Baseball Players And Fish Are Naturals At Math and Physics

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WITH the baseball season under way, fans might ponder this question. Why is an outfielder like a horsefly or teleost fish?

The answer to this odd little riddle lies at the core of an outfielder's skill, according to recently reported research.

Actually, there should be no trick to being in the right place at the right time to catch a fly ball. It's the old ballistic-missile problem. The missile -- baseball or weapon -- follows a parabolic trajectory from launch to impact. Track its initial ascent, make a few split-second calculations, and you will know where and when it will come down.

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But outfielders don't have time for fancy math, and a computer would get in their way. They have to use natural human capability that is fine tuned to accomplish the same sort of thing.

Trying to find out what that capability is has exercised psychologists for decades. Now Michael McBeath and Dennis Shaffer of Kent State University at Kent, Ohio, and Mary Kaiser of the NASA Ames Research Center at Moffett Field, Calif., think they have a plausible explanation. In their research paper published recently in the journal Science, they describe what they call their ''model'' of an outfielder's skill.

It involves a simple -- and unconscious -- strategy in which the fielder doesn't bother trying to figure out where the ball is going in three-dimensional space or when it will reach a certain point. Instead, the player is just concerned with the two-dimensional trajectory of the ball as seen against the sky or other background. In other words, the player is concerned with the perceived image of the ball moving in two dimensions. There's no need to know the distance to the ball or to home plate.

This also means the player doesn't need to know -- and, indeed, doesn't know -- where or when the ball will come down. The way the player gets to the right place at the right time to make the catch is by maintaining a balance between the vertical and lateral angular change of the image of the ball. The researchers call this following the ''optical'' ball as opposed to the actual physical ball.

In practice, according to this theory, the player runs in such a way that this optical ball follows a straight line toward the fielder. If it appears to curve up from or down toward the player's horizon, he adjusts his path and running speed to keep the optical ball moving straight. The result is that the fielder stays more or less under the ball and automatically intercepts it. This strategy also automatically corrects for deviation of the real ball from a pure parabolic trajectory because of spin, wind, or air drag. It does have the unfortunate side effect of leading an inattentive player smack into the wall if the ball goes out of the field.

The scientists tested their theory with students who were also fielders. In one experiment, they videotaped fielders' actions. In a second experiment, the fielders ran with video cameras on their shoulders that tracked the ball. The results support the theory. This may not be the only visual clue fielders use. But it does appear to be a major factor.

What does it have to do with fish and flies? The scientists explain that the ball-tracking strategy makes use of the perceptual ability to keep a constant relative angle between two objects in motion, such as the baseball and the fielder trying to catch it. The ability may be widespread among animals.

The scientists note: ''Tracking research with teleost fish ... and horseflies ... indicates that they follow the motion of their target by maintaining an optical angle that is a function of direction of movement. Our findings suggest that baseball players use a similar spatial strategy.''

That strategy involves geometry, trigonometry, and even calculus. If you can catch a fly ball, you can do that kind of math without even thinking about it.

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