|Ivars Peterson's MathTrek|
September 23, 1996
SAM (calling out while waving to another worker): Hey, Waldo, good torch work in there.
BUDDY (to SAM): You thought he did good torch work?
SAM: Heck no, but are you gonna insult a guy holding a blowtorch?
(Both laugh, pause ...)
The discussion then turns to the subject of casting, from the tight job market to the slow, boring work of manufacturing miniature souvenir replicas of the Empire State Building. They begin talking about what kinds of objects might be more interesting to cast. One wryly observes that all they ever get to cast is a deformed version of a ball. What about a doughnut or some other object with as many holes as you want?
Their topic is really topology, and much of the talk concerns what kinds of shapes can be cast using a two-piece mold. Their quick "paper napkin" sketches look suspiciously like diagrams on overhead transparencies. The discussion also takes place on a stage, and the dialog is from a two-act play called "Casting About: About Casting."
Edward Burger and Colin Adams aren't yet as well known as such famous comedy teams as Laurel and Hardy, Abbott and Costello, and Martin and Lewis, but they attracted a capacity crowd to a large auditorium at the University of Washington for a performance of their play during last month's Seattle MathFest.
Burger and Adams are not only performers but also math professors at Williams College in Williamstown, Mass. They bring antic energy, slapstick humor, and pointed satire to their presentations of mathematics, sometimes nudging and sometimes shocking their audience into grasping tricky concepts.
Continuing a discussion of doughnuts and handlebodies (apples threaded with wormholes):
SAM: Yeah, mighty tasty, but a bit on the hefty side. Once it got in your stomach, it didn't budge for days at a time. They called it a glazed handlebody. (pause) Oh, hey look, there's Mario. That guy is one of the great casters of our generation.
BUDDY: Is that right?
SAM: Yeah. One time he bronzed a pair of shoes in 37 seconds flat.
BUDDY: But I thought the record for bronzing shoes was 33 seconds.
SAM: Yeah, they didn't count it, cause someone was wearing the shoes at the time.
SAM: Yup! Broke the cardinal rule of bronzing.
BUDDY and SAM (together): Make sure no one's in them!Referring to a recent attempt at the University of Rochester to eliminate its graduate mathematics program:
SAM: You know he used to be at the plant in Rochester, casting little models of Niagara Falls. He lost his job when they downsized.
BUDDY (stunned): What?! Rochester downsized?
SAM: Yup. The company almost cut the entire casting division, but with some pressure from the MAA and the AMS, they decided to back off.
BUDDY: The MAA?
SAM: Yeah, the Metalworkers Association of America.
BUDDY: Oh yeah, and the American Molders Society. Boy, those are powerful organizations, I'm telling you.
The play also takes a poke at calculus and math education reform.
BUDDY: ....what do you think about all this hype about casting reform?
SAM: I have mixed feelings. On the one hand, I liked the old-fashioned free-form methods of casting. This new technology, the exact measurements, I don't know. What do you think? Should we use calculators in the cast room?
BUDDY: Hey, I'm all for it. Ultimately, we're in the business of molding and if technology allows you to mold a better product, then I'm all for it."
The idea of presenting a play, using character and comedy to convey mathematical theorems and proofs, is rather unconventional, Burger admits. "Perhaps this ... venture will lead into other new and creative means of sharing mathematics with others," he says. "That is our hope."
Indeed, Burger and Adams later presented a lively, illustrated lecture on how not to teach, acting out the transformation of a lackluster lecturer into a dramatic classroom presence. Their subsequent workshops on "discovering the performer in you" attracted plenty of participants.
Burger and Adams have also brought the same spirit to other endeavors related to math. Burger's main interest is in number theory and the geometry of numbers, while Adams specializes in knot theory and various aspects of topology.
In a recent article in a math journal, Burger and coauthor Thomas Struppeck wrote about infinite series and the problem of determining whether the sum of the terms of a series converges to a particular value. They gave their paper the subtitle: "You can sum some of the series some of the time and some of the series none of the time ... but can you sum some of the series all of the time?"
Adams has performed as Mel Slugbate, the irrepressible tour guide for a bus company offering reasonably priced excursions into the universe and beyond. Ever wonder if Earth is doughnut-shaped? Want to try out some alternative models of the universe? "No previous topological experience is assumed," Adams insists.
Of course, Burger and Adams aren't the first to bring humor to mathematics. At the moment, however, they're casting a wide net and ensnaring a steadily growing audience.
Now, back to the show. After a spirited description of how to "tile" a bathroom -- that is, fill the space within the bathroom -- with knotted doughnuts, Burger and Adams continue.
BUDDY: Now look. We are doing this same operation to every knotted doughnut in the bathroom. So now the entire bathroom is filled with these knotted doughnut-shaped tiles.
SAM: I love it. Seems totally pointless, but I love it. We should make and sell these tiles.
BUDDY: Hey, you know what we should do? The next time there's a big math conference, we could go there and sell these knotted tiles!
SAM: Hey yeah, but I got a better one. (laughing) Maybe at their next conference, we could go and give a presentation.
BUDDY: Yeah right. (laughing) You and me talking to an auditorium filled with mathematicians about casting and tiling. That'd be a good one. Come on, lunch is over. We better get back to work.
Mathematics and humor are really no strangers to each other. Humor arises out of understanding juxtaposed with surprise. The reward for grasping a novel concept lies in the pleasure of a smile, a loud guffaw, or a resigned groan at some ingeniously constructed use of that idea. There's plenty of room for such play in mathematics.
Copyright © 1996 by Ivars Peterson.
Burger, Edward B., and Thomas Struppeck. 1996. Does [Summation 1/n!] really converge? Infinite series and p-adic analysis. American Mathematical Monthly 103(August/September):565-577.
My thanks to Colin Adams and Edward Burger for providing excerpts from the script for "Casting About: About Casting." Adams wrote the play with help from Burger. Burger can be reached at Edward.B.Burger@williams.edu and Adams at Colin.Adams@williams.edu.
Comments are welcome. Please send messages to Ivars Peterson at email@example.com.