[From Bill Powers (950512.0100 MDT)]
I seem to be awake for a little while, so ...
Bruce Abbott (950511.1820 EST)
I definitely put you in the category of people who try to apply PCT
principles to explaining the tough cases of behavior. This has come
about, as you are no doubt aware, gradually.
···
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I said:
If you practice "on"
the target when you can see it, but can track "beside" it when you
can't see it, I think this might favor the hypothesis of remembered
target movement.
I'm not sure I see the difference. I would view "calibrating the
imagined target movement" as simply a part of building (refining)
the model.
Model-based control doesn't mean repeating specific signals that have
occurred in the past. It means constructing a model with a structure
that will create signals like those that the real environment would
create, given any actions on the environment.
The best analogy is in the control-system models we use. When we apply a
given waveform of disturbance to the model, the model produces outputs
that are opposed to the waveform. We trim the parameters of the model
until it reacts to the disturbance the same way the person does.
Now we can apply _any other_ disturbance waveform, and the model will
react just as the person will react to the new waveform. The model
doesn't contain any record of specific disturbance waveforms; actually
when we use an on-the-fly disturbance generator, neither the model nor
we knows what the next disturbance will look like. Since we use a
random-number generator as the basis for the disturbance, we can do 1000
runs and the waveform will never be the same twice. Yet the model
predicts very closely how the person will react to the same disturbance
(assuming we recorded it).
A world-model is of the same nature. What matters about it is (1) the
basic structure of the model (what variables are considered, what
relationships among them are computed), and (2) the specific values of
parameters used in the model. There is no need to record specific
behaviors of the environment, because presumably the world-model will
behave as the environment does under all specific situations.
If you memorize a specific behavior of the target, then what you have
"learned" (recorded) is only that specific behavior. No model is needed
to generate the target movements; all you need is a neural tape
recorder. To do the "Blindt1b" task, you just play back the recording,
and move the cursor according to what your present goal is. If your
present goal is to track ON the target, you can do that. If it is to
track "beside" the target, you can do that too, by changing your
present-time goal. You could even decide that you now want to make the
cursor swing in a regular pattern ahead and behind the imaginary target
as it moves. So clearly you haven't just memorized a pattern of cursor
movements. You're doing present-time control of a present-time cursor
relative to a remembered target pattern.
All this would become clear if you substituted a smoothed random
waveform for the regular sine-wave target movement that I used (for
simplicity) in the blindxxx program. If a very slow target movement
pattern were used, and you practiced with the same pattern over and
over, you would begin to memorize it, and with sufficient practice would
be able to make the cursor move in that same pattern -- or beside it, or
oscillating ahead of it and behind it, or whatever you liked. But if the
target pattern did NOT remain the same, you would have no way to keep
the cursor in any specific relationship to the invisible target.
Suppose, however, that we had a repeating target pattern, and applied a
disturbance to the cursor. Now for any disturbance pattern, you would
still be able to make the cursor move in relation to the remembered
target movements. The mouse movements by which you produced this effect
would be unpredictable, because a good part of them is opposing an
unpredictable disturbance. But the cursor would move as you want it to,
because you can see it.
And finally, what if you applied a disturbance to the cursor in the case
where the target was visible but the cursor was not? Now you would have
a real problem! How would you oppose the effects of the disturbance if
you couldn't see where the cursor is? At best, in the intermittent case,
you could keep the mouse moving with a certain acceleration and
velocity, hoping that the disturbance hadn't taken an unexpected turn
during the period of cursor invisibility. In the completely invisible
case, you'd have no luck at all.
In all of the blindxxx demos but one, the only "world-model" involved is
the assumption of proportionality of mouse movement to cursor movement.
That is a simple world model; it doesn't specify any particular cursor
or mouse movement, it just says that whatever they are, they must be
proportionally related. All you have to adjust in the world model is the
coefficient of proportionality.
The one experiment that violated this assumption and calls for a
different world-model is blindt1a, in which I used Hans' system model
from his program. This system model has a dynamic lag in it as well as a
proportional term, so the cursor does not move just proportionally to
the mouse. If you have tried it, you have already seen how much worse
your performance is, even with a lot of practice. It's very hard to
build up a new world-model even when the model needs nothing but a
proportionality constant and a time-constant in it. Perhaps with several
hundred practice trials you might be able to develop this simple world-
model to the point where it works as well as the proportional one did
(which is not excessively well, compared with real-time control).
The practice I was talking about was being done _exclusively_ with
the target invisible. Without the graph, there would be no way to
compare your actual pattern of movement to the required one, and
thus no way to detect and correct errors. On the other hand, if
you interspersed visible-target and invisible-target trials,
practice "feeling" the appropriate pattern during visible-target
trials might be sufficient by itself.
I belatedly realized, when I actually ran your program, that you were
talking about the graphical plot in the original program, not something
you had added!
This is an interesting mode of operation which I had actually used
without realizing that I was doing it. It involves higher-level
cognitive functions reasoning (from the visual graph) about the errors
you make and adjusting the reference signals for mouse movement
accordingly. It's as though you had a proprioceptive mental graph of
mouse movements versus time which you could scan to create a pattern of
mouse movements, and could redraw the graph on the basis of visually
observed errors. What really interests me is the idea of a reference
trajectory that is adjustable in detail by higher-level processes. Is
this a feature of the transition level of control? Is it a level by
itself?
Hans' model contains a method for adjusting the proportionality constant
and time-constant in the world-model, which is how his model is able to
achieve control. If there were another channel available to show
tracking errors, he could no doubt supply a more elaborate adaptive
routine that would use that information to modify the model parameters.
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Hans Blom (950511b) --
Bill Leach asks
>What do you mean by "FORWARD kinematics and dynamics
representation >..."?
And you reply:
I mean that the "world" in the demo contains an equation xt := ct
+ at * xt + bt * u + ft and that the world-model contains an
equation x := c + a * x + b * u + f
I think you are in trouble with the terms f and ft. To know f requires
that you know what external influences (outside the system you are
controlling) are going to affect the system -- and not just that you
know what they are, but that you know in detail how they are going to
behave. This, I maintain, is possible only in very limited circumstances
and only to a very limited degree in the real world.
If this is what your professor taught you so long ago, I can't help
wondering how far you have explored the properties of _non_ predictive
control systems. I need to be assured that you know their properties as
well as you know the properties of world-model based control systems.
One thing that makes me wonder is that when I say that an ordinary
negative feedback control system can control accurately without making
any predictions, and without any knowledge of external independent
influences on the controlled variable, you always come back with remarks
to the effect that no, control is not possible without having
information about those external influences.
To me, this sounds as if you are claiming that there is NO kind of
control system that can correct errors accurately without knowledge of
external disturbances. I really need to know if you're making that
claim, or if you're just more interested in predictive-adaptive control
than in the other kind.
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Best to all,
Bill P.