From: Vladimir Nesov (email@example.com)
Date: Thu Jan 24 2008 - 05:32:26 MST
On Jan 24, 2008 3:38 AM, Matt Mahoney <firstname.lastname@example.org> wrote:
> --- Vladimir Nesov <email@example.com> wrote:
> > On Jan 23, 2008 11:52 PM, Matt Mahoney <firstname.lastname@example.org> wrote:
> > >
> > >
> > > An example of uncomputable phenomena would be something like classical
> > > mechanics, in which the outcome of an experiment requires knowledge of the
> > > position and velocity of particles with infinite precision.
> > Again: how would you test that?
> We would not have probabilistic theories of physics like quantum mechanics.
What _would_ we have then? Absence of certain _theory_ hardly tells anything.
> > > > Finite state machine can perfectly well simulate itself, in any
> > > > natural interpretation that comes to mind (you'd have to additionally
> > > > define what it means for this formal construct to have a simulation of
> > > > something).
> > >
> > > A finite state machine with n states cannot model a machine with more than
> > n
> > > states.
> > Not every machine, but who needs that? And again, what do you mean by
> > modeling?
> If machine A simulates machine B, you could not run a program on B that
> simulates A. It would not have enough memory.
You keep telling that. But it's a simple question of validity of
theorem on mathematical model. Define mathematically your assertion.
You can simulate machine B of googleplex states which doesn't do
anything on a 1-state machine which also doesn't do anything.
> > > > > 2. The universe has finite entropy. It has finite age T, finite size
> > > > limited
> > > > > by the speed of light c, finite mass limited by G, and finite
> > resolution
> > > > > limited by Planck's constant h. Its quantum state can be described in
> > > > roughly
> > > > > (c^5)(T^2)/hG ~ 2^404.6 ~ 10^122 bits. (By coincidence, if the
> > universe
> > > > is
> > > > > divided into 10^122 parts, then one bit is the size of the smallest
> > stable
> > > > > particle, even though T, c, h, and G do not depend on the properties
> > of
> > > > any
> > > > > particles).
> > > >
> > > > So? If anything, it supports knowability of universe, a counterpart of
> > > > it being simulated from complex unobservable environment.
> > >
> > > Yes, that is my point.
> > Well, I meant 'counterpart' as in 'opposite'. Problem with simulated
> > worlds is (supposedly) that complex unpredicatable miracles can
> > happen. If everything is simple and observable, what is the problem?
> > 'Simulatedness' is not observable and in itself is a meaningless
> > category.
> AIXI makes complex or unusual events unlikely.
AIXI doesn't 'make' anything, it's not even an applied theory.
> > How would you test if your notion of Occam's razor didn't work?
> Occam wouldn't have made the observation, and physicists would not keep trying
> to make their theories simple and elegant.
Maybe Occam wouldn't had existed. It's not exactly a test.
> > > The fastest way to find a universe supporting intelligent life is run the
> > k'th
> > > universe for k steps. I claim that for our universe, k ~ 10^122.
> > But how does it relate to complexity of laws of physics which are much
> > simpler?
> The k'th universe will have complexity log(k), which is what we actually
> observe (very roughly).
Ah, you attribute complexity of content to runtime, as per MWI that
starts with low complexity and obtains its current complexity given
enough time. Did I get that right? Interesting.
-- Vladimir Nesov mailto:email@example.com
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