[From Bill Powers (930112.0900)]

Greg Williams (930112) --

... where does a model for tracking which uses C,H, and T as

its variables fit? And where does a model of gravitational

attraction which uses distance and mass (observationally

proportional to weight) fit?

C, H, and T (and D) are the observable variables whose behavior

we must explain, just as position, velocity, and acceleration are

the observable variables which Newton had to explain. The

explanation goes beyond the observable variables, in proposing

entities like mass, or error sensitivity.

Mass, remember, is not an observable variable (weight is not the

same thing as mass), and neither is the universal constant of

gravitation, nor the inverse-square relationship of force

(acceleration for a free body) and distance. A pound of feathers

and a pound of lead do NOT fall at the same rate. The attraction

between nonspherical objects does NOT go as the inverse square of

the distance between their centers. A cannonball does NOT travel

in an ellipse with one focus at the center of the Earth. The

observations deny Newton's laws. Newton replies, "Yes, but the

underlying relationships are as I suppose. If you calculate

viscious friction, and integrate using my universal law over all

the infinitesimal particles of irregular objects, however

imaginary those particles may be, you will see that the laws

predict exactly what we observe."

Suppose we have a simple control system with a loop gain of

1,000,000 and a slowing factor in the output function that is

sufficient for stable operation. In this case, the true steady-

state relationship between C and H is H = 1,000,000 * (C* - C).

This is not, of course, what we observe. We observe that H = -D

and C = C*, as near as we can measure, give or take random noise

and measurement error. If there are variations in C* we will see

C varying in the same way, but H will not vary a million times as

much. H will vary only as much as needed to cancel the effect of

D on (C* - C). We do NOT, in general, see H varying a million

times as much as C. Yet a generative model in which the error

sensitivity is one million explains the observations.

Still, I think Skinner's "prematurity" warning still counts for

something...

Skinner was denying the usefulness of models of the interior of

the organism at exactly the same time the principles of control

theory were being developed. He defended his views against

cybernetics and cognitive models as against any other proposals.

He took the deviations of others' views from his own as prima

facie evidence that the other views were wrong: no proof needed.

Skinner's main modes of argument were ridicule and assertion. He

did not test hypotheses. He simply offered positive instances

worded so as to support his position.

Suppose that Skinner had really believed, as he seemed to claim,

that models of the inner working of organisms might some day

provide explanatory principles not present in radical

behaviorism. In that case, all his explanations of behavior in

terms of external events and situations should have been appended

with " ... or some cause working from inside the organism."

Obviously there was no such appendage: it would have made his

bold assertions look foolish. What Skinner believed, as far as I

can see, must have been what many cognitive scientists believe

today: that if you followed all more abstract explanations down

to their fundamental bases, the causes would eventually trace

back to the environment. In other words, Skinner considered that

he was only stating in an approximate way what would some day be

shown to be the only accurate way. This was his lifelong faith.

Actually, from what I've read, they actually claim that they

DON'T WANT TO COME UP WITH AN EXPLANATION -- ONLY

PREDICTION/CONTROL. But the upshot is as you say, of course,

and they can't get as close to their professed goal as they

could with PCT models (which, as noted yet again above, might

be very difficult to generate for complex situations).

The trouble with qualitative language is that you don't get any

idea of proportions. To say that they can't get as close to

prediction as PCT can can leave the image of a footrace with PCT

winning in a final burst at the finish line. With respect to

prediction, PCT is crossing the finish line while the operant

approach still has one foot in the starting block.

Do you realize that there is no basis in the operant-conditioning

model for predicting that there will be any behavior at all in a

Skinner box? And that even if you admit as a prediction an

extrapolation from previous experience, this model can't predict

how much behavior there will be, if any? The reinforcement rate

supposedly sustains the behavior rate. But the reinforcement rate

depends on behavior, so unless you know in advance what the

behavior rate is going to be, you can't say what the

reinforcement rate will be. Not being able to predict the

reinforcement rate, you have no basis for predicting any

particular behavior rate. So there is NO PREDICTION AT ALL.

The best that the operant approach can do is to describe what has

already happened, and predict that what has happened will happen

again. All of the mathematical manipulations I have seen in the

operant literature have been manipulations of algebraic

identities; with only one equation to represent a situation

requiring two or more equations for its complete description,

that is all that can be done. It is not that the operant model

predicts less well than PCT. It does not predict AT ALL.

Skinner's extreme historical environmentalism and an extreme

"moment-by-moment" mechanistic organismism need melding into a

broader -- and I think truer -- picture.

As Dennis pointed out, "history" is not a causal mechanism. The

past can't affect the present any more than the future can.

Everything that operates on behavior is present now, or else it

has no effect. The only way for the past to seem to operate in

the present is through memory; and it's only the current contents

of memory, not what actually happened in the past, that has an

effect NOW.

This is a fundamental principle of all the hard sciences. The

history of a variable is irrelevant; the path by which it got to

its present state (including derivatives) is of no consequence.

Generative models work strictly in present time. I don't see any

possibility for a merger here.

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Avery.Andrews (930111.1905) --

Reading around in the Osherson, ed. `foundations of cognitive

science' (1989) I came across the claim that feedback is too

slow to solve inverse kinematic & dynamic problems for fast

movements.

This is a good one for the collection of myths. In fact this is a

double whammy: a myth based on a myth. In the first place, it's

not necessary to solve for the inverse kinematics because a

control system automatically does that using the environment as

its own model. So it's true that control systems aren't fast

enough to solve the inverse kinematics without feedback: no

neural system is fast enough. But solving the inverse kinematic

problem isn't necessary in any case, and control systems are

certainly fast enough to do what is necessary to control a

dynamical system.

Where can I read about why this claim is false or irrelevant

(e.g., true only for certain kinds of highly skilled movements

that people practice enough to make it plausible that they have

elaborate feedforward schemes for).

Look up analogue computer methods for solving second-order

differential equations. Korn and Korn is the only reference in my

head, and it's probably way out of date (Greg?). See also my arm

model, which controls a dynamical system without solving the

inverse kinematic or dynamic equations.

I know of no situation in which literally solving the inverse

kinematic and dynamic equations is a plausible explanation for

behavior.

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Best to all,

Bill P.