On 11/7/2012 8:18 PM, Craig Weinberg wrote:

On Wednesday, November 7, 2012 6:50:03 PM UTC-5, Stephen Paul King wrote:

    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 universe?
        > --
        Hi Craig,

             So far it seems that there is only a singular set of
        recursive functions (or equivalent) and thus a single Boolean
        for the Universal Machine. If the BA (of the Universal number or
        Machine) has an infinite number of propositions, how could it
        be divided
        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.


As far as falsifying comp though, is there any reason for Boolean algebra in and of itself to present itself as a Stone dual? Why have any new ontological presentation of equivalence at all from a pure arithmetic motive?


Hi Craig,

Comp is not false, IMHO, it is just looked as through a very limited window. It's notion of truth is what occurs in the limit of an infinite number of mutually agreeing observers. 1+1=2 has no counter example in a world that is Boolean Representable, thus it is universally true. This does not imply that all mathematical truths are so simple to prove via a method of plurality of agreement. Motl wrote something on this today: http://motls.blogspot.com/2012/11/when-truths-dont-commute-inconsistent.htm

"When truths don't commute. Inconsistent histories.

When the uncertainty principle is being presented, people usually -- if not always -- talk about the position and the momentum or analogous dimensionful quantities. That leads most people to either ignore the principle completely or think that it describes just some technicality about the accuracy of apparatuses.

However, most people don't change their idea what the information is and how it behaves. They believe that there exists some sharp objective information, after all. Nevertheless, these ideas are incompatible with the uncertainty principle. Let me explain why the uncertainty principle applies to the truth, too."

Please read the read at his website



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