Re: Anyone wanna help with a compression routine (new type)


On 18 Dez., 21:53, Virgil <Vir...@xxxxxxx> wrote:
In article <fk8hrp$3v...@xxxxxxxxxxxxxxxxxxxxxxxxx>,

WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
On 10 Dez., 12:39, Ian Parker <ianpark...@xxxxxxxxx> wrote:
On 7 Dec, 12:03, WM <mueck...@xxxxxxxxxxxxxxxxx> wrote:
But I did not find a final answer to my question whether random
strings of every finite lengths n are existing.

Pi is an infinite pseudorandom string. It will pass the standard tests
of randomness. But we know it is pseudorandom.

Yes. But if we did *not* know the short rule how to construct pi, then
we would believe in its randomness and its infinite information
contents.

Believing something contrary to 'fact' is a human failing.

My question is whether there are some (many?) more real numbers which
have "short construction rules" being unknown as yet. For that reason
I assumed the possible although improbable case of a civilization
knowing Kolmogorov complexity but not being aware of pi.

I am concerned with the question whether there may be other
expansions of real numbers which appear to be random but may follow a
short rule which has not yet been discovered though. This would reduce
their infinite Kolmogorov complexity to a small amount and it would
allow us to really address and use these real numbers.

Then the best one can be sure for most numbers is that their Kolmogorov
complexity may be smaller than we think.

In fact this would be required if we wanted to use these numbers as
individuals for some applications, because we cannot address any
number which has an infinite complexity. I think this is undisputed. I
am not so sure however, that this requirement is satisfied "for most
numbers" as you seem to believe. If you are right, then Kolmogorov was
wrong.

Regards, WM
.

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