Re: Computing Randomness

From: <juergen.domain.name.hidden>
Date: Tue, 3 Apr 2001 13:27:55 +0200

> To get to my actual Everything [roughly] first substitute an infinite
> variety of patterns each repeated an infinite number of times each with a
> family of interpretations in place of the balls. Second substitute
> shifting isomorphic links {linking interpretation to universe} for the
> caterpillars. Now stir with my Everything/Nothing alternation.

Stir how? In a computable way? You might want to try to formally describe
what you mean.

> > > If one allows an infinite repeat of each and every natural number is that
> > > not a uniform distribution?
> > >
> > > Hal
> >
> >There are many ways of repeating each natural number infinitely often.
> >But what does this have to do with a uniform distribution? How do you
> >assign probabilities to numbers?
>
> The scenario I was trying to create is where you have numbers with
> different properties say some short strings, some long strings, some simply
> patterned strings, some with complex patterns, etc. etc. Now on the number
> line numbers with one family of properties may be more or less numerous
> than numbers with another family of properties. If you put all these
> numbers in a bag and reach in and pull out a number at random the largest
> family would have the greatest probability of having a member be the one
> pulled out - an uneven distribution.

Pull out at random? The topic of this thread is precisely: where does
the randomness come from?

> Now increase the contents of the bag so that all the original numbers are
> in there with an infinite number of repeats - all families of properties
> would have the identical probability of having a member be the one pulled
> out - an even distribution.

Why? Suppose every 2^n-th number in the bag is n. Then each number is
repeated infinitely many times. But why should P(17) equal P(42)?

There is an instructive little exercise: Try to precisely describe
a probability distribution on the natural numbers such that all are
equally likely.

> Similar to some properties of my Everything but I use pattern rather than
> number. All numbers may be patterns but not all patterns are numbers.

Then try to precisely describe a probability distribution on
infinitely many patterns such that all are equally likely.

JS
Received on Tue Apr 03 2001 - 04:30:14 PDT