[From Bill Powers (2010.05.19.1725 MDT)]
Martin Taylor 2010.05.19.14.45]
RM:This is also true if r is not
constant, in which case the equation has to explicitly include r as a
variable:qo = r - 1/g()d
MMT : Well, yes, it is a function of d, but it’s a function of r
also, which would make perceptual control distinguishable from S-R in an
experiment in which r was variable in some measurable way.
BP: Only if r were sychronized with d. Too much is being said here
without reproducing the equations and showing the derivations.
RM: Your function E() is
equivalent to the feedback function, g(), in the equations I wrote.MMT: No, it isn’t. E() is the part of the loop between qo and qi. g() is
the feedback function of the entire loop.RM: You might have seen this if
I had written the complete derivation, as Bill suggested.
MMT: Actually, in my first draft
of the message to which you are responding, I did write the entire
derivation, but I decided that the detail obscured the main point, so I
deleted it.
My derivation of the
“behavioral illusion” equation – qo = r - 1/g()d – assumes
that qi = g(qo+d). Actually, in my paper describing the power law as a
possible example of a behavioral illusion
(
http://www.mindreadings.com/BehavioralIllusion.pdf), I assume that
the perceptual function itself is part of the feedback path so that p =
g(qo+d).
You guys are going all over the place. Derive the equations from the
following:
p = qi
o = f(r - p)
qi = g(o) + d
You will find that g is the function connecting the output to the
controlled variable qi, which Martin objected to, and that p is NOT g(qo
- d), as Rick said.
Do all the steps. Show your work. By this time, the best either of you
will get is a B.
Note that f(r - p) is not f(r) - f(p).
Best,
Bill P.