Galileo said, “Explain them to me.”
He felt himself become equations in the clouds inside him. Formulas described the motions of the minims, vibrating at the Planck distance and duration, thus small and brief beyond telling, and vibrating in ten different dimensions, which combined into what Bao called manifolds, each with its own qualities and characteristic actions.
“Investigations have by now found evidence for all ten dimensions,” Aurora said. “Even confirmation. The best way to conceptualize some of the extra ones is to imagine them enfolded or implicate in the dimensions we sense.” A long, flat red sheet appeared before him; it rolled lengthwise into a long thin tube. “Seen in two dimensions this looks like a ribbon, but in three dimensions it’s obviously a tube. It’s like that all through the manifolds. Dark matter has to be very weakly interacting but at the same time registering gravitationally at ten times the mass of all visible matter. That is an odd combination, but Bao considered it as a dimension we only were seeing part of, a hyperdimension or manifold that enfolds our dimensions. That manifold happens to be contracting, you could say, which gives the effect in our sensible universe of the extra gravity we detect. So that’s dimension four.”
“I thought you said time was the fourth dimension,” Galileo said.
“No. For one thing, what we call time turns out to be not a dimension but a manifold, a compound vector of three different dimensions. But put that aside for a second, and let’s finish with the spatial manifold. Dimension four we still call dark matter, as a gesture to our first awareness of it.”
“Four,” Galileo repeated.
“Yes, and dimension five in some ways counterbalances the action of four, as it is the perceived accelerating expansion of space-time. Aspects of this dimension are called dark energy.”
“Do these dimensions pass through each other, then?”
“Do length and breadth and height pass through each other?”
“I don’t know. Maybe they do.”
“Maybe the question as formulated does not have an answer, or maybe the answer is simply yes. Reality is composed of all the dimensions or manifolds, compounded or coexisting in the same universe.”
“All right.”
“Now let us come to time. Mysterious from the start, it seems mostly absent from our perception, but crucial as well. Past, present, and future are the aspects of time commonly spoken of as perceived by us, but they and other phenomena are the result of sense impressions compiled by living in three different temporal dimensions, which together make the manifold, in the same way our impression of space is a manifold. All three temporal dimensions impact on us even though we mostly have a very strong sense of moving forward in a manifold, so that we can only remember the past, and only anticipate the future, both of which remain inaccessible to us in any sensory way. Our senses are stuck in the present, which appears to move in only one direction—into the future, which does not yet exist, leaving behind the past, which exists only in memory but not in reality.
“But that present moment: how long is it, of what does it consist? How can it be as short as a single Planck interval, 1043 of a second, while even the briefest of phenomena that we are aware of takes much longer to happen than that theoretical minim? What can the present be? Is it a succession of Planck intervals, a clutch of them? Is it even real?”
“God knows,” Galileo said. “I count it in heartbeats. The beat of the moment is my present, I pray.”
“That’s a long durée, in effect. Well, look at Bao’s temporal equations, and see how neatly every present that we sense, like your long durée of a heartbeat, gets explained.”
They flew into something like a cathedral, or an immense snowflake, made of intersecting numbers and figures: a lacing of equations, the details of which now completely escaped Galileo. He tried to hold to the architectural shapes they made, but he was no longer following the math.
“Her equations postulate a temporal manifold made of three dimensions, so that what we sense as time passing, what we call time, is a compound with a vector made up of the three temporalities. We can see it here, in something like a Feynman drawing for elementary particles. Indeed we can fly in the drawing, see? The first temporality moves very fast—at the speed of light, in fact. This explains the speed of light, which is simply the rate of movement in this dimension if you consider it as a space. We call that time therefore speed of light time, or c time, from the old notation for the speed of light.”
“How fast is that again?”
“Two hundred thousand miles a second.”
“That’s fast.”
“Yes. That component of time is fast. Time flies! But the second temporal dimension is very slow, by comparison. It’s so slow that most phenomena seem suspended within it, almost as if it were that absolute grid of Newtonian—I mean Galilean—space. We call this one lateral or eternal time, thus e time, and we have found it vibrates slowly back and forth, as if the universe itself were a single string or bubble, vibrating or breathing. There is a systolic/diastolic change as it vibrates, but the vibration is weakly interacting with us, and its amplitude appears to be small.”
“All things remain in God,” Galileo said, remembering a prayer he had once learned, when as a boy he had briefly attended the monastery school.
“Yes. Although it is still a temporality, a kind of time we are moving in. We vibrate back and forth in this time.”
“I think I see.”
“Then lastly,” she went on, “the third temporal dimension we call antichronos, because it moves in the reverse direction of c time, while it also interacts with e time. The three temporalities flow through and resonate with each other, and they all pulse with vibrations of their own. We then experience the three as one, as a kind of fluctuating vector, with resonance effects when pulses from the three overlap in various ways. All those actions together create the perceived time of human consciousness. The present is a three-way interference pattern.”
“Like chips of sunlight on water. Lots of them at once, or almost at once.”
“Yes, potential moments, that wink into being when the three waves peak. The vector nature of the manifold also accounts for many of the temporal effects we experience, like entropy, action at a distance, temporal waves and their resonance and interference effects, and of course quantum entanglement and bilocation, which you yourself are experiencing because of the technology that was developed to move epileptically. In terms of what we sense, fluctuations in this manifold also account for most of our dreams, as well as less common sensations like involuntary memory, foresight, déjà vu, presque vu, jamais vu, nostalgia, precognition, Rückgriffe, Schwanung, paralipomena, mystical union with the eternal or the One, and so on.”
“I’ve felt so many of those,” Galileo said, buffeted as he flew by memories of his lost times, his secret times. “In the sleepless hours of the night, lying in bed, I feel these phenomena often.”
“Yes, and sometimes in the broad light of day too! The compound nature of the manifold creates our perception of both transience and permanence, of being and becoming. They account for that paradoxical feeling I often notice, that any moment in my past happened just a short time ago and yet is separated from me by an immense gulf of time. Both are true; these are subconscious perceptions of a delaminated e time and c time.”
“And the sense of eternity that occasionally strikes? When you ring like a bell?”
“That would be a powerful isolated sense of e time, which does in fact vibrate in a bell-like way. Then in a different way, the sense of inexorable dissolution or breakdown we sometimes call entropy, also the feeling called nostalgia, these are the perceptions of antichronos passing backward through c and e time. Indeed Bao’s work leads to a mathematical description of entropy as a kind of friction between antichronos and c time running against the grain of each other, so to speak. By their interaction.”
“Things get ground up,” Galileo agreed. “Our bodies. Our lives.”
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“That’s the effect of being in a manifold made of three different motions.”
“It’s hard to see.”
“Of course. We mainly experience time as a unified vector, much as we experience space as a plenum made up of the three spatial macro-dimensions. You don’t usually see the plenum as length, breadth, and height, you simply experience space. Time is similarly triune but whole.”
“Like tides in a river mouth,” Galileo ventured. One time as a boy he had watched the seaweed flow first one way, then the other. And at the moment the tide changed: “Sometimes there is flow both ways, and the interference chop can be either obvious or subtle. And the water is always there.”
“There are interference patterns, yes. Other people talk about Penelope’s Loom, and how we are all in our place of the tapestry busily embroidering it, and now the analepts are hopping back and re-embroidering certain parts. Anyway, time is not laminar. It shifts and flows, breaks up and eddies, percolates and resonates.”
“And you have learned to travel on these currents.”
“Yes, a little bit. We learned to shape a charge to create an eddy of antichronos, and push something along in it, and when that eddy touches c time again a complementary potentiality is created. That was enough to do a limited sort of time travel. We could perform analepses at certain resonant entanglements in the manifold. But it required very large applications of energy to make the first shift of the transference devices back in time. The required energies were so large that we were only able to move a few entanglers to bilocated past potentialities. Black holes sucked down large fractions of the gas of the outer gas giants for each entangler sent back. After that they were in place to be used as portals for entanglements of consciousness. These entanglements require much smaller energies, being a sort of field of induced or potential dreaming. The entanglements create a complementary potential time with every analepsis and prolepsis, and for this reason and others, the entire process remained controversial throughout the time it was being actively pursued. Shifting ten or a dozen entanglers required the complete sacrifice of the two outermost gas giants. That was felt to be enough, or too much. So really, this was mostly a technology of about a century ago, when analepts were going back frequently, and sometimes fighting over their changes, as Ganymede did more than anyone. It has all since been reconsidered. By no means does everyone agree it was a good idea.”
“I should think not,” Galileo said. “Why did they do it at all?”
“Some wanted to retroject science analeptically into a time earlier than it had naturally appeared, in the hope of making human history a bit less dire.”
“Why bother, now that you are here?”
“The intervening years were more dire than you know. And we are not just here; we are there too. You are not really comprehending what I have told you. We are all connected and alive in the manifold of manifolds.”
Galileo shrugged. “Things still seem to happen one after the next.”
She shook her head. “In any case, what you see here is a damaged and traumatized humanity. It was felt for a while that work on the past could make that better. A kind of redemption.”
“I see … I think. But, speaking of what you have taught me—that’s only eight dimensions, if I have not lost track. Five of space, and three of time.”
“Yes.”
“And the other two?”
“One is a truly implicate microdimension, inside all the rest. Each minim holds a universe in that dimension. Then all these and ours too exist inside a macromanifold, you might call it. This enfolds a multiplicity of universes—a kind of hyperspace of potentialities, well beyond human perception, although discoverable by observations of cosmically high energies, and of the background radiation. It’s said that in this manifold there are as many existing or potential universes as there are atoms in this universe, and some say even many orders of magnitude more than that, like 103000.”
“That’s a lot,” Galileo said.
“Yes, but it is still not infinity.”
Galileo sighed. He saw they were no longer flying, but in a room the size of a lecture hall in Padua. Aurora could point at one wall and mime writing, and equations appeared on the wall before them. She walked him through the mathematics of the tenth dimension, the manifold of manifolds, and Galileo, as he struggled to follow her, was comforted by the idea that even here her work was a kind of spatial geometry, things laid out in relationships, with proportions, just as always. Maybe that was for his sake, but it all fell into place. Everything could be explained: the bizarre paradoxes of quantum mechanics, the strange billowing of the universe out from a single point that had never been anywhere. All the laws of nature, all the forces and particles, all the constants, and all the various manifestations of time, of being and becoming, their suprachronological travel in time, the bizarre giant reality of universal entanglement, were explained. It was a whole, a quivering organism, and God was indeed a mathematician—a mathematician of such stupendous complexity, subtlety, and elegance, that the experience of contemplating Him was inhuman, beyond what any human feeling could encompass.
“My head hurts,” Galileo admitted.
“Then let’s go back,” Aurora said.
As she was flying him back into the world, Galileo experienced a moment of selfish curiosity. In his first tutorial, he had gotten a glimpse of his hero Archimedes, as clearly as if he had been through the tele-trasporta and seen the Greek face-to-face, or even lived his life. Someone had mentioned something about Ganymede visiting Archimedes before he visited Galileo; perhaps that explained it. Now, with Aurora absorbed in a private conversation with her assistants, Galileo murmured a request to the teaching machine to show him the historical background of the astronomer Galileo Galilei.
Immediately he was cast into a space like that which had surrounded Archimedes; not a moment but a life—his life. Instantly he was filled with his own life, in Florence, Pisa, Padua, then Bellos-guardo, then a smaller house he didn’t recognize, in a village. All of it filled him at once, fine-grained to the minute, and fearfully he cried out, “Stop! Take it away!”
Aurora now stood before him, looking surprised. “Why did you do that?”
“I wanted to know.”
“You thought you did. Now you will have to forget.”
“I hope I can! But I suppose you can give me an amnestic that will help me to deal with it?”
“No,” she said, looking at him curiously. “I can’t. That’s Hera’s kind of thing. You will have to cope with whatever you learned yourself.”
Galileo groaned. He struggled up from his big reclining chair, Aurora’s helmet on his head. He felt drained, frightened. The sensation of immediate powerful apprehension was still with him, but it all had to do with his life now. His past—the present moment—
People were talking. Aurora and her assistants. For a time he lost the sense of it. Thoughts in language, like the voice speaking in him; they were such simple things, like the twittering of birds. Pretty, even sometimes beautiful, but nowhere near as expressive as mathematics. Now he tried hard to remember, he tried hard to forget; some of it was there and some of it was gone, but not in the ways he would have hoped. Nothing to be done about it. The tutorial had happened in him, it had left marks; it would remain somewhere in him, in what they called e time, or in that evanescent present that always bloomed at the edge of c. Or headed back through antichronos, all the way back to the curious boy looking at the lamp swinging in the cathedral. Memory as a kind of precognition.
He regarded Aurora freshly. An ancient woman, who had, he now knew, a knowledge of mathematics, and of the physical universe, that far, far, far transcended his. That was rather amazing. He had never thought that any such person could exist.
“Do you believe in God?” he asked her.
“I don’t think so. I’m not sure I grasp the concept.” She hesitated. “Can we get something to eat? Are you hungry? Because I am.”
THEY
SAT BESIDE A LOW TABLE next to the far railing. It was an altana, it seemed to him; just as in Venice, they made their ground on their rooftops. He sat by the railing and looked at this Venice under its pulsing green-blue sky. On the table between them were plates of small cubes and slices of a vegetable substance unknown to Galileo, the bits flavored with ginger or garlic or various peppery spices he was not familiar with, which made his tongue buzz and his nose run. The water was berry-flavored; he drank deeply, feeling suddenly very thirsty. He surveyed the dim turquoise and cobalt buildings beneath them. Europa was a world of ice, Io was a world of fire. Were Ganymede and Callisto then earth and air?
“Have you had more conversation with the thing under us?” he asked Aurora. “You were telling me about it before. It seems to know gravity well, you said?”
“Yes.”
“What about the compound temporality, the vector of three times?”
“That’s been hard to determine.”
“Show me the exchanges with it.”
Aurora smiled. “It’s been eleven years since the ice was broached and the sentience confirmed. Most of the interactions have come to dead ends. But an abstract of it can be found here.”
She indicated their table, and Galileo looked at it and saw long strings of mathematical symbols and graphically organized information. The tutorial pulsed in his head like a kind of headache. He tried to pilot that knowledge into this new problem.
“Interesting,” he said at last. “What physically constitutes the sentience, do you know? Have you located the bodily source of its mind?”
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