Reconstructing the disturbance

CSGnet Archive CSG1993
1

[From Rick Marken (930616.1530)]

Martin Taylor (930616 17:15) --

Yesterday, I had completed a long response to Bill and Rick's misreading
of Allan Randall's Saturday posting, when we had a power outage, and
I lost it all. Every time we get into this information question, it
seems we have to ever deeper into basics, to try to get the fundamental
notion across. I'll try again, soon, to regenerate that posting. No
time (or inclination) now.

Hey! I've got an idea!

Why don't you guys just forget about information and information theory
for a second and just answer these three questions:

1) Can you, given a sequence of perceptual values, p, that were the input
to a control system, reconstruct the sequence of disturbance values, d,
that were present at the time? Yes or no?

2) Can you do it if I also give you the sequence of reference values present
at the time? Yes or no?

3) Can you do it if I also give you the output function that was in effect at
the
time? Yes or no?

(The last two are freebees; you would have information that the control
system itself doesn't have. I agree with Bill that if you take this
information
you are cheating -- but I'm just an easy going kinda guy).

Best

Rick

2

[Martin Taylor 930617 09:50]
(Rick Marken 930616 17:15)

Why don't you guys just forget about information and information theory
for a second and just answer these three questions:

Because it is essential to the proper understanding of the control
hierarchy (in my view).

1) Can you, given a sequence of perceptual values, p, that were the input
to a control system, reconstruct the sequence of disturbance values, d,
that were present at the time? Yes or no?

No

2) Can you do it if I also give you the sequence of reference values present
at the time? Yes or no?

No

3) Can you do it if I also give you the output function that was in effect at
the time? Yes or no?

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.

The output function normally cannot be defined precisely, though, both
because there is uncertainty about the effect of a particular output
signal on the CEV, and because the (uncertain) output function necessarily
is time variant in a cross-connected hierarchy. The problem is (at minimum)
that the effect of an ECS on its CEV is achieved through the actions of
lower ECSs, and their reference signals are derived from multiple and
varying sources (the outputs of other higher ECSs).

This variability makes it even more important to note how the information
about the disturbance (NOT the disturbing variable) is passed through
the perceptual signal. Given that the relation between the output
signal leaving the ECS and the effect of that output on the CEV is
dynamically variable, the perceptual signal also carries information back
to the output about the current relation between the output signal and
the CEV. This latter is most important for learning. The essential
issues are those of control bandwidth (information rate) and gain,
as related to the information rate of the output function itself.

(The last two are freebees; you would have information that the control
system itself doesn't have. I agree with Bill that if you take this
information
you are cheating -- but I'm just an easy going kinda guy).

The fact you say this is at the core of why we say you just don't
understand what is meant by information. Re-read Allan's posting
of last Saturday (Allan Randall 930611.1700). To show that the information
about the disturbance was available in the perceptual signal, given
the fact of control, all you need is to show that using a given language
it is shorter to describe the output function than it is to describe
the disturbance time series (or continuos waveform).

Please try to remember: the ability to reconstruct is conclusive proof
that the information about the entity is available. We demonstrated
that the disturbance could be reconstructed from the perceptual
signal, given a known output function. Inability to reconstruct is
not proof that there is no information. All an inability to reconstruct
can demonstrate is that the available information is not complete.

Martin

3

From Tom Bourbon (930617.0943)

[Martin Taylor 930617 09:50]
(Rick Marken 930616 17:15)

..

1) Can you, given a sequence of perceptual values, p, that were the input
to a control system, reconstruct the sequence of disturbance values, d,
that were present at the time? Yes or no?

No

2) Can you do it if I also give you the sequence of reference values present
at the time? Yes or no?

No

3) Can you do it if I also give you the output function that was in effect at
the time? Yes or no?

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.

But, Martin, doesn't your request for more -- I hesitate to use the word --
information about (in the sense of facts about) the output function vitiate
the claim that a modeler can reconstruct the disturbance from the perceptual
signal alone? That would be the challengs confronting the organism modeled
by the ECS. Or was the claim, not that information in p about d is
essential to the organism if it is to control, but that a modeler can
reconstruct d using p and other facts, none of which are available to the
organism modeled by the ECS?

I don't know if Rick said it, but I imagine the output quantity acted 1:1 on
the CEV, but even if it didn't, why would the modeler need to know the
output function, if the claim is that the disturbance can be reconstructed
from the perceptual signal? I was just getting connected to the net when
this particular test was proposed and I missed the details of the offer and
of the acceptance. Is the goal to reconstruct the disturbance from the
perceptual signal *and* anything else that proves necessary? For the
benefit of uninformed observers, can the parties to this demonstration
please clarify their understandings of the rules?

The output function normally cannot be defined precisely, though, both
because there is uncertainty about the effect of a particular output
signal on the CEV, and because the (uncertain) output function necessarily
is time variant in a cross-connected hierarchy. The problem is (at minimum)
that the effect of an ECS on its CEV is achieved through the actions of
lower ECSs, and their reference signals are derived from multiple and
varying sources (the outputs of other higher ECSs).

I don't know which data Rick gave you, but I'll bet they contain only the
exactly specified output function he used in the model for that run. If so,
the output function and its effect on the CEV are known exactly and the
other concerns you express here are not necessary. Again, I am speaking
from ignorance of the actual terms of the demonstration, but I suspoect
Rick gave you data from the simplest possible case, and that he did so
in order to eliminate any need for you to be concerned with uncertainties
and functions that are time variant in a cross-connected hierarchy. A
single-level, perfectly-defined loop, like the one I imagine Rick gave you,
should rule out some of those concerns, shouldn't it? (Maybe I should stop
imagining what Rick said and intended and wait for him to briefly re-state
his offer.)

This variability makes it even more important to note how the information
about the disturbance (NOT the disturbing variable) is passed through
the perceptual signal. Given that the relation between the output
signal leaving the ECS and the effect of that output on the CEV is
dynamically variable, the perceptual signal also carries information back
to the output about the current relation between the output signal and
the CEV. This latter is most important for learning. The essential
issues are those of control bandwidth (information rate) and gain,
as related to the information rate of the output function itself.

Again, if my mind-reading of Rick's offer is correct, these concerns are not
relevant to the demonstration, are they?

(The last two are freebees; you would have information that the control
system itself doesn't have. I agree with Bill that if you take this
information
you are cheating -- but I'm just an easy going kinda guy).

The fact you say this is at the core of why we say you just don't
understand what is meant by information. Re-read Allan's posting
of last Saturday (Allan Randall 930611.1700). To show that the information
about the disturbance was available in the perceptual signal, given
the fact of control, all you need is to show that using a given language
it is shorter to describe the output function than it is to describe
the disturbance time series (or continuos waveform).

Please try to remember: the ability to reconstruct is conclusive proof
that the information about the entity is available. We demonstrated
that the disturbance could be reconstructed from the perceptual
signal, given a known output function. Inability to reconstruct is
not proof that there is no information. All an inability to reconstruct

Now I am really confused. I thought the claim was an ability to reconstruct
the disturbance from the perceptual signal, and that the claim was not yet
borne out. The demonstration that the disturbance can be reconstructed from
the perceptual signal, given a known output function, mnust have appeared
before I was reliably on the net. Can someone post it again? Was the goal
to describe the output function, as you say here? When did the rules
change? By "output function" do you mean o := k(e), or are you talking
about the time series of values from the output function? Will the
parties *please* clarify the rules of the demonstration?

Until later,
   Tom Bourbon

4

[Martin Taylor 930617 13:45]
(Tom Bourbon 930617.0943)

But, Martin, doesn't your request for more -- I hesitate to use the word --
information about (in the sense of facts about) the output function vitiate
the claim that a modeler can reconstruct the disturbance from the perceptual
signal alone? That would be the challengs confronting the organism modeled
by the ECS. Or was the claim, not that information in p about d is
essential to the organism if it is to control, but that a modeler can
reconstruct d using p and other facts, none of which are available to the
organism modeled by the ECS?

There are two separate issues involved.

(1) My claim initially that I could derive the structure of the
hierarchic control system from information theory. You pointed
out that all sorts of people have claimed to be able to deduce
things from information theory that have not proved to be so. I
recognized the truth of what you said, and so have held back on that
one until I can satisfy myself that the analysis is correct. This
I have still not done. But the claim rests on a sub-claim, that
to the extent that the disturbance is countered by the output of a
control system, information about the disturbance passes through the
perceptual signal and is used to form the appropriate compensating
output. This is NOT, and never was, a claim that a modeller can
reconstruct the disturbance from the perceptual signal alone. The
claim is that information about the controlled part of the disturbance
is passed through the perceptual signal. Control itself allows the
information to be used. The control system does not have to "know"
its own output function, because that is handled by bringing the
error to zero. The "knowledge" is implicit in the fact of control.

There is also information in the perceptual signal about the part of
the disturbance that is not compensated by the control system, but
we are not talking about that, since it is accepted to be so by all
parties to the discussion.

(2) A demand by Rick, supported by Bill, that we demonstrate the
existence of information about the disturbance in the perceptual
signal by reconstructing the disturbance waveform given the perceptual
signal under the assumption that the reference signal remains zero.
We pointed out that success in this endeavour would conclusively
demonstrate that the perceptual signal contained information about
the disturbance, and Rick agreed that it would. 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).
When we ignored this irrelevant challenge, for reasons restated this
morning, Rick took that as proof of his position that there is NO
information about the disturbance in the perceptual signal.

We have tried to point out in various ways, starting from differently
phrased but equivalent bases, that failure to perform a reconstruction
was inconclusive about whether the perceptual signal contains information
about the disturbance. Despite this, we keep reading that if the
reconstruction is imperfect, then THERE IS NO INFORMATION ABOUT THE
DISTURBANCE IN THE PERCEPTUAL SIGNAL (capitals courtesy of Rick).
The point about the shape of the output function is that if the output
function can be described in a finite string, and is fixed, then
eventually its contribution to the information required to reconstruct
a disturbance waveform of indefinite length becomes negligible. Only
if the output function is changing, so that its description requires
a certain amount of information per second, does it become a serious
issue in ascertaining the contribution of the disturbance to the
information in the perceptual signal.

The two issues, reconstruction and information about the disturbance in
the perceptual signal, are separate. Success at reconstruction proves
the point that information about the disturbance is available in the
perceptual signal. Failure of reconstruction does not disprove it.

I thought the claim was an ability to reconstruct
the disturbance from the perceptual signal, and that the claim was not yet
borne out. The demonstration that the disturbance can be reconstructed from
the perceptual signal, given a known output function, mnust have appeared
before I was reliably on the net.

The demonstration is simple. Create a "mystery function" M(p-r), where
M has exactly the form of the output function O. To the extent that
the output of O is equal and opposite to the disturbance (a claim by
Rick and Bill that is simply a statement of perfect control), then
the negative of the output of M is the disturbance waveform minus an
arbitrary starting constant. It should have been sufficient simply to
point this out in order to move the discussion to the next stage, but
it wasn't. Rick said it wouldn't work as we thought. We had to (and
did) demonstrate that it worked with real data. And then the rules
kept changing in ways that confused us as much as they seem to confuse
you.

Martin

5

From Tom Bourbon (930617.1447)

[Martin Taylor 930617 13:45]
(Tom Bourbon 930617.0943)

But, Martin, doesn't your request for more -- I hesitate to use the word --
information about (in the sense of facts about) the output function vitiate
the claim that a modeler can reconstruct the disturbance from the perceptual
signal alone? That would be the challengs confronting the organism modeled
by the ECS. Or was the claim, not that information in p about d is
essential to the organism if it is to control, but that a modeler can
reconstruct d using p and other facts, none of which are available to the
organism modeled by the ECS?

There are two separate issues involved.

(1) My claim initially that I could derive the structure of the
hierarchic control system from information theory. You pointed
out that all sorts of people have claimed to be able to deduce
things from information theory that have not proved to be so. I
recognized the truth of what you said, and so have held back on that
one until I can satisfy myself that the analysis is correct. This
I have still not done.

Thank you for reporting the status of that project.

... But the claim rests on a sub-claim, that
to the extent that the disturbance is countered by the output of a
control system, information about the disturbance passes through the
perceptual signal and is used to form the appropriate compensating
output. This is NOT, and never was, a claim that a modeller can
reconstruct the disturbance from the perceptual signal alone. The
claim is that information about the controlled part of the disturbance
is passed through the perceptual signal.

Can you tell me (a) how *you* (MT) distinguish between controlled and
uncontrolled parts of a disturbance, as they occur in a perceptual signal,
and (b) whether, and if so, how, an organism, *modeled* as a PCT system,
does so in order to control? I am having a hard time imagining what you
mean. Do you mean that information about the part of the disturbance that is
*not* controlled at time t "passes through the perceptual signal" and becomes
controlled at time t+x?

...Control itself allows the
information to be used. The control system does not have to "know"
its own output function, because that is handled by bringing the
error to zero. The "knowledge" is implicit in the fact of control.

That a control system does not "know" its own output function, I agree.
You did not answer my inquiry about your definition of "output
function," but I suspect that you mean the time series of actions,
not the operator that transforms error signals into actions. Did Rick give
you the operator, or the time series? (From what you say later, I infer it
was the latter.)
..

(2) A demand by Rick, supported by Bill, that we demonstrate the
existence of information about the disturbance in the perceptual
signal by reconstructing the disturbance waveform given the perceptual
signal under the assumption that the reference signal remains zero.

This seems to be a reasonable and modest proposal.

We pointed out that success in this endeavour would conclusively
demonstrate that the perceptual signal contained information about
the disturbance, and Rick agreed that it would.

I would agree.

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).

But what you did was to construct the disturbance waveform from the output
waveform. That was not the demonstration you described in the earlier parts
of this paragraph. Had I been actively on the net when Rick gave you the
output data, I believe I would have registered a protest. The additional
data dramatically changed the nature of the demonstration, away from
showing:

existence of information about the disturbance in the perceptual
signal by reconstructing the disturbance waveform given the perceptual
signal under the assumption that the reference signal remains zero.

You demonstrated a reconstruction of the disturbance from the output time
series. If Rick protested that shift in the focus of the demonstrations,
I agree with him, but you shouldn't have been given the chance to use the
additional data in the first place.

The two issues, reconstruction and information about the disturbance in
the perceptual signal, are separate. Success at reconstruction proves
the point that information about the disturbance is available in the
perceptual signal. Failure of reconstruction does not disprove it.

That the two issues are separate, I do not agree -- not if our purpose is to
construct better generative, freely-functioning, models of control systems.
If you believe discussions *about* control systems are more complete or
satisfying or precise if you include the idea that "information about the
disturbance is available in the perceptual signal," that is one thing. It
seems quite another to claim that a PCT model would behave more realistically if
should you include an identifiable quantity that represents information
about the disturbance, as a modeled feature of the perceptual signal. The
former preference seems to be from the perspective of an observer, striving
for an aesthetically pleasing description. The latter, from the perspective
of a modeler who believes the new measure will demonstrably improve the
performance of the model. Am I very far from the mark with this
interpretation? In which sense do you think we should embrace the idea that
"information about the disturbance is available in the perceptual signal?"

Given that your demonstration is not the one originally proposed, I do not
see how it confirms your original claim.

As for the idea that a (single) failure to reconstruct does not disprove the
original claim, I agree. The claim was about a fact of nature. The failure
of a model to reconstruct the fact does not invalidate the fact. (Not any
more than a successful reconstruction offers "final" proof that a model is
"the correct one.") But a failure to reconstruct does invalidate that
particular rendering of the model.

I thought the claim was an ability to reconstruct
the disturbance from the perceptual signal, and that the claim was not yet
borne out. The demonstration that the disturbance can be reconstructed from
the perceptual signal, given a known output function, mnust have appeared
before I was reliably on the net.

The demonstration is simple. Create a "mystery function" M(p-r), where
M has exactly the form of the output function O. To the extent that
the output of O is equal and opposite to the disturbance (a claim by
Rick and Bill that is simply a statement of perfect control), then
the negative of the output of M is the disturbance waveform minus an
arbitrary starting constant. It should have been sufficient simply to
point this out in order to move the discussion to the next stage, but
it wasn't. Rick said it wouldn't work as we thought. We had to (and
did) demonstrate that it worked with real data. And then the rules
kept changing in ways that confused us as much as they seem to confuse
you.

Is M a convenient function for an observer who tries to reconstruct the
disturbance from the output function of a PCT model, or is it a feature of a
PCT model -- a feature that leads to more realistic performance by the model?

Given that you demonstrated something different from what you said (at the
beginning of (2) in your post), I have the impression you speak from the
position of an observer when you speak of M, and of the original claim about
information in the perceptual signal. Or do I misread you? Do you now
suggest that M is a function in the model of an elemental control system?

I am afraid my confusion over your interpretation of these demonstrations
has not been allayed. To me, much of my confusion comes, not from
interpretations of the meanings of theoretical terms, but from what I see
as a dramatic shift in the goal of your demonstration and in the nature of
the data you use to perform the reconstructions.

Until later,
  Tom Bourbon

6

[Allan Randall (930805.1525)]

Rick Marken:

Sorry it takes me so long to respond - I'm way behind on my reading of
this list. Anyway, I want to clear something up concerning the proposed
reconstruction demo once and for all: what I was asking for from you
was a COMPLETE description of the system (including things like
the feedback function). I'm sorry if I didn't make this clear. I want to
be able to run the program and get the same results you did. I never
accepted your challenge to do the demo blind. To make this completely
clear, I will answer the three questions:

Rick Marken (930616.1530)

1) Can you, given a sequence of perceptual values, p, that were the input
to a control system, reconstruct the sequence of disturbance values, d,
that were present at the time? Yes or no?

No.

2) Can you do it if I also give you the sequence of reference values present
at the time? Yes or no?

No.

3) Can you do it if I also give you the output function that was in effect at
the
time? Yes or no?

No.

(The last two are freebees; you would have information that the control
system itself doesn't have. I agree with Bill that if you take this
information
you are cheating -- but I'm just an easy going kinda guy).

I disagree. Both of these things are part of the control system, not the
environment. I would consider them legal.

I realize, Rick, that you have grown tired of this discussion, and you
probably don't think the demo is worthwhile if I get to see everything. But
could you just humour me and send the description? Then I can do the demo,
and you can at least see for yourself what it is I've been babbling about
all this time (even if you do think it makes no sense).

PS : hope everyone had an interesting time in Durango.

···

-----------------------------------------
Allan Randall, randall@dciem.dciem.dnd.ca
NTT Systems, Inc.
Toronto, ON