Information Theory (again)

[Allan Randall (930618.1800 EDT)]

Rick Marken (930611.2200)

You can use any kind of control system you like; or any method
you like whatsoever -- it doesn't even have to be a control system.

No, I need to know what control system to do the reconstruction for,
not what to use to do the reconstruction. Correct me if I'm
misremembering: You have stated that the simple linear example from
Powers' Primer was insufficient due to lack of nonlinearities. Therefore,
if I am going to do a demo, I absolutely need to know what kind of control
system *will* satisfy you. This seems like a simple requirement.

I will give you a sequence of numbers, P, that was an actual time
sequence of perceptual inputs to a control system. ...
I think I actually gave this data to you (and I gave Gary Cziko the
actual values of the sequence of D values) but I never got the
reconstructed values of D.

I thought I made it clear, but I'll repeat it once more: this is an
EMPTY challenge. It has nothing whatsoever to do with anything I have
claimed about information in the percept or reconstructibility. You are
asking for a completely 100% blind reconstruction. This would require 100%
of the information about the disturbance in the percept. I never claimed
this. You have said in the past that you understood this - and that you
were not looking for a complete 100% reconstruction. And yet, here you
are again acting like this challenge has some kind of meaning.

>When did you show this? You showed that it was not possible to perform
>the reconstruction?

Bill Powers and I both posted data showing that there can be a very
weak relationship between output and disturbance when there is a
varying environmental non-linearity between the output and the
controlled variable.

This is nowhere close to showing that the reconstruction is not
possible. You posted correlation figures. As far as I can remember that
was about it.

Okay, ONE MORE TIME.

Without P there is no way at all to reconstruct D except by chance,
right? What is this fewer additional bits thing?

This "fewer additional bits thing" is the whole notion of information I
have been talking about for some time. I am *not* offering to
reconstruct the disturbance blind with no additional information.
However, if I can use the percept to do the reconstruction using *fewer*
additional bits than would be required without the percept, then I have
shown that the percept contains information about the disturbance. This
is the only reconstruction demo I ever offered to do. When you posted
your blind-man challenge, I dismissed it and asked for an example of a
sufficiently nonlinear control system. I have not received this from
you, so I have not yet done the demo.

To clarify this once more, I am reposting the rules as I see them. I
have justified these in the past, so I'm not going to go on at length
about them. From a previous post:

The following is what I am assuming as given in any attempt by me to
reconstruct D from the percept p:

    - the reference r
    - the output function O()
    - a programming language, such as C

    We will all just have to agree that the C programming language
has no inherent information about d - that seems like a reasonable
assumption to me.

    The following are *not* assumed (to do so would be "cheating"):

    - the output o
    - the environmental feedback function F()
    - the disturbance d

... I'll give you a string
of numbers which I swear is P. I'll also give you r, O() and C (I really
forget why I agreed to giving C if C is values of the controlled variable;

As you can see from above, C was just the C programming language.

You give me back a string of numbers that is D. You should be able
to do this because, you claim, there is something (that you call
"information") in P that let's the control system know what D is.

The idea was to do this in FEWER bits than without P. That is crucial.

ยทยทยท

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