I have to respond to
Andukar's comment here, and specifically to his example about catching a ball. When you catch a
fly ball, you do not
calculate anything about
projectile trajectories or
air friction or
wind velocity or
anything. You use a rather simple and
beautiful motor/
perceptual hack.
Consider: when you look at a ball coming towards you in the air, it appears as a point in your
two-dimensional visual field. Now, if the ball is to the left of the center of your visual field, you move left; if it is to the right of the center you move right; if it is above the center you move back; and if it is below the center you move forward. If you keep the ball in the center of your visual field, it will run right into your face, unless you have a glove in front of it (hopefully you will!).
If you don't believe me, try catching fly balls with only one eye open sometime. It's hard, because with no
depth perception you can't figure out the ball's velocity or when it's going to hit you. There has been quite a bit of
research which indicates that this is, in fact, the actual
algorithm which baseball players use to catch fly balls.
1
So can we
generalize anything from this? Not conclusively, but I would argue that this and other similar phenomena indicate that we do not in fact do nearly as much computation as we sometimes appears to. (
Walking is another example that comes to mind; nowhere in our brain is the trajectory and landing point of our foot calculated when we take a step; we simply swing our leg and let the
physics of
gravity and
pendulums take care of the details.) On the other hand, some behaviors, such as language and social behavior, are different; we
do do a lot of complicated unconscious processing for these things. The difference is that
evolution has kindly put into our
brains a dedicated "language computer", but not a dedicated "mathematics computer". The ability we as humans have in mathematics (which is not inconsiderable) is due to the more general
cognitive capacities (
catgorization,
generalization, etc.) that we have. So, I would say, math really
is hard. On the other hand, I think it's also a lot of
fun, and I think it would get boring fast if it was always as easy as breathing.
1. I regret that I can't give any references to this research. A web search provides some discussion of this phenomenon, but no links to the original research. If anyone could provide me with some references, please /msg me.