[from Tracy Harms (19980220.08)]
First, a reply to Bruce Gregory (980219.1345 EST)]
I wrote:
> Significant discrepency in the value of o for multiple instances of the
> same value e would refute o = f(e).
>
> PCT leads us to anticipate exactly that sort of variation.
Bruce responded:
I'm not sure why you believe this. Think of a thermostat
controlling a furnace. Do the outputs of the thermostat differ
for the same values of the error? There are three possible
outputs: on, off, do nothing.
Error signal present: is the switch on?
Yes: do nothing.
No: turn switch on
Error signal absent: is switch on?
Yes: turn switch off
No: do nothing
In no case does the action differ for the same error signal.
The output "o" is not the output of the comparator, it is the output of
the *system*, i.e. everything which does not count as "environment".
To use and extend your example I direct your attention to the rather
famous book by Grady Booch, _Object Oriented Software and Design, with
Applications_. One of the application chapters is a heating system.
I've spent some time studying this chapter, in fact, because I want to
see how somebody who does not know PCT engineers such a thing, and
because I want to figure out how PCT can allow the task to be done
better. (Such efforts have convinced me that designing systems with the
help of PCT is still hard work.)
In that system there is a two-minute delay required between the turning
off of the heating elements and the turning off of the circulating fan.
Presumably this helps prevent damage to the furnace which overheating
could produce. But the incentives behind that specification are
irrelevant; the main point is that his simplified, idealized system
provides an example where output does not correlate with error signal.
The error signal can be absent while the system at large continues to
blow hot air out of its vents.
Next, Bruce Nevin (980219.1333)
Tracy Harms (980219.10)--
>It must be a false claim, that the output of a control system is a
>function of perceptual error.
You are right, it's false if taken in isolation. That is, it's incomplete.
The incompleteness is the more important point, I agree, but for now
I'll hold my ground and claim that adding the missing stuff does not
make this part true. It is just false; the "o = f(e)" equation is not a
viable part of the whole.
But Bill thinks I've misunderstood the nature of the equation, and
perhaps I have.
Bill Powers (980220.0521 MST):
>It must be a false claim, that the output of a control system is a
>function of perceptual error.
Sorry. That's an essential part of the control model. I think you've got
some definitions in your head that need to be pulled out and looked at.
Probably my notion of "function"...
Bill Powers (980220.0513 MST):
The actual output
function would in general be described by some sort of differential
equation, as it is in our models of tracking behavior (the ones that
explain 99.5% of the variance in observed behavior). But it is indeed a
single, fixed function and the output of the model is always completely
determined by the value of the error signal, in real time. If you haven't
understood this yet, you're overdue for an enjoyable insight.
Goody. Enjoyable insights are my main addiction (and they are much
harder to obtain than cigarettes...)
Along the same line I'll mention that PCT has given me my first sense of
incentive to *actually* learn calculus. (As opposed to how I dealt with
it in college.) Calculus comes up here quite regularly, and I'll admit
that I tend to get lost from the argumentation as it moves into the
math. (I'd pay for a calculus tutor who could use PCT-compliant
examples to take me through the scope of the subject. Or a
textbook/workbook.)
Bill Powers (980220.0528 MST):
Tracy Harms (980219)--
>Significant discrepency in the value of o for multiple instances of the
>same value e would refute o = f(e).
No it wouldn't (and doesn't). One form of output function that works very
well is
do/dt = k1*e - k2*o
This function can clearly yield different values of o with the same value
of e, and the same value of o for different values of e. It's a perfectly
regular and predictable function involving time.
But that equation can't be solved for o, can it? If it can't, you're
not able to talk about any o = f(e), are you?
Right about now I probably should put on my dunce cap and go sit in the
corner, but I have to ask these things if I'm going to get to the
enjoyable insights. The answer I anticipate receiving back is that when
people write "o = f(e)" they mean something like "do/dt = k1*e - k2*o",
and the fact that the former *looks* algebraic comes from that most
annoying habit of simplifying notation so that the calculus aspects are
implicit. (Such wholesale disposal of explicit detail seemed pervasive
to calculus and was a major factor in the difficulties I had with it.
Not as big a factor as neglecting to study, however.)
Finally, Marc Kurtzer (980219.1500)
With the technology currently in place its seems questionable whether we can
directly measure "e"
But I referred to a *devised* control system. When we build something
we have an opportunity to include measurement instruments at the
critical point inside the system.
Enough for now,
Tracy Harms
Bend, Oregon