Photo by Tom Campbell

Any scientist can find the volume of a bottle. But only a scientist with a sense of humor like Bernie Tao could figure out how many M&M’s it takes to fill a three-dimensional representation of a zero-volume bottle.

Bernie Tao is out to prove that science and humor can coexist.

Tao, a Purdue professor of ag engineering and food science, recently wrote an article for the bi-monthly science humor magazine The Journal of Irreproducible Results. His article was titled “Empirical Measurement of M&M’s Contained in a Standard Bottom-Mouth Erlenmeyer Klein Flask and Comparisons to Theoretical Models”.

OK, nobody said this humor thing was easy.

“The magazine is well known in the scientific community,” Tao says. “Scientists find it hilarious. Some very well-known scientists, even Nobel Laureates, have written in this publication.”

But it sometimes may take a Nobel Laureate to understand the humor.

“Well, yes,” Tao admits, “some of the humor is not generally understandable to the lay community.”

Tao saw a unique opportunity on the Internet back in 2001: “How many M&M’s does it take to fill a standard Acme bottom-mouth Klein Bottle?” a Web site asked. It provided a picture of such a bottle, filled with M&M’s, and said that whoever arrived at the correct amount would receive the bottle and the stale (by then) M&M’s.

So what’s a Klein bottle? A mathematician will tell you that it is a closed, non-orientable, boundary-free manifold. A real one can only exist in four dimensions, while our world, sadly, is three-dimensional. In lay terms, a Klein bottle is what appears to be a glass container, but since it has only one side, it really isn’t a “container” at all. Think of a Möbius strip — a strip of paper given a half twist and then joined at the ends. The paper now has only one side and only one edge.

A Klein bottle takes the concept of the paper to a third dimension, but it is only an approximation of what a real bottle would look like in four dimensions. The vessels are made by Cliff Stoll, a former professor at UC-Berkeley with a skill for glass blowing and a penchant for the ridiculous.

“The contest seemed like a good way to poke fun at the way chemists, engineers, mathematicians and liberal arts majors do things,” Tao says. “I was like a little kid looking at a jar full of jelly beans in the candy store window. I was that kid who wanted to win the prize for guessing the number of beans in a glass jar.”

But in this case, Tao wanted to win the container instead of the contents.

“This research was performed solely for the purpose of obtaining such a flask absolutely free, either with or without M&M’s,” Tao wrote in the abstract.

“It was something I banged out in a couple of hours, using four different methods of ‘analysis’ to calculate the volume of each M&M,” he says.

To sound more scientific, the M&M’s became “oblique spheroids.” And during the experimentation, Tao points out, “no M&M’s were harmed.”

Eaten, yes. But not harmed.

He attacked the problem using four different scientific methods, utilizing (1) physical chemistry, (2) mathematical estimation, (3) liberal arts estimation, and (4) engineering estimation.

Each approach yielded different results, ranging from 482.8 to 559.8. How does Tao account for the wide-ranging results? Well, scientifically, of course.

“Method 3 clearly has significant shortcomings vs. the other methods,” he analyzed. That might be because one of the primary numbers used in the calculation was 20, “the number of human digits used to eat M&M’s.” Even if human digits are valid criteria, it doesn’t take a rocket scientist to realize that you probably can count on one hand the number of people who eat M&M’s with their toes.

“The value obtained is nearly 14 percent different from the values obtained by other methods, although the methodology employed is highly appealing and very simple. It does not account for structural geometry, physical chemistry, or statistical variation, and has very little sound theoretical mathematical basis. Additionally, the veracity of the experimentalist may be in question ... due to the discovery that following the experimental procedures, approximately 25 percent of the original mass of M&M’s provided to the researcher were absent.”

Which, of course, is scientific jargon for eaten.

“I’m not sure Purdue wants a whole lot of publicity for something like this,” Tao says, “so I said the research was done at a large Midwestern university in the Soybean and Corn Belt. I just hoped people would get a chuckle out of this.”

But the joke is on Tao. For all of his work, he was published in a peer-review publication, something he has done more than 50 times in his academic career.

But no free flask was forthcoming.

Contact Tao at tao@purdue.edu