Why do you care?

CSGnet Archive CSG1993
1

[From Rick Marken (930404.1030)]

Martin Taylor (930401 12:05)--

It would not be possible to use my thought experiment to test the
experimental question as to whether there is information from the
disturbance in the perceptual signal, because we have no access to
a perceptual signal or the related reference.

Well, I guess that does it. If you won't accept your own proposal --
the one you already accepted as a test of this question -- then I'm
sure you won't accept any of ours. It looks like you're going to
believe that there is information about the disturbance in the
perceptual signal NO MATTER WHAT. We have tried several ways of show-
ing you that there is, indeed, no information about the disturbance
(or the output, for that matter -- why do we always leave that out?)
in perception. Let me count the ways:

1) p = o + d so knowing that p = 3 you can't tell whether
(o, d) is (1000, -997) or (0,3) or (-6,9) etc

2) The correlation between p and d vectors and p and o vectors in a
closed loop tracking task can be nearly 0 while the correlation between
d and o is nearly perfect (.99+)

3) The correlations between p vectors in two closed loop tracking
experiments can be nearly 0 while the output vectors are perfectly
correlated (.99+) with each other and the disturbance.

4) Simulation of Martin's Mystery function shows that the x vector
equals d vector only when p=o+d, r=o and there is no error input
to the output or to teh Mystery function.

Since it now seems impossible to demonstrate this fact to you
(that there is no information about the disturbance -- and, hence,
about how to generate output -- in a controlled perceptual variable)
perhaps you could try to explain why it is so important for you
to BELIEVE that this is true. You must consider my claim that there
is no information about the disturbance in the controlled perceptions
to be a similar BELIEF since, if there is no way for me to show that
you are wrong there is obviously no way for me to show that I am right
(I take it that a copy of the HyperCard stack wouldn't help now, either,
since you have said, above, that your thought experiment doesn't test
what it tested yesterday). I can tell you why it's important to me
to "believe" that there is no information about the disturbance in
perception; in fact, I explained why in a post some time ago on
"what's at stake" in this debate.

Why do you care whether or not there is information about the disturbance
in controlled perceptual inputs? Why are you less concerned (given
the attention it has received) about whether or not there is information
in controlled perceptual input about the system's own effects on that
input?

Gary Cziko (930401.0450 GMT) --

I would like to consider
the very idea of what an "independent" variable is.

Wonderful post. Yours is a nice way of talking about what we've
been trying to say (in harsh mathematical terms) in the "information
about the disturbance" debate. d is an independent variable (like the
"teaching methods"). But it's effects on the student (p) are not
independent of the student's own outputs (o). The student deals
only with p and if p is controlled, then there is no independent
variable (d) relevant to the student's behavior (r).

The reason our point about "no information about the disturbance"
is important is because it is the basis for claiming that the
IV-DV approach to reserach tells you nothing about what people
are actually doing, which is, controlling perceptions (p) relative
to internal references (r).

But I like your way of explaining it a LOT better than mine; I hope
you make better progress than I did.

Best

Rick

2

[Martin Taylor 930402 11:10]
(Rick Marken 930404.1030) (day after tomorrow; good predictive control)

It would not be possible to use my thought experiment to test the
experimental question as to whether there is information from the
disturbance in the perceptual signal, because we have no access to
a perceptual signal or the related reference.

Well, I guess that does it. If you won't accept your own proposal --
the one you already accepted as a test of this question -- then I'm
sure you won't accept any of ours.

Your argument was about models, as was and is ours. My comment you quoted,
as you well know, is about processes in a living control system. I
proposed and Allan executed the experiment in a simulation, and proved the
point that you cannot jointly say that the output contains information
about the disturbance but the perceptual signal does not.

Up until today (or rather two days from now), you have said that the
disturbance and the output correlate 0.99xxx in many many postings. Now,
to retain your position that there is no information about the disturbance
in the perceptual signal, you have suddenly shifted to the position that
the correlation between disturbance and output is 0.00. There is experimental
fact, determined by you and acceptable as being a scientific fact even
to Bill Powers, that the 0.99+ figure is often correct, and 0.95+ usually
correct.

You can't have it both ways. Either the disturbance and the output are
correlated, as experiment and model both show, or they are not, which you
now claim in an extreme resistance to the simulation demonstration. I
find this resistance mind-boggling.

From the same posting:

1) p = o + d so knowing that p = 3 you can't tell whether
(o, d) is (1000, -997) or (0,3) or (-6,9) etc

We have never disputed this. It is a given through the whole discussion.

2) The correlation between p and d vectors and p and o vectors in a
closed loop tracking task can be nearly 0 while the correlation between
d and o is nearly perfect (.99+)

Yes, that's the basis for the simulation.

3) The correlations between p vectors in two closed loop tracking
experiments can be nearly 0 while the output vectors are perfectly
correlated (.99+) with each other and the disturbance.

Yes, that is as one would expect, given the slightest difference in
initial conditions of the runs. However, the correlations of p1 and p2
(different runs) do differ from zero at points where the disturbance
makes a rapid excursion. p1 and p2 do track moderately well over a
short period after such an excursion.

4) Simulation of Martin's Mystery function shows that the x vector
equals d vector only when p=o+d, r=o and there is no error input
to the output or to teh Mystery function.

Not so. P = O + D was a given because that is what has always been
claimed as a basic property of the loop. The other conditions are
irrelevant. The simulation was to show that X=O, not that X=D. Provided
O and D are correlated, X has information about D, but it is not equal
to D unless the correlation of O and D is 1.000. On our side, no claim
was made about the relation between O and D or between X and D. We relied
on you for that. In a scientific argument, you are allowed to change your
claims about the properties of systems, given new evidence. But you can't
change them just to retain an inconsistent set of beliefs.

ยทยทยท

---------------------------
Bill Powers (930401.2200) has it right, when he repeats what I have been
trying to get across through this whole discussion:

When we are talking about an optimally-performing control system
that uses an integrator in its output, there are two answers:

1. The perceptual signal does not contain ANY SIGNIFICANT
information about the disturbance.

2. The perceptual signal contains ALMOST PERFECT information
about THE FIRST DERIVATIVE OF THE DISTURBANCE.

And having the value of the first derivative gives a function that
contains an integrator the actual value of the disturbance, minus an
unknown constant of integration. The constant of integration is
unknowable, since the disturbance must, in principle, be measured
on a scale with a zero point whose location has no a priori value
(is the fact that the object has an X location of 3 feet inside the
door an indication that it currently has a 60 ft disturbance of its
position?). The initial disturbance is relative only to the ECS's
reference value for the CEV. That is what provides the zero, and if
the reference shifts, so does the zero point for the disturbance scale.

You can relate the disturbance to a zero fixed in the environment, if you
want, but that zero is arbitrary. If you do that, you have to subtract
the reference from both the output and signal X to recover the disturbance
while the reference level shifts.

Now I can demur a bit from Bill's "almost perfect." There are lots of
reasons why it isn't perfect, and if this discussion is allowed to proceed,
we can develop them, and show why it is important to control theory to
understand where and why and how much information about the disturbance
is in the perceptual signal.

The reason the value of the perceptual signal at any particular moment
cannot be used to determine the current value of the disturbance is
that the information has been used for control. In other words, it
has been bled off the perceptual signal into the output signal, as I
have tried to get across in many postings.

The reasons information is important are mildly interesting in a single
control loop such as the one that has been the bone of contention in
this discussion, but are pretty fundamental when we get into the hierarchy.
Bill himself pointed the way to one reason in the posting Rick called
"really lovely." What it shows is that the degree of control, as determined
by the ratio of perceptual variability to disturbance variability, is
determined by the relative bandwidths of the perceptual system and
the disturbing variable.

If my algebra is right, then Bill's argument leads to:

log(control ratio) = (log perceptual resolution)*( 1 - BW ratio) / (BW ratio)

where control ratio is the ratio of perceptual variation to disturbance
variation, perceptual resolution is the ratio of perceptual range of variation
to the minimum resolvable perceptual variation, and BW ratio is the ratio
of disturbance bandwidth to perceptual bandwidth. This is very rough, and
depends on there being no limiting effects from output bandwidth or
transport lag. And my algebra is notorious for mathematical typos such
as sign inversion.

Anyway, that formula follows from Bill's posting, which does NOT imply
what Rick says:

We are right because this information is not used by the control
system itself.

It IS used, most explicitly and adequately.

Martin