Re: Stephen Wolfram vs. Charles Darwin on natural selection

On Mon, 15 Dec 2008 14:47:52 -0500 (EST), William Morse
<wdNOSPAmorse@xxxxxxxxxxxxxxxx> wrote:

r norman wrote:
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.

I don't understand this objection. If we are talking about a finite set
of entities, it is always possible to exactly describe any entity with a
fairly short sequence of questions. Again, it doesn't seem that this is
the thrust of your argument.

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?

At one point it was thought that genomic complexity would reinforce the
preconceived idea of humans being at the "pinnacle" of evolution. This
turned out not to be the case. But it also seems to the case that size
of the genome is not at all related to some relatively clear measures of
developmental complexity, due to (note the scary quotes) "junk"

Once you have a set of questions valid for everything you know
about, you come across (or evolution produces) something new and then
you have to add another question and then evolution produces something
yet again and then ... Actually, the set of questions we use in
dichotomous keys, for example, often enough has to be totally revised
in line with accumulating knowledge.

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?

Actually I think it is, and I think it will become more so as we
understand more about development. I think we will be able to rank
organisms on the basis of developmental complexity, i.e. on the number
of steps and subprograms in the developmental algorithm required to
produce the organism. This is probably not exactly the same as
Kolmogorov complexity, but it seems pretty close to me. Obviously there
will be a gray area when there is significant environmental input in
development, but I never promised you a rose garden :-)

Of course there is at least one other type of complexity in biota, which
I will call cytoplasmic complexity for lack of knowing whatever the real
term is. Forgoing the comparison of an amoeba with a neurocyte, how do
I compare the complexity of a human neurocyte with that of a lamprey?
Even supposing that the human is developmentally more complex than a
lamprey, that would say nothing about the relative complexity of their
neurocytes.

But I would not say that means there is no way to define that
complexity, and I would think as we learn more about proteomics we may
be able to address that question as well.

I am not so optimistic to think that we will have such a "description"
in any time soon. And my major point is that defining the notion of
complexity so as to rank order organisms is completely foolhardy at
present and will remain so for sufficient time so as not to be a
question worth asking now. My personal view is that it is not and
will never be a question worth asking. However I can't really presume
to speak for 28th century science. But for the next 50 years or so,
it is and will be meaningless.

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

And I still don't have that clue. What do you really mean by
"description" so as to evaluate just how long it is? And I really
mean a good solid formal definition that will withstand application to
a really wide range of organisms, hopefully with extension to all
life.

Some people, especially some people working in computer science, tend
to say "we are working on it and any day now..... ". We have learned
to be careful when marketing agents say that or when representatives
of the (any) government say that and we should by now be careful when
listening to anybody say that.


.

Relevant Pages

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  • Re: Stephen Wolfram vs. Charles Darwin on natural selection
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  • Re: The Intelligent Design Hypothesis.
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