Re: Stephen Wolfram vs. Charles Darwin on natural selection

On Wed, 10 Dec 2008 13:16:12 -0500 (EST), William Morse
<wdNOSPAmorse@xxxxxxxxxxxxxxxx> wrote:

r norman wrote:
On Mon, 10 Nov 2008 13:32:21 -0500 (EST), William Morse
<wdNOSPAmorse@xxxxxxxxxxxxxxxx> wrote:

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.


Let's skip all the theoretical stuff about computability of Kolmogorov
complexity of strings and get to the meat: the notion that there does
exist a "description" of an organism. The fact of the matter is that
we have absolutely no way to write one nor to verify that any claimed
description indeed describes one organism uniquely. We can often
enough verify that the description fails (for example: "dkomo is a
feathered annelid with eighteen legs") but not that it is unique.
Certainly the length of the genome does not work to describe
complexity because there are what we think of as comparable organisms
(puffer fish and any other fish) with enormously different size
genomes. Is the fingerprint pattern part of the description of a
human? I think it probably should be but it is not part of the genome
-- identical twins have different fingerprints. Is the personality?
What about all those aspects of the personality that depend on
environmental influences? What about all those aspects of human
behavior dependent on learning? Are they part of the description of
who and what we are as organisms? Is the fact that I am a retired
biologist part of my description?

Yes - but see below.

We may be able to use compressibility by some particular algorithm as
a pretty good measure of the "complexity" of a string of symbols of
defined length from a finite alphabet. Still we don't have even a
clue as to how to write an English language or genomic language or any
other language string of characters to describe an organism, let alone
select the shortest possible such description.

One of my thoughts on reading your response was that I can describe any
organism through a series similar to "twenty questions". I can say that
you are animal, that you are a homo sapiens, that you are male, that you
are a certain age, height, weight, religious background, were born in
a certain place, currently reside in a certain place, area a retired
biologist etc., etc. Most of these descriptions rely on additional
information for their specificity (I need to know what "male" means).
But fairly quickly I get to a unique description of Richard Norman. And
even though I am relying on additional information, that information is
itself bounded.

Now since I know you to be intelligent, well informed about evolution,
and thoughtful, the description I am outlining above is clearly not the
type of description you are thinking of. But from reading your
response,the "description" you are thinking of might in fact be a
Kolmogorov type description, i.e. an algorithm to create an individual.
Such an algorithm would include the genome, the environmental factors
that influence gene expression, the life experiences that further shape
personality. This doesn't seem to me to be theoretically uncomputable,
It is probably chaotic, in that I could compute the complexity of
Richard Norman, and if I reran the algorithm I could get someone as
complex as Richard Norman, but I wouldn't actually get Richard Norman -
thank God for small favors ;-)

"Twenty questions" only works if you have a predefined universe of
potential objects to define. There is also another potential entity
that satisfies all of the questions posed but differs in yet another
essential aspect.

The genome is a particularly difficult basis because there are
enormous differences in genome size that do not in any way correspond
to naive notions of organismal complexity. You have to consider only
the "meaningful" portion of the genome, ignoring true junk and
massive replications as in polyploid species. There is no way to do
that. People want to say humans are at (or at least near) the
pinnacle of complexity but our genome is far from the pinnacle of
genome size. Do you really think that the amoebas Chaos chaos or
Amoeba dubia or the most complex organisms?

Your comments to Perplexed indicate the difficulties in using
Kolmogoroff complexity. Is that really in any way a useful method for
ranking organisms by complexity?

I still don't have a clue as to what is meant by "description".


.

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