Elvis the Calculus Dog

Dr. Roland Minton, co-author of “Do Dogs Know Burifications” discusses Elvis the Calculus Dog and his Unique Problem-Solving Skills

Calculus. The word that strikes fear into the hearts of mathematically-challenged students everywhere is a breeze for Elvis, the lovable dog of Hope College professor Dr. Tim Pennings. Dr. Roland Minton, professor of math, physics and computer science at Roanoke, found an article in The College Mathematics Journal by Pennings, a professor at Hope College in Holland, Michigan, about the dog whom Pennings claimed could do calculus. Elvis is a 6-year-old Welsh-Corgie mix and has been the inspiration for much of Pennings’ calculus observations.

The article stemmed from a trip to Lake Michigan when Pennings tossed a tennis ball into the water and watched as Elvis raced to grab it. Pennings noticed that Elvis’ process of retrieving the ball could be transferred into a mathematical equation. He set up an experiment with his students to determine whether Elvis would instinctively choose the optimal path - that is, the most efficient route to the ball. The optimal path allows the person (or dog) to minimize its time of travel over different rates of speed and different mediums. Pennings found that if he threw the ball a certain distance, Elvis would swim directly to the ball if it was close to the shore. However, if the ball was further out in the lake, Elvis would run along the beach until he reached the burification point, or the point in time when he changed his mind about when to leap into the lake, and then scamper into the water.

The experiment so interested Minton that he used it as a problem for his calculus textbook and soon e-mailed Dr. Tim Pennings, quickly forming a unique friendship sown entirely through electronic communication. Minton says they were “having a lot of fun topping each other” with various calculus equations that revolved around Elvis’ innate burification point. Minton and Pennings became so enthralled with the subject that Dr. Pennings suggested Minton write his own article about their findings. Minton, however, felt that it wouldn’t have been right to take the credit, so they collaborated on the article, “Do Dogs Know Burifications?” instead, combining Minton’s ideas with Pennings’ and Elvis’ findings.

Minton and Pennings wrote the article through e-mail in about three months and it was published in The College Mathematics Journal a year later. The two never even met until well after that, when they received a prestigious award, the George Polya Award, for their work from the Mathematics Association of America. The article focuses on Elvis’ burification point and how Dr. Pennings used a general calculus equation to determine Elvis’ optimal path. Pennings’ findings show that when he mathematically calculated the optimal path of Elvis’ route, he arrived at an estimation that was very close to Elvis’ own burification point. This indicates that Elvis may in fact have the ability to problem solve.

Minton says the experiment and the application of Elvis’ actions to calculus provide an excellent visualization for the teaching of calculus and is also an entry into finding out how dogs (and possibly humans) problem solve. Pennings continued the experiment, and instead of standing on the shore, he and Elvis began in the water, and he found once again that Elvis innately found the most efficient path to the stick. This experiment cemented his belief that Elvis has the ability to think ahead when solving a problem.

In honor of Pennings and his beloved calculus dog, Hope College gave Elvis an honorary degree. Today Elvis prefers to chase large sticks rather than tennis balls, and he and Pennings continue to travel the country giving lectures about various calculus equations they have worked together. Minton, on the other hand, does not have dogs of his own, and he says he has no plans to try experiments with his cats because they would likely refuse. Minton is working on the revision of his calculus textbook with his co-author, and although he and Pennings are not officially working on anything new, they do stay in touch. Minton says that Pennings has contributed problems for the revision of his textbook, Calculus.