In my opinion, these two sculptures were such bald pro-Hylaea, anti-Deät propaganda that I was almost embarrassed by them. The Deolaters, however, seemed to take precisely the opposite view. Over the course of Apert, Deat’s pedestal had become bedizened with so many candles and charms, flowers, stuffed animals, fetishes, phototypes of dead people, and slips of paper that the One-offs would be cleaning it up for weeks after the gates closed.

“Deät and Hylaea went out searching for their father and found him lost in contemplation under the tree. Both saw the tablet on which he had recorded his impressions, and both listened to his account. Not long after, Cnoüs said something so offensive to the king that he was sent into exile, where he soon died. His daughters began telling people different stories. Deät said that Cnoüs had looked up into the sky and seen the clouds part to give him a vision of a pyramid of light, normally concealed from human eyes. He was seeing into another world: a kingdom of heaven where all was bright and perfect. According to her, Cnoüs drew the conclusion that it was a mistake to worship physical idols such as the one he had been building, for those were only crude effigies of actual gods that lived in another realm, and we ought to worship those gods themselves, not artifacts we made with our own hands.

“Hylaea said that Cnoüs had actually been having an upsight about geometry. What her sister Deät had misinterpreted as a pyramid in heaven was actually a glimpse of an isosceles triangle: not a crude and inaccurate representation of one, such as Cnoüs drew on his tablet with ruler and compass, but a pure theorical object of which one could make absolute statements. The triangles that we drew and measured here in the physical world were all merely more or less faithful representations of perfect triangles that existed in this higher world. We must stop confusing one with the other, and lend our minds to the study of pure geometrical objects.

“You’ll notice that there are two exits from this room,” I pointed out, “one on the left near the statue of Deät, the other on the right near Hylaea. This symbolizes the great forking that now took place between the followers of Deät, whom we call Deolaters, and of Hylaea, who in the early centuries were called Physiologers. If you pass through Deat’s door you’ll soon find yourself outside where you can easily find your way back to the Unarian Gate. A lot of our visitors do that because they don’t think that anything beyond this point is relevant to them. But if you follow me through the other door, it means you are continuing on the Hylaean Way.” And after giving them a few minutes to roam around and take pictures, I went out, leading all but the Deät-pilgrims into a gallery lined with pictures and artifacts of the centuries following the death of Cnoüs.

This in turn gave on to the Diorama Chamber, which was rectangular, with a vaulted ceiling, and clerestory windows letting in plenty of light to illuminate the frescoes. The centerpiece was a scale model of the Temple of Orithena. As I explained, this had been founded by Adrakhones, the discoverer of the Adrakhonic Theorem, which stated that the square of a right triangle’s hypotenuse was equal to the sum of the squares of the other two sides. To honor this, the floor of the chamber was adorned with numerous visual proofs of the said theorem, any of which you could puzzle out if you stood and stared at it for long enough.

“We’re now in the period from about 2900 years before the Reconstitution to about negative 2600,” I said. “Adrakhones turned Orithena into a temple devoted to exploration of the HTW, or the Hylaean Theoric World—the plane of existence that had been glimpsed by Cnoüs. People came from all over. You’ll notice that this chamber has a second entrance, leading in from the out of doors. This commemorates the fact that many who had taken the other fork and sojourned among the Deolaters came in from the cold, as it were, trying to reconcile their ideas with those of the Orithenans. Some were more successful than others.”

I looked over at the slines. Back in the rotunda, they had spent some time speculating as to the size of certain parts of the anatomy of Cnoüs (which were hidden under a fold of his garment) and then gotten into a debate as to which they fancied more: Deät, who was conveniently kneeling, or Hylaea, who was beginning to take her clothes off. In this chamber, they had gathered beneath the most prominent fresco, which depicted a furious dark-bearded man charging down the steps of the temple swinging a rake, striking terror in a group of deranged, eye-rolling dice-players. It was clear that the slines loved this picture. So far, they’d seemed docile enough. So I drew closer to them and explained it. “That’s Diax. He was famous for his disciplined thought. He became more and more distressed by the way Orithena was being infiltrated by Enthusiasts. Those were people who misunderstood how the Orithenans used numbers. They dreamed up all kinds of crazy number-worshipping stuff. One day Diax was coming out of the temple after the singing of the Anathem when he saw these guys casting fortunes using dice. He was so furious that he grabbed a rake from a gardener and used it to drive the Enthusiasts out of the temple. After that, he ran the place. He coined the term theorics, and his followers called themselves ‘theors’ to distinguish themselves from the Enthusiasts. Diax said something that is still very important to us, which is that you should not believe a thing only because you like to believe it. We call that ‘Diax’s Rake’ and sometimes we repeat it to ourselves as a reminder not to let subjective emotions cloud our judgment.”

This explanation was too long for the four slines, who turned their backs to me as soon as I got past the rake fight. I noticed that one of them—the one with his arm in a sling—had a curious, bony ridge running up his spine and protruding a few inches above the collar of his jersey. Normally this was concealed by his trailing burnoose, but when he turned away from me I saw it clearly. It was like a second, exoskeletal spine attached to the natural one. At its top was a rectangular tab, smaller than the palm of my hand, bearing a Kinagram in which a large stick figure struck a smaller one with his fist. It was one of the spine clamps Quin had described to me and Orolo. I guessed it had disabled the man’s right arm.

A fresco on the ceiling at the far end showed the eruption of Ecba and the destruction of the temple. The following series of galleries contained pictures and artifacts from the ensuing Peregrin period, with separate alcoves dedicated to the Forty Lesser and the Seven Great Peregrins.

From there we came out into the great elliptical chamber with its statues and frescoes of the theoric golden age centered on the city-state of Ethras. Protas, gazing up at the clouds painted on the ceiling, anchored one end. His teacher Thelenes commanded the other, striding across the Plane with his interlocutors—variously awed, charmed, chastened, or indignant. The two bringing up the rear had their heads together, conspiring—a foreshadowing of Thelenes’s trial and ritual execution. A large painting of the city made it easy for me to point out the Deolaters’ temples atop its highest hill, where Thelenes had been put to death; its market, the Periklyne, wrapped around the hill’s base; a flat open area in the center of the Periklyne, called ‘the Plane,’ where geometers would draw figures in the dust or engage in public debate; and the vine-covered bowers around the edges, in whose shade some theors would teach their fids, from which we got the word suvin, meaning “under the vines.” As far as the nun was concerned, that one moment made the whole trip worth the trouble.

As we worked our way to the farther end, we began seeing theors standing at the right hands of generals and emperors, which led naturally enough to the last of the great chambers in the Hylaean Way, which was all about the glory that was Baz, its temples, its capitol, its walls, roads, and armies, its library, and (increasingly, as we approached the end) its Ark. After a certain point it was priests and prelates of the Ark of Baz, instead of theors, advising those generals and emperors. Theors had to be sought out as small figures in the deep background, reclining on the steps of the Library or going into the Capitol to spill wise counsel into the dead ears of the high and mighty.