[From Bruce Abbott (970812.1845 EST)]
Bill Powers (970812.0555 MDT) --
The interleaving was done in your mind, allowing you to combine my
statements and Rick's as if they were part of a single argument:
Interleaving would involve reordering your statements to alternate with
Rick's, not presenting them in their actual order (Rick's after yours) as I
did. "Concatenating" is the term you want.
[Note that you are forming a logical AND in which one proposition is mine
and the other is Rick's]
Yes, that is what I did.
Rick has a way of throwing his conclusions onto the table without bothering
to explain how he justifies them. If that gets him into trouble with you,
that's his business and not my problem.
But it _is_ your problem if you do not voice your disagreement with those
conclusions. Most readers of CSGnet assume that you and Rick are of like
mind on most issues relating to theory, unless you offer a correction (as
you sometimes do). There being no such correction offered here, Rick's
addition will be accepted as if you were in complete accord with it. And
if these are the rules by which my view is to be judged, then in effect you
and Rick between you have ruled out the possibility of proof, mathematical
or otherwise. You don't see anything wrong with this?
That said, I do agree with Rick that operant-behavior analysts use a style
of mathematical analysis that can be made to reach almost any conclusion.
But we weren't discussing using "a style of mathematical analysis that can
be made to reach almost any conclusion." We were talking about analyzing a
specific model using the same style of mathematical analysis used by you and
others to establish whether a particular closed-loop system is or is not a
negative feedback system. If Rick meant some other style of mathematical
analysis, he should have said so. In the context in which it appeared, I
could only assume that he was talking about the sort of mathematical
analysis you were undertaking for e. coli. In that context, what would be
the point of switching the subject?
Given the type of analysis we were actually discussing, the rest of your
complaint about mathematical analysis as carried out by some EAB types is
irrelevant to the present discussion, although I would like to point out for
the record that you have _once again_ returned to your old myth about
Herrnstein's matching law. How many times do I have to go over this with
you? Herrnstein's matching law was formulated to describe performance on
concurrent VI VI schedules (in which case it is most definitely NOT a simple
statement that the two schedules are identical), whereas your assertion
would be correct _only_ if it were formulated to apply to concurrent ratio
schedules, which it wasn't. Apparently the charge that "any engineer" would
see the flaw is just too delicious for you to resist. Nevermind the fact
that it isn't true.
While we're on this subject, I think you need to reconsider your own E.
coli model, which you seem to remember as having settled the issue of
reinforcement theory as far as its justification is concerned. . . .
No, no, no, no, no. I never claimed any such thing. You and Rick claimed
that no reinforcement analysis could account for your simulated e. coli's
behavior; I demonstrated that one could. That is all.
You may
recall (or you may not, as you have never commented on this), your model
involved four cases, two of which increased the probability-density of a
response to an increase or decrease in the critical variable, and two of
which decreased it. Together, these four cases resulted in a slight
preponderance of changes in delay time in the right direction. However, two
of the cases worked against the other two: they went in the wrong
direction. So your model actually contained a conflict.
After two years I'm getting fuzzy about the details, but I believe it was I
who pointed this out to you, not vice versa, in one or more of my repeated
attempts to get across its logic to you and Rick. Both of you kept telling
me that the thing wouldn't work as advertised, and Rick even went so far as
to write a computer program that "proved" that the model would do no better
than a random walk. It was a nightmare, but I eventually succeeded in
getting across to you _that_ the system worked, and that it worked _as I had
described_.
I suggested that it may have been the geometry of the particular situation,
in which the gradient converged toward a point, that created enough
imbalance to give the right result. I suggested that there might be other
geometries in which the balance would go the wrong way. If I had been the
one offering your model, and had heard such suggestions, I wouldn't have
rested until I had shown _one way or the other_ whether these allegations
were true. But you seemed totally uninterested in pursuing that matter
further.
No, I believe it was I who pointed out that the model took advantage of the
geometry of the situation, and that it probably wouldn't work in some other
geometries. This business about me being uninterested in "your" allegations
and uninterested in pursuing the matter is a figment of your imagination.
There was no need for me to do so, as I had already freely admitted that
this was true.
If you will remember, your model began with the observation that if the
system were moving the wrong way, the probability that a tumble would
improve the situation was greater than 0.5, and if it were moving the right
way, the probability of a tumble making the situation worse was also
greater than 0.5. So clearly what was needed was a way of reinforcing
tumbles that were responses to a decrease in the critical variable, and
reinforcing _lack_ of tumbles that were responses to an increase in that
variable. Logic also required that a tumble in response to an increase in
the critical variable had to be punished, and _lack_ of a tumble in
response to going the wrong way had to be punished.
What was needed was a way to reinforce tumbles when the organism was going
the wrong way (away from the nutrient source) and to punish tumbles when the
organism was going in the right way (toward the nutrient source); there was
no provision for reinforcing or punishing lack of tumbles. Lack of a tumble
is not an event.
You built this logic into your model. To support this logic, you had to
assume that many detailed operations were being carried out inside the
organism: there had to be comparison of present circumstances with past
results of tumbles, and of present values of the critical variable with
past values. In short, you built into the model exactly the observations
you had made about the relationships of probabilities of improving the
situation to the effects of tumbles in the various cases. And you built
into it your own logic by which you had arrived at this understanding.
Let us imagine that I had challenged you to construct a control-system model
that would produce a certain behavior. I claim that it is impossible for
you to do so for this particular situation. It would be up to you to
specify the controlled variable and the detailed structure of the model
(e.g., single-level, two-level, proportional, proportional plus derivative,
proportional plus integral, and so on). To my surprise, you come up with a
model that exhibits the required behavior. Now I come back and cry "foul"
-- you specified just what was needed to make the model behave the way you
wanted it to! Would you accept this criticism as valid? I don't think so.
Remember, we were not talking about real e. coli. The task was not to
develop a realistic reinforcement model of e. coli (absurd, as there is no
evidence that e. coli learns to control nutrient level, and the
reinforcement model is a learning model) but to develop a model consistent
with reinforcement principles that would perform as required. Under these
conditions, I was free to invent, so long as the resulting system was so
consistent. If I had been trying to develop a model to account for real
experimental data, my modeling would have been constrained by observation;
I would have needed to demonstrate that the variables supposedly being
sensed and acted on were actually sensed, that the putative reinforcer
really was acting as the reinforcer, and so on. But this was not the case.
I had no such constraints, and therefore was free to suppose whatever I
needed to suppose to make the model work, so long as the result did not
violate basic reinforcement principles.
At best, the result was not a model of organisms in general, but only a
model of organisms capable of grasping the situation and applying logic to
it in just the way you did. You modeled an organism capable of logical
thinking.
Not really. I could easily make up a story in which simple biochemical
variables interacted so as to realize my hypothetical mechanism. But this
would be silly, as from the beginning I stated that the model was not
intended to be realistic. Remember, its purpose was only to show that a
model consistent with reinforcement theory would behave properly under the
conditions given.
As it worked out, the correct behavior was produced not by rewarding the
right changes in behavior, but by punishing the wrong changes in behavior.
There was a provision for rewarding the right change in behavior, _but it
worked the wrong way_. Fortunately, punishing the wrong change in behavior
had a somewhat larger effect on the outcome than rewarding the right change
in behavior, so -- by luck -- the overall model exhibited the right behavior.
There was no luck involved (the model converges on the right behavior,
homing in on the source of nutrients, rapidly and in every run of the
program). Furthermore, your description is grossly inaccurate. The "right"
behaviors (tumbling when going in the "wrong" direction, away from the
nutrient) were sometimes rewarded and sometimes punished; similarly, the
"wrong" behaviors (tumbling when going in the "right" direction, toward the
nutrient) were sometimes rewarded and sometimes punished. Because of the
circular geometry of the nutrient density field, right behaviors were
reinforced more often than they were punished, and wrong behaviors were
punished more often than they were reinforced. As a result, the
probabilities of the right behaviors quickly increased to a high value, and
the probabilities of the wrong behaviors quickly diminished to a low value.
Your suggestion that punishment for wrong "change in" behavior somehow
"outweighed" rewarding the right "change in" behavior is not only incorrect,
it isn't even logical. If your description were true, the model should have
perversely learned to do exactly the wrong thing.
I laid out all these problems in our original discussions, but all you have
chosen to remember is that you got the right result. If I had been in your
shoes, I would have been very concerned about these internal
contradictions, and I would have wondered if there might be situations in
which this particular arrangement of countervailing effects might come out
wrong. But I didn't see any interest on your part in pursuing that matter
any further: you got lucky and weren't about to question the result. Your
intention was to show that reinforcement theory was capable of handling the
situation just as well as a control model could, and apparently, as far as
you were concerned, you had achieved your objective. Why rock the boat?
Again, this is a total fantasy on your part. It didn't happen that way.
What _has_ happened is that you wish to demonstrate that my thinking is of
just the sort you attributed to those "operant behavior analysts" whose
faulty analytical methods were described earlier in your post. So you've
found a way to "remember" those past discussions in just the right way, so
that the parallel will be obvious to all.
Your description of our interchanges on the issue is in part a wishful
reconstruction of the facts; I stand on the record (CSGnet archives). If
you don't believe me, you can look it up.
This is the second time I have challenged you to do this; the first time,
you took up that challenge and discovered, much to your chagrin, that you
were wrong, that my description of our interchanges was accurate. You said
it was a lesson you would not soon forget. Have you forgotten it already?
Returning to our _present_ discussion, what argument would satisfy you that
Darwinian evolution involves a negative feedback loop? Bear in mind that
the argument I present will have to be verbal; I am not a mathematician.
Regards,
Bruce