# Baseball: The control of perception

[From Rick Marken (980113.2150)]

I have placed the current version of my baseball catching
program on the net at my Web site. You can run it if you have
a Java enabled Browser. Just go to:

and click on the "Baseball Catch Simulation", which is
under construction. Each time you press the "Run" button
a fly ball is hit _directly_ to the fielder. A different
hit angle (relative to the ground), hit amplitude and fielder
distance from home is randomly selected on each "Run".

I've put this demo on the net because, even in it's current
simple form (the ball moves in two rather than three
dimensions), I think it demonstrates some intersting points.

1. The fielder catches the ball by controlling a present-
time perception (of the angular velocity of the ball on
the retina) relative to a fixed reference. There is _no
prediction_ of the ball's trajectory involved in the catching
process (though its easy to see how it can _look like_ the
fielder is predicting the ball's future position). The reference
for the controlled perception (angular velocity) is positive so
the fielder's movement's are aimed at keeping the perception
of the ball moving upwards at a constant rate on the retina.

2. I tried using angular acceleration as the controlled variable
(controlled relative to a reference of zero, which is called
optical acceleration cancellation (OAC) in the baseball catching
literature) and found that the fielder doesn't catch as reliably
using this variable (especially when the ball is popped up in
front of the fielder). It doesn't seem like optical acceleration
is likely to be the variable that is actually controlled by
fielders.

2. The observed behavior of the fielder gives no obvious
clues to what the fielder is "doing" (what perceptual
variable the fielder is controlling).

3. The fielder does not always move directly to the where the
ball will land. When the ball is a pop up in front of the
fielder, the fielder actually starts by backing _away_ from
the ball. So this model of catching makes a prediction; it says
that fielders (if they are controlling angular velocity) will
initially back away from some pop ups that are hit _directly_
towards them. I looked to see if there was any evidence of
this in the baseball catching article I referenced in my
"Dancer..." paper. I was encouraged to find some _qualitative_
support for the prediction; the authors said that they didn't
include the data from the few trials where the ball was hit
_directly_ at the fielder because the fielder made "unsystematic"
_backwards_ and lateral movements. Does anyone know whether
fielders do, indeed, start by backing away from pop-ups
that are hit _directly_ at them?

4. I believe that this initial "backing away" phenomenon will
disappear when the model is extended to 3 dimensions -- at
least for the cases where the balls are not hit directly at
the fielder.

5. The fielder is limited to a maximum forward and backward
speed of movement; this maximum represents the fastest that
the fielder can run forward or backward. These fielder parameters
are currently set at "Willie Mays"; the fielder can get to almost
anything that's hit in his direction. If I lower these maxima
a bit the fielder acts more like me -- lots of balls land on
the ground in fromt of him.

Any questions, comments or suggestions would be most welcome.

Play ball!

Best

Rick DiMaggio

···

--

Richard S. Marken Phone or Fax: 310 474-0313

Loved your demo, but some questions.

You say: the fielder's movement's are aimed at keeping the perception of
the ball moving upwards at a constant rate on the retina.

When the person catches the ball, this is true?

How did you discover this?

How do you include the fear factor? Ever remember being afraid of
catching fly balls?

Does the fielder always have to be looking at the ball? What would
happen if the fielder sampled the current perception of the ball.

Neat demonstration.

Richard Marken wrote:

···

From: David Goldstein
Subject: Re:Baseball: The control of perception
Date: 1/14/97

[From Rick Marken (980113.2150)]

I have placed the current version of my baseball catching
program on the net at my Web site. You can run it if you have
a Java enabled Browser. Just go to:

and click on the "Baseball Catch Simulation", which is
under construction. Each time you press the "Run" button
a fly ball is hit _directly_ to the fielder. A different
hit angle (relative to the ground), hit amplitude and fielder
distance from home is randomly selected on each "Run".

I've put this demo on the net because, even in it's current
simple form (the ball moves in two rather than three
dimensions), I think it demonstrates some intersting points.

1. The fielder catches the ball by controlling a present-
time perception (of the angular velocity of the ball on
the retina) relative to a fixed reference. There is _no
prediction_ of the ball's trajectory involved in the catching
process (though its easy to see how it can _look like_ the
fielder is predicting the ball's future position). The reference
for the controlled perception (angular velocity) is positive so
the fielder's movement's are aimed at keeping the perception
of the ball moving upwards at a constant rate on the retina.

2. I tried using angular acceleration as the controlled variable
(controlled relative to a reference of zero, which is called
optical acceleration cancellation (OAC) in the baseball catching
literature) and found that the fielder doesn't catch as reliably
using this variable (especially when the ball is popped up in
front of the fielder). It doesn't seem like optical acceleration
is likely to be the variable that is actually controlled by
fielders.

2. The observed behavior of the fielder gives no obvious
clues to what the fielder is "doing" (what perceptual
variable the fielder is controlling).

3. The fielder does not always move directly to the where the
ball will land. When the ball is a pop up in front of the
fielder, the fielder actually starts by backing _away_ from
the ball. So this model of catching makes a prediction; it says
that fielders (if they are controlling angular velocity) will
initially back away from some pop ups that are hit _directly_
towards them. I looked to see if there was any evidence of
this in the baseball catching article I referenced in my
"Dancer..." paper. I was encouraged to find some _qualitative_
support for the prediction; the authors said that they didn't
include the data from the few trials where the ball was hit
_directly_ at the fielder because the fielder made "unsystematic"
_backwards_ and lateral movements. Does anyone know whether
fielders do, indeed, start by backing away from pop-ups
that are hit _directly_ at them?

4. I believe that this initial "backing away" phenomenon will
disappear when the model is extended to 3 dimensions -- at
least for the cases where the balls are not hit directly at
the fielder.

5. The fielder is limited to a maximum forward and backward
speed of movement; this maximum represents the fastest that
the fielder can run forward or backward. These fielder parameters
are currently set at "Willie Mays"; the fielder can get to almost
anything that's hit in his direction. If I lower these maxima
a bit the fielder acts more like me -- lots of balls land on
the ground in fromt of him.

Any questions, comments or suggestions would be most welcome.

Play ball!

Best

Rick DiMaggio
--

Richard S. Marken Phone or Fax: 310 474-0313

[From Bill Powers (980114.0419 MST)]

Rick Marken (980113.2150)--

I'll look at the demo some time today. One thing: when you say that the
ball is hit _directly_ at the outfielder, my immediate mental image is that
of a ball moving along a straight line from the bat to the outfielder: a
line drive. Of course what you mean is that the ball is hit so the plane of
its trajectory includes the outfielder, so the outfielder doesn't have to
move laterally to catch it -- only radially. Maybe "in the direction of the
outfielder?"

Best,

Bill P.

[From Bill Powers (980114.0424 MST)]

From: David Goldstein
Subject: Re:Baseball: The control of perception
Date: 1/14/97

Loved your demo, but some questions.

Does the fielder always have to be looking at the ball? What would
happen if the fielder sampled the current perception of the ball.

An interesting question. In Rick's demo, what would have to be sampled
would be the apparent velocity of rise of the baseball. But if this were
just sampling, the perceptual signal representing the rate of rise would
fall to zero between samples. What's needed would be a _sample-and-hold_
perceptual function. When the fielder glances at the ball, the perceptual
signal would change to a new value, and then would remain at that value
until the next sample. The duration of running would be based on the
constant error signal that exists between samples.

What we sometimes see is that the outfielder will watch the ball for a
moment, turn and run away from the ball's trajectory for a while, then turn
back and watch the ball, maneuvering so as to catch it. This is usually
interpreted as calculating where the ball will fall and running to the
predicted place. However, this does not, in practice, always get the
fielder to the right place -- it's a very approximate "prediction." My
impression is that the turning and running happens when the ball is clearly
rising so fast that the rate of rise can't be controlled while continuing
to keep an eye on the ball. The position required to keep an eye on the
ball limits how fast the fielder can run. The fielder turns and simply runs
as fast as possible. After running for a couple of seconds, the fielder
turns around and looks for the ball again. The running time depends on how
well the fielder perceptually estimates the relationship between rate of
rise and required running time. Or you could say that the time of running
is simply proportional to the error between the last seen rate of rise and
the reference rate. Or maybe the fielder just runs as fast as possible for
some set time, then turns and looks.

What we remember, of course, are all the times that the fielder got near
the right position before turning around. We forget the many times when the
fielder runs too far or not far enough and the ball drops in for a hit (or
a home run or foul ball). And we tend to ignore the fact that when the
fielder does turn around to look at the ball, there is most often a
considerable amount of running, either further back or toward the infield,
to make up for rather large errors in the estimate.

"Prediction" is a plausible-sounding guess about what's going on, but it's
not the only feasible explanation.

Best,

Bill P.

[From Rick Marken (980114.0820)]

David Goldstein (1/14/98) --

You say: the fielder's movement's are aimed at keeping the
perception of the ball moving upwards at a constant rate on
the retina.

When the person catches the ball, this is true?

There is evidence that this is true but no one has actually done
the appropriate tests to determine whether angular velocity is
actually one of the variables controlled by fieldersl. But the
success of this kind of model and the similarity of the model's
visible behavior to that of real fielders suggests that this is
probably a close approximation.

How did you discover this?

Bill Powers suggested angular velocity as the controlled variable
based on his recall of an old article by Chapman (I think that's
the name; by the way, Bill. I found a reference to a 1968 paper
on baseball catching by a Chapman in Am. J. Physics; could that
be the one you're remembering?). The dominant model today seesm to
be the OAC (optical acceleration cancellation) model, which
controls angular _acceleration_ (at a reference level of zero)
rather than angular _velocity_, but apparently no one has actually
tested the OAC model as a control model so they don't seem to
have noticed its shortcomings.

How do you include the fear factor? Ever remember being afraid of
catching fly balls?

They don't. My fielder is a fearless, overpaid, greedy professional;-)

Does the fielder always have to be looking at the ball? What would
happen if the fielder sampled the current perception of the ball.

My fielder does always look at the ball but I don't think it's
necessary. The real problem with looking away from the ball is
_finding_ it again in your visual field. But, if you can find it again,
you can easily regain control of angular velocity because this
variable is independent of where the ball is located on the retina.

Neat demonstration.

Thanks!

Now the real trick will be making this a 3-D demo. Right now the
ball can only be hit (as Bill Powers (980114.0419 MST) correctly
recomends that it be said) "in the direction of the outfielder".
Now I have to make it so that the ball can be hit in any direction
(between the third and first base line, say). This will not be
easy -- especially for me;-)

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313

[From Richard Kennaway (970114.1635 GMT)]

Rick Marken (980114.0820):

But, if you can find it again,
you can easily regain control of angular velocity because this
variable is independent of where the ball is located on the retina.

Not by looking in a fixed direction, and perceiving the velocity of the
retinal image of the ball, surely? The density and type of light-detecting
cells on the retina varies drastically with distance from the fovea, and I
suspect there's nothing in the signals travelling along the optic nerve
having a simple relationship with angular velocity. Besides, it's very
difficult to look at a moving object and not fixate one's gaze on it,
especially if the background is a more or less featureless sky. When
fixating on a moving object, angular velocity shows up fairly directly, in
the changing positions of the muscles that turn the eyeball.

-- Richard Kennaway, jrk@sys.uea.ac.uk, http://www.sys.uea.ac.uk/~jrk/
School of Information Systems, Univ. of East Anglia, Norwich, U.K.

[From Bill Powers (980114.0957 MST)]

Bill Powers suggested angular velocity as the controlled variable
based on his recall of an old article by Chapman (I think that's
the name; by the way, Bill. I found a reference to a 1968 paper
on baseball catching by a Chapman in Am. J. Physics; could that
be the one you're remembering?).

The article I saw was in _Science_, I believe. "Chapman" sounds right. No
reason he couldn't have got two publications out of it.

The dominant model today seesm to
be the OAC (optical acceleration cancellation) model, which
controls angular _acceleration_ (at a reference level of zero)
rather than angular _velocity_, but apparently no one has actually
tested the OAC model as a control model so they don't seem to
have noticed its shortcomings.

What shortcomings? If you control angular velocity to keep it constant, the
acceleration is being maintained near zero, isn't it? I prefer the angular
velocity definition of the CV, because motion detection is well-known,
whereas optically detecting angular acceleration would be much harder.

Aside to Richard Kennaway: my understanding is that peripheral vision is
the disadvantage (as a source of the required information) that the angular
position of the eyeball would then have to be sensed relative to the
optical background. If you're tracking the ball, there is no motion
relative to the retina. What's needed is perception of _relative_ motion of
the ball against the background, which doesn't depend on information about
eye orientation.

Best,

Bill P.

[From Rick Marken (980114.0940)]

Me:

apparently no one has actually tested the OAC [optical acceleration
cancellation] model as a control model so they don't seem to
have noticed its shortcomings.

Bill Powers (980114.0957 MST)

What shortcomings? If you control angular velocity to keep it
constant, the acceleration is being maintained near zero, isn't it?

Yes. But when you control acceleration (at zero) the velocity can
be anything. I think that's the problem I'm seeing with the OAC
model; the success of the OAC model (whether or not it catches the
ball) depends on the trajectory of the ball. The trajectory has
to be such that, when the model gets the acceleration to zero,
the velocity is increasing slightly. I think the failure of the
OAC model would become more obvious if a disturbance (wind) were
added to the ball's trajectory. I think the velocity control
system would still catch the ball but that the OAC (acceleration)
control system would fail quite often.

Bruce Nevin (980114.1205) --

The backing away false start accords with my memory of catching
flies.

Me too, though it seems that I back up less than the model does.

Me:

4. I believe that this initial "backing away" phenomenon will
disappear when the model is extended to 3 dimensions -- at
least for the cases where the balls are not hit directly at
the fielder.

Bruce:

This suggests that a second perception is controlled when lateral
motion is visible, a perception that is not available when the
rise of the ball from the bat is in a plane that includes the
fielder.

Yes. My first guess is lateral angular velocity. This variable
is affected by lateral movement of the fielder _and_ forward and
back movement (the kind involved in the demo's control of vertical
angular velocity) too. I think the back-up will be eliminated when
forward and back movement is determined by error signals from
_both_ the vertical and lateral angular control systems.

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313

[From Bill Powers (980114.1101 MST)] --

Rick Marken (980114.0940)--

What shortcomings? If you control angular velocity to keep it
constant, the acceleration is being maintained near zero, isn't it?

Yes. But when you control acceleration (at zero) the velocity can
be anything.

Beautiful. Nice catch. Of course you're right. Another triumph for The Test.

Yes. My first guess is lateral angular velocity. This variable
is affected by lateral movement of the fielder _and_ forward and
back movement (the kind involved in the demo's control of vertical
angular velocity) too. I think the back-up will be eliminated when
forward and back movement is determined by error signals from
_both_ the vertical and lateral angular control systems.

I agree with the definition of the lateral control system, but I don't
think it will eliminate the initial backing away. Let's wait for the
baseball season and watch a few games before deciding that this is a bug
rather than a feature. I predict that the second baseman will initially
back away from a pop fly. Even the outfielders may start to do so. You
might try playing with the reference signal for vertical velocity.

Best,

Bill P.

[From Rick Marken (980114.1300)]

I'm glad everyone (with the possible exception of Dan Miller
(980113.1520);-)) liked the baseball demo. I'll try to incorporate
many of the great suggestions I have received into the beta release
(which I hope will be out in a month or so;-))

Bill Powers (980114.1101 MST) --

I agree with the definition of the lateral control system, but I
don't think it will eliminate the initial backing away.

I don't think so eaither I think that it might _reduce_ or
eliminate the backward movement, but only when the ball is hit
at an angle with respect to the fielder (by far the most common
situation in a real baseball game) rather than head on.

You might try playing with the reference signal for vertical
velocity.

I have. It makes a _big_ difference. If vertical velocity is
what fielders control when they catch a ball, then one thing
they must have to _learn_ (in order to become a good fielder)
is where to set the reference for this variable. If the
reference is set too low they can't catch balls hit in front of
them; if it's set too high everything goes over their head.
The reference setting also influences how much the fielder
backs up for short fly balls; I think I can reduce the back up a
bit and still allow the fielder to catch what he should be able
to catch by raising the current reference a bit. I'll try to make
the reference (for vertical and, eventually, lateral velocity)
a parameter that can be adjusted by the user of the program.

Bruce Abbott 980114.1500 EST) --

Nice demo, Rick!

Thanks!

In a second demo, show the view as seen by the fielder, and allow
the view to change as it does when the fielder moves toward or
away from the ball. Put this view under the influence of the
mouse

This is a great idea. I had thought of doing it myself and I
will try it. But I want to get the 3-D version working first.

Dan Miller (980113.1520) --

OK! Now that he has caught the ball what does he do with it?

It looks to me like he eats it. This, of course, is one of the
liberties I have taken with the simulation. I believe that
Major League Baseball strictly forbids the eating of baseballs
by outfielders.

Yours in complexity and skepticism

Was there something in particular about the demo, other than the
fate of the ball, about which you are skeptical?

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313

[Dan Miller (980114.1600)

Bill Powers (980114.1338MST):

Hi, Bill. Thanks for the softball pitch.

I said with reference to Rick's wonderful demo:

>OK! Now that he has caught the ball
>what does he do with it?

You replied:

Obvious. He throws it at the nearest sociologist.

I meant no disrespect to Rick or his demo, but only to note
the importance of these discussions may lie in the ability to go
beyond increasingly sophisticated demonstrations of perceptual
control.

In the game of baseball, for example, once the outfielder
has caught the ball it gets interesting. Given the situation -
number of outs, if anyone is on base, and if so which base - the
outfielder's next purposive action (with respect to the game), given
his knowledge of the game and its rules, is to return the ball to the
infield without yielding further advantage to the team at bat. He
may throw to a cutoff man, ahead of a runner, or (in some cases)
behind a runner who has overrun a base and is returning to it. This
is done (at times) without looking - by anticipating that the cutoff
man will be in position, or by anticipating that he will get into
position by the time the ball arrives.

A rightfielder who catches a shallow flyball will throw to home
when an opposing player is on third base, anticipating that the
runner may tag third and run home after the catch. This is what the
rightfielder would do if he was the runner, and it is what he is
trying to prevent when he throws to home.

So, there is a lot more to catching a flyball than the demo suggests
(and I really do think it is amazing). Some sociologists are
interested in the game (the concerted purposive actions of two
groups of people), which I believe can be wonderfully described with
the Perceptual Control Perspective. My query about what comes after
the catch was an honest one - no smartalecky retort (although I am
not above it).

Yours in right field,
Dan M.

Dan Miller
miller@riker.stjoe.udayton.edu

[Dan Miller (980114.1639)]

Rick Marken (980114.1300)]

I'm glad everyone (with the possible exception of Dan Miller
(980113.1520);-)) liked the baseball demo.

Actually, I liked it. I'm really impressed. I could never do this
(the demo - I can catch a baseball).

> OK! Now that he has caught the ball what does he do with it?
>Yours in complexity and skepticism

Was there something in particular about the demo, other than the
fate of the ball, about which you are skeptical?

No. It is the game I'm interested in. I'm not sure that
increasingly sophisticated demonstrations of single purposive actions
will get us very far. I am completely convinced of the validity and
practicality of Perceptual Control Theory. But, alas, I'm an idiot
when it comes to writing programs. My Fortran 4 Prof used my
hopeless proofs for jokes in class. Even I laughed. So, speaking
for some of the sociologists lurking on the Net, I long for the game
- the interaction, the anticipation of others' actions, the concerted
play of living control systems who share reference signals, and who
have complementary ones, who in real time accomplish feats like
catching a baseball in a context of meaning and action.

I do not mean any of this as a criticism of your work. My comment
was the lament of a sociologist who has dreams, but no skill.

Even so, I am in the right field.
Dan

Dan Miller
miller@riker.stjoe.udayton.edu

[From Bruce Nevin (980114.1838 EST)]

Rick Marken (980114.1300) --

Bill Powers (980114.1101 MST) --

I agree with the definition of the lateral control system, but I
don't think it will eliminate the initial backing away.

Rick Marken (980114.1300)

I don't think so either. I think that it might _reduce_ or
eliminate the backward movement, but only when the ball is hit
at an angle with respect to the fielder (by far the most common
situation in a real baseball game) rather than head on.

The effect of backing up could manifest as running in an arc rather than a
straight line to the point of the catch.

It might not be so simple to compare the 2-D and the 3-D models in this
regard. One idea: if the fielder's run to the catch point does in fact
trace an arc, project a tangent from the starting point of the runner's arc
to the plane of the ball's trajectory. Call the intersection of the tangent
and the plane x. (Point x looks like the runner's initial guess at the
catch point, though it can't literally be that because the fielder doesn't
know the plane of the ball's trajectory, and anyway we know that's not what
the code is doing.) The distance between x and the catch point might
correspond to the amount of backing up in the corresponding case for the
2-D model. I suppose what has to correspond is the arc of the ball (or the
distance of the catch from the batter) and the distance of the fielder from
the batter at the start of the run.

Bruce

[From Hank Folson (980115)]

An intuitive guess on a 3 dimension model: I am thinking that it might be
simplest in nature to combine two independent (at one level of a hierarchy)
2-dimensional control systems that are orthogonal to each other. One control
system would be like the one Rick has modelled. The other would be a simpler one
that controls for the ball going neither right nor left. The net result is
effectively a 3 dimensional control system.

When the ball is hit at some horizontal angle to outfielder, the perception of
the angular velocity control system will be in error. The error will increase
with the magnitude of the horizontal angle away from the outfielder. However, as
the independent horizontal control system reduces its error, it will, as an
_unintended consequence_, improve the perception (and thus the accuracy) of the
vertical control system.

As I won't be doing the programming, I can glibly suggest that a simple vector
addition of the outputs of the two control systems will determine the
outfielder's path.

It is also very easy for me to suggest that another level of the control system
will recognize when the error signal between the outfielder's position and the
ball's position increases no matter what the outfielder does. The outfielder
will then emit a string of colorful expletives. This serves the useful purpose
of demonstrating what appears to be a prediction of whether the ball is
catchable.

Sincerely, Hank Folson

[From Rick Marken (980115.1100)]

Dan Miller (980114.1600) --

So, there is a lot more to catching a flyball than the demo
suggests (and I really do think it is amazing).

There is a lot more to playing _baseball_ than the demo suggests.
There is surely _some_ more to catching a flyball than the demo
suggests (lateral movement being one) but not a lot.

Some sociologists are interested in the game (the concerted
purposive actions of two groups of people), which I believe can
be wonderfully described with the Perceptual Control Perspective.

Baseball can be _described_ by anyone. What is described can probably
be _explained_ by PCT. But in order to explain what is described
(using PCT) we first have to figure out what variables baseball
players actually control. One such variable is apparently perceived
optical velocity.

We can't tell what variables are being controlled in baseball by
just watching (and describing) the behavior we see -- including
the coordinated behavior of all players. We have to do tests (like
the one I did with my demo -- comparing control of velocity to control
of acceleration) to determine what variables players control. Until
sociologists (and all other behavioral scientists) realize that
they _must_ test for controlled variables in order to have any hope
of understanding the "interesting" behaviors they can describe,
they certainly will not see anything interesting about PCT. PCT
is all about something doesn't even _exist_ in conventional
sociology, psychology, and the rest: controlled perceptual
variables.

Dan Miller (980114.1639) --

I'm not sure that increasingly sophisticated demonstrations of
single purposive actions will get us very far.

I don't think there is anything that will necessarily "get us
very far". Our little PCT demos are simply illustrations of what
I think are important principles. The baseball demo shows that
tasks that appear to require (and _look like_ they involve)
prediction and anticipation can be accomplished by systems
controlling a (rather simple) present time perception. If they
were willing, sociologists could learn an important lesson
from this demo: that behaviors that appear complex (involving
prediction, anticipation, computation, coordination, etc) can
be generated by control systems organized around the control of
rather simple perceptions.

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313

[Martin Taylor 980115 17:00]

Rick Marken (980113.2150)

Speaking as one who has spent much time in the outfield (playing cricket,
not baseball, but the problem is the same), maybe some subjective comments
are in order.

The one thing you don't want to see, as an outfielder, is a ball hit
in your direction. If you see that, the first move is to get _out of_
its line, and get a little side-angle view on the ball. So, I suspect
that when you get your 3-D simulation going, if you find the right
controlled perceptions, a by-product will be that the fielder moves
a little sideways (in the real world maybe no more than a yard or two).

The most difficult and dangerous situation is a ball hit high into a
cloudless sky. This ties in with your use of vertical velocity as a
controlled perception. In a cloudless sky, one simply cannot judge the
velocity in any direction across the "celestial sphere." The nearest
I ever came to being killed on a cricket field was when I tried to catch
a ball hit very high and almost straight up on a cloudless day. Until
I heard it land just behind me, I was sure it was going into my hands.
A foot less error, and I wouldn't be here now. In case there is any
misunderstanding, at that time I was playing cricket at an international
level, and was considered an excellent fielder. It wasn't a novice
mistake.

On prediction: I can never remember any sense of predicting where a ball
would land, but, following a suggestion of Bill P, there were many times
when I would not move to a ball I knew to be too far out of my reach.
Equally there have been many times I have caught a ball at a diving stretch
after a full run. I like the idea of Bill Powers (980114.1015 MST):

+Oh, one last suggestion, Rick. How about working in the "universal error
+curve" so when the error gets very large, the outfielder gives up and stops
+running? Now if the ball is hit too far over the outfielder's head, or in
+the infield, he will "predict that he can't catch it." By adjusting
+parameters like maximum running speed, you can limit the area within which
+the outfielder will actually try to catch the ball. And all this, still
+without any actual predictions of the ball's or the outfielder's trajectory.

Here's one item that may be different between cricket and baseball. In
baseball, the fielder catches the ball in a glove, often held quite high.
In cricket, the catch is made with two bare hands (a cricket ball has the
same specifications as a baseball for diameter and weight but is shaped
as two hemispheres rather than having a tennis-ball seam; it is also a bit
harder than a baseball). Very few cricketers catch with the hands up near
eye level unless they have to. Usually, an easy outfield catch is taken
near waist level, and that is what one is taught to do. Would this alter
the reference value for vertical velocity between the two games, or would
the reference value change during the ball's flight for a cricket outfielder?

If your 3-D simulation works well, matching what prefessional outfielders
actually do, it suggests an approach to teaching kids the trick. Line
drives hit nearly toward you are quite hard to judge. Line drives hit
where you can just reach them on a run are easy. But it would help a kid
to know what perceptions to look for, or so I should think.

Martin

[From Bruce Abbott (980120.1440 EST)]

Rick Marken (980113.2150) --

I have placed the current version of my baseball catching
program on the net at my Web site.

I've put this demo on the net because, even in it's current
simple form (the ball moves in two rather than three
dimensions), I think it demonstrates some intersting points.

1. The fielder catches the ball by controlling a present-
time perception (of the angular velocity of the ball on
the retina) relative to a fixed reference. There is _no
prediction_ of the ball's trajectory involved in the catching
process (though its easy to see how it can _look like_ the
fielder is predicting the ball's future position). The reference
for the controlled perception (angular velocity) is positive so
the fielder's movement's are aimed at keeping the perception
of the ball moving upwards at a constant rate on the retina.

How do you define "angular velocity," and what _is_ the reference value for
this angular velocity?

3. The fielder does not always move directly to the where the
ball will land. When the ball is a pop up in front of the
fielder, the fielder actually starts by backing _away_ from
the ball. So this model of catching makes a prediction; it says
that fielders (if they are controlling angular velocity) will
initially back away from some pop ups that are hit _directly_
towards them.

When the ball is hit directly towards the fielder, the fielder (in the
simulation, at least) has absolutely no information about the angle of the
ball -- a pop fly and an overhead "long ball" can look the same, given the
right velocities. For two balls traveling at the same initial velocity, the
one traveling at a tangent to the vertical arc centered on the fielder's eye
will have the greatest vertical rate of rise on the fielder's retina. The
ball's angle with respect to this tangent and its speed jointly determine
the ball's apparent motion across the retina. The more steeply the ball is
hit, the more of its velocity goes into producing vertical motion and the
less into producing horizontal motion (toward the fielder). If the pop fly
were hit straight up with sufficient velocity, it could at first produce
sufficient vertical motion on the fielder's retina to exceed the reference,
causing him to back away. As the ball's vertical velocity slowed, the
fielder would have to reverse direction and run toward the ball in an
attempt to increase the perceived vertical velocity.

A ball hit at a shallow angle toward the fielder with the same force would
tend to produce less vertical velocity on the fielder's retina (depending on
the fielder's distance), so the fielder may at first approach, but as the
ball gets more overhead and the angular velocity is mainly contributed by
the ball's horizontal component of motion, the fielder would have to run
back in the ball's direction of travel in an attempt to bring velocity
across the retina toward its reference. It is easy to see why fielders
would want to move laterally when the ball is hit directly toward them, so
as to gain information about the ball's trajectory in more than one dimension.

Regards,

Bruce