[From Bill Powers (2010.02.04.1710 MST)]
Bruce Abbott (2010.02.04.1535 EST) –
BA: Careful, Rick: You’re
starting to sound like a Skinnerian! Skinner would
have said that the rat presses the lever, not because it expects
food
thereby to be delivered, but because food delivery has followed its
lever-presses in the past. Tolman would disagree, asserting that the rat
had
learned a means-end expectation for reaching a goal. Now, wanting food,
it
presses the lever.
BP: I wouldn’t use those common-language terms or say “because”
as you say Skinner would have done when it’s a non-sequitur. OK, the
delivery has followed presses in the past. What does that have to do with
pressing the lever this time? Could it be that the rat has learned what
action to produce in order to create a given perception? That’s how we
would replace the “because” statements in PCT-compatible
language. There’s nothing about past events that can affect present
behavior in the slightest, unless there was some change in the physical
system to alter the relationship of actions to perceptions. Events don’t
cause anything; they just happen.
Terms like expectation are essentially useless to us unless you can
express the same meaning in PCT terms.
The reason your models work so
well without expectation is that the
environmental consequence of the control system’s actions (its
negative-feedback relation to the controlled variable) is already built
into
the model. The model behaves “as if” it “believed”
that moving the cursor in
a given direction would reduce the error between cursor position and
reference. But of course it doesn’t “believe” anything; it just
acts as it
was made to act. The thermostat provides another
example.
The environmental consequence is not built into the model; it stays in
the environment. What is in the model is a perceptual input function, a
comparator with a reference level, and an output function. In a
hierarchical model there are many of these things, connected in a
specific way. Unless you can connect “expectation” to something
in this model, you’d be better off finding out what the term indicates,
and starting at that level. Just saying “expectation” doesn’t
explain anything.
Behaving “as if” there is a belief is an interpretation by an
observer who wants to see beliefs whether any are actually there or not.
This is like making every corner the driver of a car encounters into an
“implicit” choice point. It’s only a choice point if the driver
makes a choice, which doesn’t happen if the driver goes that way very
often. Same for beliefs: if the driver makes an hypothesis about whether
this corner is the one where he is to turn, then whether he turns or not
depends on the credence he gives to this hypothesis. On the other hand,
he might just turn the corner without hypothesizing anything, because he
knows this is the right way to the destination.
BA: So what would distinguish a
system that developed expectations from one that did not? Perhaps a
crucial test would be to observe what the system did if the expectation
were violated.
BP: I wouldn’t start there, because I wouldn’t know how to tell if there
were an expectation at all. Maybe systems don’t ever develop expectations
– how would you know? The only way to find out what you’re talking about
is to settle down and look at something you expect, and take the
experience apart into its components. Here you sit at the train station,
expecting a train to arrive any minute. How do you do that
“expecting” thing? You don’t do it by seeing a train because
the train isn’t in sight yet. What exactly is it that you do that you
call expecting something?
By the time you’ve found the answers to all the questions that come up,
you won’t need the common-language terms any more. You can say what you
mean in PCT terms.
If you suddenly reversed
the relationship
between mouse and cursor movements, a system without an expectation
would
simply continue to act as it did before, and control would simply
fail.
There’s a partial definition of expectation. What is the expectation,
such that when it’s missing, control would fail?
A system that
“expected” the cursor to move as before (based on previous
experience) would find its expectation violated and presumably take
action
to sort out the problem.
Is that how control systems change their behavior to counteract errors?
If you venture a guess as to how this expectation thing results in taking
action, and what kind of action it would take, and what the problem is
that needs to be sorted out, you would have a useful model, perhaps, in
which the term expectation wouldn’t even appear.
BA: Although this seems like a
simple enough test for expectation, one might
have difficulty distinguishing between true expectation and
reorganization.
As in the case of expectancy, in reorganization the violation of the
usual
relation between mouse movement and cursor movement would bring about
a
change in the system’s organization; if successful, reorganization
would
restore the negative feedback relation and control over the CV would
recover.
BP: If you can’t measure an expectation by itself, how do you think
you’re going to know when an expectation is violated? What we can observe
is that when the sign of the environmental feedback function is reversed,
control at first starts to run away exponentially, and then, after about
four tenths of a second, the control system reverses its own sign and
control is recaptured. Rick and I collaborated on that experiment. I
don’t see any room there for expectation. In fact, knowing that reversals
are going to happen during a tracking run is of no help at all, since you
don’t know when they’re going to happen. If you try to prepare for
them, your tracking performance deteriorates; if you don’t prepare you
just go through the changes as usual. You just wait for the error and
then correct it. No expectations needed, and if you have any, they don’t
help.
Expectation may be a high-level
process involved in planning actions,
drawing on means-end relations learned during previous experience,
worked
out logically, or perhaps communicated to us by others. ("You want
to get to
the bank? Take Third Street to Maple and turn left." You then follow
those
directions because you expect that they will take you to the
bank.)
That’s more like it. I would say you follow the directions as the only
means you know of getting to the bank, and in the background are hoping
that you’re remembering them right or they were given right. There might
be some sense of expectancy, but I don’t know how that would change if
the destination is a bank or a grocery store. A little more work and we
could just drop the term expectancy, except as a description of a
side-effect of doing all this.
Did you really say “planning actions”?
Expectation seems less likely to
be involved in habitual activities,
although then we do behave “as if” we had
them.
The “as if” part is in the observer’s imagination. Throw it
out.
Best,
Bill P.