On 11/7/2012 10:24 AM, Craig Weinberg wrote:

On Wednesday, November 7, 2012 8:19:03 AM UTC-5, Stephen Paul King wrote:

    On 11/7/2012 7:42 AM, Craig Weinberg wrote:
    > Can anyone explain why geometry/topology would exist in a comp
    > --
    Hi Craig,

         So far it seems that there is only a singular set of countable
    recursive functions (or equivalent) and thus a single Boolean algebra
    for the Universal Machine. If the BA (of the Universal number or
    Machine) has an infinite number of propositions, how could it be
    up into finite Boolean subalgebras BA_i, where each of them has a
    mutually consistent set of propositions?
         Additionally, how is 'time' defined by comp such that
    transformations of topologies can be considered.

It occurs to me that computation can only occur where topological position is borrowed from the physical, spacetime presence of persistent bodies. Sense and static realism must exist a priori to computation.

Hi Craig,

Yes, the set of equivalent computations (equivalent in the sense of all are capable of generating the 1p content) can only occur if there is a topological position. This position is "borrowed" from the space-time that a set of persistent logics have in common. Remember, one Boolean algebra has many different but equivalent Stone spaces as its dual and each Stone space has as it dual many equivalent Boolean algebras. I am using the concept of an equivalence class. A space-time is a Stone space that has some evolution, so it is a sequence of Stone spaces. A computation is the evolution of a Boolean algebra or, equivalently, a sequence of Boolean algebras. S3nse is the 1p content/static realism of every Boolean algebra/Stone space pair - like a snapshot of an experience. What must be understood is that there is an (at least) uncountable infinity of these dual pairs and only a finite number of them can have a Boolean algebra (equivalence class) between then, so this gives the illusion of a finite universe of physical stuff for almost any finite subset of dual pairs.



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