Mathematician: Dogs do calculus

Talk at UT to address topic, focusing on games of fetch

Mathematician Dr. Tim Penning and his Welsh corgi, Elvis, will be at the University of Toledo to discuss
Mathematician Dr. Tim Penning and his Welsh corgi, Elvis, will be at the University of Toledo to discuss "Do Dogs Know Calculus?" at 7:30 p.m. Tuesday, Nov. 13 in Memorial Field House Room 2100.

Dogs are undeniably good at many activities.

Many of them are pros at catching balls and Frisbees. Would it be too much of a stretch to say it's their innate math abilities that make them so good at snagging that ball from mid-air?

Not at all, according to mathematician Tim Pennings, who ponders whether his dog, Elvis, might actually know calculus whenever he plays catch with the 6-year-old Welsh corgi.

The duo will be at The University of Toledo at 7:30 p.m. today to discuss the topic in Memorial Field House, room 2100.

Since a typical calculus problem involves finding the optimal path from one place to another while traversing two different mediums involving variable speeds, it's only logical that dogs – perhaps innately --- are practicing some form of that when they go after a Frisbee, Mr. Pennings said.

“The talk explains how Elvis (and other dogs) can instinctively find the optimal (quickest) path to a ball -- even though it is not necessarily the shortest distance,” said Mr. Pennings an associate professor of mathematics at Hope College in Holland, Mich.

When a ball is thrown from shore into the lake, Elvis always manages to find the quickest path, seeming to know that running speed is greater than swimming speed.

When the ball is thrown, Elvis could choose from among three general options, Mr. Pennings said: Hop into the water immediately and swim straight for the ball (the shortest route but slow because it involves swimming the greatest distance). Or the dog could choose to run along the shore until opposite the ball and then swim after it, yielding the shortest amount of time in the water but involving more time running. His final choice is to run along the shore partway and then swim for the ball. With repeated trials, Mr. Pennings found that Elvis chose the third option every time.

Another theme in the talk is that nature often finds optimal solutions. Using math to model nature is an interesting process and math sometimes tells things that we would not otherwise even guess at, “thus, it's good to know math,” Mr. Pennings said.

The lecture begins with Elvis demonstrating his intense desire to retrieve a ball.

“He also is involved at other points throughout,” Mr. Pennings said. “Otherwise, I try to keep him from stealing the attention. He loves it all. He is very much at home in colleges and universities.”

The pair were filmed in action for a program called “What are animals thinking” which was shown on PBS last Wednesday. The popular dog also has appeared on BBC, NPR and FOX.

“Elvis and I have given the talk about 150 times,” Mr. Pennings said. “Many of those are repeats at area high schools, but we have probably visited 20 to 30 institutions, including the University of Notre Dame, Duke, Boston University, and the University of Hawaii.”

The free, public talk is sponsored by the UT College of Natural Sciences and Mathematics, the UT Mathematics and Statistics Department, Monroe County Community College, and the Pi Mu Epsilon National Mathematics Honor Society, the Ohio Gamma Chapter, which will hold its annual induction ceremony at the start of the event.

Contact Tanya Irwin at: or 419-724-6066.