Re: Re: For Kim G. S. Øyhus

In article <1138036200.832905.107340@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Seanpit <seanpitnospam@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
>
>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.

Yes. Precisely. The minimal description of s, which is equivalent to
your functional complexity, the minimal size of DNA to achieve a
biological function.

Functional complexity is a minimal description of s, where s is a
function.

This is how you yourself has defined it.



>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.

Yes, compressibility. The shorter the description, the more compressed
it is, until it is minimal, and has reached the true Kolmogorov
Complexity, K(s). Precisely what happens in functional complexity,
where a short DNA sequence is the minimal description for a function.


>Is there a shorter way to
>describe a string of characters than the actual string?

That depends on the string.


>For a purely random string, there is no shorter description.

But we are not talking about random descriptions/strings/sequences. We
are instead talking about the shortest descriptions/strings/sequences,
which are K(s), Kolmogorov Complexity.


>And, most strings in sequence space have nearly maximum KC since they
>aren't very compressible.

Yes, and most descriptions/strings in sequence space are nonfunctional.

But we are not tolking about most sequences/descriptions. We are
primarily talking about functional sequences/descriptions, and in
particular the simplest sequences/descriptions which describes a
function/string.


>Of course, there is no way to prove that a string is
>truly uncompressible.

PRECISELY! There is no way to prove that a sequence is truly the
minimal one.


>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.

And thus Pi has low functional complexity, low Kolmogorov Complexity.


>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.

Precisely. But you DO claim that you know the minimal functional
complexity.


>This has a lot to do with chaos theory since the concept of randomness
>plays an important role in the concept of chaos.

No, it does not.

>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.

Very wrong. There are many useful ways to measure chaos, such as
measuring the dimensionality of its attractors.


>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.

You are now disregarding the definition of Kolmogorov Complexity,
which is the shortest description to generate a string. When this
description is shorter than the string, then it is NOT random.

Or are you claiming that you functional complex sequences have
functions with total randomness?


>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.

Aha! Here we have an interesting claim from you. What you just wrote
is equivalent to claiming that if one had a biological system which
could put gas molecules in precisely the same manner that they were in
that closed gas system, this biological system would NOT have random
long sequences.

So, you better come with a proof or at least some evidence that the
DNA sequence which the biological gas reconstruction system uses would
be less complicated than the description used for a Turing machine
driven physical gas reconstruction system.


>They are completely different concepts.

Not in your definiton. Your definition of functional complexity in
this case is the minimal sequence necessary for the function of
regenerating the gas molecules with the specified locations.


>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.

But your definition of functional complexity is not based on
structural order and interdependent interaction, so what you just
wrote do not follow at all. It is simply wrong.



>" . . . 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].

No, that gas was not chaotic at all.


>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]

I have already told you that chaos can be generated by short programs,
so you are wrong. Have you seen the formula for the mandelbrot set? It
is extremely short.


> 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

You still obviously do not understand or remember what I write to
you. You just parrot articles you do not understand.

Kim0

.

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