Re: Kolmorgorov Complexity and Kim Øyhus


Kim G. S. Øyhus wrote:

> >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.
>
> And you forget that K(s) is defined to use a reference machine, an
> universal computing device, say an universal Turing machine, which IS
> a function.

The Turing machine has a function, but this function is independent of
the string, which it "compresses". The string itself need not have a
particular function in order to be compressed by the function of the
Turing machine.

> I have told you this several times now, and you forget,
> again and again. Why is it so difficult for you to remember that
> something which is a function, definitively have a function, because
> it IS a function? Functions HAVE functions because they have themselves.

Again, the string is not functional here. The Turing machine has the
function - not the string.

< snip >

> >My definition of functional complexity is the minimum
> >*uncompressed* size and specificity of a string needed to gain a
> >particular type of functional system.
>
> That is NOT what you wrote earlier. It is also self
> contradictory. The minimum size is PER DEFINITION compressed. You
> clearly show that you do not understand this at all.

The minimum size for a particular function of a protein string of
residues, as part of a larger system of function, is not the same thing
as it's minimum size that could be coded for by a Turing machine.
These are different forms of potential compression. One form requires
that the function of the protein string be maintained while the other
does not.

> >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.
>
> That do not make sense at all. It seems to me that you are saying that
> compressed systems will not decompress, which is nonsens, or that
> compressed systems can fail, ignoring that decompressed systems also
> can fail.

Take a protein sequence and compress it using a Turing machine code.
That new sequence will not necessarily work, at it is, as part of the
system from which the original protein sequence was taken. In order to
work properly, the original protein sequence must maintain a certain
minimum size and specificity regardless of how it could be compressed
using this or that formula or Turing machine. It might be able to be
compressed, using a particular Turing machine, into just a few
characters, but this compressed form just wouldn't "work" if placed
back into the original system.

> > 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.
>
> If the minimal sequence do
> not work, then it is not a minimal
> sequence.

It's certainly not the minimum functional sequence although it might
actually be the minimum sequence produced by a particular Turing
machine.

> If the compressed sequence do
> not work, then it is not a compressed
> sequence.

It certainly could be a compressed sequence, per code, would could be
decompressed. However, in its compressed state it may not "work"
properly any more.

> If it do not work, then it
> is not valid.

It may still be valid as far as the Turing machine output is concerned.
It just isn't valid as far as it's original function in its original
system of function is concerned.

> It has lost its output.

It has only lost it's output as far as its original system is
concerned.

> It has lost its function.

That's true - -

> Your argument is wrong and stupid.

Actually, I believe your argument that functional minimums are the same
thing as KC is what is off base here.

< snip >

> Your definition of functional complexity did not include that it
> should be a part of a system of function, so your argument is wrong.

My definition of functional complexity always included the part a
particular sequence plays in the overall system of function. The
functional complexity of this part, as part of the whole, is determined
by the minimum size and sequence specificity requirements that are
needed in order for it to do its job in a beneficial way relative to
the system as a whole. In other words, what is the minimum size and
specificity requirement for a particular sequence to have the lactase
function to a minimally selectable benefit to the bacterium as a whole
in a lactose rich environment? Can this minimum be achieve with just 3
residues? 10 residues? 100 residues?

You see my point?

> >> >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?
>
> Yes. Chaos theory is about DETERMINISTIC systems which amplify small
> perturbations. You have not understood what chaos theory is.
> Deterministic systems are systems without randomness.

Chaotic systems are theoretically deterministic (well, not quite), but
in practice they aren't deterministic - because of those little
perturbations you mention. "A system may be perfectly deterministic in
principle, but its behavior is completely unpredictable in practice.
This phenomenon was called deterministic chaos." The resulting
"chaotic" outcome of such a theoretically deterministic system ends up
having the appearance of true randomness. In this sense then nothing
is actually random. It only has the appearance of randomness because
of the chaos problem - i.e., the starting parameters are not known and
cannot be known, even in theory, to an infinite degree. Therefore,
randomness and chaos are very closely tied together. What appears to be
"random" only has this appearance because of chaos theory - because the
starting parameters where not perfectly knowable.

http://pespmc1.vub.ac.be/CHAOS.html

< 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.
>
> NO!
>
> I have your written definition here:
>
> "Over and over again I've defined functional complexity as the minimum
> size and specificity requirement needed to achieve a specific type of
> function."
>
> There is no talk about interdependent interaction or structural order
> there. You wrote instead about the minimum size, just as in K.C.

The minimum size and specificity requirements are a big part of what it
takes for a piece of a system to be beneficial relative to the whole.
This has always been strongly implied from the get go Kim. You're just
trying to build a strawman here.

> As for specificity: You have shown that you do not know what
> specificity is, through your thorough confusion of specificity with
> density, so I ignore that part of your definition, since you do not
> know what that part means.

This is ridiculous. Sauer and Olson and even Yockey, as well as many
others, talk about the minimum sequence specificities of proteins. You
just can't change too many residues at the same time without a complete
loss of that protein's function. That's specificity. It can be
measured. All functional proteins have a minimum specificity
requirement that can be reasonable determined.

> >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.
>
> What you describe now is irreducible complexity, which is totally
> different from your functional complexity.

Irreducible complexity is not totally different from functional
complexity. IR all about the minimum size and specificity requirement
for a particular functional system. That's exactly what I'm talking
about. All functional systems have a minimum irreducible requirement
in order for a particular function of that system to be realized. What
the heck did you think I was talking about this entire time?

> But you have done that confusion several times before, and people have
> told you several times before that it is called "irreducible
> complexity".

Well obviously it is called irreducible complexity. "All functional
systems are irreducibly complex" - as I've said many times before.
There is even a title to a thread that I started by that name. It is
just that different types of functional system have different minimum
size and specificity requirements.

> I seriously thing there is something wrong with your
> mind, since you are not able to remember stuff people tell you again
> and again and again ad nauseam. It seems you have lost your ability to
> learn.

It is just that what you tell me again and again at nauseam is clearly
wrong as I see it.


> >> >" . . . 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.
>
> There was no mentioning of turbulence in any of your quotes. All
> pointed to there being ordinary stationary gas without
> turbulence. Turbulence in gas is considered the classical example of
> chaos in gas.

The type of simple gas mentioned by Baranger here, if you actually took
the time to read the paper, is actually an ordinary stationary
non-turbulent gas in a chamber. The gas molecules still move around
quite rapidly however. The movements of these molecules are indeed
non-linear or chaotic (i.e., not predictable over very short periods of
time).

> Calling a stationary gas chaotic is not right.

Sure it is. You just don't understand that Baranger is talking about
the gas molecules - since you obviously haven't read the paper.

> The normal thing to
> call the molecules of a stationary gas is "random". There is a certain
> chaotic component to the interaction of the molecules of the gas, but
> the molecules interacting chaotically does not mean that the gas is
> chaotic.

What? Molecules interacting chaotically doesn't mean that gas is
chaotic? How do you arrive at that conclusion? Baranger is talking
about this chaotic movement of the gas molecules and that is why he
said, "The simple gas mentioned earlier is highly chaotic, but it is
not complex in the present sense."

< snip >


> >> >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.
>
> You wrote above:
> "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."
>
> Which contradics your claim that That's the whole point. If true
> chaos is not the result of a very simple formula, then the point
> cannot be that true chaos IS the result of a very simple formula.

Chaos is not just the result of a simple formula with a knowable
outcome. Chaos is more than that. Chaos must contain a component of the
unknown. The same thing is true of randomness. This is why a string
that appears random or "chaotic" might actually be the result of a very
simple formula. In other words, there is no such thing as absolute
randomness or even chaos. There is only the appearance of randomness
or chaos because of the involvement of the unknown.

> >Both apparent chaos and randomness can be
> >generated by short programs, but the result is unknowable.
>
> And now you are again confusing chaos with randomness.

There you go again, thinking that chaos and randomness aren't related.


> >That's what
> >makes chaos and randomness what they are - "unknowable" or
> >"unpredictable".
>
> Chaos is deterministic. You have misunderstood, as usual.

But that's just it. Chaos isn't completely deterministic in practice.
That's why chaos theory was born, because many things just aren't
linearly deterministic. To the degree that the unknown is involved and
can affect outcome, to that degree is chaos and/or unpredictability
increased over time.

< snip >

> >Understanding and remembering are very different things Kim. I do
> >indeed remember what you write.
>
> No, you do not. You just believe you do.

Yes, I believe I do and you believe I don't. I mean, how could you
believe otherwise. Obviously someone who actually remembered the
brilliant things you say would have to agree with you. Therefore, those
who don't agree with you must not be remembering what you say! ; )

> >It just doesn't make any more sense now
> >than it did before.
>
> You are simply terrible at thinking.

Ditto ; )


> >You've directly disagreed with the author of this
> >particular article on something that seems quite obvious.
>
> You have not understood the author either.

You haven't even read the article yet, have you? Yet you know what
Baranger is saying? I guess someone who invented the notion of
Kolmogorov Complexity "independently" doesn't have to actually read
such articles to know what they say? ; )

> >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.
>
> Since you are not able to make sense of what I write, you are not able
> to judge the sense of what I write, but you do so anyway. That is
> dishonesty.

Then, by this logic, you are not able to just the "sense" of what I
write - yet you do so anyway? Is this dishonesty on your part?

< snip >

> Kim0

Sean Pitman
www.DetectingDesign.com


.

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