From: Matt Mahoney (firstname.lastname@example.org)
Date: Wed Jan 23 2008 - 21:18:49 MST
--- Daniel Burfoot <email@example.com> wrote:
> On Jan 24, 2008 1:16 AM, Vladimir Nesov <firstname.lastname@example.org> wrote:
> > Simulatedness is not directly observable, only miracles
> > are. Question of whether world is simulated is only relevant for
> > finding out if miracles can happen.
> You can imagine two versions of the simulation argument. The weak version is
> that the universe is simulated on a computer with effectively infinite
> computational power. In that case, there is no way to determine that we are
> in a simulation, because the simulation is perfect.
> The strong version is that the computer running the simulation has (vast,
> but) limited computing power. Because of this the designers need to "cheat"
> by introducing computational shortcuts. Several of the laws of physics can
> be seen as reflections of this principle:
> 1) Nature does not solve NP-hard problems.
Quantum mechanics takes exponential time to solve, at least our probabilistic
interpretation of it does.
> 2) The central mystery of quantum mechanics, as revealed by the double-slit
> experiment, can be seen as a computational shortcut: the simulation notices
> that the path of the electron does not affect anything on a "macroscopic"
> scale, so it doesn't bother to compute the real trajectory.
Paradoxes like the double slit, EPR, or Schrodinger's cat all go away if you
include the observer in the solution to Schrodinger's equations. The complete
model is not probabilistic, but it is beyond our ability to solve it. We are
the ones taking the computational shortcut.
> 3) The speed of light can be seen as a result of running a simulation on
> many machines: due to communication limits on the machines, there must be a
> limit to how rapidly an event in one machine influences an event on a
> faraway machine.
The speed of light limits the size of the universe (which must be finite in a
simulation). We can't assume that concepts like distance, time, and velocity
have any meaning in the simulating universe.
> 4) Conservation of energy can be interpreted as conservation of code length,
> due to the similarity between the Boltzmann factor and the Shannon optimal
> codelength rule.
Conservation of mass/energy limits the size of the universe. The relationship
you suggest between thermodynamic and information theoretic entropy is
unrelated to energy. It is related to the direction of time. A computation
irreversibly loses information, so its uncertainty about its environment
> 5) Fermi's paradox can be interpreted as implying that only the Earth is
> being simulated with high accuracy; in other regions the simulation is
> taking too many computational shortcuts for life to exist.
Or the universe is just big enough to form life on one planet with high
probability. Or we are not alone.
> This strong version of the simulation argument suggests new physical
> experiments. For example, there should be a point at which the simulation
> decides an effect is simply too far away to matter (e.g. the influence of
> Pluto on the Earth's gravitational field). This kind of thing should be
> testable with high-precision experiments.
The strong version would require high algorithmic complexity in the laws of
physics, which we don't observe.
> Just put yourself in the shoes of a simulation designer: you want to make it
> look "real" to the life forms, but you have limited computing power. What
> kinds of tricks do you use?
We don't know the motives of the designer, if there is one, but one trick
would be to program the simulated brains to believe without question that the
universe is real.
-- Matt Mahoney, email@example.com
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