Anathem

“That’s a little easier to take seriously,” I said. “Fine.” Because I had the sense that Criscan was getting ready to veer off into a long tedious defense of Halikaarn. “So how does this faculty figure into his account of what’s happening in this diagram?”

“There is some other type of given, other than what we can detect with our eyes, ears, and so on, that somehow reaches the Arbran Causal Domain and that is perceived by Halikaarn’s Organ,” Criscan said.

“That almost raises more questions than it answers,” Lio pointed out.

“It doesn’t answer any questions at all,” Criscan returned, “this is not really an attempt to answer questions but a way of setting one’s pieces out on the board, agreeing on terminology, and so on. So. The theorical entities in the HTW—triangles, theorems, and other pure concepts—are called cnoöns.”

“Cnoöns, check!” Lio said.

“Between us and the HTW is a relationship, the details of which are subject to further debate, which Halikaarn didn’t name, but it’s symbolized by this arrow, and so people have ended up calling it Halikaarn’s Arrow.”

“Halikaarn’s Arrow, check!”

“A Halikaarn’s Arrow is a one-way conduit for givens about the cnoöns. These givens enter the Arbran Causal Domain through a poorly understood process called the Hylaean Flow and there impinge on Halikaarn’s Organ, which is how we become aware of them.”

“Hylaean Flow, check!”

Criscan had decided that he didn’t like Lio very much, but was making a visible effort to tolerate him. I stepped into the position of interlocutor, shouldering Lio aside. Lio reacted melodramatically, sprawling off to the shoulder of the road as if he had been struck by a speeding fetch. I ignored him. “So,” I said to Criscan, “now that we have the terminology bolted down, where are we going with it?”

“Now we’re going to skip ahead a mille

“Why bother stipulating that, I wonder?”

“The property of being acyclic is required in order to preserve the fundamental doctrine of Protism: that the cnoöns are changeless. If it were possible for the arrows to go around in a circle, it would mean that events in our universe could alter things in the Hylaean Theoric World.”

“Of course,” I said, “pardon me, that’s obvious now that you mention it.”

“This diagram,” said Criscan, drawing my attention back to his two-box sketch, “just seems wrong, to a metatheorician.”

“What do you mean, just seems wrong? How can you get away with statements like that?”

“It is a legitimate move in metatheorics. You have to be continually asking yourself, ‘why are things thus, and not some other way?’ And if you apply that test to this diagram, you immediately run into a problem: there are exactly two worlds. Not one, not many, but two. One might draw such a diagram having only one world—the Arbran Causal Domain—and zero arrows. That would draw very few objections from metatheoricians (at least, those who are not Protists). One might, on the other hand, assert ‘there are lots of worlds’ and then set out to make a case for why that is plausible. But to say ‘there are two worlds—and only two!’ seems no more supportable than to say ‘there are exactly 173 worlds, and all those people who claim that there are only 172 of them are lunatics.’”

“Okay, if you put it that way, I agree that there is a certain odor of crankiness about it. Like when Deolaters claim that there are thirty-seven books making up their scripture but that anyone who proposes a different number must die.”

“Yes, and this accounts, at least in part, for the way Protism raises hackles in some quarters. So the Erasmas/Uthentine move is simply to say ‘what’s true of one DAG ought to be true of another’ and to consider other DAGs having other numbers of worlds.”

Criscan took up his stick again, and scratched out a diagram like this one:

“They called this one the Freight Train,” Criscan a

“A world is either Protan, or it isn’t,” I translated.

“Yes. Here, on the other hand, gradations of Prota

“Not just possible,” I pointed out, “they are required.”

“Yes,” Criscan said, a little distractedly, for he was already at work making another diagram.

“This is the Firing Squad,” he said. “In the Firing Squad topology, some number of Hylaean Theoric Worlds are co

He now spent a while drawing a much more complex diagram:

“The Reverse Delta,” Criscan said. “It has the topology of a river delta, but the arrows run backwards, hence the name. The Reverse Delta is most easily summed up by saying that it combines the properties of the Freight Train and Firing Squad topologies.”

“Got it,” I said, after a moment’s thought—for Criscan, I sensed, was testing me. “It’s got Analog Protism—many gradations of Prota

Criscan did not respond one way or the other, since he was busy with his stick again. “The Strider,” he proclaimed.

“Strider? In what way does it stride?” I asked.

“It’s named after a kind of tree—a tropical species that co

“Yes. Up until now, it’s always ended with arrows going to the Arbran Causal Domain. But here you are assuming a polycosmic scheme—multiple inhabited cosmi, causally disco

“That’s right. Causally disco

“And this finally leads us to the Wick.”

“The Wick is a fully generalized DAG,” Criscan said. “The Hylaean Flow moves through it from left to right—from more Protan to less Protan worlds—but here we are taking Analog Protism to its logical extreme in that no distinction is drawn between types of worlds.”

“I see ours there,” I said, pointing to the one labeled “Arbran Causal Domain.”