Re: Is the universe computable?

From: Eric Hawthorne <egh.domain.name.hidden>
Date: Tue, 06 Jan 2004 22:36:25 -0800

Frank wrote:

>Indeed, I've always thought there was a dubious assumption there.
>There isn't a universal time to pace the clock tics of a simulation.
>Relativity forbids it.
>Anyway, time is a subjective illusion.
>
>Back to the question:
>So what happens when the simulation "diverges" from regularity?
>Some possibilities:
>a) The universe ends
>b) Pink elephants pop up everywhere
>c) It's already happening
>
> I like (c)


Ok. How about:

The multiverse is a very long qubit-string. (This is an informal
statement to drive intuition.)

Being a qubit string it simultaneously exhibits all of its potential
information-states.

If there is something like this qubitstring simultaneously exhibiting
all possible information
states, then note that to do computation, within that qubit-string, no
actual computational
process need take place. Any tour through any subset of the information
states (i.e.
"visiting" one information-state after another after another...) can be
considered equivalent to a computation. Any tour through a subset of the
information
states which is such that the "direction" of the tour is restricted to
only those successor
information-states Si+1 (of the state Si we're currently at) which are
different from Si
by only a single bit-flip in a single position in the bitstring, and
where that bit-flip
would only happen based on some function of only the state of the bits
in a local vicinity
of the flipping bit, can be considered equivalent to a computation which
is comprised
solely of localized operations, similar to the kinds of computation we
understand.

So the universe (or any observable universe) could be a tour through a
subset of the
information-states of the qubit-string multiverse, which is such that
the tour
computes only self-consistent spaces and objects, perhaps using only
local computational
steps (part this computational locality is part of the secret of
ensuring consistency, locality,
metric etc properties of the space and the objects, prehaps).

Observers which were self-aware substructures WITHIN the set of objects
computed
in a "consistent" tour, maybe can only observe other information states
which are also
within that tour.

TIME AND LIGHTSPEED
As Wolfram postulates, the concept of time and speed of light c within
such an
informational universe may be related to how fast the informational
changes (from one
state to another) can propagate (across the qubitstring) using only
local computations
as the medium of state-change propagation. It is wrong to suppose that
this implies
"computational time" outside of the qubitstring. "How fast state-change
propagates"
is purely a question of how the metric spacetime that the consistent
tour defines
can evolve in form within a consistent tour.

The tour itself could be imagined to be real if you like (with the
qubitstring really in some god-quantum-computer-thingy which has a
god's-now-program-
pointer which moves from state to state in the consistent tour).
But it is better to think of the consistent tour as a virtual tour, an
abstraction,
defined by nothing more nor less than its BEING a subset of information
states, and an order
of traversal of those (very large) information states which is such that
the ordered set
of information-states IS and CONJURES reality.

OBSERVERS, AND TOUR-TRAVERSAL AS THE TIME ARROW FOR OBSERVERS

An OBSERVER is a set of local subsets of the some of the set of
information-states in the
consistent tour which is the universe. The notion of locality there is
information-distance.

OBSERVERS can observe any aspect (part) of the information states in the
tour which has
the following properties:

1. The observable substates must be within a light-cone of the observer.
Photons or waves of light are
information travelling through the set of information-states. They are
closely related to the putative
"local computations" which are imagined as defining sensible localized
change between sets of
information states. So the observable substates are those that are
reachable from the observer
states by local computations. These observation computations are
computations that can
affect the observer-part of the "now" information-state based on the
prior-to-now configuration
 of other adjacent-to-the-observer parts of the prior-to-now information
states, with the information
moving at a speed of one local computation (or is that one bitshift) per
information-state-distance
in the consistent tour. Confusing? Yes I'm confused too. This bit's
hard. (Pun intended)

2. Argument 1 implies that only parts (in some informational locality to
the observer within the
information-states) of PRIOR-IN-THE-TOUR information-states can be
observed by the observer.
That's what being in the light-cone from the observer implies: 1.
Informationally-local to the observer's
own states, and also 2. PRIOR in the consistent tour to the
"now-in-tour" state of the observer.

In fact we will stand these arguments on their heads now, and say that
the consistent-tour direction
must be one in which an observer cannot observe (via light i.e.
information packets moving by local
computation) forwards in the tour direction, but can observe (local
parts of) information-states that are
backwards in the tour direction.
--------
The time-arrow (state-tour direction) is that direction of
information-state-change in which the
changes are like local computations which can communicate information
across from one part of the
qubit string to an observer who is (is in?) another part of the qubit
string.
--------

Consistent tour direction (through a very large, or infinite?) set of
very large (or infinite) discrete information
states has a lot to do, I think, with the information-theoretic
concept of entropy, and if this whole
quantum-comp hypothesis is correct, I think we'll find that
information-theoretic entropy is in fact identical
to thermodynamic entropy.

Particle interactions are analogous to local computations.

The entropic time arrow must have to do with the fact that the
computations only appear to be
a self-consistent-classical-reality-producing set of computations when
the info-state-changes are considered
to be going in certain of the info-change directions that they could.

The direction that the consistent tour chooses (and that the particle
interactions choose when observation
from within the tour forces them to decohere into classical state) is a
direction imposed by consistency
constraints. In fact, the direction is DEFINED BY the
consistency-of-classical-reality constraints AND
BY NOTHING ELSE.

A way of thinking about where "NOW" is in the tour of information states
is that the PAST in the tour
is CLASSICAL (experiments have been conducted, quantum events have
actually chosen a path
from their probability distributions) and the FUTURE in the tour is
quantum-mechanical. The possible
successor-states have probabilities WHICH ARE BASED ON THEIR
INFORMATION-DISTANCE
from the now-state in the tour.

But the notion of the now-state in the tour is ILL-DEFINED as a global
concept (just as it is in physics).
We really just have a NOW-state of a local part of an information state
in the tour.
We can say that, as a definition,
 the consistent tour visits those information states all of whose parts
can choose a successor part-state
by local computation IN A WAY THAT IS GLOBALLY CONSISTENT AT THE SPEED OF
LOCAL-COMPUTATION INFORMATION-CHANGE (i.e. at the speed of light.)

So ALL of the choices of successor-state for each informationally local
part of the "now" information-state
in the tour must be consistent with each other, at least in the
retrospect that will happen when those
future states can be inspected (at info-lightspeed) by any observer
within the tour-states.
THAT is the transformation of quantum potentialities into classical
realities.

----------
So all in all I think I agree with Frank. The simulation DOES diverge
from regularity, but
the diverging simulation is just one of many "virtual tours" through the
"all-information-states"
qubitstring. Some other simulation, defined precisely as that one (or
few) which does not
diverge from regularity, is also simultaneously happening (or existent,
as an ordered subset)
in the qubitstring. And that non-diverging-into-noise simulation
(info-state-tour, I prefer
because it implies passivity (no computer needed)) is the universe.

So can there be other universes?

One way of rephrasing this question is to put it as the question of
whether there is
more than one "lightspeed--globally-consistent" tour through a set of
all possible
information states, where light is defined as communication, from one
part of the
qubitstring to another via local computations, of information.
Received on Wed Jan 07 2004 - 01:38:45 PST