Re: Computing Randomness

From: Hal Ruhl <>
Date: Sat, 07 Apr 2001 23:00:57 -0700

Dear Juergen:

At 4/3/01, you wrote:
> > 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.

I believe that attempting an extensive detailed formal description of the
Everything is the wrong approach. IMO - at least in this case - the more
information used to describe, the smaller the thing described.

I became convinced some time ago and before joining this list that the
actual foundation of our experience was "no information". So how does one
describe "no information" or "The Nothing"? Since it is empty it is

I hit on the idea that its very emptiness may make it Godelian
incomplete. Since The Nothing can not resolve any question whatsoever the
issue became an effort to construct a meaningful one.

That brought me to the question of its stability. Can The Nothing
endure? I do not see "Time" as entering by the back door via this question
because it is an issue of stasis not flow. I see no way for The Nothing to
escape addressing the issue of the durability i.e. stability of its own

Since The Nothing is sans logic to address this issue it must resort to
test by perturbation. IMO the minimum perturbation is for The Nothing to
directly become The Everything. According to the notion that no selection
- i.e. having all information - is identical to having no information - The
Everything is just a different configuration of "no information" - well

The interesting thing is that the Everything being a perturbation from the
Nothing does not contain the Nothing. Subtracting the Nothing from "all
information" to produce the Everything is the smallest selection
[perturbation] I can think of. The idea being that no information and all
information are identical but the Everything is not quite all
information. For this reason I prefer the name Superverse.

The perturbation is a history destroying event. The Superverse, lacking
knowledge of its origin, has exposure to the same unresolvable question re
its stability. To test this it must execute a perturbation to the
Nothing. Again a history destroying event. So here is a
Superverse/Nothing [S/N] alternation or foundation for our experience.

I also had a description of this alternation idea in an earlier post:

So having arrived at the idea that a Superverse does show up what do we do
to understand our place in it? This would be making a further
selection. Now the larger the piece of the Superverse you describe the
less information you should need to describe it. So select pieces of this
Superverse that can support our universe until one finds one with the
shortest description. This in a way brought me to the idea of pattern. A
pattern may be represented buy a binary string but need not be a
number. I select a very large piece of the Superverse by describing a no
further selection seething foamy fractal pattern of patterns. To minimize
non uniformity and selection within the fractal each pattern is present an
infinite number of times.

Each pattern has a set of isomorphic links which are either active or
possible states of universes.

Now why seething? First there is the history destroying S/N alternation so
each manifestation of the Superverse is an independent pattern of
patterns. Second to avoid a selection during a Superverse manifestation
and the resulting increase in information the active/possible status of
isomorphic links should be an uncoordinated dynamic.

Each link "j" has a self contained set of rules Rj for finding its possible
successor link(s) within the fractal. When one such possible successor
link is "encountered" during the seething it becomes the next state of that
universe. This is a link shift. There is no coordination between links.

Again avoiding selection these rules can be anything from simple to highly
complex, and completely deterministic [only one successor link is
acceptable] to totally random [all links are acceptable successors]. So
which Rj is ours? I believe the answer is a simple set of rules with some
true noise content operating in links to finite patterns.

As to my rationale for a presence of true noise in our universe see my work
in progress, George Levy style FAQ contribution at: [The intro is largely
a repeat of the above.] [ It also fixes a number of problems in the model
for those who have looked at my larger paper before.]

> > > > 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?

Rather it is evident from the above that I think the real question is how
to base our particular isomorphism on "no information". Our instinctive
reaction - to which Russell draws attention - that a random string contains
no information is in this venue perhaps the right assessment. In my model
getting a random sequence is no trouble at all - just use a "do not care"
Rj. The "pull out at random" is a valid reflection of my model since the
seething of both sorts will effect the dwell between link shifts. Any SAS
in a link so effected will not notice this.

> > 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)?

In reference to the discussion above the shifting of a link from pattern to
pattern in the fractal described is on a global basis absent preference for
a particular pattern.

>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.

Remember my point of view - minimum descriptive need [uniform distribution]
is an indicator that a very large piece of the Superverse is being described.

Received on Sat Apr 07 2001 - 20:07:10 PDT

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