Output, Perceptual information about r

[From Rick Marken (930405.1100)]

I said:

1) There IS information in the perceptual signal of an ECS!

2) The information in the perceptual signal is about the

Bill Powers (930405.0915 MDT) replies:

I think I know what you're doing. However, would you calculate
the correlation between (p - o) and d for your experiment? I
predict that it will be pretty close to 1 -- even under the
conditions you're using. If there's a feedback function between o
and p, use f(o) instead of o.

I think you know what I am doing with my "logic renunciator"
stack, yes. I do put a function between o and p (f(o)) and calculate
the correlation between the o and d. This correlation is quite
low sometimes. If I correlated f(o) with d then the correlation
would always be close to 1, as you note.

The point of doing this demo is to show why it is wrong to imagine
that there is any information (in the signal following sense) in p
about what o to generate to compensate for d. The variable, o,
is the last thing that the control system itself is responsible for;
o is directly caused by the error signal. But the effect of o on
p depends on the state of the world at the time o is generated --
and the control system can do nothing about this. The state of
the world is described by f() which is likely to be not only
nonlinear but also time varying.

Just to get tangible here: in a real control system (like a person) I
see o as the most proximal result of neural stimulation. So o might
be the degree of contraction of a group of muscle fibers. This o
variable is then translated (by physical law) into forces that move
a mouse that, ultimately, moves a cursor on a computer screen. This
last variable is the input variable, p. So there is a long causal
chain between o and p that is quite independent of the actor; the
influence of this causal chain on the effect of o on p is described
by f(). In the tracking (with a mouse) experiment, for example, part
of f is the coefficient of friction on the roller ball in the mouse;
as you move the mouse across the table (or pad) you encounter smoother
or rougher spots that influence how the muscle tensions you generate
(o) are translated into cursor positions (p). There is no way for
the actor to know , at any instant, how f() will transform their o
values into p values. So the actor's "distrubance correction" outputs
cannot depend only on disturbance produced deviations of the cursor
from the target. They must also depend on the amount of effect the
actor him or herself is having on the p. All this "information"
(about the effect of the disturbance and the actor's own outputs)
is mixed together in p; p = f(o) + d. But the actor computes
outputs that compensate for both the effects of the disturbance AND
of the actor him/herself (f(o)). So there is really no information
about o or d that is used by the actor; all the actor knows is p
(the net effect of both) and the actor continuously generates outputs
which end up keeping p near r. So it is really r that carries the
information about what p should be; not d carrying the information
about what o should be. Even the error signal (r-p) does not carry
information about what o should be because the same error value can
require very different o values to bring p back to the same r. It's
true that o is deterministically related to e; but the result of
producing that o (in terms of its effect on e) can be very different
depending on the prevailing f(o).

So "circular thinking" about the control loop leads to the idea
that a control system is continuously generating o values (based
on error) that make p match r. This is the basis of my proposed
resolution to the "information in perception" debate. All I am
saying is that p can be used as information (in both the "signal
following" and "which signal is actually occuring" senses) about
r. You can't use o to determine d but you can use p to determine r.
This is just another way of saying what PCT is all about; one of the
goal of the PCT researcher is to determine r from p in living control
systems. This is very different than the goals of the conventional
researcher, who often wants to determine o from d.