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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
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*> variety of patterns each repeated an infinite number of times each with a
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*> family of interpretations in place of the balls. Second substitute
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*> shifting isomorphic links {linking interpretation to universe} for the
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*> 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
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*> > > not a uniform distribution?
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*> > >
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*> > > Hal
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*> >
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*> >There are many ways of repeating each natural number infinitely often.
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*> >But what does this have to do with a uniform distribution? How do you
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*> >assign probabilities to numbers?
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*>
*

*> The scenario I was trying to create is where you have numbers with
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*> different properties say some short strings, some long strings, some simply
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*> patterned strings, some with complex patterns, etc. etc. Now on the number
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*> line numbers with one family of properties may be more or less numerous
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*> than numbers with another family of properties. If you put all these
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*> numbers in a bag and reach in and pull out a number at random the largest
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*> family would have the greatest probability of having a member be the one
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*> 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
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*> in there with an infinite number of repeats - all families of properties
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*> would have the identical probability of having a member be the one pulled
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*> 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
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*> 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

Date: Tue, 3 Apr 2001 13:27:55 +0200

Stir how? In a computable way? You might want to try to formally describe

what you mean.

Pull out at random? The topic of this thread is precisely: where does

the randomness come from?

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.

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

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