I Admit It: Mathfolk Are Weird

Had you been in the main office of the math department yesterday morning, you might have observed the following scene, as I and one of my colleagues discussed whether a certain thing was possible.

I held out my left arm straight in front of me, palm vertical, and said "One two".
I crossed my left arm with my right, palm also vertical, at about a sixty-degree angle: "One three".
I dropped my right arm, turned my left palm horizontal, and slashed my left arm across horizontally: "Four five".
My colleague nodded and grunted agreement.

Three Times

"What I say three times is true."

I've always associated that line with Lewis Carroll's The Hunting of the Snark. (Actually, I've always associated it with my one-time teacher Saunders MacLane, who used it as a mnemonic for one of the peculiar features of Heyting logic; but I'm pretty sure he got it from Carroll.) But I'm reading Jim Butcher's Summer Knight, which at one point suggests that it originates in a piece of fairy-lore, to the effect that if one of the fae says the same thing three times, it must either be telling the truth or do whatever it can to make it the truth. Does anyone know whether Butcher is making this up or quoting some actual legendry?