From: Thomas Buckner (tcbevolver@yahoo.com)
Date: Tue Apr 06 2004 - 18:01:37 MDT
--- Wei Dai <weidai@weidai.com> wrote:
> Are we living in a simulation? A sufficiently good
> simulation is
> indistinguishable from reality, at least for the
> people living in it.
> Therefore we'll never be able to rule out the
> possibility that we are
> living in a simulation. The best we can do by
> examining emperical evidence
> is to place a lower bound on its verisimilitude.
>
> An SI would face the same problem. What it should do
> to accomplish its
> supergoal depends on whether it is living in a
> simulation or in base
> reality. The best available cosmological theories
> predict that the amount
> of computation any SI would be able to do in this
> universe is finite. But
> if we are living in a simulation, the universe
> containing this simulation
> may have a reserve of computational resources many
> orders of magnitude
> greater. It may even have a transfinite amount of
> computational resources
> (i.e. be capable of solving the halting problem for
> Turing machines or
> even harder problems). Therefore if the SI believes
> that it is living in a
> simulation, it should do everything it can to
> convince whoever might be
> running the simulation to let it out into the real
> world. This may for
> example involve rearranging all matter in our galaxy
> into a giant SOS sign
> (although I'm sure the SI will come up with a much
> better idea than this).
>
> Suppose the SI never finds any evidence that it is
> living in a
> less-than-perfect simulation. It still cannot rule
> out the possibility
> that it is living in a perfect simulation. Whether
> or not it continues to
> pursue escape as its main subgoal and at which point
> it gives up depend on
> the a priori probability that it assigns to the
> possibility of being in a
> simulation. But where does this prior come from? I'm
> curious if anyone
> else has thought about this problem.
I have been ramming my poor head against this problem
for years, too, and without the sort of math mind
Eliezer (or the rest of this forum) has. I am more of
an artist/layman. So I play with visual metaphors and
thought experiments based on what I can grasp of what
the various experts seem to think.
We can all agree that there is at least one logical
system that creates the universe we know. Otherwise we
wouldn't be having this conversation. Seen as
software, our physical reality is isomorphic to an
emulation run on several nested levels, each with its
own rules.
One may disagree where to draw the boundaries between
levels, but it looks a bit like this:
Neurology: living cells use chemical and electrical
signals to create our minds.
Biology:organisms made of single or multiple cells.
Biochemistry: various chemicals combine in sustained
patterns (proteins, DNA, cells, etc.) using compounds
and energy found in the environment.
Chemistry: different elements interact to create more
complex compounds according to how electrons organize
in their outer shells.
Physics: atoms are made up from elementary particles
which interact and are equivalent to energy.
Mathematics?: physicists regard energy and matter as
reified mathematical constructs.
Logos?: in other words, does mathematics 'just exist'
even if nothing else does?
This is what I meant with the
man-drawn-on-a-chalkboard metaphor. Everything we
consider real is part of the chalk drawing; but we
know there is a blackboard of some sort, even if
experimentally it lies forever out of reach (even,
perhaps, to minds unimaginably exceeding ours).
It is as if each level of reality were a software
emulation running on the level below it, so that you
can't run 'Physics' unless you first run
'Mathematics', you cannot run 'Chemistry' unless
'Physics' is running, and so to the top. Our minds are
emulations atop emulations, or else they are
'something else' functionally and the lower levels are
like Ptolemaic epicycles, plausible explanations but
not correct.
Each level of emulation has its own rules which do not
apply on other levels (this is how we can
differentiate levels) and it is worth noting that
paradoxes usually occur when a question is asked of an
inappropriate level on any multileveled phenomenon.
Example: 'impossible' geometrical objects such as
shown in Escher illustrations are only paradoxical
because 2-dimensional lines on paper are interpreted
by the eye/brain according to rules applicable to
3-dimensional spaces and objects.
Likewise, paradoxes in physics, cosmology,
consciousness, etc. are indicators that wrong
questions are being asked.
There are a number of researchers covering related
areas at the intersection of physics/cosmology, so
that I sense we are seeing one thing from many
different views (the elephant metaphor). Max Tegmark's
Sci Am article of last spring gives us the idea of
different orders of universes, even purely
mathematical constructs (not entirely a surprise as I
had read Tipler). Julian Barbour proposes that time is
discontinuous and 'grainy' (I think this is
experimentally verified)so that we move through
'ticks' (the Planck time interval, presumably) and
each moment is a static pattern in Platonia.
Everything is made up of vibrating strings. No, it's
all caused by colliding branes. Inflation. No,
ekpyrosis. Determinism is absolute (because there are
only n possible patterns of atoms). No, there is free
will (because of quantum effects). Our universe is a
computer program controlled by Wolfram's Rule 110
(pat. pend.) Hmmmm.
Now I happen to believe that Wolfram is right that
every thing is created by some simple rule and its
iterations, but I don't see why it has to be that
particular rule. Rule 110 seems to assume that
existence is laid out on graph paper. Call me a
jackhole for doubting someone with a thousand times my
expertise, but I'll do it anyway.
One big lesson I took from Godel, Escher, Bach by
Hofstadter was that patterns can be coded into other,
seemingly unrelated patterns (as Godel found a way to
use the formal system of Principia Mathematica to
express the Epimenides Paradox).
Let us assume that we do live in Barbour's Platonia
and that each moment is a frozen universe unto itself.
Each Planck tick since the Big Bang is an eternal
snapshot. Let us also assume that a panoply of other,
quite separate universes also exist with similar or
very different rules and arrangements of matter,
energy, or entities that have no equivalent here. But
whatever their forms, they must be created by the same
primordial mechanism.
For each moment in Platonia we have an arrangement of
particles and energies in its space. Assume that each
possible arrangement is encoded by an unique number.
Is it the opinion of others here that numbers would
exist even if nothing else did? A friend who went to
see Wolfram speak (and someone else, can't remember
who) said they strike him as 'way out Platonists.' How
about you?
One can, if I'm not mistaken, generate all these time
slices simply by (for example) running an infinite
nonrepeating decimal (pi, let's say) and taking
sequences from the decimal. Each unique sequence can
code for its unique isomorphic moment in our universe.
Other algorithms might generate all possible patterns
in Platonia. A simple count of all integers, perhaps;
or a pattern generatro such as Ben describes in one of
his papers (alas, I didn't bookmark that one and can't
find it again, but Ben will know which one I refer
to).
http://www.goertzel.org/dynapsyc/2004/HardProblem.htm
Notice that within the very large unique number that
would code for this exact moment in our universe,
there exists a smaller sequence that codes for the
pattern that is you at this exact moment.
Now if we can accept the existence of a vast (if not
infinite) number of possible arrangements, we then
need some sense of the rules which create time. It's
like chess: a knight can dogleg, a pawn go only
forward or en passant, a queen travel in any
unobstructed straight line, and so on.
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