Pekkat

Pekkat proves things in rock. A Chthonari burrow settlement is tuned as it is dug, so that the settlement itself rings, and in the part of the Undersong Belt where Pekkat works, some of that tuning is mathematics: a relationship between parts of the structure that holds, felt directly by anyone standing on it, or does not.

The name is a struck signature, as every Chthonari name is: a strike, the same strike held, and a scrape left open to ring, spelled the way a human ear renders it. The record renders Pekkat as they, as it renders every Chthonari person.

Known History

• Born in the Undersong Belt, in a burrow settlement the record does not name. Which settlement, and what it is tuned to, is the Belt's own business.
• Tutors Federation mathematicians who come to the Belt to study under Chthonari teachers, the practice the species page records. A student who wants to learn from Pekkat has to stand on the rock. Nothing Pekkat teaches reaches a student through air, and nothing reaches a student who is not in contact with structure. How a student who cannot feel the rock receives what Pekkat teaches, the record does not describe; the students' own reports say only that they do, and that what they take home is, by Pekkat's standard, a description.
• Active in 2826 UCSD. The record does not fix how long Pekkat has taught, or how many students have come.

Character Notes

Chthonari philosophy has argued for millennia whether the distinction between a numerical ratio and a harmonic one is worth maintaining at all, since to a people who perceive resonance directly the two are close to the same fact. Pekkat keeps the distinction, and the reason is one a human mathematician would recognise. A settlement can be retuned. A theorem cannot. If retuning the rock would change the result, what was carried there was a harmony. If the result survives every retuning, it was a theorem, and the rock was only the way it was written.

That is the same line the record draws in Mathematics and Its Notations: the theorem is discovered and holds across the whole regime, and the notation is a people's own. Pekkat's students report what Federation students of Chthonari tutors have always reported. They arrive at the same theorems by a different road, and what took them years of abstraction is, for a Chthonari student, nearer to hearing.

The record does not translate Pekkat's proofs into written mathematics, and it would be wrong to. A proof carried in resonance and its written counterpart prove the same theorem. They are not the same proof, and the record keeps them as two.

What Pekkat Cannot Do

Hear a voice, or read a face. Teach anyone who will not stand on the rock. Carry a proof off the Belt except as a description of one, which, by Pekkat's own standard, is a different thing.

See also

• The Chthonari
• The Undersong Belt
• Mathematics and Its Notations
• Kettsa, a Chthonari officer of the Engineering Corps