[From Rick Marken (2008.04.04.0930)]
(Gavin Ritz, 2008.04.04.17.52NZT)
A brief aside.
What are the three experiments (like the three that more or less prove, the
Big Bang theory), that proves the PCT theory (conjecture).
I don't believe that a theory can be proven (in the mathematical
sense). However, if by "prove" you mean "critically test" (which is
one of the dictionary meanings of "prove") then my vote for the three
experiments that prove PCT are:
1. Basic compensatory tracking experiment (reported in the final
installment of Powers' 1979 _Byte_ series) that shows a low
correlation (~0) between input and output, a low correlation between
disturbance and input and a nearly perfect correlation (~.99) between
the undetectable disturbance and output. Supplement this with my
"repeated identical disturbance" version of the compensatory tracking
task (reported on p. 61-67 of _Mind Readings_) showing that the same
outputs are produced on different trials with completely different
inputs, and you have "proof" that an open loop, causal model cannot
account for output variations in a closed loop task. But the way,
these are the first two java demonstrations at my website:
http://www.mindreadings.com/demos.htm.
2. Compensatory tracking experiment where a participant secularly
changes the controlled position of cursor (reported as Experiment 2 in
Powers 1978 _Psychological Review_ paper), showing that it is the
controller, not the input display, that determines the target position
of the input. This is a very simple but powerful demonstration that
behavior is control of -- not by -- input. A variation of this is my
"Mind reading" demo when the computer is able to determine which of
three inputs is being moved "on purpose" (controlled) by the
participant. A current version of this experiment can be found at
Mindreading.
These first two experiments prove (critically test) the first "law" of
PCT which is:
(1) i ~ r
That is, input variations, i, depend on variations in reference
specifications for that input (intentions), r, rather than input being
the cause of output, o.
3. The third experiment is a demonstration of the "Behavioral
Illusion". It is presented as Exp. 4 in Powers 1978 _Psychological
Review_ paper. This is another compensatory tracking (control) study.
In this case the nature of the feedback connection from output to
input is changed. The study shows that participants automatically
compensate for this change by producing output such that the
relationship of output to input is the inverse of the feedback
function. This demonstrates the second "law" of PCT, which is:
(2) o = -1/g(d)
That is, in order to keep input under control (first law) the
controller must produce output variations, o, that oppose
disturbances, d, to that input; and these output variations must be
inversely proportional to the feedback function, g(), that connects
outputs to disturbance. Bill and I have submitted a paper (still under
review) showing that Stevens' power law (o =d^a) relating magnitude
estimates, o, to stimulus intensity, d, is an example of a behavioral
illusion if the perception of the magnitude estimates is a log
function of those estimates. In this case the feedback function
relating output (magnitude estimates) to input (perception of the size
of those estimates relative to the intensity of the stimulus being
evaluated) is logarithmic and the power function, which is the
observed relationship between i and o, is the inverse of this
logarithmic feedback function. The illusion, if course, is that the
observed relationship between d and o (1/g()) reflects characteristics
of the participant (controller) when, in fact, it is actually the
inverse of the environmental feedback connection between o and i.
Best regards
Rick
···
--
Richard S. Marken PhD
rsmarken@gmail.com