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 hpco...@hpcoders.com.au 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
