Anathem

by Neal Stephenson

  “Just as you infer that my bolt must continue all the way round me in back, from the way in which its visible part hangs.”

  “Yes, I guess it’s the same general principle.”

  “Well, it seems that this process you call consciousness is somewhat more complex than you perhaps gave it credit for at first,” Orolo said. “One must be able to take in givens from sparse dustings of probability waves in a vacuum—”

  “I.e., see stuff.”

  “Yes, and perform the trick of integrating those givens into seemingly persistent objects that can be held in consciousness. But that’s not all. You perceive only one side of me, but you are all the time drawing inferences about my other side—that my bolt continues round in back, that I have skin—inferences that reflect an innate understanding of theorical laws. You can’t seem to make these inferences without performing little thought experiments in your head: ‘if the bolt didn’t continue round in back it would hang differently,’ ‘if Orolo had no skin his guts would fall out.’ In each of those cases you are using your understanding of the laws of dynamics to explore a little counterfactual universe inside of your head, a universe where the bolt or the skin isn’t there, and you are then running that universe in fast-forward, like a speely, to see what would happen.

  “And that is not the only such activity that is going on in your mind when you describe me to the Geometers,” Orolo went on, after a pause to swallow some water, “because you are forever making allowances for the fact that you and the Geometer are in different places, seeing me from different points of view, taking in different givens. From where you’re standing you might be able to see the freckle on the left side of my nose, but you have the wit to understand that the Geometer can’t see that freckle because of where it is standing. This is another way in which your consciousness is forever building counterfactual universes: ‘if I were standing where the Geometer is, my view of the freckle would be blocked.’ Your ability to have empathy with the Geometer—to imagine what it would be like to be someone else—isn’t a mere courtesy. It is an innate process of consciousness.”

  “Wait a second,” I said, “you’re saying I can’t predict the Geometers’ inability to see the freckle without erecting a replica of the whole universe in my imagination?”

  “Not exactly a replica,” Orolo said. “Almost a replica, in which everything is the same, except for where you are standing.”

  “It seems to me that there are much simpler ways of getting that result. Perhaps I have a memory of what you look like when viewed from that side. I call up that image in my memory and say to myself, ‘Hmm, no freckle.’”

  “It is a perfectly reasonable thought,” Orolo said, “but I must warn you that it does not really buy you much, if what you seek is a simple and easy-to-understand model of how the mind works.”

  “Why not? I’m only talking about memory.”

  Orolo chortled, then composed himself, and made an effort to be tactful. “Thus far we have spoken only of the present. We’ve talked only of space—not of time. Now you would like to bring memories into the discussion. You are proposing to pull up memories of how you perceived Orolo’s nose from a different angle at a different time: ‘I sat on his right last night at supper and couldn’t see the freckle.’”

  “It seems simple enough,” I said.

  “You might ask yourself what in your brain enables you to do such things.”

  “What things?”

  “Take in some givens one evening at supper. Take in another set of givens now—or one second ago—two seconds ago—but always now! And say that all of them were—are—the same chap, Orolo.”

  “I don’t see what the big deal is,” I said. “It’s just pattern recognition. Syntactic devices can do it.”

  “Can they? Give me an example.”

  “Well…I guess a simple example would be…” I looked around, and happened to notice the contrail of an aerocraft high overhead. “Radar tracking aerocraft in a crowded sky.”

  “Tell me how it works.”

  “The antenna spins around. It sends out pulses. Echoes come back to it. From the time lag of the echo, it can calculate the bogey’s distance. And it knows in what direction the bogey lies—that’s dead easy, it’s just the same direction as the antenna is pointing when the echo hits it.”

  “It can only look in one direction at a time,” Orolo said.

  “Yeah, it’s got extreme tunnel vision, and compensates for that by spinning around.”

  “A little bit like us,” Orolo said.

  We had begun descending the mountain, and were walking side by side. Orolo went on, “I can’t see in all directions at once, but I glance to the side every so often to make sure you’re still there.”

  “Yeah, I guess so,” I said. “You have in your head a model of your surroundings that includes me off to your right side. You can maintain it for a while by holding down the fast-forward button. But every so often you have to update it with new givens, or it’ll get out of whack with what is really going on.”

  “How does the radar system manage it?”

  “Well, the antenna rotates once and takes in echoes from everything that’s in the sky. It plots their positions. Then it rotates again and collects a new set of echoes. The new set is similar to the first one. But all of the bogeys are now in slightly different positions, because all of the aerocraft are moving, each at its own speed, each in its own direction.”

  “And I can see how a human observer, watching the bogeys plotted on a screen, would be able to assemble a mental model of where the aerocraft were and how they were moving,” Orolo said, “in the same way as we stitch together frames of a speely to form a continuous story in our minds. But how does the syntactic device inside the radar system do it? It has nothing more than a list of numbers, updated from time to time.”

  “If there were only one bogey, it would be easy,” I said.

  “Agreed.”

  “Or just a few, widely separated, moving slowly, so that their paths didn’t cross.”

  “Also agreed. But what of the hard case of many fast bogeys, close together, paths crossing?”

  “A human observer could manage it easily—just like watching a speely,” I said. “A syndev would have to do some of what a human brain does.”

  “And what is that, exactly?”

  “We have a sense for what is plausible. Let’s say there are two aerocraft, full of passengers, going just under the speed of sound, and that during the interval between two radar sweeps, their paths cross at right angles. The machine can’t tell the bogeys apart. So there are a few possible interpretations of the givens. One is that both planes executed sharp right-angle turns at the same moment and veered off in new directions. Another is that they bounced off each other like rubber balls. The third interpretation is that the planes are at different altitudes, so they didn’t collide, and both simply kept flying in a straight line. That interpretation is the simplest, and the only one consistent with the laws of dynamics. So the syndev must be programmed to evaluate the different interpretations of the givens and choose the one that is most plausible.”

  “So we have taught this device a little of what we know of the action principles that govern the movement of our cosmos through Hemn space, and commanded it to filter out possibilities that diverge from a plausible world-track,” Orolo said.

  “In a very crude way, I suppose. It doesn’t really know how to apply action principles in Hemn space and all that.”

  “Do we?”

  “Some of us do.”

  “Theors, yes. But a sline playing catch knows what the ball will do—more importantly, what it can’t do—without knowing the first thing about theorics.”

  “Of course. Even animals can do that. Orolo, where is Evenedrician datonomy getting us? I see some connection to our pink dragon dialog back home, a few months ago, but—”

  Orolo got a funny look on his face. He’d forgotten. “Oh yes. About you and your worrying.
”

  “Yes.”

  “That’s something animals can’t do,” he pointed out. “They react to immediate, concrete threats, but they don’t worry about abstract threats years in the future. It takes the mind of an Erasmas to do that.”

  I laughed. “I haven’t been doing it so much lately.”

  “Good!” He reached out and gave me an affectionate thud on the shoulder.

  “Maybe it’s the Allswell.”

  “No, it’s that you have real things to worry about now. But please remind me how it went—the dialog about the pink nerve-gas-farting dragon?”

  “We developed a theory that our minds were capable of envisioning possible futures as tracks through configuration space, and then rejecting ones that didn’t follow a realistic action principle. Jesry complained it was a heavyweight solution to a lightweight problem. I agreed. Arsibalt objected.”

  “This was after Fraa Paphlagon had been Evoked, wasn’t it?”

  “Yes.”

  “Arsibalt had been reading Paphlagon.”

  “Yes.”

  “So tell me, Fraa Erasmas, are you still with Jesry, or with Arsibalt?”

  “I still think it seems fanciful to think we are all the time erecting and tearing down counterfactual universes in our minds.”

  “I’ve become so used to it that it seems fanciful to think otherwise,” Orolo said. “But perhaps we can go on another hike tomorrow and discuss it further.” We were reaching the outskirts of the math.

  “I’d like that,” I said.

  As we drew near enough to smell supper cooking, I recollected that I needed to get a message out to my friends the next day. But it was not the right moment to bring this up and so I resolved to mention it the next morning.

  I had it in my mind that this would force Orolo to make a decision, but as soon as I explained it to him, he made a point that was embarrassingly obvious, once he’d made it: the three-day deadline was perfectly arbitrary, and hence the only sound approach was to brush it aside without any further mention. He called in Fraa Landasher, who proposed that my friends be invited into the math and allowed to lodge here for as long as it might take to sort things out. This was shocking until I reminded myself that things were done differently here and that Landasher was beholden to no one except, possibly, the dowment that owned Ecba. Then I felt sure that my four friends would have no interest in biding in such a place as this. But a couple of hours later, when I walked out of the gate and down to the souvenir shop to explain matters to them, they accepted unanimously and without discussion. That in itself made me a little nervous, so I accompanied them back to the cove and helped them strike camp, using the afternoon to provide them with a running lecture on mathic etiquette. I was especially worred that Ganelial Crade would preach to them. But soon, beginning with Yul and spreading quickly to the others, they began to make fun of me for being so worried about this, and I realized that I had offended them. So I said nothing more until we got back to Orithena. Cord, Yul, Gnel, and Sammann were let in through the gate and given rooms in a sort of guest lodge, set apart from the cloister, where they were allowed to keep jeejahs and other Saecular goods. Dressed in their extramuros garb—but without the jeejahs—they joined us at dinner and were formally toasted and welcomed by Fraa Landasher.

  The next morning I rousted them early and led them down to the dig for a tour. Gnel looked as if he were having some sort of Deolatrous epiphany, though in all fairness I’d probably had a similar look on my face when Suur Spry had taken me down there.

  I asked Sammann if he’d learned anything more about who was running Ecba and he said “yes” and “it’s boring.” Some burger, just after the Third Sack, had become an Enthusiast for all things Orithenan. He was very rich and so he’d bought the island and, to run it, set up the foundation, complete with tedious bylaws that ran to a thousand pages—it was meant to last forever and so the bylaws had to cover every eventuality they could think of. Executive power lay in the hands of a mixed Saecular/Mathic board of governors, Sammann explained, warming to the task even as my attention was beginning to wander…

  So getting my friends squared away at Orithena distracted me for a couple of days. After that I resumed my walks up the mountain with Orolo.

  * * *

  Dialog: A discourse, usually in formal style, between Theors. “To be in Dialog” is to participate in such a discussion extemporaneously. The term may also apply to a written record of a historical Dialog; such documents are the cornerstone of the mathic literary tradition and are studied, re-enacted, and memorized by fids. In the classic format, a Dialog involves two principals and some number of onlookers who participate sporadically. Another common format is the Triangular, featuring a savant, an ordinary person who seeks knowledge, and an imbecile. There are countless other classifications, including the suvinian, the Periklynian, and the peregrin.

  —THE DICTIONARY, 4th edition, A.R. 3000

  “I know that our last conversation was not completely satisfactory to you, Erasmas. I apologize for that. These ideas are unfinished. I am tormented, or tantalized, by the sense that I’m almost in view of something that is at the limit of my comprehension. I dream of being in the sea, treading water, trying to see a beacon on shore. But the view is blocked by the crests of the waves. Sometimes, when conditions are perfect, I can pop up high enough to glimpse it. But then, before I can form any firm impression of what it is I’m seeing, I sink back down of my own weight, and get slapped in the face by another wave.”

  “I feel that way all the time, when I am trying to understand something new,” I said. “Then, one day, all of a sudden—”

  “You just get it,” Orolo said.

  “Yeah. The idea is just there, fully formed.”

  “Many have noted this, of course. I believe it is related, in a deep way, to the sort of mental process I was speaking of the other day. The brain takes advantage of quantum effects; I’m sure of it.”

  “I know just enough about it to know that what you just said has been controversial for a long, long time.”

  This affected him not at all; but after I looked in his eye long enough, he finally gave a shrug. So be it. “Did Sammann ever talk to you of Saunt Grod’s Machines?”

  “No. What is it?”

  “A syntactic device that made use of quantum theorics. Before the Second Sack, his forerunners and ours worked together on such things. Saunt Grod’s Machines were extremely good at solving problems that involved sifting through many possible solutions at the same time. For example, the Lazy Peregrin.”

  “That’s the one where a wandering fraa needs to visit several maths, scattered randomly around a map?”

  “Yes, and the problem is to find the shortest route that will take him to all of the destinations.”

  “I kind of see what you mean,” I said. “One could draw up an exhaustive list of every possible route—”

  “But it takes forever to do it that way,” Orolo said. “In a Saunt Grod’s Machine, you could erect a sort of generalized model of the scenario, and configure the machine so that it would, in effect, examine all possible routes at the same time.”

  “So, this kind of machine, instead of existing in one fixed, knowable state at any given time, would be in a superposition of many quantum states.”

  “Yes, it’s just like an elementary particle that might have spin up or spin down. It is in both states at the same time—”

  “Until someone observes it,” I said, “and the wavefunction collapses to one state or the other. So, I guess with a Saunt Grod’s Machine, one eventually makes some observation—”

  “And the machine’s wavefunction collapses to one particular state—which is the answer. The ‘output,’ I believe the Ita call it,” Orolo said, smiling a little as he pronounced the unfamiliar bit of jargon.

  “I agree that thinking often feels that way,” I said. “You have a jumble of vague notions in your mind. Suddenly, bang! It all collapses into one clear answer that you
know is right. But every time something happens suddenly, you can’t simply chalk it up to quantum effects.”

  “I know,” Orolo said. “Do you see where I’m going, though, when I speak of counterfactual cosmi?”

  “I didn’t really get it until you brought quantum theorics into the picture,” I said. “But it’s been obvious for a while that you have been developing a theory about how consciousness works. You have mentioned some different phenomena that any introspective person would recognize—I won’t bother to go back and list them all—and you have tried to unify them…”

  “My grand unification theory of consciousness,” Orolo joked.

  “Yes, you are saying that they are all rooted in a special ability that the brain has to erect models of counterfactual cosmi in the brain, and to play them forward in time, evaluate their plausibility, and so on. Which is utterly insane if you take the brain to be a normal syndev.”

  “Agreed,” Orolo said. “It would require an immense amount of processing power just to erect the models—to say nothing of running them forward. Nature would have found some more efficient way to get the job done.”

  “But when you play the quantum card,” I said, “it changes the game entirely. Now, all you need is to have one generalized model of the cosmos—like the generalized map that a Saunt Grod’s Machine uses to solve the Lazy Peregrin problem—permanently loaded up in your brain. That model can then exist in a vast number of possible states, and you can ask all sorts of questions of it.”

  “I’m glad that you now understand this in the same way that I do,” Orolo said. “I do have one quibble, however.”

  “Oh boy,” I said, “here goes.”

  “Traditions die hard, among the avout,” Orolo said. “And for a very long time, it has been traditional to teach quantum theorics to fids in a particular way that is based on how it was construed by the theors who discovered it, way back in the time of the Harbingers. And that, Erasmas, is how you were taught as well. Even if I had never met you before today, I would know this from the language that you use to talk about these things: ‘it exists in a superposition of states—observing it collapses the wavefunction’ and so on.”