Friday, February 24, 2006

Do Dogs Know Calculus?

I found this article from Science News fascinating:

Calculating Dogs

Ivars Peterson

It all started with Elvis.

In 2003, mathematician Tim Pennings of Hope College in Holland, Mich., revealed to the world that his Welsh corgi, Elvis, appears to be solving a calculus problem when finding the optimal path to fetch a ball. In this case, optimal path means minimizing travel time.

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.

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.

"It seems clear that in most cases Elvis chose a path that agreed remarkably closely with the optimal path," Pennings argued in the May 2003 College Mathematics Journal.

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