[From Bill Powers (940603.1015 MDT)]
Martin Taylor (940603.0930 MDT) --
Don't confuse the uncertainty used by the analyst with the
uncertainty currently under discussion when we look into Paul
Revere's head. If Paul is to perceive uncertainty, and to
control that perception, he has to have an ECS whose input
function provides a signal that is the level of uncertainty in
some other perceptual signal about its CEV. That "uncertainty-
control" ECS cannot use at all the same inputs as the analyst
would, and it probably will not get the same results the
analyst would.
We're making some progress. You have now defined subjective
uncertainty in a way that allows applying the Test. I'm
uncomfortable with drawing conclusions about what goes on in Paul
Revere's head, because you can put anything there, in imagination,
that will make the argument come out the way you want.
The easiest way to apply the Test is to set up a control task (e.g.,
every tracking task is an application of the Test). So we need first
a control system in which there is an uncertain connection between
its CEV and the perceptual signal, and of course a means of
affecting the perceptual signal via action on the CEV. Then we need
another control system which senses both the CEV and the perceptual
signal of the first system and perceives the uncertainty in the
relationship, and has some means of altering the uncertainty (which
can easily be provided by a program).
You're going to have to help out here. Suppose the CEV is the actual
relationship between a cursor and a target, and the perceptual
signal is the perceived relationship (you can substitute any other
task). We know how to model the person in this task. But I'm having
some trouble imagining how to set up the second task so the person
can monitor the CEV as well as the perceptual signal in order to
perceive the irregularity in the relationship. And come to think of
it, I'm having a problem with seeing how to introduce an uncertainty
between the CEV and the perceptual signal, so the CEV has a known
value but the perceptual signal is an uncertain representation of
it.
We have to find a way of setting up a CEV so we can know what it
"really" is, but in such a way that the participant in the
experiment gets only an uncertain perception of it. Then we have to
think of a second way for the same person to perceive the CEV, this
time accurately perceiving its actual state, and also being aware of
the uncertain perception of it.
This seems to create a logical problem. We have an uncertain
perception but a known CEV. This implies that we can define the CEV
objectively, and introduce an uncertainty such that the perceptual
signal could represent an apparent value of the CEV that is
different from the actual value. But in that case, wouldn't the Test
give the wrong definition of the CEV? When the person claims to be
maintaining a constant value of the perception, the actual CEV would
be varying. But the Test can use only the actual CEV as the basis
for judging resistance to disturbance and computing the reference
level. If we used that as the basis for defining the CEV, we would
have to conclude that the reference signal is varying.
I'm stuck on that one for the moment. Perhaps you have some
suggestions.
The second problem seems just as difficult. Somehow we have to
provide the person with a second way of perceiving the same CEV,
only this time without uncertainty. This implies a perceptual
function just like the one used in the first control system, but
free of uncertainty in its representation of the CEV. We can't use a
copy of the perceptual signal from the first system (i.e., the
perception of the CEV that the person is already getting through the
input function of the first control system), because that is the
signal we want to compare with a second signal representing the true
value of the CEV. We must duplicate the form of the function in the
first control system, but this time making sure that there is no
uncertainty in it. In experimental terms, we must provide the person
with a second way of perceiving the same CEV which will give the
person accurate information about its state.
But I confess that I can't see why, if the person had a way of
perceiving the true state of the CEV, the person wouldn't simply use
that input function for controlling it in the first place. How could
we arrange the experiment so the person would use an uncertain way
of perceiving the CEV in controlling it, and would use a certain way
of perceiving it only as a basis for adjusting the uncertainty
(using means we provide) in the first way of perceiving it? It seems
to me that in saying that the person is given some way of perceiving
the true state of the CEV, we have made it unlikely that the
experiment could be done at all.
Over to you.
···
--------------------------------------------------------------
Best,
Bill P.