# Rate Limits and Epicycles

[From Rick Marken (951215.0840)]

Bruce Abbott (951214.1635 EST) to Bill Powers (951213.0805 MST) --

Apparently I should not have telegraphed my intentions; you have used the
advance notice to launch a pre-emptive strike designed to nullify virtually
_any_ suggestion I might offer even before I have made it.

Pre-emptive strike? There was no strike at you, Bruce. Bill's on your side.
He, like you and me and the rest of us who understand PCT, is trying to show
that reinforcement theory is the "Ptolomaic" explanation of the phenomenon
called "reinforcement" (behavior and contingent reinforcement rate rise
to an asymptotic value over time); PCT is the far more elegant "Copernican"
explanation of that behavioral phenomenon.

Bill derived the simplest mathematical versions of the two models of the
reinforcemnt phenomenon:

Reinforcement: dB/dt = k1*C - k2*B

PCT: dB/dt = k1*(Co - C)

and pointed out that the solution of the differential equation for the
reinforcement model is an exponential runaway or no behavior at all, neither
of which is actually observed. Bill pointed out that the reinforcement model
could probably be salvaged by making some ad hoc assumptions about rate
limiting processes. Then Bill made a statement to which you seemed to take
considerable offense:

But to look for a "rate-limiting" process is simply to say "Even if the
basic model predicts incorrectly, I choose to defend it."

Perhaps you would find this statement less offensive if you could see that
the addition of "rate-limiting" processes to the reinforcement model is
perfectly comparable to adding epicycles to the Ptolomaic model; it can be
done -- and it might even get the model to work -- but it suggests that
something is fundamentally wrong with the model since there is no independent
basis for making these ad hoc assumptions.

The PCT model, in it's simplest form, explains the basic reinforcement
phenomenon accurately. The PCT model is not perfect yet (just as Copernicus
needed the orbits to be elliptical rather than circular); but continued
experiment comparing both models will (hopefully) show that the PCT model
requires the addition of fewer ad hoc assumptions to keep up with the data
than does the reinforcement model.

This is why we need to do the human operant conditioning experiments. We need
to design experiments that will clearly discriminate the predictions of these
two fundamentally different conceptions of the nature of living systems.
Hopefully, we will be able to do a sequence of experiments that will show
how difficult it is to maintain (via the continual addition of new ad hoc
assumptions) the concept of behavior as controlled or selected by its
consequences (the reinforcement model) and how easy it is to maintain the
concept of behavior as the control of perception (the PCT model).

This is what you want to show, too, isn't it Bruce?

Best

Rick

[From Bruce Abbott (951215.2030 EST)]

Rick Marken (951215.0840) --

Pre-emptive strike? There was no strike at you, Bruce.

Thanks for the reassurance, but no, I didn't see it as a strike at me
personally, but rather at whatever suggestion I might have offered, before I
even had a chance to offer it.

He, like you and me and the rest of us who understand PCT, is trying to show
that reinforcement theory is the "Ptolomaic" explanation of the phenomenon
called "reinforcement" (behavior and contingent reinforcement rate rise
to an asymptotic value over time); PCT is the far more elegant "Copernican"
explanation of that behavioral phenomenon.

I would like to think we're all working toward the same goal, but that
doesn't mean we're always going to agree on the best way to get there. At
the moment I'm just trying to see how all the pieces might be fit together
to produce a convincing control-system account of the empirical phenomenon
of reinforcement.

Bill derived the simplest mathematical versions of the two models of the
reinforcemnt phenomenon:

Reinforcement: dB/dt = k1*C - k2*B

PCT: dB/dt = k1*(Co - C)

and pointed out that the solution of the differential equation for the
reinforcement model is an exponential runaway or no behavior at all, neither
of which is actually observed. Bill pointed out that the reinforcement model
could probably be salvaged by making some ad hoc assumptions about rate
limiting processes. Then Bill made a statement to which you seemed to take
considerable offense:

But to look for a "rate-limiting" process is simply to say "Even if the
basic model predicts incorrectly, I choose to defend it."

I like that little model and its clear implications, but it is only the
simplest of several reasonable alternative constructions that should be
considered. When we consider different assumptions in our PCT modeling, we
call it good science. The statement above makes this same approach, when
applied to reinforcement modeling, sound like bad science.

Just to tweak your interest a little, behavior on ratio schedules has a
strong tendency to be two-valued: high rate or zero. A high rate is not
infinite, of course, but the instablility is just what the first equation
predicts. Put THAT in you snipe and poke it!

Perhaps you would find this statement less offensive if you could see that
the addition of "rate-limiting" processes to the reinforcement model is
perfectly comparable to adding epicycles to the Ptolomaic model; it can be
done -- and it might even get the model to work -- but it suggests that
something is fundamentally wrong with the model since there is no independent
basis for making these ad hoc assumptions.

Rate-limiting is perfectly reasonable: in the real world there generally are
limits to the values physical variables can attain, and examples of
rate-limited processes abound. For example, despite the steady application
of throttle your car doesn't go on accelerating forever, because the
increase in speed is associated with an increase in drag. Your suggestion
that "something is fundamentally wrong with the model SINCE THERE IS NO
INDEPENDENT BASIS FOR MAKING THESE ASSUMPTIONS" asserts as true something
which has not been demonstrated. How do you know that there is no
independent basis for them, without even knowing what they are? It's pure
question begging.

The PCT model, in it's simplest form, explains the basic reinforcement
phenomenon accurately.

That may or may not be true; I certainly have some reservations, which is
why I want to think very carefully about it.

The PCT model is not perfect yet (just as Copernicus

needed the orbits to be elliptical rather than circular); but continued
experiment comparing both models will (hopefully) show that the PCT model
requires the addition of fewer ad hoc assumptions to keep up with the data
than does the reinforcement model.

Fine, but let's not cast this discussion as a test between PCT and
reinforcement models, at least not yet. First let's see how far we can go
toward a really convincing PCT account of the empirical reinforcement
process in the context of a simple operant schedule. It think the effort
will be educational.

Regards,

Bruce