[from Mary Powers 930617.1530]
(Jeff Hunter 930617)
What bothers me about your post is
If a number of women are confined together their menstrual
cycles *will* synchronize.
They will? All of them? Always? I suspect that this is one of
the gadzillion physiological and psychological *facts* about
people in which some statistical probability has been elevated
to rock-hard 100% certainty.
I personally lived four years in a female dorm and my 5 week
cycle never budged, though I was surrounded by more typical
types. I knew 3-weekers who would have been delighted to
synchronize, but didn't. Bill's suggestion about entrainment
might explain this - in that our oscillations were too far out of
synch to be captured. But you claim that even irregular and
unusual cycles synchronize too. I suspect that the data behind
your assertion was far weaker than you thought it was when you
learned that interesting *fact*.
Mary P.
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[From Bill Powers (930617.1600 MDT)]
Martin Taylor, Rick Marken, anyone else:
I can see that this discussion of information in the perceptual
signal is settling down into a set of fixed misunderstandings. We
all seem to be talking about different things.
Martin Taylor (930617 13:45) --)
When we showed by example what should have needed no
demonstration, reconstructing the disturbance exactly, knowing
the output function exactly, Rick then said it was
insufficient, and produced a series of examples using different
output functions and/or changing reference signals (I forget
which).
Rick was holding in reserve a variable feedback function between
the output quantity and the controlled quantity. He could give
you the perceptual signal, the reference signal, and the form of
the output function because he was hiding the (variable) form of
the feedback function, rendering the task impossible. You,
however, took Rick's later comments this way:
Yes, if you assert that the output function includes the
environmental path between the ECS and the CEV to which d is
applied, and that the function is defined precisely and is
monotonic.
This is precisely the part of loop that Rick was making variable
without telling you. So Rick continues to assume that you are
excluding this part of the loop, and you continue to assume that
he is including it. End of that problem. Let's just nail it down.
Here is the diagram:
> sr
>
sp ------- [Comparator]--------- se
> >
> >
[fi] [fo]
> >
> >
qi (CEV) ------[fe]-------------- qo
> \
> <-- y
> <-- x
[fd]
>
qd
We've been assuming that fi is a unity transformation involving a
change from physical to nervous system units only. So qi is
numerically identical to sp. The comparator is a simple
subtractor, so that se = sr - sp.
Martin, you've been saying that given sp, sr, fo, and fe, and by
default fi, you can reconstruct "the disturbance", whatever that
means. I will agree that if by "disturbance" you mean fd(qd),
that is, the contribution of the disturbing variable to the state
of qi shown as x in the above diagram, you are correct. Anybody
could.
Given all functions in the closed loop, plus the reference
signal, you can compute "y" in the diagram above, the
contribution of the output to the input. As qi = y + x, and given
that you know the state of qi from the state of sp and the known
input function fi, it is trivial to compute x. qi = sp, and x = y
- qi.
In order to reconstruct the state of qd, however, you must also
know the form of the function fd, which we've been leaving out.
The variable qd is (inverse fd)(x).
When Rick and I have said that you can't reconstruct the
disturbance from the perceptual signal, we have meant that you
can't reconstruct qd just from knowing sp and sr. Unsaid was "...
unless you know the form of all the functions in the loop." But
if you know all the functions in the loop, it is trivial to
reconstruct qd from sp, because in effect you are given the
states of all the other variables in the loop. Rick allowed you
to know (he thought) all the functions in the loop but one, fe.
That automatically made the problem unsolvable and the challenge
unmeetable. You met the challenge by assuming you knew fe.
Information theory would be interesting indeed if it could
provide a way to solve for one of the variables in the loop when
insufficient information was given to do so. That is what you
seemed to be claiming you could do. And that is why I considered
that you were cheating by asking the form of the output function
(as you defined it), because being given that information made
the challenge trivial.
I hope we can consider that disagreement resolved. From my point
of view, however, there still remains a serious problem. It
starts with this:
The claim is that information about the controlled part of the
disturbance is passed through the perceptual signal.
I have no idea what you mean by "the controlled part of the
disturbance." I can't even go on describing my remaining lack of
understanding until you tell me what it means. But I will tell
you where I am going next.
Way back at the beginning I started asking for an illustration of
how information theory would be applied either to data from a
real subject or to a PCT model of the subject. I wanted to see
what the calculations looked like, thinking that would help me
understand the idea better. The next thing I knew, Allan Randall
came back with some sort of proof based on carrying out a
physically impossible (although apparently mathematically valid)
operation. I started getting lessons in why information can't
just be calculated, why a whole raft of assumptions have to be
made before you can even say what the information in a simple
signal is. Basically, I was told "here are the sources, here are
the equations, figure it out for yourself."
This is probably reprehensible of me, but I don't want to figure
it out for myself; I'm beginning to doubt that I can. What I want
is for someone to go ahead and make the necessary assumptions,
apply them to the data, and show the calculations, so I can at
least begin with one actual example. I don't care what the
assumptions are; just make them and say what they are and come up
with some sort of result. I want to see how you compute
informational measures for all parts of the control loop.
I would be perfectly happy to provide all the data from a running
model including everything: disturbance, input quantity,
perceptual signal, reference signal, error signal, and the forms
of all the functions in the model. I just want to see how the
calculations are done by somehow who knows how to do them. I
don't want any advanced understanding of theorems and
equivalences and principles. I just want to see some numbers, and
how the numbers illustrate the things you say. And I want to see
the exact assumptions that are necessary to make the calculations
possible, so I can make up my own mind about whether to accept
them as plausible.
Does this seem unreasonable?
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Best,
Bill P.