On 02 Jun 2014, at 01:50, Russell Standish wrote:
On Sun, Jun 01, 2014 at 09:19:54PM +0200, Bruno Marchal wrote:
On 01 Jun 2014, at 01:53, Russell Standish wrote:
On Sat, May 31, 2014 at 01:40:58PM -0700, meekerdb wrote:
On 5/30/2014 11:45 PM, Russell Standish wrote:
Yet it seems to me that CantGoTu environments and other non-
virtual
reality environments have measure one in the space of environments
hosted by the UD, as UD* has the cardinality of the continuum,
whereas
virtual reality environments are strictly aleph_0.
But aren't "we" as physically instantiated beings, also of the
cardinality of the continuum?
Yes, we are, but not the virtual reality environments, which must be
countable by virtue of there only being a countable number of
programs.
With COMP, and via the UDA, the number of "real" environments
experienced must be the cardinality of the continuum, and would
include all the CantGoTu environments.
We could therefore conclude (contra Bostrom), that we are most
likely
not in a simulation, but that we can never prove it by any finite
observation (Deutsch's CantGoTu argument).
I agree that sometimes we can know we're in a virtual reality -
Deutsch's chess VR example, for instance - but only by it being
logically incompatible with our existence as an observer.
The question remains - suppose someone finds a physical phenomenon
that contradicts the laws of physics derived from COMP. Does that
falsify COMP, or does it imply we're in a virtual reality? How can
you
possibly distinguish those two situations?
We can't.
But this is similar to the fact that, for accepting that we can at
least refute a theory, we still need to bet that we are not dreaming
or that we are not in some emulation (made normal by being physical,
that is built on the top of the sum on all computations).
So, to answer the question more precisely, we will need to describe
more precisely how much the physical phenomenon depart from the comp
physics, like for the case with the natural physics. If the
emulation is gross (too big pixel) we can see quickly we are
dreaming or emulated, or branched to a virtual (programmed)
environment/video-game.
By default, when I say that comp is falsifiable, I suppose we are at
the base level, and that QL and QM does describe the base levels.
Comp (and QL) saves us (normally) from the diabolical white rabbits,
but it does not save us from the human and indeed universal Löbian
consistent deception.
Bruno
I would say that COMP predicts we must be at the base level, and not
in a virtual reality, by virtue of the cardinality difference between
the set of all environments and the set of virtual ones.
Hmmm.... I see what you mean, and in "that sense" we are at the base
level.
yet, we can still belong to an emulation build on the top of that base
level, so that it inherits of the measure on all computations.
If that was not possible, we would not been able to survive with an
artificial brain. If we can, we can survive with the right relative
measure in virtual environment, like the emulation of Washington and
Moscow in step six.
But this is also what makes it possible for us to discover that we are
in virtual environment, or that we are dreaming.
Therefore if
we do discover ourselves in such a virtual variety (eg Deutsch's chess
world) violating the laws of physics derived from COMP, then COMP must
be falsified.
Not necessarily. I might have given you a pill, and then put you in a
very well done emulation, without you noticing any difference (before
comparing the comp physics and the physics of your environment).
Whilst COMP could be rescued by stating that it's just bad luck that
we are
in one of these virtual worlds, there is no epistemological benefit in
doing so, because then COMP would not provide a description of our
phenomenological physics.
Just the same is if we ever found the Anthropic Principle to be
violated (and didn't immediately wake up and realise it to be a
dream), then we'd have to declare the AP falsified, because it no
longer has any epistemological value. We could alternatively conclude
that we're living in a Sim (DD's argument), but that would be simply a
statement of faith, making the AP unfalsifiable.
I am not sure we can make something falsifiable into something non
falsifiable by an act of faith, ... except indeed by invoking a dream,
or a Daemon, but this is of course is a very weak "refutation". I
would say that it is better to bet we are not in a second order dream/
emulation by default. If the comp-QL differ from the empiric-QL, it
will be time to hesitate between the truth of comp, or of the the
classical theory of knowledge, or if we are in a simulation (that
might depends on the way the comp-QL is violated).
The fact in dispute with ghibbsa is that I am giving a precise way to
test comp (with nuance due to the vague character of "test" applied to
"reality") when translated in arithmetic. How to interpret a possible
violation by nature, will depend on the phenomenon needed to be
discovered for that effect.
It is more plausible that the comp logics fails to define a quantum
computer in the neighborhood, or that it implies modularity and
exclude infinite dimensional Hilbert spaces, or that it is
inconsistent with the different type factor (von Neuman algebra).
What if it fails, but still work with []p & <><>t in place of []p &
<>t? I would be astonished if we get directly the right logic of the
observable in one of S4Grz1, Z1* or X1*. S4Grz1 has all theorems of B
(the modal logic of QL), + the orthomodularity, but seems also very
close to S5 (as he has reflexion ([]A ->A, symmetry p -> []<>p, but
also transitivity []A -> [][]A). It is not S5 because symmetry is only
for the sigma_1 sentences p, not arbitrary formula A.
Bruno
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Principal, High Performance Coders
Visiting Professor of Mathematics [email protected]
University of New South Wales http://www.hpcoders.com.au
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