# RE: Computing Randomness

From: Hal Ruhl <hjr.domain.name.hidden>
Date: Thu, 22 Mar 2001 20:49:07 -0800

Dear Juergen:

>>Where does all the randomness come from?
>>
>>Many physicists would be content with a statistical theory of everything
>>(TOE) based on simple probabilistic physical laws allowing for stochastic
>>predictions such as "We do not know where this particular electron will
>>be in the next nanosecond, but with probability 0.04 we will find it in a
>>certain volume V".
>>
>>Any source of randomness, however, leaves us with an unsatisfactory
>>TOE, since randomness does not have a compact or simple explanation, by
>>definition.

That seems incorrect. Randomness can have a simple explanation. However, a
particular packet of random information is considered to be incompressible.

Here is what I consider to be a simple explanation for randomness in the
Everything:

The very essence of the Everything is that it contains no information. In
that case it can not internally resolve the question of its own stability
because that would be information. There is another polar expression of no
information and that is the Great Empty or the "Nothing". The Nothing is
not in the Everything because it is not a pattern. [See next
paragraph] It also cannot internally resolve the question of its own
stability for the same reason. However, the question of stability is not
avoidable. The only way to attempt to resolve it is for each to make the
only test available which is the minimum available perturbation - a
conversion into its polar opposite. The two of these must then alternate
existences. The alternation can not inject any information into either pole
so it can not have a selected particular pattern. [Neither pole can contain
a history of the process since that too would be information thus each
alternation is an independent event resulting in no pattern to the
alternation.]

Consider each manifestation of the Everything to be a particular pattern of
all patterns each repeated an infinite number of times. The Everything can
not be a fixed pattern of patterns. But it is not because each
Everything/Nothing alternation conveys no history so the particular pattern
of patterns manifest at any alternation is a random selection from all
possible patterns of patterns.

Each pattern internal to the Everything has associated with it all possible
interpretations of pattern. Each [pattern,interpretation] pair could be
isomorphic to a particular possible/actual state of a particular
"universe". Write these isomorphismic links as:
{[pattern,interpretation]/[possible/actual state of a universe]}.

Again the possible/actual pattern of these links within the Everything can
not be static or it is information. So there needs to be a no information
generating shifting of these isomorphismic links from possible to actual
and back again.

The only essential aspect is that the current pattern of all these links
can not endure. The historic active states are in no way essential to the
link shifting process. Only the active state and its possible states are
essential.

Each universe is defined by its rules of link shift. Those rules that
insist on even a partial consideration of the set of that universe's
that do not. If we live in a universe with simple rules it is unlikely our
universe's history is an issue in determining its future - only its current
state is germane.

Rules that have a "do not care" component can be even simpler than fully
deterministic rules.

The rules need just compare all nearby links vs the current one in an
increasing region of the current Everything pattern until a match is found
then the shift takes place. This process is interrupted by the
Everything/Nothing alternation which results in a new pattern of patterns
at the next manifestation of the Everything.

>>Where does the enormous information conveyed by a particular
>>history of random events come from? A TOE that cannot explain this
>>is incomplete.

No such data is essential.

>>The in hindsight obvious solution is an "ensemble TOE" which covers all
>>possible universe histories. The ensemble conveys less information than
>>most particular histories - one main motivation of this mailing list.

Since both the Everything and the Nothing have no information and thus no
history, any particular selected historic information is more more
information.

>>Which are the possible histories? Let us focus on well-defined ensembles
>>only, and ignore those that cannot be sufficiently specified to permit
>>reconstruction through a formally describable computer. In particular,
>>we may ignore uncountable ensembles such as continua, or other ensembles
>>including histories without finite descriptions.

Well you are focusing on excessively complex rules of universe evolution
IMO. Also see further comments below.

>>Is there an optimally efficient way of computing all the "randomness" in
>>all the describable (possibly infinite) universe histories? Yes, there
>>is. There exists a machine-independent ensemble-generating algorithm
>>called FAST that computes any history essentially as quickly as this
>>history's fastest algorithm. Somewhat surprisingly, FAST is not slowed
>>down much by the simultaneous computation of all the other histories.
>>
>>It turns out, however, that for any given history there is a speed
>>limit which greatly depends on the history's degree of randomness.
>>Highly random histories are extremely hard to compute, even by the optimal
>>algorithm FAST. Each new bit of a truly random history requires at least
>>twice the time required for computing the entire previous history.
>>
>>As history size grows, the speed of highly random histories (and most
>>histories are random indeed) vanishes very quickly, no matter which
>>computer we use (side note: infinite random histories would even require
>>uncountable time, which does not make any sense). On the other hand,
>>FAST keeps generating numerous nonrandom histories very quickly; the
>>fastest ones come out at a rate of a constant number of bits per fixed
>>time interval.
>>
>>Now consider an observer evolving in some universe history. He does not
>>know in which, but as history size increases it becomes less and less
>>likely that he is located in one of the slowly computable, highly random
>>universes: after sufficient time most long histories involving him will
>>be fast ones.

As I said I currently see no essential role for "history". Further the
Everything/Nothing alternation can inject no historic information into the
Everything there is no way to detect its actual individual
alternations. Any SAS that can conclude it exists seems to be in a
universe with undecidables.

The Everything/Nothing alternation is in effect the transporter operating
at the lowest level.

Hal
Received on Thu Mar 22 2001 - 18:06:26 PST

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