From: Matt Mahoney (firstname.lastname@example.org)
Date: Tue Aug 14 2007 - 13:40:51 MDT
--- Byrne Hobart <email@example.com> wrote:
> How do you know? All we know is that the universe is consistent with a
> > simulation. For example, AIXI theory predicts that if the universe is
> > Turing
> > computable, then the algorithmically simplest models consistent with past
> > observations will be the best predictors of future results, regardless of
> > the
> > experiment. This is in agreement with our observation of Occam's Razor.
> I'd need to know more about this theory to respond. Do you have a link? My
> first question would be: how do you define algorithmic simplicity? It can't
> be Kolmogorov Complexity, because the simplest algorithm will be the one
> that discards inputs and returns nil.
Marcus Hutter has some papers on AIXI.
Hutter models an agent and an environment as a pair of interacting Turing
machines exchanging bits of information. In addition, the environment outputs
a reward signal. The agent has a goal of maximizing the accumulated reward.
Hutter proves that the optimal (although uncomputable) strategy is for the
agent to guess at each step that the environment is simulated by the shortest
program consistent with the interaction observed so far.
The proof of AIXI requires that the environment have a computable probability
distribution. Of course this is not a proof that the universe actually has
such a distribution, but the fact the the result is observed in our reality
(i.e. Occam's Razor) suggests that it does.
> This is a good rephrasing of Nietzsche (or Groundhog Day
> http://rightreason.ektopos.com/archives/2007/06/nietzsche_and_t_1.html ).
> Assume you are a post-singularity entity living in a simulation: how does
> this affect your behavior? If you'd act differently in that case -- why?
I don't think it matters. From the point of view of the simulator, your
behavior is deterministic. You were programmed to guess that the universe
might be a simulation, and probably to misguess what the real world is like.
Our thinking is constrained by our model of the universe. In the real world,
concepts such as people, space, time, and mass might be meaningless, just
BTW Groundhog Day was interesting, but differed from Nietzsche in that the
subject remembered each repeated existence. From Nietzsche's point of view,
it is irrelevant, just as it is irrelevant whether there is a past and a
future, or whether there is only a single point in time right now, and all of
your memories were created to simulate a past and a belief in a future.
-- Matt Mahoney, firstname.lastname@example.org
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