Jesse Mazer writes:
> Hal Finney wrote:
> >I imagine that multiple universes could exist, a la Schmidhuber's ensemble
> >or Tegmark's level 4 multiverse.  Time does not play a special role in
> >the descriptions of these universes.
> Doesn't Schmidhuber consider only universes that are the results of 
> computations? Can't we consider any computation as having an intrinsic 
> "causal structure"? How would it be possible to write an algorithm that 
> describes a "Life" universe where there's no time, where the t-axis is 
> replaced by a z-axis, for example?

Well, you could just replace the letter t with the letter z, but of course
that wouldn't change the underlying nature of things.  You might well
say that there was still a time axis, just that it had a different name.

But the bigger question is whether the order in which a universe is
computed must match the concept of "time" within that universe.  It is
true that for universes like ours, it seems difficult to compute them
in any way other than starting at the past and working our way into
the future.  In that case, the order of computation is the same as the
within-universe time axis.

However it might be dangerous to generalize and to assume that this is
always the case, or that one can go so far as to define the concept of
time within a universe to be the order in which things were computed.

It is not difficult to come up with universes that can be computed in
a different order than the "natural" within-universe direction of time.
Even our own universe appears to be time-symmetric at the micro-scale.
The only reason we have an arrow of time is apparently because the
universe was created in a special low-entropy state.  A universe without
such a special state at one end could be computed in either direction.
Or we could start in the middle and compute forward and backward from
that point.  Or maybe we could even compute it sideways, taking a
particular timelike line as the "initial conditions".

Further, in our own universe there appears to be quite a bit of ambiguity
about time ordering, and many different computational strategies will
work equally well.  Relativity theory shows that events either have a
timelike separation, in which case it is clear which one is in the past,
or a spacelike separation, which makes it ambiguous which one is farther
in the past.

It was suggested here a while back that a Life universe could be
computed using an algorithm which ran around somewhat randomly and made
localized changes to cells in order to make them match the Life rules.
Eventually this would converge to a stable and consistent Life universe.
Any observers living in that universe would have a perceived direction
of time that was very different from the actual order in which it was

However although this is possible, I think it is likely that any
high-measure universe containing observers like us will pretty much
have to be computed in the past-to-future direction of time.  That seems
to be the best way to specify a universe like ours with simple initial
conditions, using a simple algorithm.  So I imagine that in practice,
for most universes that we are interested in, it will be correct to
identify subjective (within-universe) time with computational ordering.
But this is not true in general.

> >Tegmark in one of his papers considers universes with two or more
> >time dimensions.
> If this universe is computable, it can be simulated by an algorithm that can 
> run in a universe with only one time dimension. Perhaps the algorithm would 
> go back and forth between simulating time increments in different 
> directions, like how a regular computer can simulate a parallel computer.

Yes, but there is still a difference between two time dimensions and one,
just as there is a difference between two spatial dimensions and one.
An interesting question is whether there would be any algorithms possible
in a universe with two dimensional time that would run fundamentally
faster than in a universe with one dimensional time.  I don't understand
the concept well enough to address that.  But if so, a being who evolved
in such a universe might deny that one dimensional time observers could
exist, that such a limited notion of time would be rich enough to support
the computational complexity necessary for life and intelligence to exist.

Hal Finney

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