Math Experts Split the CheckAuthor(s): Ben OrlinSource: Math Horizons, Vol. 21, No. 3 (February 2014), pp. 18-19Published by: Mathematical Association of AmericaStable URL: http://www.jstor.org/stable/10.4169/mathhorizons.21.3.18 .

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Math Experts Split the Check

Ben Orlin

E ngineer: Remember to tip 18 percent, everybody.Mathematician: Is that 18 percent of the pretax total, or of the total with tax?

Physicist: You know, it’s simpler if we assume the system doesn’t have tax.Computer Scientist: But it does have tax.Phys: Sure, but the numbers work out more cleanly if we don’t pay tax and tip. It’s a pretty small error term. Eng: What you call a “small error,” I call a “collapsed bridge.”Economist: Don’t get me started on taxes! If there were no taxes, I would have ordered a second soda. But instead, the government intervened, and by increasing transaction costs, prevented an exchange that would have benefited both the restaurant and me.Eng: You did order a second soda.Econ: In practice, yes. But my argument still holds in theory.

The computer scientist lays a smart phone on the table.CS: OK, I’ve coded a program to help us compute the check.Math: Hmmph. Any idiot could do that. It’s a trivial problem.

CS: Do you even know how to code?Math: Why bother? Learning to code is also a trivial problem.Eng: Uh . . . your program says we each owe $8,400.CS: Well, I

haven’t debugged it yet, if that’s what you’re getting at.Phys: This is a waste of time. Let’s just split it evenly.Econ: No! That’s so ineffcient. Let’s each write down the amount we’re willing to put in, then auction off the remainder at some point on the contract curve.Phys: Huh?Math: Like most economics, that’s just gibberish with the word “auction” in it.Eng: Look, it’s simple. Total your items, add 8 percent tax, and 18 percent tip.Math: Sure. Does anybody know 12 plus 7?CS: You don’t?Math: What do I look like, a human calculator? Numbers are for children, half-wits, and bored cats.

The engineer looks at the cash they’ve gathered.Eng: Is everyone’s money in? It seems we’re a little short . . .Phys: How short?Eng: Well, the total was $104, not including tip . . . and so far we’ve got $31.07 and an old lottery ticket.Phys: Close enough, right? It’s a small error term.Math: Which of you idiots wasted your money on a lot-tery ticket?Econ: I should mention that I’m not planning to eat here again. Are any of you?CS: What does that matter?Econ: Well, in a noniterated prisoner’s dilemma, the dominant strategy is to defect.Eng: Meaning?Econ: We should be tipping 0 percent, since we’ll never see that waiter again.Math: That’s awful.

18 February 2014 : : Math Horizons : : www.maa.org/mathhorizons

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Phys: Will the waiter really care—0 percent, 20 percent? Let’s not split hairs. It’s a small error term.

The engineer looks up from a graphing calculator.Eng: All right. I’ve computed the precise amount each of us should pay, using double integrals and partial derivatives. I triple-checked my work.Math: Didn’t we all order the same thing? You could have just divided the total by fi ve.Eng: I could? I mean . . . of course I could! Shut up! You think you’re so clever!Econ: So, we’re all agreed on a 0 percent tip?CS: Well . . . the waiter did bring only two orders of fries for the table.Phys: We only ordered two.CS: Exactly. We got the 1st order, and the 2nd, but never the 0th.Econ: I’ll be frank. At this point, my self-interest lies in not paying at all. And the economy prospers when we each pur-sue our individual self-interest. See you later!

The economist dashes off . The engineer and computer scientist glance at one another, then follow.Math: Looks like it’s just you and me now.Phys: Good. The two-body problem will be easier to solve.Math: How?Phys: By reducing it to a one-body problem.

The physicist scampers away.Math: Wait! Come back here!Waiter: I notice your friends have gone. Are you done with paying the check?Math: Well, I’ve got a proof that we can pay. But I warn you: It’s not constructive. ■

Since completing his BA in math in 2009, Ben Orlin has taught high school courses including calculus, sta-tistics, psychology, biology, and (somewhat dubiously) earth science. He has written for Slate and The Atlantic, and he blogs at Math with Bad Drawings (http://mathwithbaddrawings.com/).Email: ben.orlin@gmail.com

http://dx.doi.org/10.4169/mathhorizons.21.3.18

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Ty Devries, somethingofthatilk.com

Uncountable sets

“ . . . Infi nity-one! Infi nity-two! Infi nity . . . “

Grant Snider, incidentalcomics.com

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