Re: Predicting the Future and Kolmogorov Complexity

On 26 Mar, 16:41, "Seanpit" <seanpitnos...@naturalselection.
0catch.com> wrote:
On Mar 14, 8:29 pm, "Nic" <harrisonda...@xxxxxxxxxxx> wrote:

I made two more replies yesterday in addition to the ones that you
see, but they have been lost in the system.

I had divided your message up in to sections:

k
Shannon Information
Symmetry in Nature
SETI
Non-beneficial Gap

I attempted to give a reply to each of them with the others snipped
for clarity. Unfortunately Google Groups was nasty and vindictive.

What I had to say about k was illuminating and entertaining, whilst
all the time pushing you further and further into your corner.

Hey ho, can't remember any of it now.

Save to say, your explanation of k and Shannon Information accords
with my original understanding of these things, and so my original
post still stands.

I can paraphrase it as: complexity may well be quantifiable, but how
does that help you with designedness? Being designed doesn't make
something complex, and being complex doesn't make something designed.
Perhaps you (and I think you are likely to) say extant complexity is
beyond naturalistic explanation, and so requires design. Fair
enough. But having a formal definition of complexity gets you only
half way there - you still have to demonstrate how naturalistic
explanation is too limited to account for it. Surely the Darwinian
approach can account for anything, given enough time?

So, you see, if your selected UTM has to increase its size as the size
of the string increases in order to make the string's KCC equal to
zero, then there seems to be a relationship here to predictability.
For example, certain UTMs do not have to increase in size to reproduce
a specific sequence of increasing size. Such a situation is capable
of providing a great deal of predictive value with regard to what will
come next.

This paragraph seems to be a rebuttal of the previous one about k.
Specifically that for favourably chosen reference machines (favourable
to the source string), k scales with the string, thus destroying the
argument.

If the KC of U relative to U0 starts out at zero plus k and then stays
that way as the length of the string in question increases, one can be
more and more certain (though never perfectly certain) of the
hypothesis that states that the string is unlikely the be the result
of a truly random source. If, on the other hand, the KC of U relative
to U0 starts to increase toward maximum KC or algorithmic entropy, one
becomes less and less able to use the program in question as a better-
than-even-odds martingale or predictor. At the same time, the ability
to say that the string is most likely non-random decreases (but never
reaches absolute certainty).

Is your actual position that patterns in a string are *not* reference
machine relative, and that there is therefore such a thing as complex
specified information?

If the UTM is selected based on a small subsection of a string, then
the KC of the entire string is not significantly subject to the choice
of UTM. Regardless of the UTM chosen a randomly produced string will
show increasing KC toward maximum as more and more of the string is
evaluated - as noted above.

Leaving aside the obvious corollary that such
strings seem to be distinguished by *lack* of information, what
exactly do you want to argue for?

The term "information" is relative to the type of information you are
talking about. In this particular thread, we are talking about
"information" in the Shannon sense of the term.

Shannon information is not really a theory of information in the usual
sense of the word. Rather, it is more a theory of maximum information
transmission or sequence "complexity" or "randomness". For example,
consider a short children's storybook. Such a book contains more
Shannon information than a book of equal size composed entirely of a
string of As, but less Shannon information that a book of randomly
produced letters. In other words, a series of random letters has more
Shannon information than is contained in a meaningful storybook. Of
course, for most people, this description is very confusing since it
seems counterintuitive for a string of random letters to have more
information content than a meaningful storybook with the same number
of letters.

Richard Feynman summed up this little problem in his 1999 Lectures on
Computation when he asked, "How can a random string contain any
information, let alone the maximum amount? Surely we must be using the
wrong definition of 'information'?" In fact, it seems to me quite
unfortunate that Shannon used the term "information" at all when it
might have saved a lot of confusion to use the term "compressibility"
or "maximum information transfer" instead. In fact, Warren Weaver
(coauthor with Shannon of The Mathematical Theory of Communication)
noted, "The word information, in Shannon's theory, is used in a
special sense that must not be confused with its ordinary usage. In
particular, information must not be confused with meaning..."

http://www.detectingdesign.com/meaningfulinformation.html#Shannon


<snip On Symmetry in Nature>

<snip SETI>

<snip Non-beneficial Gap>


Nic



.

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