We spiraled up and around to a point where we could look down into Samble and wave to our friends below. The service in the ark showed no sign of winding down. We had assumed that the vehicles would catch up with us soon into our hike. In other words, we were only doing this to get some exercise—not as a way of getting to the top. But now it seemed we might get there before our vehicles did. For some reason this aroused our competitive instincts and made us hike faster. We found a shortcut that had been used by other hikers, and cut off one whole circuit of the mountain by scrambling straight up the slope for a couple of hundred feet.

“Did you know Fraa Paphlagon?” I asked Criscan when we stopped at the top of the shortcut to drink water and marvel at our progress. The view was worth a few minutes.

“I was his fid,” Criscan said. “You were Orolo’s?”

I nodded. “Are you aware that Orolo was a fid of Paphlagon before Paphlagon came to you through the labyrinth?”

Fraa Criscan said nothing. For Paphlagon to have mentioned Orolo—or anything about his former life among the Tenners—to Criscan would have been a violation of the Discipline. But it was the sort of thing that could easily leak out when talking about one’s work. I went on, “Paphlagon and another Tenner named Estemard worked together and raised Orolo. They left at the same time: Paphlagon via the labyrinth and Estemard via the Day Gate. Estemard came here.”

Criscan asked, “What was Orolo’s reputation? Before his Anathem, I mean.”

“He was our best,” I said—surprised by the question. “Why? What was Paphlagon’s reputation?”

“Similar.”

“But—?” Because I could tell that there was a “but” coming.

“His avocation was a bit strange. Instead of doing something with his hands like most people, he made a hobby of studying—”

“We know,” I said. “The polycosm. And/or the Hylaean Theoric World.”

“You looked at his writings,” Criscan said.

“Twenty-year-old writings,” I reminded him. “We have no idea what he’s been up to recently.”

Criscan said nothing for a few moments, then shrugged. “It seems highly relevant to the Convox, so I guess it’s okay for me to talk to you about it.”

“We won’t tell on you,” Lio promised him.

Criscan didn’t catch the humor. “Have you ever noticed that when people are talking about the idea of the Hylaean Theoric World, they always end up drawing the same diagram?”

“Yeah—now that you mention it,” I said.

“Two circles or boxes,” Lio said. “An arrow from one to the other.”

“One circle or box represents the Hylaean Theoric World,” I said. “The arrow starts there and points to the other one, which represents this world.”

“This cosmos,” Criscan corrected me. “Or causal domain, if you will. And the arrow represents—?”

“A flow of information,” Lio said. “Knowledge of triangles pouring into our brains.”

“Cause-and-effect relationship,” was my guess. I was recalling Orolo’s talk of Causal Domain Shear.

“Those two amount to the same thing,” Criscan reminded us. “That kind of diagram is an assertion that information about theorical forms can get to our cosmos from the HTW, and cause measurable effects here.”

“Hold on, measurable? What kind of measurable are you talking about?” Lio asked. “You can’t weigh a triangle. You can’t pound in a nail with the Adrakhonic Theorem.”

“But you can think about those things,” Criscan said, “and thinking is a physical process that goes on in your nerve tissue.”

“You can stick probes into the brain and measure it,” I said.

“That’s right,” Criscan said, “and the whole premise of Protism is that those brain probes would show different results if there weren’t this flow of information coming in from the Hylaean Theoric World.”

“I guess that’s so,” Lio admitted, “but it sounds pretty sketchy when you put it that way.”

“Never mind about that for now,” Criscan said. We were on a steep part of the road, breathing hard and sweating as the sun shone down on us, and he didn’t want to expend much energy on it. “Let’s get back to that two-box diagram. Paphlagon was part of a tradition, going back to one Suur Uthentine at Saunt Baritoe’s in the fourteenth century A.R., that asks ‘why only two?’ Supposedly it all started when Uthentine walked into a chalk hall and happened to see the conventional two-box diagram where it had been drawn up on a slate by one Fraa Erasmas.”

Lio turned and looked at me.

“Yes,” I said, “my namesake.”

Criscan went on, “Uthentine said to Erasmas, ‘I see you are teaching your fids about Directed Acyclic Graphs; when are you going to move on to ones that are a little more interesting?’ To which Erasmas said, ‘I beg your pardon, but that’s no DAG, it is something else entirely.’ This affronted Suur Uthentine, who was a theor who had devoted her whole career to the study of such things. ‘I know a DAG when I see one,’ she said. Erasmas was exasperated, but on reflection, he decided it might be worth following up on his suur’s upsight. So Uthentine and Erasmas developed Complex Protism.”

“As opposed to Simple?” I asked.

“Yes,” Criscan said, “where Simple is the two-box kind. Complex can have any number of boxes and arrows, as long as the arrows never go round in a circle.”

We had spiraled around to the shady side of the butte, and come to a stretch of road that had been covered with silt during seasonal rains—perfect for drawing diagrams. While we rested and sipped water, Criscan went on to give us a calca* about Complex Protism. The gist of it was that our cosmos, far from being the one and only causal domain reached by information from a unique and solitary Hylaean Theoric World, might be only one node in a web of cosmi through which information percolated, always moving in the same direction, as lamp oil moves through a wick. Other cosmi—perhaps not so different from ours—might reside up-Wick from ours, and feed information to us. And yet others might be down-Wick from us, and we might be supplying information to them. All of which was pretty far out—but at least it helped me understand why Paphlagon had been Evoked.

“Now I have a question for you Tenners,” Criscan said, as we set out again. “What was Estemard like?”

“He walked out before we were Collected,” I said, “so we didn’t know him.”

“Oh, that’s all right,” Criscan said, “we’ll know soon enough.”

We walked on silently for a few steps before Lio—casting a wary glance to the top of the butte, not so far away now—said, “I’ve been looking into Estemard a little. Maybe I should tell you what I know before we barge into his house.”

“Good for you. What did you learn?” I asked.

“This might be one of those cases where someone walked out before he could be Thrown Back,” Lio said.

“Really!? What was he doing?”

“His avocation was tiles,” Lio said. “The really ornate tile work in the New Laundry was done by him.”

“The geometric stuff,” I said.

“Yes. But it seems he was using that as a sort of cover story to pursue an ancient geometry problem called the Teglon. It’s a tiling problem, and it dates all the way back to the Temple of Orithena.”

“Isn’t that the problem that made a bunch of people crazy?” I asked.

“Metekoranes was standing on the Decagon in front of the Temple of Orithena, contemplating the Teglon, when the ash rolled over him,” Criscan said.

I said, “It’s the problem that Rabemekes was thinking about on the beach when the Bazian soldier ran him through with a spear.”

Lio said, “Suur Charla of the Daughters of Hylaea thought she had the answer, scratched out on the dust of the road to Upper Colbon, when King Rooda’s army marched through on their way to getting massacred. She never recovered her sanity. People’s efforts to solve it have spun off entire sub-disciplines of theorics. And there are—have always been—some who paid more attention to it than was really good for them. The obsession gets passed down from one generation to the next.”