Friday, February 24, 2006
Mathematics of fetch
At Science News, Ivars Peterson explores the mathematics of dogs playing fetch. Specifically, dogs attempt to identify the optimal path toward the ball or stick they're fetching. That canine approach isn't unlike using calculus to model and solve the problem. Peterson's story starts with an introduction to Hope College mathematician Tim Pennings and his dog Elvis. From the article:
When Elvis and Pennings go to the beach, they always play fetch. Standing at the water's edge, Pennings throws a tennis ball out into the waves, and Elvis eagerly retrieves it. When Pennings throws the ball at an angle to the shoreline, Elvis has several options. He can run along the beach until he is directly opposite the ball, then swim out to get it. Or he can plunge into the water right away and swim all the way to the ball. What happens most the time, however, is that Elvis runs part of the way along the beach, then swims out to the ball.Link
Depending on the dog's running and swimming speeds, the strategy that Elvis follows appears to minimize the time that it takes to get to the ball. Indeed, Pennings found by experiment that Elvis performs in a way that closely matches a calculus-based mathematical model of the situation.
UPDATE: I'm aware that others, including Richard Feynman, have explored similar, er, waters. (For example, a lifeguard racing to save someone who is drowning.)
UPDATE: For more on animals and math, check out Keith Devlin's book The Math Instinct. Link
posted by David Pescovitz at 11:20:15 AM permalink | Other blogs' comments
