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. -- ---------------------------------------------------------------------------- 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 ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
