Re: For Kim G. S. Øyhus


Kim G. S. Øyhus wrote:

> >> And
> >> it was that bit which had the calculations. The title did not have
> >> calculations. So, the part with the calculations refer to just
> >> structure, not function.
> >
> >That's a very odd conclusion. Why don't you read the paper yourself?
> >Or, why don't you get someone, like, say, Leonid, to support you on
> >this one. See if he will come and tell me I'm wrong about this. He
> >disagrees with me on a lot of things, even on what the significance of
> >the author's calculations mean, but he agrees that the authors were
> >actually presenting calculations dealing with the limits of functional
> >changes to structure - not just structure alone. Think about it.
>
> You could provide the entire article as evidence, or an easy reference
> to it.

I have provided a large part of the article dealing with the particular
estimates we are discussing. There is no easy online reference to the
article. You could, however, go to the library and copy it for yourself
like I did.

As far as Kolmogorov Complexity, let's look at the basic definition one
more time. When discussion a string (s) of characters.

K(s) is the length of the minimal description of s.

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

That's very basic. As I undersand this statement, this is a measure of
the degree of a string's compressibility. Is there a shorter way to
describe a string of characters than the actual string? For a purely
random string, there is no shorter description. And, most strings in
sequence space have nearly maximum KC since they aren't very
compressible. Of course, there is no way to prove that a string is
truly uncompressible. A common example of this is Pi. Written out,
the number sequence of Pi looks quite random and uncompressible. But,
it actually is very compressible - the product of a very "simple"
formula Pi. The fact that uncompressibility cannot be prove does not,
however, make KC a worthless concept because you can always say that at
string has at least a certain degree of compressbility. For example,
if you find a way to compress a string to a certain point, you can say
that it has at least that degree of compressbility - which is actually
measureable. You can also know, mathematically, that most postential
sequences have high KC.

This has a lot to do with chaos theory since the concept of randomness
plays an important role in the concept of chaos. Yet, what appears to
be chaotic might actually be the result of a very simple formula
repeated over and over. As with KC, chaos is impossible to measure in
any sort of absulte way, but order is possible to measure. You can
say, "at least this amount of non-chaos" is present.

Note that Kolmogorov "Complexity" deals with randomness, order, and
chaos. The term "complexity", in this sense, is all about the notion
of randomness or disorder. This is quite different from the use of the
term "complexity" to describe a highly ordered system of function -
like a space ship.

For example, would the KC of the locations of gas molecules in a closed
system by high or low? What is the shortest string you could use to
describe the location of each gas molecule if they were all given
different numbers? It would appear that these numbers, if written
down, would be highly random and well mixed - right? The KC of such a
system would appear to be very high - right? But, this sort of
"complexity" although high, is not the same type of complexity as when
one talks about a highly ordered interactive system of functional
complexity. They are completely different concepts. The gas system is
highly chaotic, but has little functional interdetpendent complexity.
The space ship, on the other hand, requires a great deal of structural
order and interdependent interaction to achieve its high level of
functional complexity.

" . . . The simple gas mentioned earlier is highly chaotic, but it is
not complex in the present sense [although it does have apparently high
Kolmogorov Complexity]. We already saw that complexity and chaos have
in common the property of nonlinearity. Since practically every
nonlinear system is chaotic some of the time, this means that
complexity implies the presence of chaos. But the reverse is not true.
Chaos is a very big subject. There are many technical papers. Many
theorems have been proved. But complexity is much, much bigger. It
contains lots of ideas, which have nothing to do with chaos. . . [i.e.,
Kolmogorov Complexity]
So the field of chaos is a very small sub-field of the field of
complexity. Perhaps the most striking difference between the two is the
following. A complex system always has several scales. While chaos may
reign on scale n, the coarser scale above it (scale n - 1) may be
self-organizing [i.e., greater than the sum of its parts], which in a
sense is the opposite of chaos. Therefore, let us add [another] item to
the list of the properties of complex systems: Complexity involves an
interplay between chaos and non-chaos." In fact, many people have
suggested "that complexity occurs 'at the edge of chaos', but no one
has been able to make this totally clear."

http://necsi.org/projects/baranger/cce.pdf

< snip >

> Kim0

Sean Pitman
www.DetectingDesign.com


.

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