Simultaneous vs sequential

CSGnet Archive CSG1993
1

[From Rick Marken (930621.1200)]

Martin Taylor (930621 11:00) --

Do you see the contradiction? We keep trying to tell you that we NEED the
circle, and you keep trying to tie us up with the chain.

Greg Williams (930621) --

Good for you! I would have brought this up, too, but I already know where
things would probably head:

Well, I think you were wrong about where things would head. But I think
there is a better (more accurate) way to characterize the difference
between the PCT and information theory of control: rather than circle
vs chain I think it is more accurate to characterize it as simultaneous
vs sequential.

Both PCT and information theory recognize a circular chain of events
occuring in control:

p --> (r-p) --> o --> g(o) --> p

Since p is at the beginning and end of the chain, there is an implicit circle.

What the information theory view seems to miss is that all the variables
in this circle are changing simulataneously; it is by simultaneously solving
the system and environmental equations that we end up finding that

o = p*-1/g(d)

with no contribution to the output, o, from perception, p. This is not
only because the perceptual variable is part of a causal circle; it is
because all variables in this circle have an effect on all others AT THE
SAME TIME.

I think the information theorists must imagine that the events in the
loop occur sequentially; perception is compared to reference which
leads to output which is transformed by the feedback function, g(o),
into a new perception; there is sort of an assembly line with the infor-
mation in perception serving as the blueprint for what should be done
to counter the disturbance. This may be why they imagine that something
is extracted from p -- the information that is used to produce the
next item in the sequence, o. At least, this is what I think they must
be thinking -- otherwise they would see that there is obviously no
information in p about d; p is just one of several simultaneously varying
variables that happens (due to the negative feedback, high gain
SIMUTANEOUS relationship between all the variables) to be kept equal
to one of the variables --r.

Note that g(o) -- the feedback function -- is separate from the control
system itself in both the information theory and PCT versions of the
control loop. Thus, I fail to see the contradiction that you and Martin
seem to see. Help me out here.

Best

Rick

2

[Martin Taylor 930621 18:50]
(Rick Marken 930621.1200)

I think
there is a better (more accurate) way to characterize the difference
between the PCT and information theory of control: rather than circle
vs chain I think it is more accurate to characterize it as simultaneous
vs sequential.

I don't think you can say this either. We (I, anyway) take for granted
that all the variables are changing simultaneously, but unlike you, we
do recognize that there is a construct "loop delay." If you try

simultaneously solving
the system and environmental equations that we end up finding that

o = p*-1/g(d)

with no contribution to the output, o, from perception, p.

you are working with no loop delay, which is unrealistic. You have
to include in your analyses not just p or o or d, but p(t), o(t), d(t).
If you do that, you get part-relations like o(t1) = f(e(t1-delta t))
and the like. As you work your way around the loop, you then run into
problems of stability at critical frequencies, so you have to do some
sort of spectral compensation (e.g. integration in the output function).
There's a lot that happens when you don't allow infinities in the analysis,
such as infinite speed and infinite resolution.

But we do agree that all this is happening simultaneously.

Martin