On 25 Apr 2017, at 04:49, Russell Standish wrote:
On Mon, Apr 24, 2017 at 07:12:38PM -0700, Brent Meeker wrote:
On 4/24/2017 2:15 AM, Bruno Marchal wrote:
This world is 'objective' in the sense that there is
intersubjective agreement about it.
That happens in multi-user video games, and all the multi-user
games are implemented by all universal numbers, with all players
in arithmetic. The only problem is the relative measure, but we
have already that the measure one obeys a quantum logic.
How do we "have" that? Can you derive, from computationalism, that
the description of the world must be in terms of vectors in a
complex Hilbert space?
I looked into that claim, so maybe I can offer a different
perspective. Quantum logics are the logic of events in a complex
Hilbert space that have probability 1, ie the logic of Hilbert
subspaces. For example, if x is the statement that the system is in
subspace X and y the statement that the system is in subspace Y, we
can speak of x∧y being the statement that the system is in the
subspace X∩Y, and x∨y being the statement that the system is in
X⊕Y
(X∪Y is not a subspace). It turns out that these logics
(apparentally
a family of them, all quite distinct from classical logic) satisfy the
same axioms as Z and X, modal logics describing two of Bruno's
hypostases
(that of the believer and the observer IIRC).
The significance of all of this? Bit hard to say - it would be nice to
handle the more usual QM statements where probability is less than
1. Also, it is open whether Z describes exactly Birkhoff and Neumann's
quantum logic, or merely something like it.
Nevertheless an intriguing result.
Well thanks, Russell. Of course the Quantum Logic (QL) appears only
when we restrict the modal logic on the universal dovetailing (X1, Z1)
and look at the true part (and thus we need X1* and Z1* to get the
QL). This is what eventually justifies the first person plural nature
of the cosmos. We enter all in the same "teleportation boxes" when we
do quantum measurement. It corresponds well to the contagion of the
superposition. That is also what makes QM, and the comp physics
completely local and (normally reversible and linear, but a lot
remains to be done to assess this). Sorry for Brent, but we don't have
vectors yet, still less tensor. (But we have first person, and that's
the goal).
Note that the logic does handle a bit the less than 1 probability,
thanks to the presence of negation ([]p = proba(p) = 1; ~[]p =
proba(p) ≠ 1, []~p should be proba(p) = 0, but is really proba(p)
near 0 for some technical reason related to the lack of necessitation
and the fact that the measure is more a measure of credibility than
probability).
bruno
--
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Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellow [email protected]
Economics, Kingston University http://www.hpcoders.com.au
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