From: shenkin@avogadro.barnard.columbia.edu (Peter S. Shenkin)
Subject: Re: More wacky theory
Organization: Dept. of Chem, Barnard College, Columbia U, New York
Distribution: bionet
Date: Tue, 15 Sep 1992 14:06:35 GMT
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In article <6078@m1.cs.man.ac.uk> mshute@cs.man.ac.uk (Malcolm Shute) writes:

>This then comes back to my comment last week, from Richard Dawkins' "The Blind
>Watchmaker".  Mont Blanc is a complex structure... with millions of fragments
>of intricately shaped rocks making it up.  However, much of this complexity
>is random.  Mont Blanc would still do the same job if someone where to come
>along and muddle up some of its rocks, or even replace some of them.  However,
>a CPU would not work if you swapped a couple of its leads over, or replaced
>them with something else.

It seems to me that in order to measure information quantitatively you
always need a context.  A context is implicit in both your Mont Blanc
example and in your CPU example;  namely, you assume that the "job" of
Mont Blanc is to simply sit there and look pretty, and that of a CPU
is to function as a computer.  Similarly, when we talk about the information
content of a stretch of DNA, we assume that its "job" is to code for 
a protein, and we measure its information content in a manner consistent
with the job we have in mind.

Let me now present counterexamples for all these cases -- atypical but
imaginable "jobs" for Mont Blanc, a CPU and a stretch of DNA -- in the
context of which their respective "complexities" are "random,", in the 
same sense in which, using Malcolm's word, Mont Blanc's complexity is 
"random."

Suppose you were designing a terrain recognition system for a missile
whose target was Mont Blanc.  In the memory of the missile you have a
coding of enough of the complexities of Mont Blanc to distinguish it
from its neighbors.  In this case, the complexities of Mont Blanc
are far from random, and the only way in which a mountain can do its
"job" -- to be recognized by the guidance system -- is to have enough 
of the actual features of Mont Blanc that Mont Blanc itself has.  This 
sort of problem could be discussed from the point of view of information 
theory, and the amount of information needed to recognize Mont Blanc and 
reliably distinguish it from its neighbors could be calculated.

Similarly, if the CPU were part of a scrap-heap from which it was
desired to extract some element, the specifics of its wiring scheme
would be of no more relevance to the "job" of having, say, the gold-plating
of its leads extracted than are the specifics of Mont Blanc's complexities
to the "job" of being a mountain.  

Similarly, if the DNA is to be burned in a calorimeter in an effort to
measure its heat capacity, the specifics of its complexity as a gene
are (to a very, very good approximation) irrelevant to the task at hand.

Thus, "information" requires a context.  The specifics of Mont Blanc's 
complexities are "meaningless" with respect to most, but not all, contexts 
in which Mont Blanc normally occurs.  DNA's complexities are "meaningful" 
in the context of most, but, but not all, contexts in which DNA is considered. 

	-P.

-- 
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Peter S. Shenkin, Department of Chemistry, Columbia Univ.,  New York, NY 10027
(212)854-8402    shenkin@avogadro.barnard.columbia.edu   shenkin@cunixf.BITNET
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