Re: Less is not More

On Nov 11, 7:52 pm, "R. Baldwin" <res0k...@xxxxxxxxxxxxxxxxxxxx>
wrote:

Now you are heading off base again. The phrase "additions to the string
do
not produce an increase in the string's KC toward its maximum upper
bound"
is wrong. You are implying that larger substrings have constant or
decreasing Kolmogorov Complexity, which mathematically cannot be tendancy
due to the pigeonhole principle. If you have a program "print the first n
digits of computable constant X" with n as an argument, its description
increases as log n.

An increase of description length of only log n is always well shy of
the string's maximum KC or "upper bound" - as I've already pointed
out.

Please re-read what I wrote, more carefully this time. I am taking issue
with one specific incorrect statement. If you are planning to continue
pontificating about Kolmogorov Complexity, you ought at least to get the
terminology correct.

Who is "pontificating" here? - and coming up with all kinds of
irrelevant quibbles? If you go back and re-read what I actually
wrote, and more carefully this time, you will see that I didn't say
that there was no increase in KC, but that there wasn't an increase
toward the upper bound with increasing n. That's in fact true. The
increase in the upper bound with increasing n outpaces the increase in
KC if the prediction of n is perfect.

If you found that KC only increased according to log n, with
perfect predictability beyond that as to what binary digit the next n
would be, that would be very good indication of non-random bias with
increasing n.

Well, it might, and it might not, and whether it did would depend on
precisely what you meant by "non-random bias". You've been awful difficult
to pin down on this.

Oh come on! You know exactly what I mean by non-random bias. Again,
we are talking about the KC definition of random here.

Beyond this, for infinite computable sequences like pi,
the program could read "print n of computable constant X to
infinity".

What? Print n what? Digits? If you are going to print a finite number of
digits, infinity never factors in.

Print infinitely many digits . . . and don't stop until I say so or
enter the command to stop printing digits . . .

There is no need to specify any particular end to the
print function.

Man, you really don't get it, do you? A computable constant wiith an
infinite number of digits has one and only one value for Kolmogorov
Complexity, which is DIFFERENT FROM the Kolmogorov Complexity of its finite
substrings.

I know . . . But you don't get the concept that you cannot ever know
if an incoming string is in fact a computable constant with an
infinite number of digits. This is where hypothesis comes into play -
a hypothesis that can never be 100%.

Suppose I have the following four strings: A, B, C, and D. Here are the
4! =
24 ways I can concatenate them once each into a single string, without
interweaving:
ABCD ABDC ACBD ACDB ADBC ADCB
BACD BADC BCAD BCDA BDAC BDCA
CABD CADB CBAD CBDA CDAB CDBA
DABC DACB DBAC DBCA DCAB DCBA

Which ordering should I choose, Sean? And why?

Knowing the actual order of how the substrings appear in the overall
single string is completely irrelevant to the fact that all of them
could be represented by a single string.

Which of the k! single strings that could represent them ought to be used,
Sean? That is the question. They each have different Kolmogorov Complexity,
and by the pigeonhole principle, we expect most of them to be
algorithmically random.

Don't you understand that this is completely irrelevant to the
particular concept at hand? The point is that you have access to a
limited finite amount of information. You ask for additional
information outside of the string that you are analyzing. The problem
with this request is that it is equivalent to asking for more sections
of the same string. Arguing that your mind works in parallel is
completely irrelevant. Arguing that the order of known string
subsections can be concatenated in a vast number of ways is also
completely irrelevant. Not knowing which of k! ways should be used to
link the strings together is completely irrelevant to the concept that
you do in fact have access to only limited amounts of information that
could in fact be represented by a single finite binary string.

There could be additional
substrings which you have no knowledge of that separate the few finite
substrings of which you are aware. These additional unknown
substrings are of both unknown size and composition. This also
doesn't matter when it comes to the point at hand. What you are
asking for is additional finite information concerning the nature of a
single string. What you are doing is asking for nothing more than
having access to a longer portion of substring. How you can argue
that your *lack of knowledge* as to where the substrings where in fact
originated in the main string means that you actually have more
information as to the true character of the string in question is
beyond me. Less knowledge concerning the true order of substrings
that are in fact known is not more informative when it comes to
hypothesizing a biased vs. a non-biased origin for the string in
question.

This is complete nonsense. It is clear that you haven't got the remotest
grasp on this subject.

Likewise . . .

Sean Pitman
www.DetectingDesign.com


.

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