[From Bill Powers (980410.1107 MDT)]
Jeff Vancouver 980409.1723 EST--
You might be equally able to answer this next question then (there is
actually several assumption checking questions before I get to the real
one). I am assuming "a" is action, "p" is perception, "r" is reference
signal, "K" is gain in the system, "d" is disturbance, and "E" is gain in
the environment, correct? Your point in the note is that K or E (but not
both) must be negative, and that "E" will always be less than "K" because
of the nature of the agential systems (organism v. environment). Thus, the
answer to my original question is that the math is the same (as you
describe in the note), but that the level of the numbers must be different
because of the differences between environment and organism.
That's all correct as I see it.
Further, the
note anticipates the point of my question, which is that only one thing,
"p" can be described as controlled; "a" cannot. So you say "r" affects the
environment, not "d" affecting the system (and by environment you mean "a"
and by system you mean "p," correct?).
I would say r determines the state of p while the disturbance has hardly
any effect on p. That's because p is controlled by variations in the
action. Because the environmental feedback function normally has a much
lower gain, I would say that d _influences_ the output a, but that a is
also influenced by r, so we wouldn't say that the environment _controls_ a.
Maybe a brief glossary might help here.
Control: A is said to control B if for every disturbance tending to change
B, A changes so as to keep B very near a specific state called the
reference level of B. This implies that A has some influence or effect on
B. Usually we say that the control system as a whole does the controlling,
but we can also say that the action fits the definition: the action varies
so as to keep the perception very near a specific state or level, so the
action controls the perception. The rest of the control system explains how
this happens.
Influence or affect: A is said to influence or affect B if there is a
nonzero correlation between changes in A and changes in B, with A being the
independent variable (i.e., arbitrarily changing B need not change A). Note
that other variables, C, D... X, might also affect B at the same time. It
is not possible to reason backward from B to A, because the state of A
might be caused by something other than A.
Determine: A is said to determine B if we can calculate B on the basis of
knowing A alone. To say that A determines B is a much stronger statement
than saying A affects or influences B. If A determines B, it doesn't matter
what the values of any other variables are. If we specify the state of A,
the state of B is automatically specified as well. Furthermore, if we know
the state of B we also know the state of A, because B is not influenced by
anything but A.
Apply this to the discussion above. The reference signal _determines_ p,
because knowing r is sufficient to allow us to predict p (d has essentially
no effect on p). The disturbance _influences_ or _affects_ the action a; it
doesn't _determine_ a, because r also influences or affects a, by
approximately the same amount that d affects it. A change in a might be
caused by a change in the disturbance, but it can also be caused by a
change in the reference signal. We can't tell just from seeing a change in
the action whether the cause was a change in r or in d or in both. [All
this assumes a reasonably tight control system in a normal environment]
And finally, the action _controls_ p by varying to oppose the effects of d
on p while maintaining p near a specific state or value which we call the
reference level.
I hope that will make things clearer instead of less clear.
My question is this: If a = K(r + p), where is the comparator? That is, I
thought it was r - p. Is this because K is really the negative valued
gain? Thus, it is a = -Kr - Kp where K is now positive?
The comparator is a place where p has one effect on the error signal and r
has the opposite effect, so it is possible to these two influences to
cancel, leaving an error signal of zero.
In the environment, the input quantity is a place where the disturbance has
one effect and the action has the opposite effect, so it is possible for
these two influences to cancel, leaving a net effect of zero. We don't draw
a box to represent the joining of effects, but we could.
Upon further reflection, I wonder if this can explain a problem I have on
the net. I have suggested that one of the main perceptions I am trying to
control is the respect of others. Rick (and I think you) suggest that I
should look for an internal variable that I am trying to control. That I
am >trying to control my own "self-respect" for instance.
That isn't quite it. We are suggesting that "the respect of others" is
perception of yours. You perceive a variable you call "respect," which is
based on more detailed perceptions of what others say and do relative to
you. What you perceive has no necessary objective relation to what they
actually feel toward you. If you were to change the way you perceive
respect, others could go on behaving as they do while your perception of
their respect for you changed.
As I read your
note in the LCSI, I think I see why you reject the idea that another person
be the EV that my actions affect and feedback to my perception. For if
that were the case then the environment would be another organism. If the
environment were another organism, then K and E are likely to be very large
numbers. This would give me the symmetry I suspected. However, only one
can be negative for stability. So if Rick really were trying to control
the perception of something about me while I was trying to control the
perception of something about him we will be highly unstable. That
certainly does explain a lot.
Very nice inference, and quite correct. One additional note that might be
useful: this is a problem only if the variables each person is trying to
control are the same, so you can't have them in two different states at once.
In the meantime I have tried to implement symmetry in a model. I think I
have, but I must be doing something wrong. Unfortunately, I do not know
how to show you what I have done very well. Below is a posting of the
Visual Basic program I wrote, but I am not sure how clear it will be.
Perhaps you can find the flaw (it is a simple program).
I find your model very hard to understand, much less find any flaws in. I
think I'll leave that to you.
Best,
Bill P.