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Posted-Date: Fri, 09 Oct 92 12:27:07 PDT
Newsgroups: bit.listserv.csg-l
Date:         Fri, 9 Oct 1992 12:27:07 PDT
From:         marken@AERO.ORG
Subject: Re: Why 99%, hierarchical perception

[From Rick Marken (921009.1230)]

Martin Taylor (921008 20:30)

>In response to Rick Marken's suggestion that we
>continue a private discussion via CSG-L.  In view of his suggestion, I hope
>he will not object if I quote from that mail.  If I'm wrong, I apologise in
>advance.

I don't object, I rejoice (well, anyway, yes, that's what I wanted).

>I think you might be tempted to believe that you have shown the possibility
>that perceptual input functions (PIFs) can include multiplication operators,
>x and y both (presumably) being controllable CEVs in themselves.  Now I
>propose to you that this is false, and I propose as a counter-possibility
>that addition operators and logarithm operators are possible, and that
>the "correct" PIF is log(x)+log(y).

No problemo. I was just trying to show that the variable being controlled
was more like x*y than x+y; I didn't care how the neural signal was derived
from the sensory inputs, though I think it might be interesting to try to
figure it out -- especially if you are interested in how neural processing
works.

>It is (conceivably) important to distinguish these
>possibilities, because they may have strong implications for the brain
>structures involved not only with this percept, but with many other percepts.

OK.

>What to do?

Probabaly try to find the neural signal that corresponds to the controlled
variable and start dropping some single cell recorders in there.

>But now let's introduce a new reference size, in which x and y are both
>doubled.  So the new level of (x*y) is four times the old reference level.
>But the gain is, we assume, undisturbed, so we expect to see much the same
>error in prediction.  We have only changed the reference level, an additive
>variable in the equation.  The same is true if the subject is controlling
>log(x)+log(y), but instead of multiplying the reference signal by 4, we have
>added 0.6 units to whatever it was beforehand.  If we now refer the variance
>of our estimates to the size set as a reference for the subject, we find that
>if the logarithmic hypothesis is correct, the residual variance is constant
>in log size units, whereas if there is a multiplier operator in the PIF, the
>residual variance is constant in area units.

I'm not sure I buy this derivation. What is the "variance of our estimates"
by the way? What is the "residual variance" here? the variance of the
the size of the quadrilateral relative to the reference size? In what
way is the residual variance "constant" in log size or area units. I don't
understand the analysis, I suppose. If you explain it to me I could do it
in a second since it's easy as pie to do the experiment -- I already
have the area control program ready to go and it's pretty easy to change the
size of the reference square. Maybe it's my bias but why not have the
reference square vary continuously in size?  Then you could look at the
size of the error as a function of the size of the reference area. Maybe
that's what you want anyway -- maybe you are saying that the size of the
error will be constant with respect to log size rather than size?? Is that
it? I still don't get WHY this would be true if their is a log transform
applied to the inputs to the perceptual function. Maybe you could give
a simple mathematcal reason for this prediciton -- but keep it simple; I'm
certainly no math whiz, as, I imagine, you can tell.

>I think the results would be contaminated by other effects, but the main idea
>should be valid.  It's a very simple kind of case, but it is typical of the
>sort of thing that psychologists want to know.

Yes, and they miss the whole point. The fact that the person is controlling
a variable and that it took some doing to figure out what it is just goes
right by. Early astronomers wanted to know how the patterns they saw in
the night sky were related to one's personality. I know it's rude but,
frankly, I could care less what conventional psychologists want to know.
What they want to know is based on their preconceptions about how people
work; so they think it is important to know how reinforcement affects
behavior or which behavioral/cognitive capabilities are in the right
brain and which are in the left, etc etc. Since their preconceptions
about how people work are wrong (because they don't understand the
consequences of the fact that organisms are locked in a negative feedback
situation with respect to their environment -- cf. the blind men paper)
it is only by chance that anything psychologists might want to know about is
anything more than an illusion from the point of view of PCT.

Have a nice weekend all

Rick


     **************************************************************

Richard S. Marken                   USMail: 10459 Holman Ave
The Aerospace Corporation                   Los Angeles, CA 90024
E-mail: marken@aero.org
(310) 336-6214 (day)
(310) 474-0313 (evening)
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU