[Martin Taylor 931221 18:00]
(Bob Clark 931221.1620)
Misunderstandings abound. I apologize for assuming your message was
tongue in cheek, but I could not believe it otherwise, since you were
responding to a message in which I tried to show the difference between
our positions. And I assumed that you were aware that I have been trying
to make sure people continue to know that I do think information theory is
important to PCT while trying not to get once more into the long process
of explaining how, which I tried to do last year. (Though I have today
opened the floodgates again with a message in response to Tom Bourbon).
I don't think there is much point in an "I said, and then you said"
kind of dialogue. But I will try to explain.
I said that your description of Information Theory did not add much to
understanding of PCT, intending to emphasize the words "your description."
The reason for this is your insertion of "the sender" which implies
that information is implicit only in messages intentionally sent by
one person to another. My point was and is that the existence of a
sender is irrelevant. Information is determinable only in respect of
a receiver, and it is measured by how an observation affects the
probability distribution of the receiver about some aspect of the world.
Information capacity is an externally determinable quantity in many
cases, but the information received often is not. To determine the
information about something that is received requires determining the
change of uncertainty in the receiver. Limits are often discoverable,
and are useful in determining what can be achieved.
My initial discussion of Info Theory was in terms of the reduction in
uncertainty experienced by the receiver. This post was received
favorably by you. Therefore I thought I had the basic concept
essentially correct.
I thought so, allowing for the caveats I originally mentioned about
quantization and uniform probability distrbutions.
I then tried to apply that concept to communication situations and
thus to PCT. "Messages," I observed, "imply both a sender and a
receiver."
To object to this was the point of my next posting, and remains so.
I hope you now understand why.
But I failed to find anything "in" or "from" Info Theory that
modified the conclusions already included in PCT. Hence I thought to
summarize the situation with:we agree that Info Theory is not useful to PCT.
I fail to see how any conclusions that are correct within any form of
control theory, or are obtained from careful simulations, could be modified
by any other correct theory. Does that mean that all other approaches
are "not useful?" Looking at things in different lights often shows
up different aspects that might otherwise be overlooked, without any
of the views invalidating the others.
Does this help?
Martin