# Control, determination, influence; retrofaction equations

[From Bill Powers (960201.0500 MST)]

Bruce Abbott (960131.1630 EST) --

Re: Retrofaction tutorial.

Well done! I have very few quibbles. One is about your statement that
_action_ is the retrofaction of perception. "Behavior" is the better
word because it doesn't refer specifically either to action or the
consequences of actions. Spontefaction or retrofaction (Ugh, I agree) is
a result of whole-loop operation, so shouldn't be causally identified
with any one element of the loop.

The most interesting result of your recasting of the theory is what
happens to the word control when it is used "as in EAB:"

There, to control is to influence or determine the state of a
variable. I will use "control" in that sense here.

No distinction appears to be made in EAB between influencing and
determining; this seems a fair inference if the same term can be used in
place of either.

When I looked up "influence" in my Webster's I got a surprise. The first
meaning as a verb is "to affect or alter by indirect or intangible
means;" the second meaning is more like the one I have used: "to have an
effect on the condition or development of". I had forgotten that
"influence" is most often used in the magical sense.

The first meaning of "determine" was more familiar: "to fix conclusively
or authoritatively."

In system analysis, the distinction is rather critical, as I was
pointing out a day or so ago.

In Newton's laws of motion, the acceleration of an object is said to be
_determined_ by the vector sum of all forces acting on the object, and
the mass of the object. Given knowledge of the mass and of every force,
one can then state what the acceleration of the object will be.

Any one force is said to _influence_ the acceleration. That is, if one
of the forces is increased, the acceleration vector will swing at least
slightly toward the direction of that force, and will increase slightly,
or become less negative, in the new direction.

The distinction is this: if you know ALL the forces that influence, and
together determine, the acceleration, you can calculated the
acceleration. If you know only _some_ of the forces, you cannot
calculate the acceleration.

In any mathematical analysis of a system, every variable must be
accounted for in one of two ways. Either all the other variables on
which it depends must be explicitly stated together with the functional
relationship, or the variable must be treated as an independent variable
with an arbitrary value. In other words, variables are either completely
determined, or they are arbitrary and may have any value. There is no
place in a system analysis for the concept of "influence", because the
term implies an incomplete enumeration of the determining variables. If
the enumeration is not complete, the system equations can't be solved.

You say,

The retrofaction forward function (forward system function) shows
how the input variable controls the action variable (assuming a
constant reference). In this example it is:

(1) a = (r - k1*i)*k2.

We have here an equation that _determines_ the value of _a_. That is,
everything on which _a_ depends is stated in the equation. So _a_ is
_determined_ by the reference signal, the input variable, and two system
constants. Given all four values we can calculate the value of _a_. If
we assume a constant reference we still can't calculate _a_ unless we
know the arbitrary value of the reference, not just that it is constant.

You say, however, that the _input variable_ i "controls" the action
variable. Since the variable r also influences the value of _a_, this is
clearly a case in which the meaning of "control" is like the meaning of
"influence." The input variable i is _one_ of the influences that acts
on _a_, but not the only one.

In your definition of the retrofactive input function, you say

p = k1*i

Here, p is clearly _determined_ by i, given the system constant k1. That
is, given i and the value of k1, we can unambiguously calculate p. The
perceptual signal p depends on no other variable but i, so the value of
p is "conclusively fixed" by the value of i. So now we have "control"
being used in the sense of "determine."

Again:

Sometimes analysts will unwittingly solve Equation 2 for a,
yielding:

i + k4*d (5)
a = -------------
k3

The equation seems to show how input controls output through the
mediation of the system, but in reality it only describes the
environment.

Since there are two variables influencing a (i and d), "control" is
being used here in the sense of influence. Knowing only the system
constants and i, it is not possible to calculate a. One must also know
the value of d, which might have any value.

Using the term "control" to mean either "determine" or "influence"
allows making the following generalization:

For all variables within the loop, it is easy to see that each
variable both controls and is controlled by every other variable in
the loop, including itself.

To make this statement true, the meaning of "control" must shift from
"influence" to "determine" as required for every variable in the diagram
of the loop. The perceptual signal is determined by the input variable,
but the input variable is only influenced by the action variable. The
action variable is determined by the error signal, but the error signal
is only influenced by the perceptual signal. However, since the term
control does not, in this usage, distinguish between influence and
determination, the same word can be used everywhere in the loop.

I think we agree that i, the input variable, is where the reinforcer or
incentive would be placed. We can see now how it is possible to say that
the reinforcer controls behavior. In this case, the meaning of control
is not "determine" but "influence", because the reference signal also
influences the action variable _a_. The reinforcer or incentive
influences behavior, which in EAB usage is the same as saying it
controls behavior.

Perhaps you can see why I have introduced a new term to replace
"control." When control can mean either determination or influence, and
in neither case means what my new term means, it is clear that we can't
communicate my theory to EABers by using the word control.

All this would be unnecessary if EABers would say "influence" when they
mean influence and "determine" when they mean determine, and release the
term "control" to mean the result of the operation of a closed-loop
negative feedback system. Then I could go back to using reasonable
language and everybody would be happy again.

···

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Martin Taylor 960131 16:00 --

RE: Turing test

I don't think Bill P will want to be given credit for being either
cleverer or more competent than Alan Turing.

That's right.

I agree with your assessment. All Turing asked was whether it is
possible, through verbal/symbolic communication alone, to determine
whether you are interacting with a machine or a human being. The Turing
Test was conceived as a way of evaluating how well symbol-manipulating
programs behaved like human symbol-manipulators. If human judges
couldn't tell the difference, the programs were probably pretty good.
Given the goal, I think this was a pretty reasonable test.

We have a variant on the Turing Test in PCT. It is called a tracking
experiment. The object is to build a model which will reproduce a record
of handle movements and cursor movements that a human being can't
distinguish from a record of a real person's behavior. We haven't
actually put it to that test, but we could. Actually, to make the
model's data look more like the human's data, we would have to add some
random noise to the model. If we did that, I don't think that most
people could say which data plot comes from the human being.
--------------------------------
Oh, dear. I hope we aren't going to start into another fruitless
"information IN perception" round of postings.

I can tell you that I'M not going to.
--------------------------------
A general remark: what is said is what is said. What is heard and what
is meant can be quite different.
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Remi Cote 310196.2012(EST) --

To whom it may retrofit:

In a post(960130.0730(MST)) Bill P. just make it clear, as always:
"So a second functional relationship must exist: X1 = g(y-yo)"

Does this function exist in E.Coli too?

Yes. The function g describes the organism. In E. coli's case, we have

x1 = time between tumbles
x2 = speed of swimmming
x3 = direction of swimming

Y = rate of change of concentration of attractant, where

Y = f(x1,x2,x3,x4)

The function f describes how the environmental variable Y depends on
those four variables.

Inside e. coli, there is a sensor that detects rate of change of
concentration. The tumbles themselves are a stereotyped event, the speed
of swimming is constant,the direction of swimming is randomly selected
by a tumble, and the direction of the gradient is a property of the
environment. The only output variable that can be systematically related
to the input variable Y is the time between tumbles, x1 in the list
above. As Daniel Koshland showed, the time between tumbles increases as
the rate of change of attractant increases. This relationship can be
expressed approximately as

x1 = k*(Y - Y0),

which corresponds to x1 = g(Y - Y0) above.
---------------------------------
So when we look at output of a retrofaction (presumed) we may also
look at a imitation of retrofaction. That is retrofaction without
the second functional relationship X1=g(y-yo).

Ah, HAH! I've found another one. I'm sorry, Remi (actually, not), but
you are not allowed to call any system without the second function a
"retrofactive" system. To define retrofaction you must show two
functions, the environment equation and the equation of the behaving
system, and a closed negative feedback loop must exist. If you talk
about a system in which you have only Y = f(x1..xn), you are talking
about a deterministic system but not a retrofactive system.

You can see the problem I would have if I were still using the word
"control." We would start arguing about whether Y is controlled by the
variables on which it depends, x1..xn. But since I defined retrofaction,
you can't argue with me. My definition is the only one allowed.

An imitation of retrofaction would have to work like this:

1. Given Y = f(x1,x2...xn).

2. Vary x2 and predict the effect on Y from the form of the function f.

3. Predict that x1 will change so as to prevent the value of Y from
changing as much as predicted (ideally, the change will be almost zero).

Without the second function, there is no way to predict that x1 will
change in the required direction and by the required amount.

And it is easier to conceive a pseudoretrofaction model than a
retrofaction model.

I know. That is what a lot of people insist on doing. They can get away
with it if we use the word "control," but not if we say "retrofaction."

Am I right in saying retrofaction without X1=g(y-yo) is
pseudoretrofaction or worst the manifestation of an evil s-r.

You are right. Without X1 = g(y - yo) you don't even have
pseudoretrofaction. You can't imitate the effect without the closed
loop. Remember, if you change any variable x2..xn on which Y depends,
then for retrofaction to occur, x1 must change so its effect on Y
maintains Y near some specific value Y0.
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Best to all,

Bill P.