Anathem

“After I landed at Bly’s Butte,” Orolo said, “I was like one of those poor cosmographers, just after the Reconstitution, who couldn’t use his atom smasher any more.”

“Yes, I saw that telescope,” I told him, “the pictures you tried to take of the icosahedron…”

He was shaking his head. “I could not see a thing with that. So, my work concerning the aliens had to be based on what I could observe.”

This didn’t make sense to me. “All right,” I said, “what was that?”

He looked at me, mildly startled, as if it ought to have been obvious. “Myself.”

I was nonplussed. Which only showed that I was dealing with the same old Orolo. “How would self-observation help you understand the Geometers?” I asked. For I had already mentioned to him that this was the term people were now using to denote the aliens.

“Well…the Sconics are not a bad place to start. Remember fly-bat-worm?”

I laughed. “Just got a refresher on that a couple of weeks ago. Arsibalt was explaining it to an extra who wanted to know why we didn’t believe in God.”

“Ah, but that’s not what fly-bat-worm says,” said Orolo. “It says only that pure thought alone doesn’t enable us to draw any conclusions one way or another about things that are non-spatiotemporal-such as God.”

“True.”

“The same observations that the Sconics made about themselves must also be true of aliens’ brains. No matter how different they might be from us in other respects, they must integrate sensory givens into a coherent model of what is around them-a model that must be hung on a spatiotemporal frame. And that, in a nutshell, is how they come to share our ideas about geometry.”

“But they share more than that,” I pointed out, “they appear to share the idea of Truth and of Proof.”

“It is a reasonable enough supposition,” Orolo said with a cautious shrug.

“More than that!” I protested. “They emblazoned the Adrakhonic Theorem on their ship!”

This was news to him. “Oh, really? How cheeky!”

“Didn’t you see it?”

“I remind you that I was Thrown Back before I saw the last picture that I took of the alien ship.”

“Of course. But I assumed you had taken other pictures before then-had been taking them for a long time.”

“Streaks and blobs!” Orolo scoffed. “I was only learning how to capture a decent image of the thing.”

“So you never saw the geometric proof-or the letters-or the four planets.”

“That’s correct,” Orolo said.

“Well, there’s much more that you have to know, if you want to think about the Geometers! All kinds of new givens!”

“I can see how excited you are about those new givens, Erasmas, and I wish you all the best in your study of them, but I’m afraid that for me it would all prove a distraction from the main line of the inquiry.”

“The main line-I don’t know what you mean.”

“Evenedrician datonomy,” Orolo said, as if this ought to have been quite obvious.

“Datonomy,” I translated, “that would be study, or identification, of what is given?”

“Yes-givens in the sense of the basic thoughts and impressions that our minds have to work with. Saunt Evenedric pursued it late in his life, after he got locked out of his atom smasher. His immediate forerunner, of course, was Saunt Halikaarn. Halikaarn thought that Sconic thought was badly in need of an overhaul to bring it in line with all that had been discovered, since the time of Baritoe, about theorics and its marvelous applicability to the physical world.”

“Well-how’d he make out?”

Orolo grimaced. “Many of the records were vaporized, but we think he was too busy demolishing Proc and kicking away all the ankle-biters Proc sent after him. The work fell to Evenedric.”

“Has it been an important thing to the Lineage?”

Orolo gave me a queer look. “Not really. Oh, it’s important in principle. But notoriously unsatisfying to work on. Except when great alien ships appear in orbit around one’s planet.”

“So, then…are you finding it satisfying now?”

“Let’s be quite direct and say what we mean,” Orolo said. “You fear that I’m navel-gazing. That on Bly’s Butte I pursued this line of inquiry, not because it was really worthwhile, but simply because I didn’t have hard givens about the Geometers. And that now that we have evidence that they are, or were, physically and mentally similar to us, this line of inquiry should be dropped.”

“Yes,” I said, “that’s what I think.”

“I happen to disagree,” Orolo said. “But things have changed between us. We are no longer Pa and Fid but Fraa and Fraa, and fraas disagree, cordially, all the time.”

“Thank you but it has certainly felt like a Pa/Fid conversation to this point.”

“Largely because I have a bit of a head start on you.”

I let this polite nothing pass without comment. “Listen, if I can tear you away from Evenedrician datonomy, we have to talk about Sæcular stuff for a minute.”

“By all means,” Orolo said.

“Several of us were Evoked to a Convox at Tredegarh,” I said, for, unbelievably, Orolo had not yet expressed any curiosity as to why or how I’d turned up at Orithena. “One of the others was Fraa Jad, a Thousander. He accompanied me and Arsibalt and Lio to Bly’s Butte-”

“And saw the leaves on the wall of my cell there.”

“He-Jad-figured out quickly-weirdly quickly-that you had gone to Ecba and, I guess, that you had ideas about the Geometers that he wanted to know more of.”

“It was neither quick nor weird,” Orolo said. “All of these matters are connected. It would have been obvious to Fraa Jad as soon as he walked in.”

“How? Do you guys communicate? Violate the Discipline?”

“What do you mean, ‘you guys’? You are carrying around some melodramatic idea of the Lineage, aren’t you?” Orolo said.

“Well, just look at this place!” I protested. “What is going on?”

“If I got interested in meteorology,” Orolo said, “I’d spend a lot of time observing the weather. I would come to have much in common with other weather-watchers whom I’d never met. We would think similar thoughts as a natural result of observing the same phenomena. Nine-tenths of what you think of as mysterious Lineage machinations is explained by this.”

“Except that instead of watching the weather you’re thinking about Evendrician datonomy?”

“Close enough.”

“But there was nothing about Evenedric or datonomy on the wall of your cell for Fraa Jad to see. Just material pertaining to Orithena, and a chart of the Lineage.”

“What you identified as a chart of the Lineage was really a sort of family tree of those who have tried to make sense of the Hylaean Theoric World. And it turns out that if you trace the branches of that tree and, so to speak, prune off all the branches populated by fanatics, Enthusiasts, Deolaters, and dead-enders, you end up with something that doesn’t look so much like a tree any more. It looks like a dowel. It starts with Cnous and runs through Metekoranes and Protas and some others, and about halfway along you encounter Evenedric.”

“So Fraa Jad, looking at your tree-pruned-down-to-a-dowel, would guess immediately that you must be working on Evenedrician datonomy.”

“And would assume I was doing so in hopes of gaining upsight as to how the Geometers’ minds must be organized.”

“What about Ecba? How’d he guess you went to Ecba?”

“This math was founded by people who lived in the same cells where Fraa Jad has spent his whole life. He would know or surmise that if I could get to this place they would let me in the gates and provide me with food and shelter-quite obviously a better existence than what I could manage at Bly’s Butte.”

“Okay.” I was feeling relieved of a burden I’d been carrying since that day above Samble. “So there’s not a conspiracy. The Lineage doesn’t communicate through coded messages.”

“We communicate all the time,” Orolo said, “in the way I mentioned.”

“Meteorologists watching the same cloud.”

“That’s good enough for this stage of our conversation,” Orolo said. “But you haven’t yet unburdened yourself of whatever terribly important-seeming message or mission you brought in the gates with you. What errand has Fraa Jad sent you on?”

“He said ‘go north until you understand.’ And I guess that part of the mission is accomplished now.”

“Oh really? I’m pleased that you understand. I’m afraid I am still full of questions about these matters.”

“You know what I mean!” I snapped. “He also implied I was to come back to Tredegarh later. That he’d see to it I didn’t get in trouble. I guess he wanted me to fetch you. To bring you back to the Convox.”

“In case I’d developed any ideas, concerning the Geometers, that might be useful,” Orolo hazarded.

“Well, that’s the point of a Convox,” I reminded him, “to be useful.”

Orolo shrugged. “I’m afraid I don’t have enough givens to work with, concerning the Geometers.”

“I’m sure that all the givens that there are to be had, are available at Tredegarh.”

“They are probably collecting exactly the wrong sort of information,” he said.

“So go there and tell them what to collect! Fraa Jad could use your help.”

“For me and Fraa Jad and some others of like mind to try to change the behavior of this Sæcular/Mathic monstrosity called a Convox sounds like politics, which I am infamously bad at.”

“Then let me try to help!” I said. “Tell me what you’ve been doing. I’ll go back to the Convox and look for ways to use it.”

The most charitable way to interpret the look Orolo now gave me was affectionate but concerned. He waited for my brain to catch up with my mouth.

“Okay,” I said, “with a little help from some of the others, maybe.” I was thinking of the conversation I’d had with Tulia before Eliger.

“I can’t advise you on what to do at the Convox,” he finally said, “however, I am happy to explain what I’ve been up to.”

“Okay-I’ll settle for that.”

“It won’t help you-in fact, it’ll probably hurt you-at the Convox. Because it will sound crazy.”

“Fine. I’m used to people thinking that we are crazy because of the whole HTW thing!”

Orolo raised an eyebrow. “You know, on balance I think that what I’m about to discuss with you is less crazy than that. But the HTW”-he nodded in the direction of the Orithena dig-“is a cozy and familiar form of craziness.” He paused for a few moments, returning his gaze to me.

“Who are you talking to?” Orolo asked.

I was wrong-footed by this bizarre question, and took a moment to be certain I’d heard the question right. “I’m talking to Orolo,” I said.

“What is this Orolo? If a Geometer landed here and engaged you in conversation, how would you characterize Orolo to it?”

“As the man-the very complicated, bipedal, slightly hot, animated entity-standing right over there.”

“But depending on how a Geometer sees things, it might respond, ‘I see nothing there but vacuum with a sparse dusting of probability waves.’”

“Well, ‘vacuum with a sparse dusting of probability waves’ is an accurate description of just about everything in the universe,” I pointed out, “so if the Geometer was not able to recognize objects any more effectively than that, it could scarcely be considered a conscious being. After all, if it’s having a conversation with me, it must recognize me as-”

“Not so fast,” Orolo said, “let’s say you are talking to the Geometer by typing into a jeejah, or something. It knows you only as a stream of digits. Now you have to use those digits to supply a description of Orolo-or of yourself-that it would recognize.”

“Okay, I’d agree with the Geometer on some way to describe space. Then I’d say, ‘Consider the volume of space five feet in front of my position, about six feet high, two wide, and two deep. The probability waves that we call matter are somewhat denser inside of that box than they are outside of it.’ And so on.”

“Denser, because there’s a lot of meat in that box,” Orolo said, slapping his abdomen, “but outside of it, only air.”

“Yes. I should think any conscious entity should be able to recognize the meat/air boundary. What’s on the inside of the boundary is Orolo.”

“Funny that you have such firm opinions on what conscious beings ought to be able to do,” Orolo warned me. “Let me see…what about this?” He held up a fold of his bolt.

“Just as I can describe the meat/air boundary, I can describe how bolt-stuff differs from both meat and air, and explain that Orolo is wrapped in bolt-stuff.”

“There you go making assumptions!” Orolo chided me.

“Such as?”

“Let’s say that the Geometer you’re talking to has been inculcated in his civilization’s equivalent of the Sconics. He’ll say, ‘Wait a minute, you can’t really know, you’re not allowed to make statements about, things in themselves-only about your perceptions.’”

“True.”

“So you need to rephrase your statement in terms of the givens that are actually available to you.”

“All right,” I said, “instead of saying, ‘Orolo is wrapped in bolt-stuff,’ I’ll say, ‘When I gaze at Orolo from where I’m standing, I see mostly bolt, with bits of Orolo-his head and his hands-peeking out.’ But I don’t see why it matters.”

“It matters because the Geometer can’t stand where you are standing. It has to stand somewhere else, and see me from a different angle.”

“Yes, but the bolt wraps all the way around your body!”

“How do you know I’m not naked in back?”

“Because I’ve seen a lot of bolts and I know how they work.”

“But if you were a Geometer, seeing one for the first time-”

“I’d still be able to surmise that you were not naked in back, because if you were, the bolt would hang differently.”

“What if I got rid of the bolt and stood here naked?”

“What if you did?”

“How would you describe me to the Geometer, then? What would meet your eye, and the Geometer’s?”

“I would say to the Geometer ‘From where I stand, all I see is Orolo-skin. From where you stand, O Geometer, the same is likely true.’”

“And why is it likely?”

“Because without skin your blood and guts would fall out. Since I can’t see a puddle of blood and guts behind you, I can infer that your skin must be in place.”

“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 Sæcular 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 Sæcular/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.