Matt Mahoney wrote:
--- Eugen Leitl <[EMAIL PROTECTED]> wrote:
On Tue, Mar 27, 2007 at 06:50:59PM -0700, Matt Mahoney wrote:
Of course it could be that a singularity has already happened, and what
you
perceive as the universe is actually a simulation within the resulting
superintelligence.
Is this a falsifyable theory?
Unfortunately, no. You would have to prove that the universe is not
computable, for example, that your observations are a function of the halting
probability Omega or some other uncomputable number. I don't know that that
would even be mathematically possible.
But everything we know about it suggests that the universe is computable. For
one, the universe has finite entropy*. For another, Occam's Razor seems to
work in practice, consistent with AIXI's assumption of a computable
environment (abductive reasoning, I know). For a third, there is nothing
going on in the human brain that we believe is not computable, so it would be
impossible to distinguish reality from a simulation, and we are simply
programmed to reject such a possibility.
*The entropy of the universe is of the order T^2 c^5/hG ~ 10^122 bits, where T
is the age of the universe, c is the speed of light, h is Planck's constant
and G is the gravitational constant. By coincidence (or not?), each bit would
occupy the volume of a proton. (The physical constants do not depend on any
particle properties).
A small but crucial point: this is the entropy of everything within the
horizon visible from *here*. What about the stuff (possibly infinite
amounts of stuff) that lies beyond the curvature horizon?
Richard Loosemore
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