Anathem

Paphlagon’s plate was clean; Lodoghir hadn’t even picked up his fork. Hunger at last succeeded where throat-clearing, glares, exasperated sighs, and the en masse departure of the servitors had failed: Lodoghir fell silent, picked up his glass, and doused his flaming vocal chords.

Paphlagon was eerily calm-almost jolly. “If one were to examine a transcript of that, one would see an extraordinary, and quite lengthy, catalog of every rhetorical trick in the Sphenic book. We’ve seen appeals to mob sentiment: ‘no one believes in the HTW any more,’ ‘everyone thinks Protism is crazy.’ We’ve seen appeals to authority: ‘refuted in the Twenty-ninth Century by no less than Saunt So-and-so.’ Efforts to play on our personal insecurity: ‘how can any person of sound mind take this seriously?’ And many other techniques that I have forgotten the names of, as it has been so long since I studied the Sphenics. So. I must begin by applauding the rhetorical mastery that has given the rest of us an opportunity to enjoy this excellent meal and rest our voices. But I would be remiss if I did not point out that Fraa Lodoghir has yet to offer up a single argument, worthy of the name, against the proposition that there is a Hylaean Theoric World, that it is populated by mathematical entities-cnoons, as we call them-that are non-spatial and non-temporal in nature, and that our minds have some capability of accessing them.”

“Nor could I-ever!” exclaimed Fraa Lodoghir, whose jaw had been working at an astounding pace during the last few moments to get a bite of food squared away. “You Protists are ever so careful to frame the discussion so that it can’t be touched by rational debate. I can’t prove you’re wrong any more than I can prove the non-existence of God!”

Paphlagon had some infighting skills of his own; he simply ignored what Lodoghir had just said. “A couple of weeks ago, at a Plenary, you and some of the other Procians floated the suggestion that the diagram of the Adrakhonic Theorem on the Geometers’ ship was a forgery, inserted into Saunt Orolo’s Phototype by Orolo himself, or someone else at Edhar. Do you now retract that allegation?” And Paphlagon glanced over his shoulder at an astoundingly high-resolution phototype of the Geometers’ ship, taken last night by the largest optical telescope on Arbre, on which the diagram was clearly visible. The walls of the messallan were papered with such. The table was scattered with more.

“There is nothing wrong with mentioning hypotheses in the course of a discussion,” Lodoghir said. “Clearly that particular one happened to be incorrect.”

“I think he just said ‘yes, I withdraw the allegation,’ said Tris, in the kitchen. I had gone back there ostensibly to fulfill my duties, but really to plow through heaps of more phototypes. Everyone in the Convox had been looking at them all day, but we weren’t even close to being tired of it.

“It is such good fortune that this gambit worked,” Emman reflected, gazing fixedly at a grainy close-up of a strut.

“You mean, that we did not get rodded?” Barb asked-sincerely.

“No, that we got pictures,” Emman said. “Got them by doing something clever, here.”

“Oh-you mean it is good fortune politically?” Karvall asked, a little uncertain.

“Yes! Yes!” Emman exclaimed. “The Convox is expensive! It makes the Powers That Be happy when it yields discernible results.”

“Why is it expensive?” Tris asked. “We grow our own food.”

Emman finally looked up from his pictures. He was checking Tris’s face, in order to see whether she could possibly be serious.

Over the speaker, Paphlagon was saying: “the Adrakhonic Theorem is true here. It’s apparently true in the four cosmi the Geometers came from. If their ship had turned up in some other cosmos, the same as ours, but devoid of sentient beings, would it be true there?”

“Not until the Geometers arrived to say it was true,” said Lodoghir.

Back in the kitchen, I intervened before Emman could blurt out anything he might have to apologize for. “It must be expensive for people like Emman and Ignetha Foral to keep tabs on it,” I pointed out.

“Of course,” Emman said, “but even if you ignore that: there is a huge amount of mathic effort going into it. Thousands of avout working night and day. S?culars don’t like wasted effort. That goes double for S?culars who know a thing or two about management.”

Management was a Fluccish word. Faces went blank around the kitchen. I stepped in to translate: “Just because the Panjandrums know how to run cheeseburg stands, they think they know how to run a Convox. Lots of people putting in time with no results makes them nervous.”

“Oh, I see,” Tris said, uncertainly.

“How funny!” Karvall said, and went back to work.

Emman rolled his eyes.

“I admit I am no theor,” Ignetha Foral was saying on the speaker, “but the more I hear of this, the less I understand your position, Fraa Lodoghir. Three is a prime number. It is prime today, was prime yesterday. A billion years ago, before there were brains to think about it, it was prime. And if all the brains were destroyed tomorrow, it would still be prime. Clearly its primeness has nothing to do with our brains.”

“It has everything to do with our brains,” Lodoghir insisted, “because we supply the definition of what it is to be a prime number!”

“No theor who attends to these matters can long escape the conclusion that the cnoons exist independently of what may or may not be going on in peoples’ brains at any given moment,” Paphlagon said. “It is a simple application of the Steelyard. What is the simplest way of explaining the fact that theors working independently in different eras, different sub-disciplines, different cosmi even, time and time again prove the same results-results that do not contradict each other, even though reached by different proof-chains-results, some of which can be turned into theories that perfectly describe the behavior of the physical universe? The simplest answer is that the cnoons really exist, and are not of this causal domain.”

Arsibalt’s bell jingled. I decided to go in with him. We took down a huge rendering of the icosahedron that had been pinned to a tapestry behind Paphlagon. Karvall and Tris came out and helped take the tapestry down, exposing a wall of dark grey slate, and a basket of chalk. The dialog had turned to an exposition of Complex versus Simple Protism, and so Arsibalt was called upon to draw on that slate the same sorts of diagrams that Fraa Criscan had drawn in the dust of the road up Bly’s Butte when he had explained this topic to me and Lio some weeks earlier: the Freight Train, the Firing Squad, the Wick, and so on. I drifted back and forth between there and the kitchen as the exposition went on. Ignetha Foral had long been familiar with this material, but it was new to several of the others. Zh’vaern, in particular, asked several questions. Emman, for once, understood less of what was going on than his doyn, and so as he and I worked on garnishes for the desserts, I watched his face, and jumped in with little explanations when his eyes went out of focus.

I returned to the messallan to clear plates just as Paphlagon was explaining the Wick: “A fully generalized Directed Acyclic Graph, with no distinction made any more between, on the one hand, so-called theoric worlds, and, on the other, inhabited ones such as Arbre, Quator, and the rest. For the first time, we have arrows leading away from the Arbran Causal Domain towards other inhabited worlds.”

“Do you mean to suggest,” Lodoghir asked, as though not quite believing his ears, “that Arbre might be the Hylaean Theoric World of some other world that has people living on it?”

“Of any number of such worlds,” Paphlagon said, “which might themselves be the HTWs of still other worlds.”

“But how could we possibly verify such a hypothesis?” Lodoghir demanded.

“We could not,” Jad admitted, in his first utterance of the whole evening, “unless those worlds came to us.”

Lodoghir broke into rich laughter. “Fraa Jad! I commend you! What would this messal be without your punch lines? I don’t agree with a word of what you’re saying, but it does make for an entertaining-because completely unpredictable-mealtime!”

I heard the first part of this in person, the back half over the speaker in the kitchen, to which I had repaired with an armload of plates. Emman was standing over the counter where we had spread out the phototypes, thumbing something into his jeejah. He ignored me, but he did glance up and fix his gaze on nothing in particular as Ignetha Foral began to speak: “The material is interesting, the explanation well carried off, but I am at a loss, now. Yesterday evening we were told one story about how Plurality of Worlds might be understood, and it had to do with Hemn space and worldtracks.”

“Which I spent all day explaining to rooms full of bureaucrats,” Emman complained, with a theatrical yawn. “And now this!”

“Now,” Ignetha Foral was saying, “we are hearing an altogether different account of it, which seems to have nothing to do with the first. I cannot help but wonder whether tomorrow’s Messal will bring another story, and the day after that, yet another.”

This touched off a round of not very interesting conversation in the messallan. The servitors pounced and cleared. Arsibalt trudged to the kitchen and busied himself at the keg. “I’d best fortify myself,” he explained, to no one in particular, “as I am condemned to spend the remainder of the evening drawing light bubbles.”

“What’s a light bubble?” Emman asked me quietly.

“A diagram that shows how information-cause-and-effect-moves across space and time.”

“Time, which doesn’t exist?” Emman said, repeating what had become a stock joke.

“Yeah. But it’s okay. Space doesn’t exist either,” I said. Emman threw me a sharp look, and decided I must be pulling his leg.

“So how’s your friend Lio doing?” Emman asked, apropos of yesterday evening. It was noteworthy that he remembered Lio’s name, since there had been no formal introduction, and little conversation. In the Convox, people met one another in myriad ways, though, so they might have crossed paths anywhere. I would not have given this a second thought if not for the substance of what Lio and I had talked about. Yesterday I’d felt easy around Emman. Today it was different. People I cared about were being drawn into-in Ala’s case, perhaps leading-a subversive movement. Lio was trying to draw me into it even as Emman wanted to follow me to Lucub. Could it be that the Sæcular Power had got wind of it, and that Emman’s real mission was to ferret it out, using me as a way in? Not a very nice way to think-but that was the way I was going to have to think from now on.

I’d lain awake in my cell all night from a combination of jet lag and fear of a Fourth Sack. Good thing that most of the day had been a huge Plenary at which the story of last night’s satellite gambit had been told, and phototypes and speelies exhibited. The back pews of the Unarian nave were dark, and roomy enough that I and scores of Lucub-weary avout had been able to stretch out full-length and catch up on sleep. When it was over, someone had shaken me awake. I had stood up, rubbed my eyes, looked across the Nave, and caught sight of Ala-the first time I’d seen her since she had stepped through the screen at Voco. She had been a hundred feet away, standing in a circle of taller avout, mostly men, all older, but seemingly holding her own in some kind of serious conversation. Some of the men had been S?culars in military uniforms. I had decided that now was not the best time for me to bounce up to her and say hello.

“Hey! Raz! Raz! How many fingers am I holding up?” Emman was demanding. Tris and Karvall thought that was funny. “How’s Lio doing?” he repeated.

“Busy,” I said, “busy like all of us. He’s been working out quite a bit with the Ringing Vale avout.”

Emman shook his head. “Nice that they’re getting exercise,” he said. “Love to know what joint locks and nerve pinches are going to do against the World Burner.”

My gaze went to the stack of phototypes. Emman slid a few out of the way and came up with a detail shot of a detachable pod bracketed to one of the shock absorbers. It was a squat grey metal egg, unmarked and undecorated. A structural lattice had been built around it to provide mountings for antennae, thrusters, and spherical tanks. Clearly the thing was meant to detach and move around under its own power. Holding it to the shock absorber was a system of brackets that reached through the lattice to engage the grey egg directly. This detail had drawn notice from the Convox. Calculations had been done on the size of those brackets. They were strangely oversized. They only needed to be so large if the thing they were holding-the grey egg-were massive. Unbelievably massive. This was no ordinary pressure vessel. Perhaps it had extremely thick walls? But the calculations made no sense if you assumed any sort of ordinary metal. The only way to sort it-to account for the sheer number of protons and neutrons in that thing-was to assume it was made from a metal so far out at the end of the table of elements that its nuclei-in any cosmos-were unstable. Fissionable.

This object was not just a tank. It was a thermonuclear device several orders of magnitude larger than the largest ever made on Arbre. The propellant tanks carried enough reaction mass to move it to an orbit antipodal to that of the mother ship. If it were detonated, it would shine enough radiant energy onto Arbre to set fire to whatever half of the planet could see it.

“I don’t think that the Valers are really expecting to swarm over the World Burner in space suits and subdue it with fisticuffs,” I said. “Actually, what impressed me most about them was their knowledge of military history and tactics.”

Emman held up his hands in surrender. “Don’t get me wrong. I would like to have them on my side.”

Again, I couldn’t help but see a hidden meaning. But then a bell rang. Like animals in a lab, we had learned to tell the bells apart, so we didn’t have to look to know who it was for. Arsibalt took a final gulp from his flagon and hustled out.

Moyra’s voice was coming through on the speaker: “Uthentine and Erasmas were Thousanders, so their treatise was not copied out into the mathic world until the Second Millennial Convox.” She was speaking of the two avout who had developed the notion of Complex Protism. “Even then, it received scant notice until the Twenty-seventh Century, when Fraa Clathrand, a Centenarian-later in his life, a Millenarian-at Saunt Edhar, casting an eye over these diagrams, remarked on the isomorphism between the causality-arrows in these networks, and the flow of time.”

“Isomorphism meaning-?” asked Zh’vaern.

“Sameness of form. Time flows, or seems to flow, in one direction,” Paphlagon said. “Events in the past can cause events in the present, but not vice versa, and time never loops round in a circle. Fraa Clathrand pointed out something noteworthy, which is that information about the cnoons-the givens that flow along all of these arrows-behaves as if the cnoons were in the past.”

Again, Emman was staring off into space, drawing connections in his head. “Paphlagon is also a Hundreder from Edhar, right?”

“Yeah,” I said. “That’s probably how he got interested in this topic-probably found Clathrand’s manuscripts lying around somewhere.”

“Twenty-seventh Century,” Emman repeated. “So, Clathrand’s works would’ve been distributed to the mathic world at large at the Apert of 2700?”

I nodded.

“Just eight decades before the rise of…” But he cut himself short and flicked his eyes nervously in my direction.

“Before the Third Sack,” I corrected him.

In the messallan, Lodoghir had been demanding an explanation. Moyra finally settled him down: “The entire premise of Protism is that the cnoons can change us, in the quite literal and physical sense that they make our nerve tissue behave differently. But the reverse is not true. Nothing that goes on in our nerve tissue can make four into a prime number. All Clathrand was saying was that things in our past can likewise affect us in the present, but nothing we do in the present can affect the events of the past. And so here it seems we might have a perfectly commonplace explanation of something in these diagrams that might otherwise seem a bit mystical-namely, the purity and changelessness of cnoons.”

And here, just as Arsibalt had predicted, the conversation turned into a tutorial about light bubbles, which was an old scheme used by theors to keep track of how knowledge, and cause-and-effect relationships, propagated from place to place over time.

“Very well,” said Zh’vaern eventually, “I’ll give you Clathrand’s Contention that any one of these DAGs-the Strider, the Wick, and so on-can be isomorphic to some arrangement of things in spacetime, influencing one another through propagation of information at the speed of light. But what does Clathrand’s Contention get us? Is he really asserting that the cnoons are in the past? That we are just, somehow, remembering them?”

“Perceiving-not remembering,” Paphlagon corrected him. “A cosmographer who sees a star blow up perceives everything about it in his present-though intellectually he knows it happened thousands of years ago and the givens are only now reaching the objective of his telescope.”

“Fine-but my question stands.”

It was unusual for Zh’vaern to become so involved in the dialog. Emman and I confirmed as much by giving each other quizzical looks. Perhaps the Matarrhite was actually getting ready to say something?

“After the Apert of 2700, various theors tried to do various things with Clathrand’s Contention,” Moyra said, “each pursuing a different approach, depending on their understanding of time and their general approach to metatheorics. For example-”

“It is too late in the evening for a recitation of examples,” said Ignetha Foral.

Which chilled the whole room, and seemed to end the discussion, until Zh’vaern, in the ensuing silence, blurted out: “Does this have anything to do with the Third Sack?”

A much longer silence followed.

It was one thing for me and Emman, standing back in the kitchen, to mention this under our breath. Even then, I’d felt excruciatingly awkward. But for Zh’vaern to raise the topic in a messal attended (and under surveillance) by S?culars, went far, far beyond disastrously rude. To imply that the avout were in any way to blame for the Third Sack-that was mere dinner-party-wrecking rudeness. But to plant such notions in the minds of extremely powerful S?culars was a kind of recklessness verging on treason.

Fraa Jad finally broke the silence with a chortling noise, so deep that it hardly came through on the sound system. “Zh’vaern violates a taboo!” he observed.

“I see no reason why the topic should be off limits,” Zh’vaern said, not in the least embarrassed.

“How fared the Matarrhites in the Third Sack?” Jad asked.

“According to the iconography of the time, we, as Deolaters, had nothing to do with Rhetors or Incanters and so were considered-”

“Innocent of what we were guilty of?” said Asquin, who seemed to have chosen this moment to stop being nice.

“Anyway,” Zh’vaern said, “we evacuated to an island, deep in the southern polar regions, and lived off the available plants, birds, and insects. That is where we developed our cuisine, which I know many of you find distasteful. We remember the Third Sack with every bite of food we take.”

On the speaker I heard shifting, throat-clearing, and the clink of utensils for the first time since Zh’vaern had rolled his big stink-bomb into the middle of the table. But then he ruined it all by the way he volleyed the question back at Jad: “And your people? Edhar was one of the Inviolates, was it not?” Everyone tensed up again. Clathrand had come from Edhar; Zh’vaern seemed to have been developing a theory that Clathrand’s work had been the basis for the exploits of the Incanters; now he was drawing attention to the fact that Jad’s math had somehow managed to fend off the Sack for seven decades.

“Fascinating!” Emman exclaimed. “How could this get any worse?”

“I’m glad I’m not in there,” Tris said.

“Arsibalt must be dying,” I said. A small noise in the back of the kitchen drew our notice: Orhan, Zh’vaern’s servitor, had been standing there silently the whole time. It was easy to forget he was there when you couldn’t see his face.

“You just got to the Convox, Fraa Zh’vaern,” said Suur Asquin, “and so we’ll forgive you for not having heard, yet, what has become an open secret in the last few weeks: that the Three Inviolates are nuclear waste repositories, and as such were probably protected by the Sæcular Power.”

If this was news to Zh’vaern, he didn’t seem to find it very remarkable.

“This is going nowhere,” announced Ignetha Foral. “Time to move on. The purpose of the Convox-and of this messal-is to get things done. Not to make friends or have polite conversations. The policy of what you call the Sæcular Power toward the mathic world is what it is, and shall not be altered by a faux pas over dessert. The World Burner, you must know, has quite focused people’s minds-at least where I work.”

“Where would you like the conversation to go tomorrow, Madame Secretary?” asked Suur Asquin. I didn’t have to see her face to know that the rebuke had really burned her.

“I want to know who-what-the Geometers are, and where they came from,” said Ignetha Foral. “How they got here. If we have to discuss polycosmic metatheorics all evening long in order to answer those questions, so be it! But let us not speak of anything more that is not relevant to the matter at hand.”