From: Matt Mahoney (firstname.lastname@example.org)
Date: Wed Jan 23 2008 - 17:38:17 MST
--- 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.
> > > 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
> > states.
> Not every machine, but who needs that? And again, what do you mean by
If machine A simulates machine B, you could not run a program on B that
simulates A. It would not have enough memory.
> > > > 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
> > > > 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
> > > is
> > > > divided into 10^122 parts, then one bit is the size of the smallest
> > > > particle, even though T, c, h, and G do not depend on the properties
> > > 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
AIXI makes complex or unusual events unlikely.
> 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.
> > The fastest way to find a universe supporting intelligent life is run the
> > 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
The k'th universe will have complexity log(k), which is what we actually
observe (very roughly).
-- Matt Mahoney, email@example.com
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