On 27 Feb 2012, at 21:38, meekerdb wrote:
On 2/27/2012 11:56 AM, Bruno Marchal wrote:
You can make matter behave in any way relatively to virtual reality
that you are building, but the 3-creature, relative to you, will be
able to deduce from their observation that they are in a simulated
reality, by comparing what they can measure with what can
relatively emerge from *all* computations.
That sounds good but its implementation is problematic. What can
relatively emerge from all computations is not something we can know
if your theory if correct.
Why?
On the contrary we can know that by interviewing simple machine that
we can prove to be correct, like PA.
And if what can emerge is essentially anything (which I think is
likely)
The propositional logic of the observable have already been derived.
It is not *anything* at all. It is a precise arithmetical orthologic,
or minimal quantum logic.
Let me give you an example how to test comp in practice. You can take
a quantum-empirical tautology, like a Bell inequality:
A & B => (A & C) V (B & ~C)
which is true in the Boolean algebra, but not necessarily satisfied in
"physical" comp, as it is not in the natural quantum ortholattice of
quantum propositions.
You need to represent it in modal terms, by using the quantization
translation of Goldblatt, this gives:
[]<>A & []<>B => []<>([]<>A & []<>B) V ([]<>B & []<>(~[]<>C)
This should be seen as a formula in the material hypostases, so you
need to translate this in G*, this will give a very long formula,
because just []<>A becomes []([]A v <>A) & <>([]A v <>A), so we get
[]([]A v <>A) & <>([]A v <>A) & []([]B v <>B) & <>([]B v <>B) => etc
(very long due to the double nesting of the quantizations []<>#).
This gives a long formula that you can test in G*, more exactly in G*1
(G + p->[]p, need to makes the machine assuming comp, and restricting
herself on the UD accessible states).
The whole formula is already to complex for my 1990 modal theorem
prover, unfortunately. My translation above is also not completely
correct because the deduction "=>" should be replaced by "->", which
itself is rather long to translate. But my point was only illustrative.
If G* does not find a counter-example to the last, corrected, formula,
it means that the comp-physics does not violate the simple Bell
inequality. If G* finds a counter-example, then you can read it as a
description of a possible experience in the comp physics which
violates that Bell's inequality. G* is complete, and you can ask it
all experiences/counter-examples to that Bell inequality.
In 1990 I predicted that comp (+ classical knowledge theory) would be
refuted before 2000. This has not yet happened, though.
From a paper of Rawling and Selesnick there are evidences that comp
might define a canonical quantum computer in the background physics of
all universal machine. That is some comp-physics tautologies seems to
be rich enough to implement universal quantum gate.
Anyway, by the UDA reasoning you can know that we should get the whole
physics in the corresponding, non necessarily propositional, logics,
so it is hard to imagine a more "refutable" theory than comp, once we
accept Theaetetus or the classical theory of knowledge (verified
notably by the Theaetetus idea when applied on the notion of comp
belief).
Bruno
then no observation can falsify the theory.
Brent
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