[From Bill Powers (980124.1656 MST)]
I want to make a point about model-based control and the question that Jeff
Vancouver raised, of perceptual systems as models of the environment. This
discussion, appropriately enough, will go in a big circle.
What gets overlooked here is the relationship of perceptual signals to the
environment that is basic to PCT. The view that is taken outside of PCT is
that the environment, the world, is just what is out there, and the brain
has to construct some kind of model of it inside the head, so as to be able
to predict or control it. But in PCT, as I conceive it, the world of
perception _is_ the world that seems to be "out there." The problem is not
to understand how the brain forms a model of the world we observe, but how
the world we observe is constructed from the physical reality on which we
assume it's based. We're already looking at the perceptions; the real
problem is to figure out how they're related to the physics.
All this came to mind again as I was working on a refinement of Rick's 3-D
baseball model. This problem gets a bit complicated when you try to get the
details right. The natural thing to do is to split the control systems up
into one that controls in radius, and another that controls laterally.
Relating this to the physics of the "real" baseball diamond gets
complicated because the control is always relative to the fielder, but we
have to express the motions in a fixed physical coordinate system. When the
fielder moves radially or laterally in relation to the line of sight to the
baseball or home plate, that motion is not in the x-y coordinates of the
playing field "out there;" it has to be projected onto the external
cartesian coordinates. The right fielder, for example, is off to one side,
so when he moves straight away from home plate he is moving in one
dimension relative to himself, radially, but in both x and y in relation to
the external coordinate system.
This gets more complicated when we realize that the ball player can move
only in one direction at a time, the direction of running. This direction
can change, but from the ball player's point of view he is always running
in a given direction. Of course he can be running sideways, his body
twisted, or even backward, backpedaling relative to the ball. The
orientation of the body or its direction of motion have no fixed
relationship to the direction the legs are moving relative to the body.
The fact that there is only one body and one pair of legs also makes it
hard to see how the fielder could have two separate control systems, one
controlling laterally and the other radially. He can't move his legs in two
different ways at once, and his body can move in only one direction at a
time. What the player actually does is to vary his speed of running and his
direction of running, not his x-y coordinates or even his polar coordinates
as we see the situation from outside him.
Finally, we have the problem that the fielder is perceiving the world
through eyes that are mobile in a head that swivels on a neck attached to a
body that can change its orientation relative to the playing field. Yet
what the fielder has to perceive, to catch the ball in the way we think he
does it, is the direction and velocity of the ball in a fixed external
space, even if he's running away from the ball and glimpsing it by looking
back over his shoulder. He has to perceive the ballpark, the ball, and
himself as movable objects in this fixed space, keeping track of horizontal
and vertical.
The only way I can even imagine this to work is to suppose that in the
ball-player's head, there is a common spatial framework into which all
sensory modalities are translated. Touch, kinesthesis, vision, and sound
all are transformed so they are mutually consistent within this common
space. If I reach out to touch something, I see it as having a location in
an external space. When I touch it, the sensation of touch is also located
in this same external space, at the same place where I see the object and
my finger. If the object makes a noise, I hear the sound coming from the
direction in which I feel and see the object. And when I reach toward it, I
feel the location of my arm and hand in that same space, and my direction
of reaching feels as if it is in the same direction as the object,
consistent with where I hear it, see it, and will eventually touch it. If I
walk toward the object, I feel my own position in this space as changing
toward the visual, tactile, kinesthetic, and auditory location of the object.
Of course as I move toward the object, it moves toward me; somehow I sense
my changing position in this common space, yet I am always at the center of
it. When I turn to face in another direction, I sense myself turning, yet
everything in the space is revolving around me the other way, and I always
end up looking straight ahead. I can look left and right, yet if I am
looking left by turning my eyes, I can instantly redefine where I am
looking as being straight ahead and feel my body and head as pointed to the
right. And I can then turn my head and body while keeping my eyes pointed
straight ahead until body and head, too, are oriented straight ahead, in
the direction that was, until a moment ago, off to the left. I turn my head
and body while holding my gaze -- and my eyeballs -- straight ahead.
None of this seems to be happening in a model in my head, yet it obviously
can be happening nowhere else. It is truly all perception.
So what we seem to have happening here is model-based control -- only it's
control _of_ a model, not control_through_ a model. When I turn my head to
look at something, I am making this perceptual model swing around me, which
I also interpret as turning my eyes and head toward it. But I have no idea
how I do that -- that is, the "how" is not modeled or experienced.
What is not experienced is the nervous system that sends signals to my
muscles, or the muscles themselves that make me (or the world) turn, or the
physics involved in converting torques into angular accelerations,
velocities, and positions, or the optical laws involved in generating
images on my retinas. All I experience are the effects that wanting to look
has on the appearance of my perceptual world. I want to look at an object;
the world swings around; and there is the object -- right where it has
always been, with me turned to look at it.
So this is very clearly and definitely not a situation in which the
properties of the world between my actions and my perceptions are
represented as an internal world-model. This is not Hans Blom's model of
how behavior works. The model we are talking about now, this common
framework within which all modalities of perception are adapted to agree
with each other, is a perceptual model of what lies outside us. It is, in
fact, the world that we experience as being objective and outside. But it
is neither objective nor outside.
Let's climb back inside this outfielder, then, and see how the world he is
controlling looks to him. He is in a large space, his body at a particular
location in the outfield, yet still at the center of everything. Home plate
is over there, in a direction he can see, to which he can point. There is
the foul territory to the left of first base, toward which he can walk when
the inning is over, bringing the dugout close enough to step into. He hears
the crack of the bat coming from the place where home base is, and sees a
ball rising into space at some angle from the vertical. He waits to make
sure the ball might be coming toward him, and then moves himself in this
space until he has turned the ball's slanted rise into a vertical rise, and
is keeping the rate of rise at some small value. He maintains the ball
rising vertically, even though he has to turn his body and head and eyes
and move himself in this common space, so part of the time he has to
imagine that the rising of the ball is continuing somewhere behind him.
He's not imagining the physics of objects moving through air in a
gravitational field; he's just imagining a rising-ness continuing behind
and above him. He turns, makes any corrections of the ball's place in this
space that are necessary to keep it rising vertically at a slow rate, and
when the ball gets close enough, moves his glove in front of it and catches
it.
At no time does this outfielder have to think about how to get his body
moving in a given direction or with a given orientation. That is left up to
all the lower-level control systems, which vary the directions of movement
of the legs and the body's orientation to maintain the sensed direction and
speed of running in the specified state. All those lower systems at all the
lower levels just produce whatever perceptions are demanded from above.
Obviously, working out the details at the lower levels would be a
incredibly difficult task. But to model the higher-level systems that catch
the ball, we don't have to do that.
At the higher level, all we have to do is decide what state of affairs is
to be controlled in this common perceptual framework. The ball is to rise
steadily in the vertical direction. To make it do this, we have to convert
rate-of-rise and angle-of-rise error signals into appropriate directions of
movement of the body, to keep the angle of rise at vertical and the rate of
rise at a small positive value. We can do this just as if we were measuring
the position and velocity of the ball from the standpoint of the
outfielder. We don't have to consider the details of how the error signals
produce the right motions, any more than the outfielder has to pay
attention to such things. We don't have to know how this common perceptual
framework is generated by the brain, and of course neither does the
outfielder.
So my conclusion is that we _can_ model the ball-catcher as a pair of
control systems working radially and at right angles to the direction to
the ball, and these control systems can produce orthogonal directions of
motion. Since we don't hope to model all the lower-level systems that must
be involved, we can simply propose an organization that produces the right
effect, knowing that however the real systems work, they must produce the
same effect. In this way we will answer the question of how the higher
systems might work, without getting hung up on all the lower levels of
organization.
Well, that leaves me about where I started, but I think with a better grasp
of what we're trying to do. And I think this discussion helps to make clear
the difference between control through an internal model of the
environment's _properties_, and control through an inner perceptual
representation of the _behavior_ of the world.
Best,
Bill P.
