From Greg Williams (930107)

Bill Powers (930106.2100)

Control theory is more akin to classical physics, which deals

with a continuous macroscopic world.

As I've said before, Newton was the Skinner of his day: "Hypotheses non

fingo!" I think we must admit that he guessed right that his trying to make a

generative model for gravity -- and then being able to test it -- would have

been fruitless. It isn't so clear that Skinner's claim that, giving the

current state-of-the-art (between the Thirties and the Eighties) in

physiology, making generative models of behavior is misguided. We don't yet

have 20-20 hindsight. At any rate, future historians will be able to judge,

since the "cognitive movement" (which includes PCT) has called Skinner's hand.

I'm reminded of the

quote that Rick (or was it Tom) came up with, in which Skinner

admitted that it would be better to understand how the insides of

the organism work. He was really battling against people who

tossed off glib and question-begging explanations in terms of

traits and tendencies, and of course I'm with him all the way,

there. Unfortunately, he persuaded a lot of people that

successful models of the insides were millenia off, and not worth

thinking about.

I found that quote, and I still have considerable sympathy for Skinner's

pragmatism and humility. The question really boils down to whether, at a given

time, generative models work better FOR THE PURPOSES OF THE INVESTIGATORS than

do descriptive "models." Even in the long run, generative models simply might

be too complicated to actually make, or you might run into chaos (hair-

trigger) problems.

It's not worthwhile trying to make a model fit every anomaly.

There goes the PCT standard of "accept nothing less 99.9999999...

correlations." Right out the window. The high correlation between PCT-model-

predicted handle movements and actual handle movements begins to look less

spectacular, doesn't it? In principle, underlying generative models are more

complete than descriptions at the level of the phenomena. But in practice, the

former might not be able to predict better than the latter, due to the

complexity of the underlying mechanisms and/or hair-trigger situations.

Well, I think I do, but if you want to put your model where your

mouth is, I will pay attention. Of course I expect it to be a

real S-R model -- no feedback allowed!

I think you better be explicit about what you mean by "real S-R model." The

kind of model a behaviorist would make is one which is a function of

observables in the external world; in this case, cursor position and velocity,

target position, and handle position and velocity. He/she would curve-fit with

parametric variation a function relating cursor position and velocity and

target position to handle position and velocity through time. Is that OK? If

this is not a "real" S-R "model" (or at least a "real" "model" AT THE LEVEL OF

THE OBSERVABLE PHENOMENA) because there is a feedback connection in the

computer from the handle to the cursor, then you are right, I can't come up

with a "real" "model." I can only come up with a mathematical description

relating observable inputs and outputs, which, I contend, can be as predictive

as the most predictive PCT model. In fact, as the behaviorist and the PCTer

both "zero in" on the most predictive models, I think the mathematics will

converge in all but perhaps one respect: the PCT model might include an

underlying generative model for the "noise," while the behaviorist model will

use probability formulae DESCRIBING the noise as observed. It isn't clear,

given current knowledge of the nervous system, whether generative models for

such "noise" can be more predictive than descriptive "models." I do agree, of

course, that an underlying generative model is needed to EXPLAIN the "noise."

But explaining and predicting are two different things, as Newton knew so long

ago.

It seems to me that a large number of models (PCT and S-R, each

differing from the others in parameters and/or basic forms) can

produce equally high correlations between actual handle

position and model-predicted handle position, because the

moment-to-moment differences in the predictions of the various

models get "washed out" in computing those correlations.

In one sense this is certainly true, at least of PCT models.

Then you go through a long list of red herrings. What I meant to say is that

various PCT models such as proportional, proportional-integral, and

proportional-integral-derivative, with various nonlinearities and various

parameters, and various descriptive "models" with various functions and

parameters, ALL give about equally high correlations between predicted handle

positions and actual handle positions, but all do NOT give equally high

correlations between predicted cursor positions and actual cursor positions.

But I deny that any S-R model will be able to predict the

behavior of the handle and the cursor with any interesting degree

of accuracy. It's up to you to show that I'm wrong, and you're

not going to accomplish that with words.

It will save me a lot of trouble if I know in advance that a descriptive

function which includes a subtraction of cursor position from target position

won't count for you as a "real" descriptive "model." Two different

distinctions are being interwoven here, and they need separating: feedback vs.

non-feedback (S-R, I take it) models, and underlying generative models vs.

descriptive "models" at the level of the observable phenomena (behaviorist

functional "models"). I believe that the PCT models used to predict tracking

can be interpreted also as functional "models" -- the choice of interpretation

(underlying generative model or function "model") depends only on whether one

envisions a reference signal for target position inside the organism (thus

explaining why cursor position is subtracted from target position) or one

simply notes that prediction is good if there is such a subtraction in the

function relating "input" to "output" at each moment and doesn't care about

explaining why.

As ever,

Greg