[From Rick Marken (940206.2030)]
Bill Leach (06 Feb 1994 10:35:18)--
Rick; I'm really having trouble with this one!
Excellent! You are probably having trouble with it because you
understand it. It IS rather amazing.
If there indeed ARE the exact same signals "disturbing" the cursor
then there should be NO perceptual difference.
This is not quite true. It is true that the disturbing variables (we only
refer to variables inside the system as "signals") are exactly the
same in the two cases: time variations in d are composed of EXACTLY
the same numbers in both cases. But this does not mean that the
perceptual signal will be the same in both cases. There are two reasons
for this: first, remember that p = o + d so even if you present the same
series of d values twice the outputs may be different (with an integral
controller this results from starting the control process with a
different value of o each time); second, in real control systems there
is always some noise in the system, so p = o + d + noise, where the
noise is a random variable; the size of the noise is typically very
small relative to o and d but since, when control is good, p is nearly
a constant (if there is a constant reference), most of the observed
variance in p is actually noise. So even if both o and d are the same on
two trials, the perceptual signal will not be the same.
There is an experiment in my book "Mind Readings" (p. 61) that
illustrates this point. The experiment shows that, when the same
disturbance is present on two different trials, the subject produces
nearly the same outputs in both cases (since o=-d when control is good)
even though the perceptual signal (p) on both trails is completely
different (the correlation between the series of p values on the two
trials is completely uncorrelated). I did this experiment to show that
perceptual input is NOT the cause (or the informational basis) of
response output in a closed loop control task. This experiment (done
years ago and one of my first PCT research projects) should have
been the end of the "information about the disturbance in perception"
debate -- after all, the subjects were clearly making highly correlated
responses (r=.99+) on two differnent trials when what they were
seeing was completely different on each trial (correlation between
perceptual signals typically on the order of .2). But NOOOO.
Anyway, the Marken effect has nothing to do with output differences
or noise in the perceptual signal. The Marken effect depends on the
dynamics of the way the disturbance is generated. In the "live"
case, the d values depend on the dynamics of the output of the subject
as much as the dynamics of the output of the subject depend on the d
values. When the exact same sequence of d values is produced
"independently" of the behavior of the subject (the usual way disturbances
occur), the behavior of the subject is different. I cannot describe why
this works, analytically, using differential equations and Laplace
transforms, but I know that it DOES work because I have run a computer
model of a control system (with a transport lag -- it doesn't work without
the transport lag) in the same situation as the subjects (controlling a cursor
against exactly the same sequence of d values on two occasions -- first when
they are generated live, second when they are played back from a table)
and the model behaves exactly like the subjects.
At the moment, I personally discount the idea that the time of occurance
for each of the "runs" being different has any significant bearing on
your results [but reserve any sort of "final" judgement].
Your suggested "reverse" order version of the experiment cannot be done;
the "live" disturbance values must be obtained first. They cannot be obtained
from a model becuase the model will not have EXACTLY the same dynamic
behavior as the subject (the subject won't show the same dynamic behavior
twice in a row either). The model runs I did (where the model controls against
both the live and played back version of the same disturbance) really confirm
that this is a real effect.
Additionally, I still think that there is a possibility that the two runs
actually ARE different.
They ARE different in terms of how d is generated each time. But there is
no question that the actual series of d values that the subject opposes is
EXACTLY the same on each trial. On the first trial, the d values were
generated from a program statement like:
d(i) := d(i) + k*(r-p) (1)
This statement was in a loop with i as the index. On each iteration of the
loop, the cursor position seen by the subject, c, was set equal to:
c = d(i) + H (2)
where H is the mouse value at that moment and d(i) is the value obtained from
(1). The d(i) values are being stored in an array, d(N). On the next run
the subject does the tracking again (starting the loop over with i = 1) but
this time the d(i) values are the ones that were stored during the previous
run; equation (1) is not used during the second run. So, on the second run,
the subject tracks again and the cursor position is determined by equation
(2) again, with the d(i) values from the prior run. The RMS deviation of
cursor from target during this second runs is ALWAYS at least TWO TIMES
LARGER than it was on the first run -- with EXACTLY the same d(i) values.
This happens even if the subject is told that the disturbance on the
second run will be the SAME as on the first run (not surprising since the
subject cannot perceive the disturbance ON EITHER RUN -- there is NO
INFORMATION about it in the subject's perception of the cursor movements.
This result seems like magic -- I agree. But it's not -- it's just control
dynamics; a surprising result of control dynamics, all right. It seems like
this should not happen. But it does happen, and we understand why it happens.
And it shows that there is no information about the disturbance in perception.
If there were, then the perception should have the SAME information both times
because the disturbance is the same both times. And the subject should track
the same both times. But, in fact, the subect does much better the first
time -- with the "live" version of the disturbance.
Best
Rick