Eric Hawthorne, <[EMAIL PROTECTED]>, writes some great and thought-provoking
questions, to which I can offer only partial answers.

> 1. What test could determine if a computational hypothesis holds?

I assume in the context of this list you mean some version of the
hypothesis that the universe we live in is actually the execution of a
computer program.  List member Jacques Mallah argued that this question
is not falsifiable in http://www.escribe.com/science/theory/m1951.html.
He suggests that any observation is consistent with the hypothesis.

> 2. Is it enough that a theory be elegant and explain all the known physics
> observations, or does the test of the theory also have to rule out all
> competing theories, or at least force all known competing theories to
> add ugly complex terms to themselves to continue to work?

Most people accept the principle of Occam's Razor, so that the simplest
successful theory will be accepted.  Therefore the "ugly complex terms"
necessary for other theories to work would disqualify them.

> 3. Is it not true that the kind of computation that computes the universe
> or multiverse must be an energy-free computation, because energy itself
> is INSIDE the computed universe, and it would be paradoxical if it also
> had to be OUTSIDE.

That makes sense.  Energy as we know it is a conserved quantity, and
our deepest theories relate it to a symmetry of the mathematics that
appears to describe the universe.  Other universes would have different
symmetries, or none at all, and the putative computation that creates
the universe would be entirely outside of the system.

> 4. What range of energy regimes and physical laws are required to produce
> spontaneous order where the order retains the dynamism required for
> life. (e.g. as opposed to producing one big, boring crystal.)

Max Tegmark has published some speculations along these
lines.  He argues that we need to have the 3+1 dimensionality in
http://www.hep.upenn.edu/~max/dimensions.html, and about the strengths
of various physical constants in http://www.hep.upenn.edu/~max/toe.html.
His conclusion is that our universe is quite "special" and that even
small variations would not plausibly produce the balance between order
and chaos that would seem to be necessary for life.

I also find relevance in Stephen Wolfram's work,
http://www.wolframscience.com/, where he runs computer simulations of a
wide variety of different simple computational systems to see which ones
might have a sort of dynamism.  My interepretation is that, depending
on the computational framework, from about one in a million to one in
a hundred randomly selected computational systems appear to allow for
some semblance of structure (i.e. particle-like objects) to exist.
However I suspect that of these, only a small fraction will have the
further properties necessary for life.
>
> 5. Do these "special" energy regimes and physical law sets NECESSARILY
> produce spontaneous order with the required dynamism?

Presumably the question of spontaneous order is a function of the laws
and the initial conditions.  If the IC's are random, then it would
come down to how big the universe is.  If we assume that all possible
universes exist, so that all initial conditions are realized for any
given set of physical laws, then I would say that the answer is yes,
if the laws allow it, order will necessarily arise somewhere among the
universes that follow those laws.

> 6. Why does spontaneous order emerge in these energy/law regimes?

Extending Wolfram's work, it appears to be a property of mathematics
that a substantial fraction of computational systems allow for some
kind of structure.  Let us further suppose that some smaller fraction of
these systems allow for spontaneous order.  Then this is fundamentally
an inherent property of mathematics; not contingent on the properties
of our universe, or any universe.  It is not something that could be
controlled even by God, for He could not have created mathematics to be
different from it is.  It is simply inevitable, that among chaos there
is automatically a subset called order.

> 7. If we were in a "possible world" where thermodynamics ran backwards
> (entropy decreased), would the time-perception of observers within
> that world also run backwards? Would these backwards worlds (as far as
> classical physical observations go, anyway) thus be equivalent to and
> theoretically equatable with the corresponding possible world which was
> the same except that thermodynamics runs forwards as we are used to?

I suppose so, although your question assumes a sort of "absolute time"
relative to which we can say that entropy is decreasing.  It might be
more correct to say that "time" is simply that direction towards which
entropy increases and that there is no inherent arrow of time that we
can compare entropy changes to.

> 8. What is the significance of the fact that observers like ourselves
> (possibly with some notion of free will) are separated in space and can
> only communicate / cooperate with each other at the speed of light. They
> cannot interfere with some decisions that the other makes, because the
> other has already made the decision before a lightspeed communication
> can tell them or force them to stop. Imagine Jane on Venus and Joe on
> Mars getting into an argument.  Immediately after receiving Joe's last
> communication (which he sent an hour ago), Jane decides to detonate her
> solar-system bomb in frustration and spite. Nothing Joe can say or do
> can stop her, because it will take two hours for him to know she's about
> to push the button, and communicate his desperate and well-crafted plea
> for forgiveness. The idea of FUNDAMENTALLY independent decision makers
> "co-existing" seems interesting. Open ended question.  It's just as if
> Joe and Jane lived at different times. (And yet they CAN communicate
> with each other, just slowly. Hmmm)

I speculate that the speed of light limitation preserves diversity by
preventing an intelligence from expanding infinitely fast throughout
the universe and turning the whole thing into a single consciousness.
Elsewhere in the universe are expanding minds, but they have not gotten
here yet because of the speed of light limitation; and further, that
limitation makes those minds themselves become fragmented.  Perhaps,
on some versions of the anthropic principle, this could increase the
"mental measure" of our universe relative to those that become singleton
minds, making it more likely.

A perhaps more plausible speculation is simply that relativity theory
exists as a side effect of a simple set of equations that guides our
universe (the unified theory our physicists seek).  Once that set
of equations is found, it will be seen to be very simple, but the
ramifications of that theory lead to all of the complexity and order
that is necessary for life to evolve.  The speed of light limitation
just falls out of the theory as a side effect of its inherent simplicity,
one which doesn't impair the formation of life and hence has no anthropic
implications.  It just happened to happen.

Hal Finney

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