[From Bill Powers (960130.0730 MST)]
Bruce Abbott (960129.1235 EST) says
I believe that Bill has opened up a whole new world of terminology
for us to explore, and hereby offer the following candidates for
addition to our dictionary:
Hans Blom (960130c) says
I like it! I like it! With one stroke of genius, one brilliantly
incisive insight, you have completely solved the problem! I admire
you! Thank you, now I understand that I'm in complete retrofaction!
Martin Taylor (960129 16:50) says
... how are you going to prove a negative? Just because you can't
see an organism's-altitude-sensing-system in the environment
doesn't mean there isn't one.
Somehow I get the feeling that my proposal about retrofaction isn't
being taken seriously.
One brief aside: Martin, the burden of proof is on the one who proposes
that there is an altitute-sensing system in the environment.
Rick Marken (960129.1100) says
I think we have more than a definitional problem here. I don't
think anyone would have trouble understanding why the environment
does not _control_ (or _retrofact_) if they had a feeling for the
nature of the phenomenon to which these words (control, retrofact)
refer.
Could it be that my little stratagem has elicited responses from the
three people on the net who thought they understood the phenomenon I now
call retrofaction, but who don't actually distinguish it from influence,
determination, cause, and so on?
Let's review some of those other terms. I can't tell you what they
really mean, but I can tell you how I understand them.
1. The value of Y is _determined_ by the set of values of x1, x2, .. xn
(an enumerated set) if Y = f(x1..xn). This means that given x1..xn, the
value of Y can be calculated exactly and Y can have no other value. The
set x1..xn consists of _all_ the variables having an immediate
(unmediated by any other variable) effect on Y.
2. The value of Y is _influenced_ by x1 in the above set. However, at
any given time a change in x1 may produce no change in Y because the
influences from changes in other variables x2 .. xn might cancel or
exceed the influence of x1.
3. A change of x1 _affects_ Y if the influence of a change in x1 is not
completely cancelled by the influences of changes in the other variables
x2..xn.
An influence is calculated as a partial derivative, which is the
_effect_ of variations in any x on variations in Y when all other x's
are held constant.
4. To say that x1 _causes_ Y is to say that x2..xn do not exist, so that
x1 _determines_ Y.
5. "Partial determination" is a contradition. To say that Y is
"partially determined" by x1 means only that Y is _influenced_ or
_affected_ by x1. To say that Y is partially determined by x1 is to say
nothing about the value of Y, or even of changes in Y. Regardless of the
value or rate of change of x1, Y could have any value or any rate of
change.
6. The same holds for saying that Y "depends" on x1. If x2..xn exist,
this has meaning only if "depends on" is used in the sense of "is
influenced by" x1 -- the partial derivative of Y with respect to x1.
In the above list, you will not find the relationship I am calling
retrofaction. To say that x1 retrofacts Y is to say that for any
variation in Y due to changes in x2..xn, x1 will change so as to restore
Y to a specific value. That is a crude way of expressing retrofaction,
because it doesn't bring out the fact that x1 will be changing its
influence on Y at the same time that the other variables x2..xn are
changing their influences on Y.
If x1 is the variable involved in retrofaction, then the set of other
variables x2..xn is known collectively as "the disturbance." The
variable x1 is the "means of retrofaction," and Y is the "retrofacted
variable."
For retrofaction of Y by (or though) x1 to occur, x1 must be a function
of Y - Y0, where Y0 is the specific value toward which x1 influences the
value of Y. So a second functional relationship must exist (in the
mathematical meaning of function, not the EAB meaning): x1 = g(Y - Y0).
Of all the possible functions g, only a subset of them will result in
retrofaction. The particular subset depends on the form of f in Y =
f(x1..xn).
Retrofaction is therefore a phenomenon that depends simultaneously on
the forms of the two functions f and g.
···
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In 1972 and 1973, I gave a series of student-sponsored seminars, backed
by Hugh Petrie, Don Campbell, and (for anthropoplogy students), P. J.
Bonhannan at Northwestern University. One of the things I did to give
the students the feel of a retrofactive system was to bring an x-y
recorder to the sessions, so the students could physically interact with
it. This was not the modern type in which a stepper motor generates the
pen positions, but the old-fashioned analog type in which DC servomotors
moved the pen carriage in x and y, and the position was sensed by a
linear slidewire potentiometer along each axis.
The first lesson consisted simply of taking the pen carriage between
thumb and forefinger and trying to move it. Until he or she actually
tried this, it was clear that each student had understood my
introductory descriptions of negative feedback systems in some way that
was off the mark. I could tell, because every one of them, on grasping
the pen carriage and trying to move it, looked startled or surprised --
even after having just seen another student doing the same thing. What
surprised them the most was that the carriage _resisted_ them,
energetically enough that they could hardly feel (or see) any motion of
the carriage at all. With enough applied force, the carriage would seem
to break loose and move without any further increase in resistance, as
if it had come out of a detent, but always pushing back toward the
original position. The motor had a slip-clutch on it to prevent damage,
and when enough force was applied to the carriage, the motor could be
heard to hum louder and louder and then start spinning at high speed.
The experience was one of being resisted by a very active system. All of
the students said that it "felt alive."
The next demonstration was to have each student take hold of the x or y
offset control and turn it. This control actually varied the reference
signal for the retrofactive system that positioned the carriage. Again
the students were surprised, because there was no perceptible lag
between the turning of the knob and the movement of the carriage, unless
a real effort was made to turn the knob by a large amount in as little
time as possible. And then the lag was less than a quarter of a second
from the initial position to the final position. One student
hypothesized that there was a direct mechanical connection between the
knob and the carriage, and refused to believe that no such connection
existed until I took the control panel off and showed him the
potentiometer and the wiring, and operated the knob.
The next demonstration consisted of having one student turn the
reference-signal knob while another (or the same) student tried to move
the carriage by pushing on it. This quickly got across the idea that the
reference signal _determined_ the pen position, with influences from
disturbances having no perceptible effect until the disturbance exceeded
the ability of the servo motors to resist it. So a feeble electrical
signal could swiftly and precisely move the pen carriage, while the
hidden retrofactive system prevented gross mechanical disturbances from
having any important effect.
For the final demonstration, I mounted four temperature-sensitive
thermistors and two photoelectric cells (looking in different
directions) on the pen carriage. I wired the outputs of these sensors
to the x and y reference signal inputs. There was no attempt to create
any sensible retrofactive systems; I just wanted to create some sort of
higher-level systems that worked through the reference inputs of the
lower-level retrofactive system.
This was a big hit. If you held a hand near a thermistor, the heat would
alter the pen position reference signals and the pen would move, either
toward or away from the hand. At the same time, light falling on the
photocells would contribute to the motions, so the shadow of the hand
also had a large effect. The whole system would very rapidly seek
positions where the balances of heat and light came into equilibrium
with the carriage position. Both heat and light disturbances, such as
from a cigarette lighter, would seem to make the carriage move in
strange ways to new positions, sometimes slowly and sometimes very
rapidly. If approached from the right direction, the thermistors would
do nothing until actual contact was made, and then jerk suddenly away
from the finger, or into it and beyond it (the thermistors were sticking
up on the ends of flexible wires). All kinds of purposive
interpretations could be offered: the carriage was trying to keep the
finger between itself and the window, the touch caused a startle
response, the carriage was chasing the finger or fleeing from it, and so
forth. But the students, having seen how each part of the system worked
and having gained a personal intuition of the system through physical
interaction with it, quickly arrived on their own at the _correct_
purposive interpretation: that the system was controlling some function
of heat and light sensor signals. Of course now they would all have to
be told that the system was retrofacting light and sensor signals, since
if they said "control" some people would interpret this to mean "react"
or "affect" or "influence" or "determine" or "cause." The students knew
that what they had experienced was none of these. What they had been
experiencing had never been mentioned in any of their psychology or
philosophy courses.
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I still try to teach through demonstration, but it's hard to get people
on the internet to explore the simple demos to get the kind of
understanding my students eventually got. Everyone wants to go on to
more interesting topics, big complicated systems doing big dramatic
things, and generally doing things that are deliberately made so complex
that they can't be done well, or be understood in any clear way. It's
almost as if people want to avoid the simple issues, the clear
phenomena, the explanations that either fit or don't fit with no
quibbling. As long as we flounder around with complex behaviors, any
theory about them can seem right -- who can prove they're wrong?
Bill Leach at one time was considering building some real
servomechanisms to use as demonstrations of real retrofactive systems
that people could physically interact with. I hope, Bill, that when your
current situation comes to some sort of even keel you can get back to
this project. Even if they cost $500 apiece, they would be worth it in
educational power. People who are serious about wanting to learn and
teach retrofaction theory would willingly pay the price to buy or rent
such devices.
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Best,
Bill P.
