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Monday, April 18, 2005
catching a fly ball / doing physics in my head
Earlier this evening, I spent a little time with my two-year old playing ball. I threw long arcs with a very soft ball and although he couldn't catch it, he was starting to track the ball in the air.
This reminded me of something I read that discussed how smart we must be to be able to compute 2-dimensional physics equations in our head. Somehow, we know where the ball will land and place ourselves there well before the ball actually arrives. Of course, this is done through experience (trial & error), since most of us will not take measurements, count steps and do s = ut + 1/2 at2 in our head. As I was throwing this green soft ball in large arcs, I thought that in reality the problem is actually much easier and at the same time much more difficult.
The problem is made more difficult than our Physics 101 problem since we have to deal with things like wind and terminal velocity. Also, we have height (y<>0), and our eyesight is not connected to the glove itself. In order to do the actual math, we would have to take all these (and a few more) factors into account. But we have a secret weapon. It's more powerful than the equations and ability to accurately measure things on the "fly".
It's called feedback. We can make a good guess (from experience), and make adjustments as the ball is in the air. There's a reason why Coach told us to "keep our eye on the ball". We don't have to recalculate -- we don't even have to do the initial calculation. We can guess, and make smart adjustments.
Now, this is not earthshattering news. This is Baseball 101, Chapter 3: "how to play outfield". Feedback is built into our human nature. It's amazing how well we learn and solve how to do things.
Unfortunately, many models ignore such feedback mechanisms. Think of pricing models that ignore competitor's responses; tax models without the ability of people giving up their US citizenship to avoid taxes. Feedback is an important part of many systems. The world is not static -- the agents in a system are not static either. They react, they learn, they try different things, they fail, they succeed.
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Howard--great post, and a wonderful illustration. You have really captured the challenge in what we do.
Take your ball playing with your son as an example. Even a child can learn by direct experience the complex physics of projectile motion. But let's say that you had to describe this to someone on another planet where there is no gravity, no intuitive sense to work from. Moreover you are required to generalize this to tennis balls, cannon balls, or cow chips. For that audience, much like the business community we work with, it is necessary to break down the observable into the learnable, using the medium of mathematics. Insanely hard, yes...but infinitely rewarding.
George Danner
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Take your ball playing with your son as an example. Even a child can learn by direct experience the complex physics of projectile motion. But let's say that you had to describe this to someone on another planet where there is no gravity, no intuitive sense to work from. Moreover you are required to generalize this to tennis balls, cannon balls, or cow chips. For that audience, much like the business community we work with, it is necessary to break down the observable into the learnable, using the medium of mathematics. Insanely hard, yes...but infinitely rewarding.
George Danner
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