So what?, Distinguising control systems

[From Rick Marken (940123.0815 PST)]

Bruce Abbott (950122.1340 EST) --

Rick Marken and Tom Bourbon have both indicated that the most common
response of colleagues to this demo is "So what?". Once you have identified
the correlation between disturbance and handle position, you would seem to
have demonstrated a simple case of cause-and-effect, so I can understand why
they would respond in this way. Nothing earth-shaking here: when the cursor
goes that way, you move the mouse in the opposite direction. So what? How
do you respond to that? Get out your coin and rubber bands?

Bill Powers (950122.1550 MST) replies --

If you really want to cause some head-scratching, show this diagram:

                     0.05 0.03
       disturbance <------> cursor <----------> handle position
           > >
            <---------------------------------------->

                              -0.996

Yep. This is the penultimate answer to the experimental psychologist who
says "the disturbance causes the response; so what?". The first answer is
"but the subject cannot SEE the disturbance; only the cursor". The clever
experimental psychologist will then reply "Yeah. But there is information
about the disturbance in the cursor movements". That's when you pull out the
above graph and show that there is no correlation between disturbance and
cursor.

But the REALLY clever experimental psychologist (like me) will then say
"well, the low corrlation between disturbance and cursor doesn't mean that
the cursor doesn't have SOME kind of information in it about the disturbance;
it's just a kind of information that is not linearly related to the
disturbance itself. For example, there might be a lag between variations in
d and c that correlate with one another; and/or the relationship between d
and c may be grossly non-linear.

You reply to the REALLY clever experimental psychologist by doing the study I
describe in the "Cause of control movements..." paper in my "Mind Readings"
book. You have subjects make exactly the same response on two trials by
presenting the same disturbance on each trial (correlation between response
variations are typically > .99). If the cursor has information about the
disturbance, then it must be the same information on both trials. So there
should be a very high correlation between cursor variations on the two
trials when responses are the same. In fact, the correlation between cursor
variations on the two trials rarely exceeds .6, is typically about .2 and is
often close to 0.0, even though the correlation between responses in all
these cases is > .99.

A control model behaves just like the subjects; a high correlation between
response variations when there is the same disturbance on both trials; a low
correlation (ranging from 0 to .6) between cursor variation on the two
trials. So there is clearly no magic involved in control -- but there is
no lineal cause-effect relationship between cursor and output (stimulus and
response) either. Bad news for experimental psychology.

After this demonstration, the REALLY REALLY clever experimental psychologist
just ignores PCT and continues with business as usual. I wasn't THAT clever;-)

Bill Powers (950122.1550 MST)--

Let's simplify. Suppose you see a target moving in a nice triangular
waveform, and you see the cursor moving in the same waveform but with a
10-pixel displacement: simple pursuit tracking. The question is, is this
person controlling the cursor to make it maintain a 10-pixel displacement,
or a 0-pixel displacement?

This is related to one of the little demos I gave in Wales. I showed that the
behavior (in terms of cursor movement and handle movement) of two rather
different control systems was essentially indistinguishable. The two systems
were 1) a low gain system that was trying to keep a cursor in a fixed
position and 2) a high gain system that was trying to keep the cursor
at a reference position correspondeding to the cursor positions produced by
the low gain system. I don't think that you could distinguish the two systems
(from the "outside") without some pretty accurate information about the
physical situation in which they were operating. But if you had this
information, I think they could distinguish the two systems using modelling.

Best

Rick