## The failure of Uresh

Mmm. There’s an excerpt of Patrick Rothfuss‘s the Wise Man’s Fear over on the Tor site.

One: Eagerly waiting, oh yes. Just a few more days.

“You can divide infinity an infinite number of times, and the resulting pieces will still be infinitely large,” Uresh said in his odd Lenatti accent. “But if you divide a non-infinite number an infinite number of times the resulting pieces are non-infinitely small. Since they are non-infinitely small, but there are an infinite number of them, if you add them back together, their sum is infinite. This implies any number is, in fact, infinite.”

“Wow,” Elodin said after a long pause. He leveled a serious finger at the Lenatti man. “Uresh. Your next assignment is to have sex. If you do not know how to do this, see me after class.”

Which I could, if I was feeling uncharacteristically umbrage-ready, take as an insult to all mathematicians, ever, even to Gottfried Leibniz, “the Amor-Goat of Hanover”. But I won’t, because obviously Uresh is so ordered to seek out the opposite or the same sex because he’s been at work for so long he no longer thinks straight. (Or even rigorously bent.)

Well, that, or then the mathematics of Kvothe’s world aren’t yet up to the Cantorian level of understanding infinities, c. 1874; Uresh may be agreeing with one of the so-called “paradoxes” of Greek mathematics, most of which were just the result of too much common sense. (In mathematics, “common sense” is a dangerously misleading tool. Common sense doesn’t work for uncommon subjects!)

Or then Uresh’s just trying a fairly despicable bit of sleight-of-hand, hoping Mr. Elodin isn’t a mathematics professional (professorial?) thought he acts like one.

Namely, his second assertion is all wrong. He’s saying that you can take a finite number and break it into an infinite number of non-zero pieces. This is true, though only for some infinite divisions.

This division would then make the pieces add up to infinity, which would be highly peculiar. This ain’t so, which can be illustrated with an easy example.

Take the number one. (A stick one foot in length if that helps you.) Split it into two pieces, 1/2 and 1/2.

Split the second half (but not the first) into two more pieces, 1/4 and 1/4. You have 1/2, 1/4 and 1/4.

Split the second fourth into two more pieces, 1/8 and 1/8. You have 1/2, 1/4, 1/8 and 1/8.

Go on likewise, and don’t worry about stopping.

Doing so, you get the pieces 1/2, 1/4, 1/8, 1/16, 1/32 and so on; you get infinitely many pieces, each of which is of a finite, fixed, non-zero size. And adding them all back together clearly (?) leads back to the same one-piece, not to some bogus infinity!

We must refrain from splitting both pieces, because we want pieces of non-zero size. If we ever split every piece, we would get first two halves, then four fourths, then eight eighths, and so on; clearly if this went on no piece could be of any size greater than zero: after $n$ splits, each piece is a one-$2^n$th and this is, for large enough $n$, smaller than any fixed non-zero size you might fancy.

So Uresh was thinking, “Infinite times a non-zero thing is infinity. Holy smokes!” — but he failed to think that “Damn! But I always get either just zero things, and then infinite times zero is an Amyr-awful mess; or then I get things which are of different non-zero sizes, and those sizes don’t add up to infinity!”

So if we were sticklers for mathematical accuracy and assuming Pat meant Uresh to be right and in full possession of modern mathematical rectitudes (I don’t feel he did), Uresh would have said something like this:

“You can divide infinity an infinite number of times, and the resulting pieces will still be infinitely large,” Uresh said in his odd Lenatti accent. “But if you can divide a non-infinite number an infinite number of times so that the resulting pieces are non-infinitely small, though this is not true for every division. Since they are non-infinitely small, but there are an infinite number of them, if you add them back together, their sum is infinite. This implies any number is, in fact, infinite.the original number obviously; what do you take me for, some Lenatti lackwit, eh? This is math, not magic.

“Wow,” Elodin said after a long pause. He leveled a serious finger at the Lenatti man. “Uresh. Your next assignment is to have sex. If you do not know how to do this, see me after class.Your mathematical prowess impresses me. Please tell me how to get some sweet, sweet loving from the math-hungry girls of Imre.

“Sure thing”, Uresh said. “Here’s how you prove Hölder’s inequality —“

— but that’s where I stop, before this devolves into fanfic about Uresh the Integrator, whom you may have heard of: Uresh the Bloodless, Uresh the Arcane, Uresh Kingkiller — Uresh that burned down the conjecture of Trullheim; Uresh who spent a night with the Rectorian and left with both his sanity and his life; he that gained tenure at the University at an age younger than most people are allowed in; the same Uresh that has talked to Administrators, loved numbers, and written exercises that make the students weep.

Like I said, that’s where I stop.

### 2 Responses to “The failure of Uresh”

1. krysjez Says:

heh, that was interesting! can’t wait for WMF to come out.

2. scubabob Says:

That was hilarious XD