"Wirt Atmar"  wrote in message
>
> I'm not so sure that Shannon would think that Dawkins is all that wrong.
> Shannon saw the "surprise" measure of
"information" that you're mentioning
in
> an inverse manner, as a depature from the monotonous signal.
>
> When all of the redundancy has been sucked out of a completely meaningful
> signal, in a lossless manner, the compression algorithm is said to have
> achieved "maximum entropy," but that term does not mean to
imply that any
> part of that "entropy" is necessarily the result of meaningless noise.
>
> Mutation (meaningless error) does the Shannonian entropy of an encoding
> program, but it also quite obviously decreases the "true information
content"
> of the program, to use Dawkins' phrase above.
>
The point is that a high-information signal, in Shannon's terms, is likely
to be pretty useless in human terms.

For instance let's say I toss a coin a large number of times. I can send the
results to you as a sequence 101110100001101 and this cannot be compressed
in any way. In Shannon's terms it is a minimum-entropy signal. However in
practical terms it is pretty useless and boring.

Now let's say we spin an American cent. I have heard (don't know if it true
or not) that there is a slight bias towards tails, due to Abe Lincoln's head
beign in bass-relief. Let's say our results are 11011111011001111  (1 is
tails). This is a far more interesting result. However it can be compressed,
because 1s are clearly dominant (the naive way would be to encode runs of
1s, better compression can be achieved by representing the number as an
arithmetical value and giving 1 a bigger representation).

Human language is highly redundant. You can do terrible violence to written
text and still have something intelligble. This indicates that redundancy
isn't in fact a fault in information systems. As a thought experiment, take
a Usenet post and scramble the order of the sentences. Obviously much will
be destroyed. However virtually nothing is known about this type of
redundancy.

Mutation is like the coin toss. The information is useful only for a very
restricted set of purposes. What we are interested in is the accumulation of
favourable mutations, which build up coherent structures. This is caused by
natural selection. However selection, by definition, works by eliminating
some mutations from the gene pool. "Coherent structure" is
something that we
can all recognise, but is hard to define formally.
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