# Signal Paths (was Hebbian learning)

[Martin Taylor 2009.06.04.09.12]

[From Bill Powers (2009.06.04.0624 MDT)]

Martin Taylor 2009.06.04.00.46–

``````I don't really see any value in continuing
``````

that discussion, which hinged around a claim that if (as is true in any
control system) o = f(d), and one can work with d = g(x), then o =
(f(g(x)).

That’s not quite the argument.

o = f(qi)

qi = g(o) + d

o = f(g(o) + d)

Suppose

o = k*qi and

qi = -o^2 + d

where o^2 means o*o

then

``````1 + SQRT(1 + 4k^2d)
``````

o = ------------------

``````        2k
``````

So the output will be observes as that rather complicated function of
d, and the appearance is that a stimulus produces a response according
to that formula. In fact, the forward (organism) function is a simple
proportionality but the feedback effect greatly modifies the
relationship between d and o.

If k (the forward gain) is large, and d does not go negative, we have
the approximation

``````1 + 2k*SQRT(d)
``````

o ~ --------------, or

``````      2k
``````

o ~ SQRT(d)

so the output appears to be related to the disturbance as the inverse
of the relationship in the feedback path, and the forward relationship
between qi and o is not visible at all.

Whether we use the approximation or not, the apparent relationship
between d and o is different from the forward equation describing the
behaving system. That is the basis of Rick’s objections to the proposed
analysis of the Schouten experiment. To work around this problem it is
necessary to identify qi, the controlled variable, which was not done
in the Schouten experiment. My objection is also based on lack of
identification of qi – in fact, on the impossibility of identifying it
given only the experimental results. Your proposed analysis of the
information content of the perceptual signal is based on using the
apparent relationship between d and o, which is not the same as the
actual relationship between qi and o. Without additional data, it’s not
possible to deduce the value of qi or the form of the forward function,
though of course by assuming a form of the forward function one can
deduce the rest. However, every different assumption will yield a
different value of the measured information, so the model is
underspecified.

I believe I understood this argument, and agree with all of it except
for the last sentence: “However, every different assumption will yield
a different value of the measured information, so the model is
underspecified.”
This sentence is false when substituting one monotonic function for
another. It is not totally false, since there exist functions y = f(x)
that have regions of x for which dy/dx = 0, or for which more than one
value of x can give the same value of y. These are functions that have
saturation or threshold plateaus, or that
are non-monotonic. Such functions will give different results for
H(y|x) than will the monotonic functions that are more likely “f” in qi
= f(o, d) in any experiment on perception. Control become problematic
in case where d(qi)/do = 0 or switches sign as a function of the
magnitude of qi, so we usually assume d(qi)/do retains a constant sign.
Since qi = f(d,o), we make the same assumption in respect of
d(qi)/d(d).
Your specific example of a proportional control system in which d
cannot go negative is not likely to represent many real-world control
situations. The principle you use it to illustrate, of nonlinear
relationships in various pathways of the control system, is likely to
represent almost all real-world situations, but so long as the loop
gain doesn’t change sign as a function of the magnitude of the
disturbance, it won’t affect the informational argument, which starts
with the relationship H(o | d) that is computed from the experimental
data, and in the Schouten experiment d(H(o | d))/dt.
Unless there are separate influences from a common source on o and d,
the maximum information rate d(H(o | d))/dt is determined by the lowest
channel capacity of any influential link connecting them.
One possible, though highly improbable, interpretation of the Schouten
experiment is that the form of the function perception =
f(presentation) changes consistently as a function of the time after a
light is turned on. It is more parsimonious, following Occam’s razor
and the usual principles of PCT, to assume that the form of the
function does not change when its argument (the turning on of a light
in the “presentation”) changes.

If this is true, then d(H(o | d))/dt as actually measured from
Schouten’s data is a fair measure of the lowest channel capacity in the
forward path from presentation to output. That path contains complete
control loops, but it also contains one uncontrolled link from
presentation to perception. One may argue about the functions in the
control loops, and about what perception precisely is being controlled,
but the resolution of such arguments has no influence on the analysis
of the information transmission unless it can be shown that the form of
the control loop changes as a function of time since the onset of the
light. It could, however, be argued that the limiting channel capacity
is in the control loop rather than in the link from presentation to
perception. That’s a different argument than the one you present above,
and I would suggest that it, too, is implausible. I have argued against
it in the earlier discussions.

Since you read Science, I assume you have studied the paper by Kiani
and Shedlen, May 8 2009, Vol 324 p 759. It most certainly is not done
or interpreted within the PCT framework, but I found it interesting,
last part.

Martin

[From Rick Marken (2009.06.04.1400)]

Martin Taylor (2009.06.04.09.12)--

Bill Powers (2009.06.04.0624 MDT)--

If k (the forward gain) is large, and d does not go negative, we have the
approximation

ï¿½ï¿½ï¿½ 1 + 2k*SQRT(d)
o ~ --------------, or
ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ï¿½ 2k

o ~ SQRT(d)

so the output appears to be related to the disturbance as the inverse of the
relationship in the feedback path, and the forward relationship between qi
and o is not visible at all.

I believe I understood this argument, and agree with all of it

So you must now agree with Bill and I that a conventional experiment
like Schouten's, which does not take into account the fact that the
system is closed-loop with respect to it's perceptual input, provides
a misleading picture (as per the "behavioral illusion" described
above) of the nature of the open-loop perceptual component (p = f(qi))
of the path from d to o: d-->qi-->p-->o. Welcome aboard (I wish)!

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

[Martin Taylor 2009.06.04.23.37]

``````[From Rick Marken (2009.06.04.1400)]
``````
``````Martin Taylor (2009.06.04.09.12)--
``````
``````Bill Powers (2009.06.04.0624 MDT)--
``````
``````
``````
``````
If k (the forward gain) is large, and d does not go negative, we have the
approximation
1 + 2k*SQRT(d)
o ~ --------------, or
2k
o ~ SQRT(d)
so the output appears to be related to the disturbance as the inverse of the
relationship in the feedback path, and the forward relationship between qi
and o is not visible at all.
``````
``````
``````
``````I believe I understood this argument, and agree with all of it
``````
``````So you must now agree with Bill and I that a conventional experiment
like Schouten's, which does not take into account the fact that the
system is closed-loop with respect to it's perceptual input, provides
a misleading picture (as per the "behavioral illusion" described
above) of the nature of the open-loop perceptual component (p = f(qi))
of the path from d to o: d-->qi-->p-->o. Welcome aboard (I wish)!
``````

Unfortunately for your wish, the system is not closed-loop with respect
to the input from the presentation of the left or right light. Also
unfortunately for your wish, neither Schouten nor I have made any claim
as to just what is perceived, so the issue of the behavioural illusion
does not arise. The claim he made was about the change of detectability
of the difference between “left” and “right” light on, as measured by
the relation of the output button pushes to the actual light, as a
function of the time between the light onset and the button-push. The
claim I made is that one can convert detectability measures directly
into information measures, and thereby measure the channel capacity of
the pathway, whatever it might be, between the light and the button.
The obvious fact that the button pushes are behaviour that controls
some perception is irrelevant to either claim.

Incidentally, I wonder why you omitted the end of the sentence whose
start you quoted? For the record, my sentence concluded …‘except
for the last sentence: “However, every different assumption will yield
a different value of the measured information, so the model is
underspecified.”’ That was what I disagreed with, and what my message

The rest of the message to which you are responding explains precisely
why the behavioural illusion is irrelevant to the claims. If you have
read it, the only reason I can think of as to why you wrote what you
did was that you were trying to be “amusingly” mischievous. Not

A little advanced philosophy for you, Rick: “All A is B” does NOT imply
"All B is A’. “All behaviour is the control of perception” does not
imply “All perception is controlled by behaviour”.

I hope that’s not too difficult to understand. If it is, I’ll try to
find a way to make it easier.

Martin

[From Bill Powers (2009.06.05.0703 MDT)]

Martin Taylor 2009.06.04.23.37 –

David Goldstein said, “Looks like Martin and Rick are at it again.
Those two ought to get married.” I’m not quite sure what that means,
but it’s funny anyway.

MT to Rick: Unfortunately for
your wish, the system is not closed-loop with respect to the input from
the presentation of the left or right light.

BP:Not if you define the input quantity as a function of the presentation
of the light alone. However, if the controlled input quantity is a
specific relationship between light intensity and state of a
button-press, the perception of the actual controlled quantity can be
disturbed by a change in either variable, and can be corrected by a
change in whichever variable can be affected by the actions of the
system. So while it is true that the state of the light bulb is not
affected by the action, that is irrelevant if perception of the
light-bulb alone is not the effective input variable.
You might be able to measure the channel capacity of the path between the
intensity of the light, measured at the bulb, and the illumination of the
retina which is the last we can measure of the input information by
external means. But the behavior is not based on the illumination of the
retina; it’s based on some function of that illumination, which is
unknown. The function is probably something like p = (light and press) or
(no light and no press), which is affected by the action of the system
and has a reference level of “true.” In some experiments I have
seen (including one reported by Dick Robertson and designed by me),
pressing the right button actually turned off the light, so there was an
effect on the light-bulb. That could easily have been done in the
Schouten experiment. Would the results have been any different?
The channel capacity implied by the Schouten experiment is that between
the light bulb and some stage of perception after the retina. What you
measure is not the channel capacity (the maximum possible rate of
information transfer) but the rate at which information is actually
transferred. From that, you infer the channel capacity under certain
assumptions about the nature of the significant variables.
I posted a model, on which you still have not commented, in which I
assume that there is a first stage of perception where the identity of
the light is instantly and correctly found, being indicated by a
perceptual signal being turned on. So the channel capacity up to that
point is very large. The next stage consists of a forced guess as to the
state of the perceptual signal indicating the decision, the observation
occurring at some time delay after the light actually turns on. The
perceptual decision-signal has a finite rise time so it takes a while
after the decision-signal is turned on for the amplitude of the signal to
rise to a steady state indicating the choice of “left” or
“right.” If the decision-signal is observed before that signal
has risen to its final magnitude, there will be some uncertainty in
the relationship of the signal to the decision
, the amount depending
on the amplitude of the signal relative to the noise in the channel. The
channel capacity you measure, therefore, would not be the capacity of the
channel from the light-bulb to the perceived decision, but only the
part of the channel between the decision and the state of the signal
representing it. You would be measuring not the “detectability”
of the light-event, but the “reportability” of an infallible
detection of which light turned on.

I pointed out a rather long time ago that under my alternate model, the
rise-time of the decision-signal could be quite long, several seconds,
with the forced sampling occurring while that signal had only a small
fraction of its ultimate amplitude. My diagrams explain what I mean. The
setup of the Schouten experiment precludes changing the state of the
light more than one or two times per second, since there must be a pause
between trials to allow the effect of the press, if any, to be observed,
and each trial involves delays as long as 2/3 second before a
button-press occurs. So clearly the actual channel capacity is not being
measured, but is inferred from widely-spaced observations. In fact this
channel capacity could not be realized in the Schouten experiment because
if the lights are turned on and off too rapidly, the subject can’t
perceive their relation to the button presses (imagine turning the next
light on before the button press related to the previous event had been
completed and the button was released again).

MT to Rick: Also
unfortunately for your wish, neither Schouten nor I have made any claim
as to just what is perceived, so the issue of the behavioural illusion
does not arise. The claim he made was about the change of detectability
of the difference between “left” and “right” light
on, as measured by the relation of the output button pushes to the actual
light, as a function of the time between the light onset and the
button-push. The claim I made is that one can convert detectability
measures directly into information measures, and thereby measure the
channel capacity of the pathway, whatever it might be, between the light
and the button. The obvious fact that the button pushes are behaviour
that controls some perception is irrelevant to either claim.

BP: On the contrary, it is crucial. The experiment can’t distinguish
between the detectability of a light-event and the reportability of a
correct detection. Furthermore, the measure of probability of a correct
guess could be the same in either case, but in neither case would it
represent the maximum rate at which information could be seen to pass
from light bulb to button press. Only the actual rate could be observed,
and its meaning would be ambiguous.

It seems odd to me that you can measure the information in a signal
without knowing what the information is about. That would be like a
meter-reading of 2.00, without any indication of whether it meant 2 volts
or 2 pounds per square inch. I have no doubt that there are computations
you can carry out that yield a number; my problem is with the meaning of
that number. Calling it information does not mean that it is about
anything.

It’s interesting that your remarks to Rick are coming more and more to
resemble his remarks to you. Perhaps some form of civil union is indeed
being foretold.

Best,

Bill P.

[From Rick Marken (2009.06.05.0800)]

Martin Taylor (2009.06.04.23.37) --

Rick Marken (2009.06.04.1400)]

So you must now agree with Bill and I that a conventional experiment
like Schouten's, which does not take into account the fact that the
system is closed-loop with respect to it's perceptual input, provides
a misleading picture (as per the "behavioral illusion" described

>above) of the nature of the open-loop perceptual component (p = f(qi))
of the path from d to o: d-->qi-->p-->o. Welcome aboard (I wish)!

Unfortunately for your wish, the system is not closed-loop with respect to
the input from the presentation of the left or right light.

I presume this is more of your "supporting artillery". I presume you
are thinking of the "input from the presentation of the left or right
light" as d and the button press as o. So there is, indeed, an
open-loop connection between d and o as I diagrammed above:
d-->qi-->p-->o. As I've noted before, this seems to to be the
situation in every psychological experiment. The IV (such as
presentation of a light, presentation of a sound, presentation of
pairs of block objects, presentation of a drug, etc) is a disturbance
to a controlled variable that is also influenced by the subject's
output, the DV. The loop, of course, is closed with respect to qi:

d--->qi-->p-->o
^ |
> ______|

But you seem to think the Schouten experiment is unique in the sense
that it has been set up so that, as you say: "The system is not
closed-loop with respect to the input from the presentation of the
left or right light". Now this whole discussion came up in the context
of my "Revolution" paper, in which I argued that it is impossible to
study open loop causal components of a closed loop system using the
conventional experimental methods of psychology because they fail to
take into account the fact that the system is controlling some
perceptual variable. You said you liked the paper but you tempered
your praise by pointing out that there were conventional experiments,
Schouten's being an example, which are designed so that they are
exempt from the criticisms made in my paper. Bill and I have been
trying to convince you ( with no apparent success and to the
considerable amusement of David Goldstein) that this is not the case;
that the Schouten experiment is no different than any other psychology
experiment. But you seem committed to your point of view. So let me
ask you this: Since you did say you liked my paper you must, then,
agree that the arguments apply to experiments other than the Schouten
experiment. So could you give an example of one -- just one --
psychological experiment to which the arguments in my paper do
correctly apply and explain how the design of the Schouten experiment
differs from the design of that experiment, making it possible to
determine open loop causal components of the subjects in the former
(Schouten) experiment but not the latter (your example) experiment.

Thanks a bunch.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

[From Rick Marken (2009.06.05.0830)]

Bill Powers (2009.06.05.0703 MDT)--

David Goldstein said, "Looks like Martin and Rick are at it again. Those two
ought to get married." I'm not quite sure what that means, but it's funny
anyway.

Apparently the sense of humor is the second thing to go. But we
couldn't get married in California anyway and, I'm afraid Martin's not
really my type. Now if Barak Obama wasn't already married I'd be
planning my move to New Hampshire right away. That's my kind of guy!

MT to Rick: Unfortunately for your wish, the system is not closed-loop with
respect to the input from the presentation of the left or right light.

BP:Not if you define the input quantity as a function of the presentation of
the light alone.

You're just trying to steal Martin away from me by going at it again
with him yourself (saying what I would say, only better) and then
blaming me for being a meany. Masher!

ï¿½MT to Rick: Also unfortunately for your wish, neither Schouten nor I have
made any claim as to just what is perceived, so the issue of the behavioural
illusion does not arise... The obvious
fact that the button pushes are behaviour that controls some perception is
irrelevant to either claim.

BP: On the contrary, it is crucial.

Hey, buddy, stop beating my time. Oh, never mind, he's yours ;-(

It's interesting that your remarks to Rick are coming more and more to
resemble his remarks to you. Perhaps some form of civil union is indeed
being foretold.

No need to play the brave loser. I told you, you can have him.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com

[From Bill Powers (2009.06.05.1521 MDT)]

Martin Taylor 2009.06.04.09.12 –

Since you read Science, I assume
you have studied the paper by Kiani and Shedlen, May 8 2009, Vol 324 p
759. It most certainly is not done or interpreted within the PCT
framework, but I found it interesting, nevertheless. I’d be interested in

I think that conventional brain research of this kind with nonhuman
species is extremely difficult, if not impossible. There is simply no way
to verify what the animal is doing or experiencing, without the test for
the controlled variable. The anthropomorphising and guessing in that
article is not a valid substitute. I don’t think the authors have made
any sort of case for saying that the monkeys were making
“decisions”, that they were “opting for the sure
target,” that they perceived “probability” or
“belief”, or just about anything else the authors claimed was
going on in the monkey’s brain. If the experiments had been done on
humans, we could at least have interviewed the subjects and found out
what they thought they were doing. Perhaps the test for the controlled
variable might have helped figure out what the monkey’s goals (and
perceptions) were, in some sort of neutral terms that didn’t force the
attribution of human perceptions to them. But the authors seem to have no
qualms about supposing that the significance of the displays was the same
to the monkeys as it was to the human observers. That bespeaks the
Gibsonian theory of perceptions, in which we and other organisms simply
look through our “transparent” perceptual systems and see the
world as it really is. I didn’t think anyone believed that any more, but
I guess I’m wrong.

There has been a spate of articles in Science, lately, about many
similar approaches to brain research. It’s very peculiar, as if we had
gone back a hundred years to naive realism and behaviorism and
reductionism of the crudest sort. In every issue lately, it seems, there
is at least one article in which the experimenters do brain scans or
measure EEGs or trace out impulse pathways and draw conclusions about
psychological or social phenomena, sometimes in humans and sometimes in
other species. The idea seems to be that if brain activity correlates
with some external situation or action, it must indicate the same
perception at the same level that the experimenter experiences. Of course
the idea of levels of perception is completely missing from such
writings, as is the implication that the same external situation could be
represented many times in the brain, simultaneously and at different
levels.

I think this whole line of research is way off the track and is more
imaginative than scientific.

Best,

Bill P.