[From Bill Powers (950901.1430 MDT)]
Bruce Abbott (950901.1045 EST) --
Yet in the aggregrate, it is possible to learn some important
lessons about traffic flow if one simply imagines that each car is
a particle responding to "forces" impressed on it by the particles
around it (e.g., a repulsive force falling off with the square of
the distance to the particle ahead, to take a simple case).
The question is whether you want to explain natural phenomena with
analogies or by making models which are intended to show how the
phenomena actually work.
Although, at this stage of development, we don't see the evidence very
often, the control model is far more than an analogy. It is a proposal
about the way the real physical living system is organized inside. In
modeling tracking behavior, for example, we might just say that the
person behaves AS IF the basic control diagram and the equations that
describe its operations applied. From that point of view, there are many
mathematical expressions that would work; as long as they predicted the
same observations there would be no way to choose among them.
But in the control model, we are saying that each box and each arrow
corresponds to a specific function or signal that really, physically,
exists in the controlling person, with neural signals corresponding to
the signals in the model. We claim, for example, that the box we draw
that is labeled "input function" corresponds to a real device that we
can find in the person doing the tracking. We claim that this device
produces actual neural signals, which enter neural comparators and
generate real neural signals, and that those neural signals get
transformed into signals that operate muscles corresponding to the
output function box.
In the case of tracking the correspondence is incomplete because we
don't know enough about the visual systems. All we can really say is
that we expect real neural functions and signals to be discovered,
eventually, which do the _equivalent_ of what the signals and functions
in the model do. But for simpler aspects of behavior we can come much
closer than that. The Little Man version 2 model is designed to match
the anatomy of the nervous system and muscles at the spinal level,
function by function and signal by signal. In this model we can
indentify two input functions, the stretch receptors and the tendon
organs, and we can trace the signals from these input functions to a
comparator, and from the comparator to the output function, and from the
output function through physical aspects of the local environment back
to the input functions again. At every step the model conforms exactly
to the known anatomy and functions, including the signs of effects of
neural signals where they reach the spinal motor neuron, the comparator.
There is very little choice about what model to use, and no need at all
for analogies. These systems are not LIKE control systems: they ARE
control systems.
When we learn enough about the brain, the nervous system, and the
biochemical systems, we are not going to have any choice about the model
to use. Only one model will match the real system signal by signal and
function by function. At that point it won't matter how many other
models or mathematical forms might fit the same behavior. Only one of
the models can be correct.
If all you want is some empirical formula that will predict various
forms of traffic flow, you can use any analogy or any arbitrary
equations you like. Understanding what is causing those patterns is not
then the point; the point is merely to fit some mathematical form to the
data that is easier to deal with than the data themselves. Neither the
varibles not the constants in the equations have to have any physical
meaning; they are there simply to allow adjusting the curves described
by the equations to fit the data points.
If you want understanding, however, you have to try to solve the problem
a different way. You have to use the actual braking and acceleration
properties of cars; you have to study visual perception of distance of
objects; you have to study delays between disturbances and actions that
oppose them; you have to study how drivers hold their hands on steering
wheels and how much gain there is between the spinal neurons and the
front tires that do the steering. You have to come up with a model of
each driver and car, and by some means study how these independent
models interact with each other, without any superordinate guidance.
If you approach it this way you're going to come up with a good model at
much greater expense of money and labor and much later than the guy who
is just trying to fit curves to data. But when you do arrive at a good
model, you're going to know a lot more, and be able to predict at a lot
more, than the other guy who went for the quick answer.
Yet in the aggregrate, it is possible to learn some important
lessons about traffic flow if one simply imagines that each car is
a particle responding to "forces" impressed on it by the particles
around it (e.g., a repulsive force falling off with the square of
the distance to the particle ahead, to take a simple case). The
laws of fluid dynamics then apply, and you can predict traffic
jambs around construction sites (restrictions to flow), standing
waves, and even multiple-car pileups by applying these laws to the
right set of initial conditions. The drivers are not being modeled
as control systems, yet the (admittedly faulty) analogy holds well
enough to be useful. It is at this level that the physicists'
model operates. It may provide a useful description so long as it
is not taken too literally.
You put it very well, and I have a very simple reply. Cars are not
particles responding to external forces between them. The laws of fluid
dynamics do not apply. This model is simply wrong. The only thing it can
claim is that it can reproduce the same behaviors of the centroids of
the cars. That is trivial; it is just curve-fitting. Any number of
models could do that. What we want is a model that uses the _right_
physics, the _real_ properties of all the systems involved, the _actual_
sources of all the forces being generated. With a little more respect
for epistemology, we want our explanation to be consistent with
_everything_ we know, not just with a few highlights picked up at a
superficial level of observation.
···
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Martin Taylor (950901.1140)--
1. Is it possible to show that there CAN BE any model-based control
system whose behaviour cannot be reproduced in exact detail by a
non-model-based perceptual control system?
Yes. A model which can continue behaving in an approximately right way
when the perceptual system is arbitrarily turned off for a short time.
2. Is it possible to show that there CAN BE any perceptual control
system whose behaviour cannot be reproduced in detail by some
model-based control system?
Yes. A perceptual control system that can counteract the effects of
arbitrary independent disturbances with an accuracy greater than the
theoretical accuracy with which the disturbance could be deduced and
extrapolated into the future by any means of prediction.
... the controllers you deal with hide their "model" within their
structure of perceptual functions, output functions, and linkage
weights. Bill's Artificial Cerebellum improves control some, when
the output function learns a specific model of the feedback
function.
A model is supposed to duplicate the input-output relationships in the
real system, isn't it? In fact, the input, comparison, and output
functions do not duplicate the properties of the plant, the external
feedback function. Not only does the plant fail to contain any
comparator or reference signal, but its properties do not resemble those
of the input function, the output function, or the two combined. For any
given organization of the control system, there is a wide range of plant
properties over which control will remain very good.
The dynamical properties of the control system must been certain minimum
criteria in order for control of a given plant to be stable. Other than
that, there is no requirement that the control system have properties in
any wayt resembling those of the plant. The plant, for example, could be
a linear transducer. The control system, however, could be controlling
the square or square root or logarithm of the plant output, or any other
reasonably monotonic function of it. The control system in that case
would have properties that the plant does not have, and would impose its
own properties on the apparent response of the plant to disturbances.
You are using the term "model" in such a vague and elastic way that it
hardly has any meaning left.
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RE: method of levels
Without knowing it, I find that this is what I often do to myself,
not previously having realized what was happening. Very often if I
am distressed and hopeless, and want to talk to someone about it, I
imagine what I would say, and exactly the kind of questions Bill
proposes are what come to mind as ones the "other" might ask.
I think that this way of handling problems is used by practically
everyone, without giving it any formal name. It's natural to go up a
level, if you can. Doing it by oneself, however, and especially going up
several levels in a row, doesn't seem to be easy. The hardest viewpoint
to grasp is the one you're in right now.
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Rick Marken (950901.0930) --
Your post will go a long way toward relieving feelings of guilt among
PCTers. If we're so goddam smart about human nature, why do we so often
act as if we'd never heard of PCT?
Marc Abrams has given some of the right answers, and so has Tom Bourbon
(and so have you). Learning about PCT is something like learning about
gravity and aerodynamics. It's only when you're halfway between the
garage roof and the ground, flapping your orange-crate wings like mad
and watching the driveway rapidly approaching, that you think "Oh, yeah,
_gravity_! Oh, yeah, _aerodynamics_!"
The full understanding of PCT comes only when you're in the middle of
doing something based on your lifetime of experience and custom and you
see what difference it would make if you had applied PCT. By then it's
usually too late: you've gone and done it. You pick yourself up off the
driveway and vow never again to ignore what you know. Four or five tries
later, or six or seven or eight, you finally manage to have the crucial
insight _before_ you start to act.
PCT applies to absolutely every aspect of behavior and experience. There
is no way that anyone is going to sit down and in one massive session of
self-analysis alter every single aspect of behavior, thought, and belief
at every level that is based on a different understanding of how people
work. Everything we have been told about how we do or should behave and
about what makes other people tick has been drilled into us from infancy
by parents, teachers, baby-sitters, cops, professors, preachers, books,
movies, TV, Nobel laureates, friends, enemies, and lovers. This complex
and vast structure of beliefs and thoughts can't change overnight, or in
a month, or a year, or 40 years. The overlapping generations now
learning about PCT are the very first. No custom, tradition, or
inherited wisdom is there to help apply the theory. We are on our own.
So let us remind each other what we are about, and pick each other up
when we stumble, and try to keep our sense of humor.
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Best to all,
Bill P.