Re: Kolmorgorov Complexity and Kim Øyhus


Kim G. S. Øyhus wrote:

> >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.

You forget that K(s) does not concern itself with the functional aspect
of the string. My definition does concern itself with this aspect of
the string. My definition of functional complexity is the minimum
*uncompressed* size and specificity of a string needed to gain a
particular type of functional system.

KC is only concerned with the compressibility of a string given a
system that could decompress it to its original state. A particular
functional system may not be able to sustain such sequence compression
because it needs the uncompressed sequence in order to realize its
function. The compressed state of a functional string would not
necessarily be able to maintain a particular function, such as
flagellar motility.

> >http://en.wikipedia.org/wiki/Kolmogorov_complexity
> >
> >That's very basic. As I understand 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.

It's not the same. The shortest description of a string may not be
translatable into the functional system that the uncompressed string
actually coded for. In fact, it is quite likely that significant
compression of the DNA code for the flagellar system would destroy this
functional ability.

< snip >

> >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.

Actually, there is when you are talking about a particular functional
aspect of a system. There is most certainly a most likely minimum that
can be quite reasonably approximated. This is not the same thing as
KC. KC is a whole different ball game since it is not concerned with
the function of a string, only the compressibility of a string without
regard to maintaining its functional qualities.

> >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.

You can't say anything about the "function" of Pi without understanding
the system that defines Pi or requires Pi to be "functional". The KC
of Pi has nothing to do with weather it has a "function", as part of a
system of function, or not. Don't you get it? KC is not the same
thing as functional complexity. They are very different concepts.

< snip >

> >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.

Are you serious? You are arguing that chaos theory has nothing at all
to do with the concept of randomness?

> >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 absolute 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.

As with KC, you can never prove that a particular sequence or structure
is truly chaotic rather than the result of a very simple formula.

< snip >

> >The gas system is
> >highly chaotic, but has little functional interdependent 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.

You are mistaken. My definition of functional complexity IS based on
structural order and interdependent interaction to achieve a particular
type of function - like flagellar motility. The structural order of
such a system and interdependent interaction of the parts of such a
system cannot be reduced or changed beyond a certain very high minimum
threshold without a complete loss of the flagellar motility function.
It is this minimum threshold that I'm talking about. Without this
minimum in place, flagellar motility will not happen at all - period.
Not even a tiny little bit. This minimum can indeed be approximated.
It is not an impossibility like it is for figuring out the maximum
compressibility of a character string.

> >" . . . 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.

Did you notice that this is a direct quote from Baranger's paper? You
are disagreeing with Baranger here, not me.

Beyond this, it is obvious that the molecules in a gas chamber are
highly chaotic with regard to their known or knowable "order" relative
to each other. This is basically a definition of chaos. Knowing the
precise location of all the gas molecules after a certain space of time
gets more and more impossible to predict as time increases. It is
kinda like being able to predict where each pool ball will end up after
the initial break of the Q-ball. The "order" of the pool balls will be
pretty much unknowable or "chaotic" or "random" after they are shaken
around for a while on the table.

> >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.

That's the whole point. Both apparent chaos and randomness can be
generated by short programs, but the result is unknowable. That's what
makes chaos and randomness what they are - "unknowable" or
"unpredictable". The fact that what appears to be unknowably
chaotic/random may in fact be generated by a very simple program or
formula, like Pi, is what makes it impossible to really determine if a
particular string is truly random or "chaotic".

> >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.

Understanding and remembering are very different things Kim. I do
indeed remember what you write. It just doesn't make any more sense now
than it did before. You've directly disagreed with the author of this
particular article on something that seems quite obvious. It seems to
me, then, that it is you who doesn't grasp the concepts presented in
this article and therefore do not understand the fundamental
differences between Kolmogorov Complexity and functional complexity.
They are not the same Kim. They really aren't.

> Kim0

Sean Pitman
www.DetectingDesign.com


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