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# Preposterous Universe

Thursday, July 15, 2004

Is that a Riemann or Lebesgue integral?

Terry Teachout has a nice reflection on the social disapprobation that accompanies an unseemly regard for the artistic and intellectual side of life (especially for children). I have nothing deep to add, except that his mention of a hypothetical waitress who could quiz him knowledgeably on what he was reading reminded me of this well-known math joke:
The first mathematician says to the second that the average person knows very little about basic mathematics.
The second one disagrees, and claims that most people can cope with a reasonable amount of math.
The first mathematician goes off to the washroom, and in his absence the second calls over the waitress.
He tells her that in a few minutes, after his friend has returned, he will call her over and ask her a question.
All she has to do is answer: `one third x cubed'.
She repeats `one thir -- dex cue'? He repeats `one third x cubed'.
Her: `one thir dex cuebd'? Yes, that's right, he says.
So she agrees, and goes off mumbling to herself, `one thir dex cuebd...'.
The first guy returns and the second proposes a bet to prove his point, that most people do know something about basic math. He says he will ask the blonde waitress an integral, and the first laughingly agrees.
The second man calls over the waitress and asks `what is the integral of x squared?'.
The waitress says `one third x cubed' and while walking away, turns back and says over her shoulder `plus a constant'!
Okay, it's not very funny if you don't know much calculus (the waitress was giving a more precisely correct answer than the mathematicians had any right to expect, demonstrating that they were both handicapped by inaccurate stereotypes). But I noticed something else: looking for a copy of the joke through Google, the version I just transcribed is only the second-most-popular version. More popular is the following:
Two mathematicians were having dinner in a restaurant, arguing about the average mathematical knowledge of the American public. One mathematician claimed that this average was woefully inadequate, the other maintained that it was surprisingly high.
"I'll tell you what," said the cynic. "Ask that waitress a simple math question. If she gets it right, I'll pick up dinner. If not, you do."
He then excused himself to visit the men's room, and the other called the waitress over.
"When my friend returns," he told her, "I'm going to ask you a question, and I want you to respond 'one third x cubed.' There's twenty bucks in it for you." She agreed.
The cynic returned from the bathroom and called the waitress over. "The food was wonderful, thank you," the mathematician started. "Incidentally, do you know what the integral of x squared is?"
The waitress looked pensive, almost pained. She looked around the room, at her feet, made gurgling noises, and finally said, "Um, one third x cubed?"
So the cynic paid the check. The waitress wheeled around, walked a few paces away, looked back at the two men, and muttered under her breath, "...plus a constant."
You see the difference? In the first version, with which I was familiar, I always imagined that the waitress was having fun teasing the mathematicians, and walked away smiling. But in the second version it's clear she is just pissed off and grumbling. Now it seems much less funny to me, although obviously a lot of people prefer this version.

It's amazing what psychological insights you can reach just be wandering through the web with Google as your only guide. The internet isn't anything weird and scary, it's just a window into our brains. Okay, that is pretty scary.

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