On 31 May 2014, at 13:21, Russell Standish wrote:
On Sat, May 31, 2014 at 10:07:00AM +0200, Bruno Marchal wrote:
On 31 May 2014, at 08:45, Russell Standish wrote:
I gather you think it might be possible to distinguish between being
in a virtual reality, and being in the real reality.
David Deutsch introduced the concept of a CantGoTu environment.
It is unclear if this contains only total functions or partial one.
Neither. A CantGoTu environment by construction is not the result of
any program.
I reread DD on this, but it is unclear. But a part of this is made non
relevant by the FPI. As the DU dovetails on the oracles (the real)
too. We can come back on this. On the partial functions, we have the
closure for the diagonalization. The way the CantgTu are defined, it
is unclear what complexity it can have in the arithmetical hierarchy.
I can stretch in different way to get different correct sense, but it
is unclear which one is meant.
...
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 we can never
know that we're in one.
What is a non-virtual reality environments in the UD*?
UD* is not a set, so cardinality notion does not apply. But with the
rule Y = II, we can associate a set of computations which has the
cardinality of the continuum to UD*, but this can make the virtual
reality environments into a continuum (and I think it should, to get
rid of the white rabbits).
I think the way virtual reality is defined in FoR, there can only ever
be a countable number of them. It is the environment that is
simulated, not the observer.
In his glossary, he propose a more general definition, but in some
paragraph it looks it is like you say.
He is not at ease with logic/computability theory.
By contrast with the UD, it is the observer that is "simulated",
leading to a continuum of environments by FPI.
The UD emulates all the 3p observers, in all environment (computable
or not a priori). This leads to a continuum of environment by FPI
(being enough naive, and open for equivalence classes of computations
and states, notably structured by the use of the Theaetetus definitions.
DD does later in the chapter speculate about VR environments that
one
can know one is trapped in a VR, such as being inside a game of
chess. This is because the "rules of physics" of such an environment
are inconsistent, especially with the presence of an observer. But
provided the rules of physics are consistent with yourself as an
observer, then there doesn't appear to be any way of knowing whether
you're in a simulation of not, as per the CantGoTu argument above.
But DD ignores the FPI.
Sure - but I'm not sure of the relevance...
An environment is defined by the probability on the computations, or
the sigma_1 sentences, as believe, ([]p), known ([]p & p), observe
([]p & <>p), felt ([]p & <>p & p).
Physics is given by the laws governing our consistent extensions,
which is describable in terms of elementary machine's beliefs (like
the belief in Robinson arithmetic and the induction axioms).
The rules of physics (whether under COMP or not) must be those that
allow the presence of observers, and of observation. All else
_has_ to
be geography.
The only way we can prove we're actually in a simulation is if the
Anthropic Principle were to suddenly fail.
You need to take into account the comp RSSA, based on the FPI. All
computations emulating an observer, even if contradicting the
physical laws, have to be taken into account, and that is why
physics is a sum on all computation (going through your states),
OK - but how does the following follow?
so
you can (in principle) find out if you are in a simulation (assuming
comp all along).
It is like in the lucid dream. You believe that the physical laws
prevent you to fly by will, then you observe yourself flying at will,
and conclude that you are dreaming (i.e. you are in a second order
simulation, sustained by the physical reality).
But now, imagine I want fake you more subtly, by making an emulation
of the known physics. Well in that sense we will have the []p & p
together and you are not failed. Indeed, from the 3-1 view, you are in
all computations, and no more in that second order than in the first
order (relatively to the UD*).
Now, I have to fail you at some level in that simulation, because I
can't emulate all the computations done in UD* to get all the decimal
correct in the FPI on the whole Sigma_1 truth, so, in principle, if
you have all the time, and if I don't make change to the system
(except adding the needed memories for your exploration, you (from my
1-view of your 3p being in the computer) will at some point get the
decimal wrong from the prediction of some details in his environment.
More happily, he could discovered some set of observable in his
environment not obeying to the comp-quantum logic. In any case, if he
keeps the comp hypothesis, he can say that he is in a simulation.
Bruno
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