Spring 2007

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From the Director

30 Second Math Lessons, or
Math Encounters Madison Avenue

Douglas N. Arnold
Doug Arnold,
IMA Director

Four times a year I recruit a top mathematician to come to the IMA for our Math Matters public lecture series. I lay before him or her a daunting challenge: to get across a message about math—how important, connected, exciting, and just plain fun it is—to a very diverse and mostly non-expert audience. The 50 minute academic hour can seem very short for the task. The remarkable success our lecturers have achieved (we have built up a loyal audience of several hundred people) is thanks to lots of planning and preparation as well as talent and skill on the part of the speakers. Expectations of how much can be communicated must be reigned in and every minute made to count.

I recently experienced this sort of challenge myself, concentrated to nth degree, when I had a chance to collaborate with creative professionals working with one of the world's leading advertising agencies and a top production company to produce television ads for the 2007 Masters Golf tournament. The goal: to get out a message about math—how important, connected, exciting, and just plain fun it is—in 30 seconds.

If you want to see the results before reading further, you can see the ads at this site (although the resolution is very low, so check the stills below), or, more clearly, at The Science of a Drive educational web site, which is discussed below.

The occasion was the 2007 Masters Golf Tournament held in Augusta, Georgia in April. ExxonMobil, the advertiser, seized this opportunity to pitch a simple message to the TV audience of millions of people. The message: Math and science are everywhere. ExxonMobil has been an active supporter of efforts to improve math and science training in U.S. schools, and has teamed up with two-times Masters Golf Champion Phil Mickelson and his wife Amy to create the Mickelson ExxonMobil Teachers Academies. These ads were part of a related public relations effort.

My connection with the campaign began with an inquiry at the end of January from the advertising conglomerate Euro RSCG Worldwide which was developing the ads. (My thanks to Joe Gallian, the president of the Mathematical Association of America, for the referral.) The agency had at this time the basic story line for the two ads, to be called "Swing" and "Eraser." Yes, a 30 second ad has a story line, with a beginning, development, and finale. Here is the beginning of the story line for "Swing:"

Open on Phil Mickelson about to drive his ball off the tee. As he begins his swing, the action slows down, and all kinds of graphs and equations suddenly appear around his club as it rotates up and then down to strike the ball. The equations and graphs rapidly change, appearing to track the math and physics that equate to the angle of Phil's swing, the force it generates, etc.


The second ad, "Eraser," begins with a nine-year old girl erasing a chalk board and then banging the chalk dust from the erasers at the window of her urban school. As from Phil's swing, equations, graphs, and diagrams swirl out of the chalk dust and constantly metamorphize, form, and reform as the dust blows away, leading to a whirlwind tour of the world, passing by striking venues and a variety of human activities from Lisbon to Shanghai harbor (pictured here with one of Maxwell's equations visible in the lower right).

My role, which I eagerly accepted, was to provide the equations, graphs, and diagrams which would deliver the message "math and science are everywhere." I worked with several artists from the production company, Motion Theory, who were simultaneously filming and interacting with me on the equations. I was very impressed by the importance they placed on getting the math right. The equations had to be correct and had to be relevant, even though they would swirl by so quickly almost no one would know. For "Swing," I researched such articles as "On the flight of a golf ball in the vertical plane," R. Stengel, Dynamics and Control 1992, and "The vibrational mode structure of a golf ball", J. Axe et. al., J. Sports Sciences 2002.

One challenge was to come up with an equation that not only related to golf, but would somehow convey the relationship to the audience. Not easy! After all, even most mathematicians would have a hard time recognizing the equations for a double pendulum in the first image above, and even a harder time recognizing them as a reasonable mechanical model of the shoulder-arm-club dynamical system. The typical viewer of the Masters tournament, I would claim, is unlikely to recognize any equation whatever, except perhaps e=mc2, which is not highly relevant to golf. (The equation does appear in the Shanghai harbor image above, since nuclear power is a source of electricity there.) My approach to this conundrum is the same I take to achieve readability in my research papers: a careful choice of notation. Thus a key equation in "Swing" is


which relates the launch velocity of the ball to the velocity of the club head and their relative masses. (Here is an exercise for the mathematically inclined reader: using conservation of momentum and energy, derive this formula with the coefficient of restitution, cR, equal to unity, and conclude from it that the ball will never launch at more than twice the speed of the impacting club head. Math is indeed everywhere!)

The final part of this work was to provide the mathematical support to the web team at Euro RSCG in the design of an educational web site called The Science of a Drive. The web site builds on the message of "Swing" with explanations of some of the math and physics behind a golf drive: the double pendulum, energy transfer, drag and lift, and similar concepts. The web designers were amazing, and the speed with which this went from rough concept to polished online site—in just a few weeks—took my breath away. The site is aimed at a grade school audience but has proven interesting even to mathematicians. I encourage you to visit the site. Maybe you can guess which parts are based on my Matlab simulations.

This mathematician encountered Madison Avenue and Hollywood, and came away very impressed. And convinced: you can deliver a lesson about math in 30 seconds flat—that it is important, connected, exciting, and just plain fun.