Uncommon ground

[From Rick Marken (930317.0800)]

Avery Andrews (930317.1514) --

People just don't care about the input-output model of behavior as
much as Rick thinks they do.

Multi-millions of dollars are spent in the US (and probably
Australia too) in support of behavioral science research (psych,
sociology, econ, poli sci, etc) where the data is collected
and analyzed in the context of the general linear model; multiple
regression, ANOVA, etc. I bet few of these people would consciously
say "I assume that the basic model underlying behavior is a
cause-effect model" but they sure ACT like this is what they
assume-- and big bucks are being spent in tacit support of this
assumption. I believe it is important to know that this is the
model that behaviooral scientists are "controlling for" -- consciously
or not -- because I am sure that it is the reason why PCT -- after,
what, 30 or so years on the scene -- has made virtually NO headway
in the behavioral sciences. Its either that PCT is just a stupid
model and all the behavioral scientists have been smart enough to
notice that (but there are some other obviously stupid "models"
running around in the behavioral sciences and, nevertheless, they
get a lot of attention) or it is because of active resistence. I
think PCT has made no headway because there IS active resistence
and I think the underlying reason for this resistence is that PCT
is a disturbance to the assumption in the behavioral sciences of a
cause-effect model.

Indeed, I suspect that one of the reasons
linguists don't spend much time in the psych lab is that the
input-ouput, IV-DV stuff just seems stupid and boring to them, w.r.t.
the things they are interested in, but that's the only thing that people
seem to know how to do in labs.

Well, I don't know if I would brag about not having any model
at all. Just observing is very genteel and all -- but unless you
try to predict and explain what you see with a model, what have you
learned? I think that linguists do have implicit models -- cause
effect models. If they don't want to test them then that's there
problem. I don't care if they test them in labs or in the real world;
but I don't think you have much of a science unless you test models.
If linguists don't know how to do anything other than IV-DV research
when they do it it's because their basic (unconscious model) is
cause-effect. If they don't go into the lab to do IV-DV research it
must be because they don't like the implications of their own models.
If their models were not cause-effect -- if, for example, they were
control of input models -- I'm sure these bright folks would have
noticed very quickly that there is an alternative to the IV-DV
approach to research and they would have very quickly understood
research based on testing for controlled variables.

Avery Andrews (930317.1830) --

Suppose we add to our system
two random noise generators, one into p(t), one into o(t), both
downstream from where we are taking our measurements. Switching
either of these generators on will clearly degrade our information
about d(t),

Wait a minute. What do you mean "clearly degrade"? I thought we
finally agreed that d(t) is "information" only in the sense that
it is part of the perceptual signal. When you add noise to p(t)
you now have p(t) = d(t)+o(t)+ e(t) where e(t) is the noise.
Notice that d(t) is still part of p(t) in all it's glory and
o(t) will be proportional to d(t) + e(t). Now all you can find out
from p(t) by knowing o(t) is the sum, d(t) + e(t) which means
that information about d(t) is not degraded -- it is eliminated
(in the sense of usable information). But the information about
d(t) -- in the sense in which we agreed that the information
about d(t) exists -- is still there.

The idea being if we can
damage the info by injecting noise into a channel, it must in some
sense be there. But in what sense is kinda mysterious, isn't it.

Well, now you've confused things completely. How do you measure
the amount by which the information (about d(t) I presume) is
"damaged" by injecting noise? We seem to be back to square one
(despite Bill P.'s diligent attempts at reconciliation this
morning -- I'll get to that in a second).

You are saying that the information ABOUT d(t) is DAMAGED by
addition of noise, e(t), to the perceptual signal. This is
completely inconsistent with my understanding of what we had
agreed to be the information available about d(t) in p(t).
I thought we agreed 1) that information about d(t) is available
in p(t) simply because p(t) = o(t)+d(t) 2) you can recover
this information if you know o(t) and 3) since the control
system itself does not have access to information about its
own o(t) [Bill's proposal this morning requires multiple
control systems, some of which have, as input, the o(t) of
other control systems] the information about d(t) that is in
p(t) in not informative -- IT MIGHT AS WELL NOT EVEN BE THERE

Now you are saying that information about d(t) is degraded by
addition of e(t) to p(t). If you go by meaning 2) above of inform-
ation then the best you can get out of p(t) is d(t) + e(t) --
in other words a signal that is the sum of two signals. So,
unless you can now get a hold of e(t), you are in the
same position as you are given definition 3) of information --
the information about d(t) in d(t) + e(t) is uninformative.

Bill Powers (930317.0700) --

Now it's time for all of us to
start saying, "OOOOH! I thought you meant ..."

Well, after Avery's last couple of posts its clear to me that
what I thought the "opposition" meant by information is
what they mean by information. Avery clearly believes (see
above) that there is USABLE information about d(t) in p(t)--
otherwise, why would noise "degrade" that information.

The combination of Cliff's and Avery's posts suddenly showed me
that my own view has been too narrow. It is perfectly possible
for a _hierarchical_ control system to deduce the actual state of
a disturbance of one lower-level control system.

This was a very interesting discussion -- and I think it is
definitely worth more development. I never doubted that a
hierarchical system could deduce d(t); since it could get
information about p(t) and o(t) (well, actually, as you
said, the error signal -- the function relating output to
input -- the physical world tranformation -- would have to be
a guess). But I don't think that is what Avery or Martin
have in mind when they talk about the information in p(t);
although I think it would be a nice plateau on which to settle
their reorganization.

Based on Avery's comments above, it seems to me that there
is still some cause-effect thinkingabout control system lurking
around in the background. I think that some people still think that,
in a control system, there is USABLE information about d(t) in p(t).
I have conceded that information about d(t) EXISTS in p(t). But I
am arguing that that is a matter of supreme irrelevance to
the system that is controlling p(t) because there is no
way (or need) for that system (in and of itself) to get the
information about d(t) that is in p(t) -- because it has no
way (or need) to know o(t). So there IS information about d(t)
in p(t) but, as I said about a week ago to Allan Randall --
SO WHAT? It is completely invisible to the control system; its
just like it wasn't there. It can be MADE visible by the clever
hierarchical combination of several control systems (that's why
clever hierarchical control systems like us can do science).

I'm pushing on this because I want Avery to appreciate the
magnitude of what Uncle Bill hath wrought.