Abandoning the .9999999+ standard?

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