Anathem

Two hours later I was standing alone at the gates of Orithena.

The wall was twenty feet high, made of blocks of fine-grained, grey-brown stone that were all the same size and shape. As I stood there, sweating in the sun, waiting for an answer to my knock, I had more than enough time to examine these and to conclude that they had been cast in molds, using some process that fused loose volcanic ash into a sort of concrete. Each was about the size of a small wheelbarrow, say the largest that a couple of avout could move around using simple tools. Anyway the courses were extremely regular, since all of the blocks were clones. Some were slightly browner, some slightly greyer, but on the whole the wall looked as if it had been snapped together out of a child’s building toy kit. The gates themselves were steel plates, which would last a good long while in this climate. After knocking, I stepped well back to get clear of the stored heat radiating from those panels, which were large enough to admit two of the largest drummons abreast. I turned and looked back at the souvenir stand, a few hundred feet down the hill. Cord, leaning back against the shady side of Yul’s fetch, waved at me. Sammann took a picture on his jeejah.

The gate was framed between a pair of cylindrical bastions perforated with small gridded windows. The one on the left sported a tiny door, also of steel. After some time had passed, I ambled over and knocked on it. Framed in its upper half was a hatch, just about the size of my hand. Ten minutes or so later, I heard movement on the other side. A door opened, then slammed shut within the bastion. A latch scrabbled. The little hatch creaked open. The room on the other side of it was dark and, I guessed, delightfully cool. But my eyes were adjusted to the blasting sun of an Ecba noon, and I could see nothing.

“Know that you address a world that is not your own and into which you may not pass save that you make a solemn vow not to leave it again,” said a woman’s voice, speaking in locally accented Fluccish. This was what she was supposed to do. Gatekeepers in places like this had been saying this, or some variant of it, since Cartas.

“Greetings, my suur,” I said, “let us speak in Orth if you please. I am Fraa Erasmas of the Edharian chapter of the Decenarian math of the Concent of Saunt Edhar.”

A pause, then the hatch closed and was latched. I waited for a while. Then the hatch opened again and I heard a deeper, older woman’s voice.

“I am Dymma,” she said.

“Greetings, Suur Dymma. Fraa Erasmas at your service.”

“That I am your suur, or you my fraa, is very much undecided in my mind, as you come so attired.”

“I have traveled far,” I returned. “My bolt, chord, and sphere were stolen from me as I made peregrin across the S?culum.”

“No Convox is summoned hither. We do not look for peregrins.”

“It seems inhospitable,” I said, “that Orithena, whence the first Peregrins departed, should not open her gates for one who has returned.”

“Our duty is to the Discipline, not to any custom of hospitality. There are hotels in town; hospitality is their business.” The little hatch made a noise as if she were getting ready to close it.

“What part of the Discipline permits avout to sell soap extramuros?” I asked. “Where does the Discipline state that bolted fraas may stroll about yonder town?”

“Your discourse belies your claim to be avout,” said Dymma, “as a fraa would know that there are variations in the Discipline from one math to the next.”

“Many avout would not know it since they never leave their own maths,” I demurred.

“Precisely,” Dymma said, and I could imagine her smirking in the dark at how deftly she had turned the point to her advantage-for I was on the outside, where no avout should be.

“I grant that your customs may differ from those of the rest of the mathic world,” I began.

She interrupted me. “Not so much so that we would admit one who had not sworn the Vow.”

“Did Orolo swear the Vow, then?”

A few seconds of silence. Then she closed the hatch.

I waited. After a while I turned back, waved to my friends, and pantomimed a big shrug. It was strangely difficult to reconnect with them, even in such a simple gesture, after having stared over the threshold of the math. I’d bid goodbye to them a few minutes ago as if I’d be back in time for lunch. But for all I knew I might end up spending the rest of my life there.

The hatch again. “State your business, you who style yourself Fraa Erasmas,” said a man in Orth.

“Fraa Jad, Millenarian, would know Orolo’s mind on certain matters, and sends me in quest of him.”

“Orolo who was Thrown Back?”

“The same.”

“One on whom the Anathem has been rung down may never more go into a math,” the man pointed out. “And for that matter, one who has been Evoked, and despatched to Convox at Tredegarh, may not suddenly present himself at a different math on the other side of the world.”

I had already suspected the answer before we reached Ecba. Certain clues had bolstered my hypothesis. But, strangely, what clinched it for me was the architecture of the place. No concessions to the Mathic style here. “The riddle that you pose is a trying one,” I admitted, “however, on reflection, its answer is clear.”

“Oh? What is its answer then?”

“This is not a math,” I said.

“What is it if not a math?”

“The cloister of a lineage that was born a thousand years before Cartas and her Discipline.”

“You are well come to Orithena, Fraa Erasmas.”

Heavy bolts moved and the door swung open.

I stepped forward into Orithena, and into the Lineage.

At Saunt Edhar, Orolo had grown a little doughy, though he kept in decent shape by working in his vineyard and climbing the steps to the starhenge. At Bly’s Butte, according to Estemard’s phototypes, he had lost some of that weight and gone shaggy-headed and grown the obligatory Feral beard. But when I picked him up at the gates of Orithena and spun him around five times, his body felt solid, neither fat nor emaciated, and when I finally let him go, tears were making wet tracks down his tanned and clean-shaven cheeks. That was all I saw before my vision was blurred with tears, and then I had to break away and walk to and fro in the shade of the great wall to get my composure back. The Discipline had taught me nothing of how to cope with such an event: throwing my arms around a dead man. Perhaps it meant that I too was now dead to the mathic world, and had moved on to a sort of afterlife. Cord, Yul, Gnel and Sammann had served as my pallbearers.

It took a powerful effort of will to remember that they were still out there, wondering what was going on.

There was a little fountain in the cloister. Orolo fetched me a ladle of water. We sat together in the shade of the clock-tower as I drank. It tasted of sulfur.

Where to begin? “There’s so much I would have said to you, Pa, if I could have, when you were Thrown Back. So much I wanted to say to you in the weeks following. But…”

“It all flows back.”

“Beg pardon?”

“Those things flow back in time and as they do they change-your mind changes them-so that they no longer need talking about quite so much. Fine. Let’s talk of what is fresh and interesting.”

“All right. You’re looking well.”

“You aren’t. Scars honorably earned, I hope?”

“Not really. Learned a lot though.” But I did not really feel like telling him the story. We made idle chitchat for a few minutes until we both realized how ridiculous it was, then got up and began to prowl around. A younger fraa-if that was the correct term for one who lived in a math-that-was-not-a-math-brought me a bolt and chord, which I traded for my Sæcular clothes. Then Orolo led me away from the cloister along a broad path, beaten down by countless sandaled feet and barrow-wheels, to the edge of a pit big enough to swallow the Mynster of Saunt Edhar several times over. If we had built our monument by piling stone on stone, building up from the ground, they had built theirs by digging down, a shovel-load at a time. The walls of the hole were too steep, the soil too loose to be stable; they had shored it up using slabs of fused ash. A ramp spiraled down to the bottom. I started down it, but Orolo held me back. “You’ll notice there are no people down there. It gets hotter as you descend. We dig at night. If you insist on going for a hike, we’ll ascend.” And he gestured up the mountainside.

I already knew from Sammann’s pictures and from yesterday’s scouting trip that Orithena had two wall-systems, an inner and an outer. They coincided along the road, where the main gate stood. The huge twenty-foot wall enclosed the cloister where the avout lived, and the hole in the ground where they delved. The outer wall was much lower-perhaps six feet high-so, more symbolic than anything else. It reached thousands of feet up the mountainside, embracing a strip of ground that ran all the way to the volcano’s caldera. It was clear from the pictures that mine-works had been created up at the top, possibly to extract energy from the volcano’s heat. So there I reckoned it would be hot, foul-smelling, and dangerous. But the territory in between-what Orolo and I walked through-had been transformed into an oasis by the labor of the Lineage. Somehow they had found water and used it to raise vines, grain, and all manner of trees that yielded fruits and oils while casting dappled shade on the path up the mountain. The temperature dropped a little, the breeze freshened, with every step. The effort of climbing kept me warm, but when we reached a suitable altitude to stop, enjoy the view, and nibble at the fruits we’d pilfered along the way, my sweat dried instantly in the cool dry wind off the sea and I had to wrap myself up.

We passed beyond the upper limit of Orithena’s orchards and wandered through a belt of twisted, gnarled trees to a sloping meadow dusted with what had looked, from a distance, like frost. But it was actually a carpet of tiny white wildflowers that somehow found a way to grow here. Colorful insects flew around but there weren’t enough of them to be obnoxious. They were kept in check, I guessed, by the birds, who sang from perches in scrub-trees and bursts of spiky vegetation. We sat on the exposed root of a tree that must have been planted the spring after the volcano had gone off. Orolo explained that these trees, which were no taller than I, were in fact the oldest living things on Arbre.

Most of our conversation that afternoon consisted of such tour-guide stuff. In a way it was a great relief to chatter about birds and trees, and how many cubic feet of earth had been removed from the dig and how many of the Temple buildings had been excavated, rather than talking of such weighty affairs as the Geometers, the Convox, and the Lineage. Later we hiked down and supped at the Refectory with the hundred or so fraas and suurs who lived here. Their FAE, Fraa Landasher, the third of the three who’d interrogated me at the gate, formally bade me welcome and made a toast in my name. I drank more than my share of their wine, which was infinitely better than what Orolo made in his frostbitten vineyard at Saunt Edhar, and slept it off in a private cell.

I awoke sour, hung over, out of sorts, thinking it was late and that I’d overslept-but no, it was early, and the night shift of diggers were coming up out of the pit with their picks, trowels, brushes, and notebooks, singing hilarious marching-songs. They’d constructed a bathhouse where hot water was sluiced down from volcanic springs and routed through vertical shafts where you could get blasted clean in about ten seconds. I stood in one of those until I could no longer breathe, then stepped out and let my newmatter bolt pull the water off my skin. This helped a little. But what was really throwing me for a loop was the re-entry shock of being back in the mathic world, with its view of time so different from what I’d grown used to extramuros. Making it worse was that no one had explained the place’s rules to me yet. In most ways it was like a Cartasian math. But they’d not made me swear a vow, and I got the sense that I could walk out the door whenever I chose. They just pretended it was a math when they were dealing with anyone who might not understand. Being avout was their cover story. And yet it was no lie, for they were as dedicated to their work as any who lived in Saunt Edhar. Perhaps more so, in that they wouldn’t suffer that work to be impeded by rules, would not submit to the dictates of any Inquisition.

Fraa Landasher intercepted me coming out of the sluice-bath and introduced me to Suur Spry, a girl of about my age. Or rather reintroduced me, since she was the first person I’d spoken with yesterday at the gate. She reminded me disconcertingly of Ala. It was now or never, explained Landasher, for me to descend and see the ruins, for if we waited any longer it would be too hot. Suur Spry was to be my guide; she’d packed a basket of food that we could nibble on as we went. It was clear from the looks on their faces that they expected I’d be thrilled. And what would be more reasonable? Yet I had to feign gratitude because what I really wanted was to awaken Orolo and talk to him of pressing Sæcular matters.

Not having known what might happen at the gate, I’d made the plan yesterday with Cord, Yul, Gnel, and Sammann that if I was allowed to go inside, they should wait for an hour and then, if nothing happened, come back three days later, at which time I’d try to get word out to them as to what ought to be done next. I felt that my three days were flying by, and so in truth I did not want to go on a long tourist hike with some girl I’d only just met. It was in a peevish mood that I began to descend the ramp, carrying Suur Spry’s picnic-basket on one arm.

It was in an altogether different mood, though, that I reached the bottom, kicked off my sandals, and felt under my bare feet the paving-stones on which Adrakhones had walked. The Temple steps where Diax had brandished his Rake. The Analemma where generations of physiologer-priests had celebrated Provener. And the tile-strewn Decagon where Metekoranes had stood, lost in thought, as the whole place was buried under ash.

“Did you find him?” I asked Spry, a few minutes later, as we were munching on some fruit and drinking water from the basket.

“Who-Metekoranes?”

“Yes.”

“Yes. He was the first one we-I mean they, my forerunners-looked for. They found, standing upright, a-” She balked, looking awed and disgusted.

“Skeleton?”

“A cast,” she said, “a cast of his whole body. You can look at it if you want. Of course it’s just speculation that it is the actual Metekoranes. But it fits perfectly with the legend. He even had his head bowed, you know, as if he were looking at the tiles.”

The plaza where we were enjoying our little picnic-the one where Metekoranes had been buried and cast in stone-was the Teglon made real. It was flat, decagonal, maybe two hundred feet across, paved in smooth slabs of marble. In ancient times the plaza had been plentifully supplied with tiles made of clay baked in molds. There were seven molds, hence seven different shapes of tile. Their shapes were such that it was possible to fit them together in an infinite number of patterns. That’s not possible with squares, or equilateral triangles; those fit together in repeating patterns, so there are no choices to make. But as long as you had more copies of the Teglon tiles, you could go on making choices forever. Hundreds of tiles were scattered around the place even now, and from place to place the modern-day Orithenans had been putting them together in little arrangements. I squatted down and looked at one, then looked questioningly at Spry. “Go ahead,” she said, “it’s a modern reproduction. We found the original molds!”

I picked up a tile for a closer look. This one happened to be four-sided: a rhombus. A groove was molded into its surface, curving from one of its sides to another. I carried it over to the nearest vertex of the Decagon and set it down; its obtuse angle fit perfectly into the corner.

“Ah,” Suur Spry teased me, “going straight to the most difficult problem of all, huh?”

She was talking, of course, of the Teglon. She turned away and walked to the opposite vertex and set a tile down there. Meanwhile I scavenged a few other tiles, getting samples of all seven shapes. I chose one at random and set it next to the first. This one also had a groove curving from one side to another-all of the tiles were so made-and I rotated it until its groove mated with, and became a continuation of, the one on the first tile. Into the angle between them I was able to place a third. That created opportunities to slide in a fourth, a fifth, and so on. I was playing the Teglon. The objective of the game was to build the pattern outward from one vertex and pave the entire Decagon in such a way that the groove formed a continuous, unbroken curve from the first vertex to the last-the one directly opposite, where Suur Spry had put down a tile. Along the way, the curve had to pass across every tile in the entire Decagon. For the first little while, it was easy-it came naturally. But beyond a certain point, the two objectives-that of tiling the whole surface, and that of keeping the curve going-began to conflict. I had to leave a stretch of groove hanging unconnected for a while, then work my way back to it, steering the groove around to make the connection. That was satisfying. But a few minutes later I found myself with three such segments of marooned groove in different parts of the pattern, and despaired of ever finding an arrangement that would connect them all. On one level, this was all about the shape of the outer boundary, and how it developed. Tiles trapped in the middle were of no further interest to the game-or so you might think. But on the other hand, the way in which an interior tile had been laid down ended up determining the location of every other tile in the whole Decagon.

The ancient Orithenans suspected, but didn’t know how to prove, that the tiles of the Teglon were aperiodic: that no pattern would ever repeat. Again, solving the Teglon would have been easy-it would have been automatic-with square or triangular tiles, or any tile system that was periodic. With aperiodic tiles, it was impossible, or at least very unlikely, unless you had some Godlike ability to see the whole pattern in your head at once. Metekoranes had believed that the final pattern existed in the Hylaean Theoric World, and that the Teglon could only be solved by one who had developed the power of seeing into it.

Suur Spry was clearing her throat. I looked up. I was squatting at the edge of a system of tiles fifty feet wide. It was getting hot.

“Sorry,” I said.

“Some people use sticks to push them around. Saves wear and tear on the back.”

“We should probably get out of here, huh?”

“Soon,” she allowed.

First, though, I followed her about as she showed me the remnants of the ancient buildings. All the roofs were gone, of course. Some pillars still stood, and a few courses of stone that had once been walls, now half-buried in blocks that had tumbled down from above. But mostly we were looking at foundations, floors, stairs, and plazas. Active parts of the dig were gridded with string, a geometric touch Adrakhones would have appreciated. The rocks were annotated with neatly brushed letters and numbers put down by diggers of centuries past. Up above, I knew, was a sort of museum where they’d placed many of the artifacts they had found, including presumably the cast of Metekoranes. I imagined that museum should be dark. Nicely ventilated. And cool. “Okay, let’s get out of this barbecue pit,” I proposed, and heard no argument from Suur Spry.

We had stayed later than expected. Partly because it had been fascinating. But-and this probably didn’t say much for my character-mainly because this was the one thing I could do on this journey that would seem almost as cool as Jesry’s space adventure.

My body had healed to the point where it was willing to cut me a little bit of slack, and so during the early part of the climb I was babbling about the Teglon just like all of those geometers of yore who’d gone crazy over it. Soon enough, though, my injuries began talking to me, and excitement was snuffed out by pain. The remainder of the hike was a long silent trudge. Another sluice-bath was called for. I fell asleep. When I woke up it was late afternoon. Orolo was on kitchen duty. I helped him. But we didn’t really get to talk about anything. So more than one of my three days had been gobbled up just like that. Before we retired that evening I warned Orolo we must speak of important things the next day. So after breakfast the next morning we hiked back up to the meadow.