## Tuesday, December 22, 2009

### Does your dog know calculus?

Friday night, Prof. Orzel talked to us about how to teach your dog physics.

Perhaps Elvis, pictured above, would make a good student of physics. His owner, Prof. Tim Pennings of Hope College, has verified experimentally that Elvis "knows" calculus, or at least that he behaves as if he knows calculus.

Prof. Pennings reached his conclusions by taking measurements of Elvis running and swimming to fetch balls he threw into Lake Michigan, but he also suggests that you could conduct the same kind of experiment on your dog by throwing a stick into some deep snow near a cleared sidewalk.

We confess that although he made good choices, Elvis does not know calculus. In fact, he has trouble differentiating even simple polynomials. More seriously, although he does not do the calculations, Elvis’s behavior is an example of the uncanny way in which nature (or Nature) often finds optimal solutions. Consider how soap bubbles minimize surface area, for example. It is fascinating that this optimizing ability seems to extend even to animal behavior. (It could be a consequence of natural selection, which gives a slight but consequential advantage to those animals that exhibit better judgment.)

Finally, for those intrigued by this general study, there are further experiments that are available, other than using your own favorite dog. One might do a similar experiment with a dog running in deep snow versus a cleared sidewalk. Even more interesting, one might test to determine whether the optimal path is found by six-year-old children, junior high aged pupils, or college students. For the sake of their pride, it might be best not to include professors in the study.

Do dogs know calculus? College Mathematics Journal