Re: Dawkins gives incorrect answer

From: CurtAdams (curtadams_at_aol.com)
Date: 08/19/04 

Date: Thu, 19 Aug 2004 23:35:54 +0000 (UTC)

tim@tt1lock.org

>This bit:

>``Mutation is not an increase in true information content, rather the
> reverse, for mutation, in the Shannon analogy, contributes to increasing
> the prior uncertainty.''

>...is not correct. Mutation typically *increases* the information in the
>genome, by increasing its suprise value.

I'm with Wirt Atmar on this one. I agree that Dawkins seems to have tripped up
in the application of Shannon's definition of "information". The problem is
that
Shannon's definition of "information", while a mighty handy and useful concept,
isn't close to the common-sense meaning of "information". "Data" would be a
far better term.

Consider a video of pure random white noise vs. a video of a movie. The movie
will be highly compressable, and by the Shannon definition contains less
"information".
But ask almost anybody how much information they contain, and they'll say the
movie has some and the white noise none. Saying the white noise has more
information is nonsense in the common sense of the word. "Data" is also vague,
but there's a commonsense distinction between "data" and "information" which
corresponds passably to the distinction between Shannon-sense "information"
and common-sense information. Shannon-sense "information" is a reasonable
formalization of common-sense "data" by this interpretation.

If you want a mathematical formalization of common-sense "information",
Bayesian/likelihood "support" is much closer. "Support" tells you to what
extent a given message is more compatible with one model than another.
Messages
equally compatible with all models, ie noise, carry no "support", and hence
no information. Messages exclusively compatible with only one model carry
a lot of information, even if quite short. (say, a measurement "proving" a
scientific
theory". But the terms are already out there and I'm not sure what's to be
done.

If you consider a likelihood definition of "information" Dawkins' statement
makes perfect
sense.

Curt Adams (curtadams@aol.com)
"It is better to be wrong than to be vague" - Freeman Dyson

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