The H, you say!

<Martin Taylor 940204 12:00>

On January 31, I tried to post the following to Tom Bourbon in private
response to a posting of his. It was private because I thought that
the general CSG-L readership would know most of what it contains, having
read the material as it went by. This morning, the message was returned
to me on the grounds that Tom's machine is down. I hope that he will
receive it when his machine returns to life, if I send it via CSG-L.
And maybe it isn't totally redundant as a public posting.




Perhaps I misunderstand your posts, Martin. It seems to me that you claim
to have used information theory to successfully reconstruct the disturbance
function that accompanies the data Rick sent to you.

Not at all. The claim always was that if there is no information about
the disturbance in the perceptual signal, it should never be possible to
use the perceptual signal in any way to reconstruct the disturbance signal.

It's a limiting case. In the general case, there is some information
about the disturbance in the perceptual signal, but not normally enough
to permit reconstruction of the disturbance signal. The interesting
aspects are how the uncertainty of the disturbance given the perceptual
signal might affect the usable gain in the loop, the need for, and
effectiveness of, higher levels of control, and the like.

To my mind, the reconstruction test was always a red-herring, apart from
what I originally conceived would have to be an in-your-face demonstration
that there MUST be information about the disturbance in the perceptual
signal if one could do the reconstruction over unlimited time, given a
finite amount of extra information. The test conditions were prespecified
by Rick to be acceptable. When we did that demonstration, the grounds
shifted very rapidly under our feet, and instead of the obvious conditional:
IF reconstruction THEN information, the reverse was and continues to be
claimed: IF imperfect reconstruction THEN no information, which is, on the
face of it nonsensical.

But the tar baby seems to have crawled back into my lap. I'm going to try
to avoid handling it by approaching the issue from a different direction,
based not so much on information flow as entropy import and export. To
follow the forthcoming argument, you will have to understand my posting
<Martin Taylor 940125 11:30>, which Bill Powers called a "fine posting"
on the nature of Boltzmann's entropy.

Too bad about your disconnect. It's very disturbing to lose your contact
with the world, isn't it?