Hal Finney wrote:
> 
> Georges Quenot writes:
> > I would be interested in reading the opinions of the participants
> > about that point and about the sense that could be given to the
> > question of what "happens" (in the simulated universe) in any non-
> > synchronous simulation "when" the simulation diverges ?
> 
> I'll make two points.  First, you're right that there are other ways of
> computing a universe than simply starting with some initial conditions
> and evolving "time" forward step by step, computing the state of the
> universe at each subsequent instant.  You list several ways this might
> happen and I agree that this concept makes sense.  We might call this
> "non-sequential" or "non-temporal" simulation.
> 
> But, given the specific temporal structures that exist in our universe,
> there are limitations to how this computation can be done.  Specifically,
> we are able to construct physical computers in this universe which perform
> complex calculations.  And among these calculations are those which are
> believed to be inherently sequential and lengthy, calculations for which
> the answer cannot be computed without spending a great deal of time from
> the initial values.

I'll make two subpoints. First, I don't believe in any way that
it is possible to simulate our (and probably any) universe within
itself. I would say that the universe in which we would simulate
another universe have to be much larger than the simluated one.
Even if it could be conceived in some compact and general way,
it could not be expanded within itself.

Second, I do not share the view that there are things like
"temporal structures" that place constraints on how computations
could be done (in other universes or in appropriate mathematical
structures if the distinction makes sense). I believe this view
is biased by our anthropomorphic perception of nature and
sepcifcally of causality (you can refer to my reply to John M. 
http://www.escribe.com/science/theory/m4962.html). I see
"temporal structures" as emergent properties and not as a basic
underlying mechanism. The emegence of these properties should
be simulated as well and not be used in the simulation process
(possibly making the simulation work much more complicated but
the alternative appears simplistic and meaningless to me).

Given a set of equations, we could solve them either using initial
conditions, using final conditions, or using any appropriate
possibly much more complicated set of conditions. It is well
known that tiny variations in initial conditions can lead to
huge variations at some point later (known as the butterfly wing
flap effect, possibly a non standard translation of the french
equivalent). It *might* seem simpler to start with initial
contitions and to go forward instead of any alternative but it
is not sure that, if we are to do the computations with the
appropriate accuracy to get sound result at any time later,
it well really reduce the complexity or the required execution
time.

Intuitively, If we wish to reach a given level of accuracy at
all "places", I see the problem equally complex whether we start
with an initial condition and go forward, we start with a final
condition and go backward, we use any appropriate combination of
initial, internal and final conditions or even we use any higher
level consideradion among which I particularly like that one
(which has the additional advantage to be consistent with
Hawging's hypothesis that the universe does not have boundaries):

  Given the set of rule and equations, choose the solution in
  which the universe is "as much as possible more ordered on one
  side than on the other".

This might well be a sound additional condition to the set of
equation/rules to define a limited set of possible universes
and one would notice at once that this kind of condition is
very well appropriate to select those in which SASs have a
chance to emerge. This condition does not seem alone enough
to define a unique mathematical structure but there might be
a little number of ways according to which the remaining
symmetries could be canonically broken.

I would be interested in knowing whether this idea is original
and, if not, in getting earlier references.

> Given that our universe contains systems like this, it constrains the
> amount of computation which must be done in any kind of non-sequential
> simulation.  Specifically, the non-sequential simulation must do at
> least as much computation in order to produce our universe as the more
> traditional kind of sequential simulation.  This demonstrates a limit
> on the power of non-sequential simulation.
> 
> My second point is with regard to your specific question, what would
> happen if we tried to simulate a universe which diverged in some
> space-time region from the conventional physical laws?  This is our
> often-discussed "flying rabbit" paradox (we have other names as well),

The oldest one I know of is about somebody walking on water,
possibly 2500+ years ago. I always perfer to give credit to
the more original reference (might be Zoroastre).

> where it seems that if all universes exist, we might as well be living
> in a universe which was lawful everywhere except in some small region,
> or up until a certain time, as in one where the laws are truly universal.

I am not sure this would require violation of universal laws.
Alternatively, it could be something like a "singularity" in
"boundary conditions". This involves a distinction between
truly unisersal (basic) laws and statistically/macroscopically
emergent laws (like the 2nd law of thermodynamics). Violation
of the seconds does not imply violation of the firsts. The
second type of laws seems more relative to boundary conditions
than to first type of laws. There is not reason for ma than
"men walking on water" constitute a violation of the first type
(basic, universal) laws. It could just arise from "biased"
"boundary conditions".

> Your question is whether this concept makes sense in a non-sequential
> simulation, or whether it assumes sequential simulation.

Not exactly. My question was not merely whether "men walking
on water" happen more or less in sequential than in non-sequential
simulation but what sense it makes to link that to a *divergence
of the simulation* in a sense that this view makes a link between
the time in the computer in which the simulation is carried out
and "the" time in the universe which is simulated. In other words:
what sense would it make to postulate that "men walk on water" when
the simulation reaches a given level of accuracy ?

> I think it makes just as much sense in the context of non-sequential
> simulation.  The non-sequential simulator is trying to find or create a
> universe which satisfies certain physical laws.  It may be iteratively
> solving a differential equation or using some other non-temporal method,
> but that is its goal, its mechanism.  The case at hand is simply
> a matter of defining the physical laws to be different in different
> regions of space-time.
> 
> We could define the physical laws which the non-sequential simulator is
> trying to solve in some such terms.  We'd say, observe these laws in this
> region, but these other laws in that region.  For example, we might say
> to observe the true laws of our universe (whatever they turn out to be)
> up to simulated time T, and then to observe other laws after time T.
> Or similarly we could have one set of laws up to spatial coordiate X,
> and another set of laws on the other side of X.
> 
> The non-sequential simulator would have no more difficulty in creating
> a universe which satisfied such non-uniform physical laws than in one
> where the laws were the same everywhere.  So I'd say that the issue of
> sequential vs non-sequential simulation is irrelevant to the question
> of the existence of "flying rabbit" universes and does not shed light
> on the issue.

See above.

Georges Quénot.

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