[From Bruce Abbott (980204.0505 EST)] <---way too early
Rick Marken (980203.1950 LALA TIME) --
Bruce Abbott (980203.1840 EST)
I think you understand the reasoning; you just can't accept the
conclusion. For example, you know that:
I understand the reasoning and therefore can't accept _your_ conclusion.
When serving as a participant in a psychophysical study, I am
controlling for producing statements that accurately reflect
the state of the relevant perception
So you know that, in a psychophysical experiment, you are controlling
a perception (p) that depends on both environmental stimuli (s) and
you own outputs (o):
(1) p = f(g(o) + h(s))
where g() is the "feedback function" relating your own output
to the controlled input; h() is the function relating the stimulus
to the controlled input and f() is the perceptual function,
relating controlled input to controlled perception.
In the psychophysical example I used, we get into logic-level control and
the exposition becomes rather complicated. To keep things relatively
simple, imagine a psychophysical experiment in which the person is asked to
rotate a knob so as to keep a tone at a level that, for this person, is just
at the margin between perceptible and imperceptible, while the apparatus
applies a smoothly-varying disturbance to the tone's physical intensity. In
that case,
(1) i = g(o) + h(s)
where i is the physical intensity of the tone, o is the knob setting, g is
the function giving the influence of knob setting on tone intensity, s is an
intensity setting that is varying independently of the participant's actions
(disturbance) and h is the function giving the influence of this disturbance
on the tone's intensity.
(2) p = f(i)
This is the perceptual input function (PIF) relating the tone's physical
intensity to its perceived intensity. It is a property of the person
(system), not of the environment.
Putting (1) and (2) together gives Rick's equation: p = f(g(o) + h(s))
So you know that you are trying to keep the perception at
a target (reference) level. So you know that the controller
in this experiment can be modeled by the following equation:
(2) o = k(r-p)
Where k() is the "organism" function mapping error into output.
Yes.
You probably even know that when you perform this experiment,
the observed relationship between o and s is proportional to
-h()/g() (both characteristics of the environment). So the
observed relationship between stimuli (s) and responses (o)
in a psychophysical experiment reflects characteristics of
the environment [h()/g()], not characteristics of the organism
[f() and k()]. Concluding that the results of such experiments
_do_ tell you about the organism [f() and k()] is the behavioral
illusion.
Yes. So?
By varying the tone intensity, an investigator could determine
the limits of my ability to sense the presence of the tone
Surprisingly, no (it's a compelling illusion -- like the illusion
that the earth is flat). To determine the limits of your ability
to sense the presense of a tone the investigator would have to
be able to determine the function f(h()) relating tone (s) to
perception (p). But we have seen that all we get from this
experiment is h()/g(), not h() or f(h()). And the h() and
g() we get depend on what perception (p) you actually happen
to be controlling.
It is not the point of the experiment to find the function k coverting error
into output. It is the point of the experiment to find out something about
f(i).
In this example, I am controlling the perception of tone intensity, and,
following instructions, I am attempting to keep the tone at a level that is
just on the edge of perceptibility (r), against the disturbances to that
perception produced by the apparatus. You will find that my output pattern
will be the inverse of the disturbance pattern (allowing for scaling
differences). But you will also discover the intensity of tone that I can
just barely perceive (the delivered tone intensity will be varying closely
around this value), and that is a property of my perceptual input function,
not of the environment. In further work, you will discover that when you
ask me to maintain the tone at a particular intensity that is well below
this value, I will be unable to vary my output so as to track the changing
physical intensity of the tone, because within this range of values the
function f(i) is flat: all values of i yield p = 0. The intensity at which
the function f(i) ceases to be flat will be at the r inferred from the tone
intensity which the participant maintains against disturbances.
In yet other experiments, I could similarly determine the amount of _change_
in the tone's intensity that you could just barely detect, and could do so
at a variety of absolute tone intensities. Your ability to discriminate
such changes certainly must impact on your ability to maintain the tone's
intensity at a particular value against very small disturbances to that
intensity, and that ability is a characteristic of you, not the environment.
Making such determinations is what psychophysics is all about.
So you see, Rick, when I perform psychophysical studies I am learning a good
deal about the characteristics of the organism, contrary your assertion that
I am only learning about the characteristics of the environment. This is no
"behavioral illusion."
Regards,
Bruce