From: Hal Finney (hal@finney.org)
Date: Wed Mar 05 2003 - 15:19:07 MST
There's actually another level of parallelism implied by modern physics
beyond Tegmark's four, at least if we accept certain philosophical views.
This comes from Hans Moravec's ideas of instantiation or re-instantiation
of conscious entities via simulation.
If we accept that simulated beings can be conscious at all (that's
the philosopical leap), then the forms of parallelism discussed by
Tegmark all imply that there are worlds where beings are simulating
other possible worlds. In fact, there are an infinite number of such
simulation-containing worlds, and an infinite number of such simulations.
Hence everything exists both as a real world in reality, and as a
simulated world in any number of simulations.
We can then ask, what percentage of instantiations of a given world X
exist in the real universe versus in simulations? This is a question
that is answerable in principle, at least if we stick to a simple form
of parallelism like Tegmark's level one (namely that in a spatially
infinite universe, all possible worlds exist an infinite number of times).
You'd have to estimate what fraction of worlds evolve intelligent life
forms capable of performing such simulations. These would include worlds
whose past history is identical to our own but which are farther along
their developmental path because they got started a little earlier.
They would have seen a slightly younger universe than we do now, but
given the uncertainties, they could easily be at least many thousands
of years ahead of us and still have us be a valid model of their past.
If we assume that we are "almost there" as far as having simulation
capability adequate to simulate ourselves, this suggests that about
half of all worlds like us will be enough advanced to be running such
simulations (i.e. the half which is older than us). If each one runs
exactly one simulation of its past that includes us, then that would imply
that the chances of us presently being in such a simulation are about 1/3
(because each such advanced world represents two instantiations of our
consciousness, and half of all worlds are advanced like that).
However if these worlds (which, remember, are like us but thousands
of years more advanced) are also capable of marshalling sufficient
resources to run multiple simulations of pasts that include us, then
the odds become even larger that we are in one of those simulations.
So I'd suggest that the assumption that the universe is infinite in
extent, and/or that cosmic inflation exists, combined with the assumption
that simulations are consciousness, gives us good reason to believe that
we are presently in such a simulation.
Moravec argued the same thing with respect to future civilizations,
I think. Even if there is only one world, if it eventually runs many
simulations then we are probably in one such. The variant based on
multiple worlds makes the argument a bit more concrete, in that these
simulations might actually be occuring "now".
The big question is how much of the universe's computational resources
are being devoted to running simulations of worlds that contain conscious
observers, versus the number of actual worlds containing such observers.
I think it's likely that simulations would be biased towards such worlds,
so even if a relatively small fraction of conscious-observer-containing
worlds are presently running such simulations, they might still account
for a large fraction of the total instantiations of consciousness.
Hal
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