Re: Stephen Wolfram vs. Charles Darwin on natural selection


"William Morse" <wdNOSPAmorse@xxxxxxxxxxxxxxxx> wrote in message news:gf9unl$1sfb$1@xxxxxxxxxxxxxxxxxxxxxx
dkomo wrote:
Tim Tyler wrote:

dkomo wrote:


Richard Dawkins proposed that a rough measure of complexity for an organism
is the length of its description. [...]

That's http://en.wikipedia.org/wiki/Kolmogorov_complexity
--

LOL.

"Incomputability of Kolmogorov complexity

The first result is that there is no way to effectively compute K.

Theorem. K is not a computable function.

In other words, there is no program which takes a string s as input and
produces the integer K(s) as output."

http://en.wikipedia.org/wiki/Kolmogorov_complexity#Incomputability_of_Kolmogorov_complexity

http://tinyurl.com/5vjtkl

But if you follow further on that wikipedia entry you encounter the
obvious, that many compression programs do exactly what you say there is
no program to do - they take a string s as input and produce as output a
file (which could be expressed as an integer K) that contains all the
information in s. Not exactly the same as Kolmogorov complexity, but an
indication that incomputablity may be true in the abstract but it may be
possible to come very close to computability in the concrete.

For Kolmogorov complexity, it is not difficult to come up with cases in
which 'zip' programs do not 'come very close'. For example, the binary
digits of pi or of sqrt(2). Low Kolmogorov complexity because these
strings can be computed by a simple algorithm. But very high 'zip-complexity".

For 'Dawkins complexity', the question is more interesting. My guess is that
zipping an organism description (in some formal language) would probably
get pretty close to the optimal data compression. But Mr. Cabej, who
occasionally posts here, seems to believe that the complexity of the wiring
of the human brain is reproducible enough that it represents real complexity
(signal, rather than noise) but (like pi) it can be encoded in an algorithm
which does not require huge quantities of (genetic) information. Personally,
I am not convinced that it is all signal, but if it turns out that it is, then I
think that the way that wiring unfolds during development is quite analogous
to the way that the digits of pi might unfold from the execution of a Turing
machine program.

.

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