[From Bill Powers (970428.2106 MST)]
I've been studying how I play Microsoft Golf on the Torrey Pines course. I
once used to play real golf, occasionally, just enough to be able to compare
the computer game with the real thing -- it's pretty good, even on the
putting greens. The actual output is different; timed hits on a mouse button
instead of a real swing. But for this post, the important part is the
imagination and planning that goes on.
Off the tee on par 4's or more, it's easy: pick the direction and hit it
with as precise timing as possible. Fudge a little for the wind. But
basically just hit it with as good form as possible, which means hit it as
far and straight as you can, which means use a big but not too big backswing
(set by when you release the mouse buttom) and make contact exactly at the
bottom of the swing (set by when you do the second click as a marker sweeps
down around a circle).
For approach shots or par 3's, accuracy still counts but there's a new
consideration. The basic thing is to know how far a standard swing will send
the ball using different clubs. This is a matter of remembering what has
happened before. Nine iron the way I hit it, about 90 to 100 yards, and so
on for each club. If I played this game every day, I would know -- in about
a year -- just how far each club would send the ball. It would help to keep
a notebook, because this is a matter of symbolic memory. There's a window
with a table showing the relationship, but I never use it. Nothing to be
computed: just remember or record the results. 120 yards = 8-iron, if the
ball is hit right with a standard backswing.
There's also a wind gauge, showing velocity and relative direction. I don't
have this down yet, but it would translate eventually into a deviation of
the aiming angle from the pin as a function of direction and velocity of
wind. This also seems to be a matter of memory, only now it's an association
of an analog wind gauge reading (direction arrow and velocity bar)
associated with an analog deviation of aiming direction. Very crude, about 2
bits, just now. Also, at my stage of enlightenment, if the wind's hard
against me I use one club lower, and if with me, one club higher (in
number). That's a cognitive symbolic rule.
On the green it gets more interesting. The greens have grid lines that show
the bumps, hollows, and tilts, which can be read pretty well, about as well
as I ever read a real green, anyway. What I do is imagine a trajectory; it's
just like running an analog model. I see an imaginary ball moving toward the
hole, the speed and direction being affected by the slopes as it moves
toward the pin. I adjust the direction of the putt, running the model over
and over, until the run ends up with the ball near the hole ("in" is asking
a little much), and not going too fast. Once I've decided on the direction,
I set the direction marker that determines where the putt will go when I hit
the ball -- I pick an aiming point. I obviously have some computer in my
head that does a pretty good job of relating the surface of the green to the
effect on the ball, as the program computes it. I actually imagine the ball
as it moves, following its motion with my eyes -- only of course I don't see
any ball. I don't imagine at that low a level. I wasn't terribly bad at this
on real greens, so the program seems to be quite realistic. I had trouble
gauging distance when there were uphill and downhill slopes on real greens,
and I have the same trouble with the game. Pretty good simulation -- I mean
the program. My own mental simulation of the ball's trajectory is so-so as a
predictor of where the ball will actually go. It's fun to get it right on a
long putt.
When you putt, the distance to the hole is given in numbers, and the speed
of the stroke is set by releasing the mouse button when a pointer gets to
where you think it should be on an uncalibrated circular scale. This sets
the backswing. So this is like deciding that the hole is X feet away,
correctly, and then gauging how hard to hit the ball, which is fairly
inexact. This is a digital-to-analog association. "3" feet means a certain
amount of backswing on a continuous scale marked off with ticks but not
calibrated. If I were judging the distance by eye, it would be an
analog-to-analog association. Again, this has to be modified for uphill and
downhill putts, an analog judgement.
I don't know how the analog model is implemented, or how the memory
associations, digital and analog, happen, but I can see the results as they
unfold. I'm conscious of trying to link up the associations that are needed
-- that is, I want them linked up, and sometimes they do link up. I'm very
conscious of running that analog simulation of the ball moving on the green
in imagination. And the more I play the game, the better I get. After
perhaps a dozen games (18 holes each), I was shooting about 120. A few
months ago I broke 100. Now I'm shooting in the 80s, and starting to make a
couple of birdies per game. So however these associations and computations
work, they're getting better, with very scattered practice.
The interesting thing about all this is the way the mental operations relate
to the act of hitting the ball. They don't occur at the same time. In fact,
all the mental model-running and associations of things like wind with
aiming direction produce actions only after they are all finished. Once I've
gauged the head or tail wind and the distance, I click on the club I want to
use -- pull it out of the bag. After going through all the analog runs in
imagination on the green, or after judging distance and wind on approach
shots, I pick an aiming point and an amount of backswing.
Only when I've picked how hard to hit the ball and where to aim it, and set
up these reference levels, do I actually execute the swing. I've reduced the
problem to making the actual swing match the reference swing that was
established while setting up the shot, in imagination and by using cognitive
functions. The only low-level real-time control problem occurs during
execution of the plan.
This is how model-based control seems to work in at least one person, me, in
one sport, golf. There's lots more that could be noticed and said,
especially about playing a REAL game of golf, but I think even this much
shows that however model-based control works in a real person, it doesn't
much resemble what goes on in an MCT model, or the kind that Hans Blom has
shown us. While there is an internal model, it doesn't run at the same time
the actual control processes go on at lower levels, and it's focused on
establishing a limited set of critical reference conditions for lower-order
systems to bring about.
I'd like to hear from others what they observe when doing similar things,
including golf but also bowling and any other sport that calls for this kind
of cognitive planning. The more detail, the better (short of the point where
the eyes glaze over). But nothing hypothetical, please: just a description
of what you actually observe when you're actually doing it.
Best,
Bill P.