Re: Computing Randomness

From: Hal Ruhl <hjr.domain.name.hidden>
Date: Fri, 30 Mar 2001 21:58:08 -0800

Dear Juergen:

At 3/30/01, you wrote: [I reverse the order of your comments]

> (Admittedly I also was not able to
>follow your earlier reply dated Thu, 22 Mar 2001 19:47:35)

Here is a semi analog of my view of the Everything:

Take some differently colored balls say red, green, and black. Put a lot
of each in a big bag. Now add some caterpillars to the bag. Each
caterpillar is provided with a different set of rules for deciding what
color ball it will crawl onto next. These rules may use the color of the
ball it is currently on as data. Further make sure the bag of balls is
slowly stirred in a way to avoid damage to the caterpillars

Now - without regard to the pattern of ball transfers each caterpillar's
rules dictate from random to highly non random - all these patterns will be
produced equally fast.

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.

> > 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.

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.

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.

Hal
Received on Fri Mar 30 2001 - 19:14:33 PST