device I am.

  No doubt about it, I am a perfect fool.

  17. INFINITY

  AS THE RADIUS of the nearest sun suddenly shrinks and disappears into the fourth spatial dimension, evening arrives in this area. Once again, Rita finds herself in love with this familiar scene.

  As this fourth-dimensional sun travels in uniform motion through the fourth dimension, the
radius it displays in Rita’s space-time appears to change in a pattern described by the formula √R2−t2, where t = time and R = the true radius of the star. When this sun seems to suddenly disappear, Rita gets a satisfied look on her face and continues to gaze up at the sky where the sun just was.

  Her father shows no interest in listening to her talk about this, and her friends at school are the same way. Her teacher is a little different, but Rita knows he sees her as the kind of girl who always asks one more question than is strictly necessary.

  It seems the only one Rita can depend on to listen to what she has to say and to teach her things is her grandfather. But lately her grandfather has been mostly sick in bed. When Rita visits his expression brightens, but his body is unable to follow suit. Rita knows her grandfather waits for her with all his heart between visits, but considering the state of his health, her family members have decided it might be best if she doesn’t visit too often.

  Rita’s grandfather was a wanderer his whole life, and her other relatives, who still live right near the place where they were born and who are still not bored by that, cannot think of him as anything but a crazy person. Nor can they even understand why he finally came back to this place. The reason is clear—Rita’s birth. But even something so obvious, her kin just don’t get.

  One day, Rita visited her grandfather for the first time in a week. From his sickbed, one eye closing slowly, he reached out a bloodless hand to her. Once a week, thirty minutes. That was all the time Rita and her grandfather were allowed to spend with one another.

  “I have a fun game,” her grandfather said, and he explained the rules. “The game is to find the words I need to say to you in twenty-five hours, in the roughly fifty visits we have left to us.”

  Grandfather had decided he had about a year left to live. He had always decided everything on his own, and he would probably stand by this decision as well. He was stubborn about his own decisions. And he was even more stubborn about things people decided for him.

  “Twenty-five hours is not nearly enough for the things I have to teach you. So once a week, I am going to give you homework problems. You will think about these problems during the week. If you have an answer, I will give you the next problem. If you don’t have an answer, I will give you a hint. For my last year, let this be the game we play together.”

  As he nodded vigorously at his own decision about his final days, the sight of her grandfather made Rita smile. He was a man who had lived his life always trying to do the correct thing and to do it correctly. This had probably involved a lot of arbitrary decisions.

  Of course, there was no saying no to this game. If her grandfather overestimated her abilities and gave her a problem that was too hard, Rita could spend the whole next week working again on the same problem. Or if he gave her a problem that was too easy, Rita would have extra free time. The way to win the game would be if he kept giving her problems that took exactly one week to solve, and she took exactly one week to solve them, and this pattern repeated itself fifty times. Both Rita and her grandfather would be winners, and if anyone was a loser it would be both Rita and her grandfather. Rita loved the idea. And her grandfather wore a broad grin.

  “For me, the game will be to see if I can come up with fifty problems that are just right,” her grandfather said.

  Quietly, Rita prayed that her grandfather’s final pleasure, something only he could do, would come off without a hitch. She placed her hand on his chest, and he put his hand on her head.

  And that is how the game began.

  To date, they’ve been through twenty-three of these simple, weekly thought exercises gauged to quietly stir up Rita’s brain circuits. She has done well, for the most part, even if her grandfather does tend to err on the side of slightly overestimating her abilities.

  To solve the twelfth problem, Rita had to skip breakfast for three days, and on the twentieth problem, Rita did not fully grasp the solution until she stood by his sickbed discussing it with him.

  Now, Rita is preoccupied with the twenty-fourth problem.

  “In this planar universe, does there exist a girl almost surely just like you?”

  That is the problem her grandfather had given her three days before.

  Rita is not even sure she understands the premise, the first part of the problem.

  Clearly, the problem has something to do with infinity. This universe is believed to be planar. Infinite planes. And on these planes live an infinite number of humans. That is the conventional view of the post-Event universe.

  No one knows if that is really true. All that can be said is that it seems to be true for the space within at least thirty light years. The Event took place thirty years before. Regarding what lies beyond the space that can be traversed in thirty years at the speed of light, nothing is known, and there is no way of knowing anything.

  A plane with a radius of thirty light years. Seventy percent of it is said to be the sea, but Rita has no idea how many people are living there. Without question, though, it was an awful lot.

  Among that awful lot of people, what would it mean for there to be someone who was almost surely just like her? Almost surely just like. This phrase is one her grandfather uses a lot, but it is seldom heard in ordinary life. It must be the key. Grandfather had not said, “Exactly the same as.”

  Rita wonders just how much of herself is herself.

  A person with the same array of DNA would be an awful lot like Rita. But even twins are not the same person, so such a person would still be a little bit different from Rita.

  A person with a very similar arrangement of neurons. That may be close too. Such a person might think the same way as Rita, may even be thinking the same thing Rita is right now. Even her own family might think that other person was Rita. But if her face was different they would figure it out right away.

  Still, she can’t quite get her thoughts in a row. Thinking the matter through like this is just a way of wondering, if there is a person who is an awful lot like Rita, what would that person be like? Something is backwards. The answer that Grandfather is looking for must be something different.

  She sighs and rolls her shoulders, freeing her thoughts from the maze that has been going around and around in her head for the past three days. She has to change her whole approach. A lake is not the same as the ocean. Some lakes are not even connected to the ocean.

  Right. Everything is made of molecules—DNA, neurons, everything. Molecules are combined in particular ways. If all of those ways could be written down, the number of combinations would certainly be extremely large but less than infinite. No need for an infinite number of pages of notes. Rita is made up of a finite number of molecules.

  In other words, it is like this. No human has an infinite number of molecules. A human made up of an infinite number of molecules would be infinitely large. Whatever that would be, it would not be human.

  Rita reads out two propositions in her head. One: the number of people in this universe is infinite. Two: There is no person of infinite size.

  And Rita thinks this is enough. No proof, but maybe these are the assumptions Grandpa made.

  Rita doesn’t want to think about exactly how many, but she supposes the number of molecules she contains is finite. With molecules, it is the way they combine that is important. Imagine a space that has as many dimensions as there are molecules. A space where an enormous number of suns can flit about, willy-nilly, in any dimension they please. One point in that space corresponds to the position of the molecules that make up Rita. All the other innumerable points are the infinite number of other people in existence. In this space, at a point marked infinitely close to Rita, there is a person almost surely like Rita. An infinite number of points marked in space. How close are they to one another? That is the problem Grandpa posed.

  Rita’s body stiffens, and she furrows her brow and continues thinking. But the dimensionality of the structure she is trying to envision is too complex, and her imagination is unable to
keep up. The universe Rita occupies is known to have thirty-two dimensions, perhaps, or so it is said, though not all are accessible to humans. The space of people’s everyday lives is still the same as before the Event, three dimensions. Add in what is necessary for astronomical phenomena and you come to four dimensions.

  An infinitely expansive plane, illuminated periodically by an infinite number of suns approaching from the fourth dimension. More precisely, by the three-dimensional cross-sections of those four-dimensional spheres. That is what Rita and her peers know as the Suns.

  Strongly influenced as she has been by her grandfather, Rita can somehow see the sky as a four-dimensional space. But even with all the quizzes her grandfather has given her, for now the scale of Rita’s imagination is stuck at the fourth dimension.

  Modern physicists say the universe is now adding dimensions as necessary, as people come to think on a grander scale. Thirty-two should be the end of that. Anyway, the scientists say this 3+1-dimensional space where the infinite number of people live is a little pocket of sub-space within the thirty-two-dimensional space. Grandfather always shrugs his shoulders as if to say, honestly, who knows.

  The number of dimensions scientists are now trying to deal with is not a number remotely like four or even thirty. They want to slap a label on every molecule. It’s a ten with a whole lot of zeroes after it. A number so big it hurts to think about it; that’s how many dimensions they are interested in. It may be that by the end of the exercise, a day will come when Rita will be able to picture five or six dimensions. Now, though, she cannot, no matter how hard she thinks about it. At least not until her next meeting with her grandfather. Or maybe not until Grandfather passes away.