It's a Math World for Animals（2）

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    Pennings wondered if Elvis was instinctively taking the fastest possible route to the ball.First,he measured how fast Elvis runs and swims.Then,he threw a tennis ball into the water and let the little Welsh corgi go.

    "I ran after Elvis with a screwdriver,"says Pennings,who works at Hope College in Holland , Michigan ."Where he turned toward the water,I drove a screwdriver into the sand.While he was swimming to the ball,I ran and grabbed a tape measure and beat him to the ball."Man and dog ran back and forth like this for more than 3 hours.After throwing out trials with bad tosses or high waves,Pennings had 35 sets of measurements.Then,he went home and did some calculations,using calculus to find the fastest route.

    "I did all the math,"Pennings says,"and I figured out that where Elvis jumps in is pretty much perfect.He kind of naturally knows the right spot to jump in."

    It took the grown man about an hour to come up with the same solution that the 3-year-old dog could figure out in a fraction of a second.But is the dog really doing the math? "Elvis is doing calculus in the sense that he somehow knows how to find the minimum time to get to the ball,"Pennings says.

   Pennings suspects that other creatures have naturally learned the most efficient ways to do things over millions of years of evolution."There might be all sorts of things like that in nature,"he says.