Anathem

Theor: Any practitioner of theorics, which see.

Theorician: Nearly equivalent to theor, but with slightly different co

Theorics: Roughly equivalent to mathematics, logic, science, and philosophy on Earth. The term can fairly be applied to any intellectual work that is pursued in a rigorous and disciplined ma

Thousander: Informal term for a Millenarian (see).

Throw Back: An informal term meaning to subject an avout to the aut of Anathem.

Throwback: An ex-avout who was Anathematized.

Tredegarh: One of the Big Three concents, named after Lord Tredegarh, a mid-to-late Praxic Age theor responsible for fundamental advances in thermodynamics.

Triangle Ark: Alternate term for the Kelx faith or one of its arks.

Unarian: An avout sworn not to emerge from the math or to have contact with the outside world until the next A

Upsight: A sudden, usually unlooked-for moment of clear understanding.

Uraloabus: Prominent Sphenic theor of the Golden Age of Ethras who, if the account of Protas is to be credited, committed suicide after being planed by Thelenes.

Uthentine: A suur at Saunt Baritoe’s in the Fourteenth Century A.R. who, along with Erasmas, founded the branch of metatheorics called Complex Protism.

Vale-lore: Martial arts. Associated with the Ringing Vale (see).

Valer: An avout of the Ringing Vale; one who has, therefore, devoted his or her entire life to the martial arts.

Vlor: An informal contraction of Vale-lore (see).

Voco: A rarely celebrated aut by which the Sæcular Power Evokes (calls forth from the math) an avout whose talents are needed in the Sæcular world. Except in very unusual cases, the one Evoked never returns to the mathic world.

Vout: An avout. Derogatory term used extramuros. Associated with Sæculars who subscribe to iconographies that paint the avout in an extremely negative way.

Warden Fendant: A hierarch charged with defending the math or concent from Sæcular interlopers, by all means up to and including physical violence, and typically overseeing a staff of more junior hierarchs trained to carry out such functions.

Warden of Heaven: During the years leading up to the time in which Anathem is set, a popular religious leader who obtained Sæcular power by claiming to embody the wisdom of the mathic world.

Warden Regulant: A hierarch charged with maintaining the Discipline intramuros, empowered to conduct investigations and to mete out penance. Technically subordinate to the Primate but ultimately answerable to the Inquisition, and empowered to depose the Primate in certain exceptional circumstances.

Wick: In Complex Protism, a fully generalized Directed Acyclic Graph in which a large (possibly infinite) number of cosmi are linked by a more or less complicated web of cause-and-effect relationships. Information flows from cosmi that are more “up-Wick” to those that are more “down-Wick” but not vice versa.

CALCA 1: Cutting the Cake

A supplement to Anathem by Neal Stephenson

“LET’S SAY THAT EACH serving will be a square, the same width as the spatula. Go ahead and cut in one corner of the pan.”

Dath cut the cake thus:

and then made more cuts thus, to produce the four servings I’d asked for:

“I can’t believe you’re doing this!” Arsibalt muttered.

“If it worked for Thelenes…” I muttered back. “Now shut up,” and I turned my attention back to Dath who was awaiting further instructions. “How many servings do we have there?” I asked him.

“Four,” he said, slightly u

“Now, what if you cut a similar figure but with sides twice as long? So instead of each side being two units—two spatula-widths—it would be—?”

“Four units?”

“Yes. We have four servings here already—if you doubled the size of the figure, how many people could we serve then?”

“Well, two times four would be eight.”

“I agree that two times four is eight. Go ahead and try it,” I said. Dath made more cuts thus:

Halfway through, he saw his error and made a wry face, but I encouraged him to keep going until he was finished. “Sixteen,” he said. “We actually have sixteen servings. Not eight.”

“So, just to review: when we cut a square grid that is two units on a side, we get how many servings?”

“Four.”

“And you just told me that a four-unit grid gives us sixteen. But what if we only wanted eight servings? How many units would our grid have to be?”

“Three?” Dath said, cautiously. Then his eyes dropped to the cake and he counted it out. “No, that gives nine servings.”

“But we’re getting warmer. And now an important thing has changed, which is that you know you don’t know.”

Dath’s eyebrows went up. “That’s important?”

“It’s important to us in here,” I said.

I couldn’t remember what Thelenes had done next when he had done this with a slave-boy on the Plane six mille

I spun the cake around, presenting Dath with an unmarked corner. “Go ahead and cut one square big enough for four servings. You don’t have to cut the individual servings out of it.”

“Can I make lines on the frosting?” he asked.

“If it helps.”

With some hints and nudges from Cord, Dath produced a square like this:

“Good,” I said, “now add three more squares just like it.”

Extending lines he’d already made and adding some new ones, Dath enlarged it to this:

“Now, remind me, how many servings can we get out of that whole area?”

“Sixteen.”

“All right. Now look only at the square in the lower right-hand corner.”

“Is there a way you can divide it exactly in half with only one cut?”

He got ready to slice along one of the dotted lines, but I shook my head. “Arsibalt here is very particular about his cake and he wants to be sure no one gets a larger slice than him.”

“Thank you very much, wise Thelenes,” Arsibalt put in.

I ignored him. “Can you make one cut that’s guaranteed to satisfy him? The pieces don’t have to be square. Other shapes are okay—like triangles.”

With that hint, Dath made a cut like this:

“Now, do the others the same,” I said. He made it like this:

“When you made the first diagonal cut, you cut a square exactly in half, right?”

“Right.”

“And is the same true of the other three diagonal cuts and the other three squares?”

“Of course.”

“So, let’s say I rotate the pan and you look at it this way”:

“What shape do you see in the middle there?”

“A square.”

“And how many servings worth of cake are contained in that square?”

“I don’t know.”

“Well, it’s made up of four triangles, right?”

“Yeah.”

“Each of those triangles is half of a small square, right?”