[From Rick Marken (930316.0800)]
Allan Randall said:
How can you say this, when the sole purpose of the control
system is to oppose the disturbance? It can't oppose something
it has NO information about. It simply cannot.
(Bill Powers 930315.0700) replied:
When you get this figured out, you can finally claim to
understand PCT.
and Martin Taylor (930315 18:30) says:
Bill, your comment is exactly saying that PCT applies only to entities
that operate in a universe thermodynamically isolated from the disturbing
variable. It would make for a very uninteresting area of application
for PCT. Let's deal in possible worlds, shall we? I think PCT applies
to a very interesting part of the real world. If what you say is true,
then I am much less interested in PCT, which has suddenly become a branch
of abstract mathematics.
How could I let this statement go by last night; clearly, Martin
has confronted my razor's edge, and balked.
Martin Taylor (930316 10:00) re:(Bill Powers 930315.1900)
I agree with everything in Bill's posting, at least at first reading.
If Rick also agrees with Bill's posting, we can see that our apparent
disagreements are based more on misunderstandings of language than of
principle.
I agree with Bill's posting, of course. I agree that there must be
some confusion about language. That's why I tried to get quantitative
in my last post. But that didn't seem to help. For example, I said:
(1) p(t) = d(t) + o(t)
What the control system perceives (and controls) is a time varying signal,
p(t) that is at any instant the result of the combined effects of an
indepedent disturbance variable, d(t) and an output being generated
by the system itself, o(t). All the system perceives is p(t); it has no
way of knowing "how much" of p(t) is at any instant the result of d(t)
or o(t). In other words, it has no information about d(t) -- all it has
is p(t)
And Martin Taylor (930316 10:20) replies:
Fine, except that the last sentence is a non-sequitur. It indicates that
the core of the argument is a misunderstanding about the nature of
information.
OK. I'm waiting to have my understanding of "information"
non-sequitized. But instead, here's what I get:
p(t) = d(t) + o(t), and therefore p(t) contains information
derived from d(t).
Another assertion; where the hell is this information? How can it
be USED. p(t) is a series of numbers -- here's part of it
23,25,30,21, -10, 3, 8 ... Now, could you please explain to
me where, in those numbers, is the information about d(t)?
If you just say ITS THERE then I might break my computer screen.
Isn't information a measure of what a message (which I take p(t)
to be) tells you about the source, which I take d(t) to be. Or
is this view of information a non-sequiter and thermodynamically
impossible. I think your response to disturbance is showing.
This in no way implies that d(t) can be recovered
from p(t) without knowledge of (as distinct from information
from) o(t).
So there is information about d(t) in p(t) but it cannot be
recovered from p(t) without knowledge of o(t) -- is that it.
So you are saying that there is information about d(t) in
p(t) but it is useless without knowledge of o(t).
I'll buy this. So you are saying that the subject get's information
about d(t) from p(t) because they know o(t)? Is that your position?
If so, then I suppose I've got to develop a demonstration to
show that the subject DOES NOT need to know about o(t) in order
to produce o(t) = -d(t). I actually presented one non-experimental
proof of this fact some time ago in the context of the "control of
error" discussion. In that discussion, I showed that perception, p(t)
was controlled (kept equal to r(t)) even when the disturbance
was added before the trasformation of output into an effect on
the controlled variable. That is, I added the disturbance to the
error signal so that o(t) = k(r-p(t))+d(t). I showed both
mathematically and with simulation that the disturbance is
compensated for; in this case, by adjustments to the error signal.
An interesting feature of this demonstration is that d(t) doesn't
enter the loop directly through p(t). In fact, d(t) enters
the loop as part of the effect of o(t), the very variable
that we had to know in order to extract the information about
d(t) from p(t).
So I'll tell you what -- how about this concession on MY part.
There IS information about d(t) in p(t) [when p(t) = d(t) + o(t)]
but it is useless and uninformative. In other words, there is
uninformative information about d(t) in p(t). How's that?
I said:
Nevertheless, it generates outputs, o(t) that are a precise mirror
or d(t)
Martin says:
That word "precise" is an argument killer. o(t) is NOT a precise mirror
of d(t). It differs by an proportion that is roughly 1/Gain. In an
integrating control, 1/Gain approaches infinity at infinite time, and
then you can talk about o(t) being a precise mirror of d(t), but only
if no disturbing "events" have happened in the interim. You can't use
infinite gain without going to zero bandwidth, because otherwise you would
be infinitely amplifying the least little noise in the comparator or
perceptual input function. That again is a question of information.
Well my statement may have been an argument killer for you but your
paragraph above is gobbldygook to me. What in the world is the point
of all this? If it's a question of information then WHAT IS THE ANSWER.
What does the lack of precision that comes from having a loop gain
of 1,000,000 instead of infinity have to do with INFORMATION.
The best I can do with this is assume that you believe that the
lack of precision of control leaves a remnent of variance in the
input, p(t), that is the INFORMATION used to guide o(t). Thus,
my challenge for you to find that remnent and reconstruct d(t)
from it. But you say this is a straw man challenge. So please
tell me what in the world is your point.
Best
Rick