Slightly indignant murmuring from avout—not at all certain that they agreed with him—was drowned out by applause from the majority of visitors. Poor Suur Frandling had to get up next and say a few words for the Reformed Old Faanians, but she could have been reading from an economic database for all anyone cared. Most of the avout were peeved by Corlandin’s eloquence—or glibness—and Orolo was among them. But to his credit he pointed out that Corlandin had smoothed over an awkward moment and probably won us some sympathy extramuros.

“How do you know when someone is really glib?” Jesry muttered to me.

“I’ll bite. How?”

“It doesn’t cross your mind that he’s glib until someone older and wiser points it out. And then, your face turns hot with shame.”

More music then, as most of us avout got up to clear plates and fetch dessert. The entertainment, which earlier had been so intimidating, had become a little easier to enjoy. Many of the carols traditionally played over loudspeakers in stores and elevators at this time of year were derived from liturgical music that had originated in the maths and filtered out at Apert, and so many of the visitors were pleasantly surprised to hear familiar melodies spilling from the lips of these bolt-wrapped weirdos.

Dessert was sheet cakes baked and served in broad trays. One of them ended up in front of Arsibalt—not a coincidence. He picked up the spatula that had arrived with it: a flat metal blade about the size of the palm of a child’s hand. Just before he plunged it into the cake, I had an idea, and stopped him. “Let’s have Dath do it,” I said.

“As hosts, it is our duty to serve,” Arsibalt demurred.

“Then you can serve, but I want Dath to do the cutting,” I insisted. I wrenched the spatula from Arsibalt’s grip and handed it across to Dath, who took it a little uncertainly.

I then talked him through cutting the cake; but I had him go about it in a very specific way, working through the steps of an old geometry proof* that Orolo had taught me when I had been a brand-new fid, up all night crying because I missed my old life. This took a little while, but when all was said and done, it was clear from the look on Dath’s face that he understood it, and I was able to tell him: “Congratulations. You have just worked out a geometric proof that is thousands of years old.”

“They had sheet cakes back then?”

“No, but they had land and other things they needed to measure, and the same trick works for those things too.”

“Uh huh,” Dath said, gobbling a vertex from his serving.

“You say uh huh like it is not a big deal, but it is a big deal to us,” I said. “Why should a proof that works for sheet cake work as well for a plot of land? Cake and land are different things.”

We had gone a little over the head of Dath, who just wanted to eat his cake, but Cord saw it. “I guess I have an unfair advantage here since I spend so much time thinking about geometry in my work. But the answer is that geometry is…well…geometry. It’s pure. It doesn’t matter what you’re applying it to.”

“And it turns out that the same is true for other kinds of theorics besides geometry,” I said. “You can prove something. Later the same thing might be proved in a totally different way; but you always end up with the same answer. No matter who is discussing these proofs, in what age, whether they are speaking of sheet cake or pasture-land, they always arrive at the same answer. These truths seem to come out of another world or plane of existence. It’s hard not to believe that this other world really exists in some sense—not just in our imaginations! And we would like to go there.”

“Preferably without having to die first,” Arsibalt put in.

“When I’m cutting a part, sometimes I get obsessed with it,” Cord said. “I lie awake in my bed thinking about its shape. Is that—perhaps—related to how you all feel about what you study?”

“Why not? You’re carrying this geometry around in your head that fascinates you. Some would say it’s only a pattern of neurons firing in your brain. But it has an independent reality. And for you, thinking about that reality is an interesting and rewarding way to spend your life.”

Rosk was a manual therapist—he put his hands on people to fix them. “I’ve been working on someone who has a pinched nerve because he has lousy posture,” he said. “I was discussing it with my teacher, over the jeejah—no pictures, just our voices. We had this long talk about this nerve and the muscles and ligaments around it and how I should manipulate them to help alleviate the problem, and suddenly I just flashed on how weird the whole thing was—two of us both relating to this image—this model—of another person’s body that was in his mind and in my mind, but—”

“Also seemingly in a third place,” I suggested, “a shared place.”

“That’s what it felt like. It freaked me out for a little while, but then I put it out of my mind because I thought I was just being weird.”

“Well, it’s been freaking people out since Cnoüs and this is like an asylum for people who can’t stop thinking about it,” I said. “It’s not for everyone, but it’s harmless.”

“Since the Third Sack anyway,” Rosk said.

That he said it so innocently made it ten times as rude as it was to begin with. I saw Cord’s face flush, and guessed she’d probably have words with him after dinner. It was anyone’s guess whether he’d ever really understand why it was such an abhorrent thing to say.

People were shushing us because we had reached that part of the aut where the newcomers were presented at the high table.

Eight foundlings had been Collected. One was sickly and would stay in the Unarian math where it would be easier for the physicians to keep an eye on her. Two of them still had the stumps of their umbilical cords attached, which meant that they were destined for the Millenarian math, by way of a brief sojourn among the Hundreders. We would pass them along via our upper labyrinth. The remaining five were a little bit older, and so would be passed to the Hundreders.

Thirty-six youngsters were to be Collected. Seventeen of these, including Barb, would come directly to our math. The others would stay with the One-offs, at least at first. With any luck, some of them might graduate to our math later.

Twelve of the One-offs had decided to graduate to our math. Nine more had arrived from another, smaller concent in the mountains that acted as a feeder to ours.

All of these were brought up before the high table, welcomed, and applauded. Tomorrow, after the gate closed, we would celebrate their arrival in a much more tedious ceremony. Tonight was the time for the extramuros authorities to supply their own special brand of tedium. By ancient tradition, the highest-ranking Panjandrum present at this dinner was supposed to stand up and formally hand the newcomers over to us. At that moment, they passed out of Sæcular, and into mathic jurisdiction. We became responsible for housing them and feeding them, caring for them when they ailed, burying them when they died, and punishing them when they misbehaved. It was as if they ceased in this moment to be citizens of one country and became citizens of another. It was, in other words, a big deal from a legal standpoint, and it had to be solemnized by the speaking of certain oaths and the ringing of a bell. And there was an almost as ancient tradition that the official in question would use it as an excuse to “deliver some remarks.”

This turned out to be the rope-draped oddity who had appeared at the Decade Gate with his contingent on the first morning of Apert. He was, as it turned out, the mayor.

After thanking everyone from God on down and then back up to God again, and then, as a precaution, tacking on a blanket thank-you for any persons or supernatural beings he had left out, he began: “Even those of you who live at Saunt Edhar must be aware by now that the extraordinary re-configuration of prefectural boundaries mandated by the Eleventh Circle of Arch-Magistrates has literally transformed the political landscape. The Plenary Council of the Recovered Satrapies has passed through a tipping point of no return, placing five of the eight Tetrarchies within the grasp of a new generation of leaders who I can promise you will be far more sensitive than their predecessors to the values and priorities of New Counterbazian constituencies and our many friends who may belong to other Arks, or even to no Ark at all, but who share our concerns…”