Hi Roger,

On 8/20/2012 6:48 AM, Roger wrote:
Hi Stephen P. King
Mereology is part and parcel of Leibniz's system, to use a limp pun.

I like puns! They show us that existence does not just have one side/form/pattern/perspective...

1) Although unproven, but because God is good while the world is contingent (imperfect, misfitting), Leibniz, like Augustine and Paul, believed that things as a whole work for good, but unfortunately not all parts
have to be equally good. This is essentially his theodicy.

OK, I agree with the spirit of this statement but I am trying to find the canonical mereology of the monads. We can get lost in the many rabbit trails of concepts chains that this idea can lead off to... In the words of Red Leader " Stay on Target!" ;-)

2). Everything is nonlocal: The monads are arranged like a tree structure leading up to
the Supreme Monad, above which is God, causing all things to happen
and perceiving all things.

Yes, but I think that it is a non-Archimedean <http://en.wikipedia.org/wiki/Non-Archimedean> arrangement and, to be specific, an ultrametric <http://en.wikipedia.org/wiki/Ultrametric_space> that can be represented as a Bethe lattice <http://en.wikipedia.org/wiki/Bethe_lattice>.

Bethe lattice

Each "node" represents a monad and the edges represent connections to other monads that it is partly bisimilar to. All composition is given in terms of relative wholes, as there are no "parts" in the Archimedean sense in a monadology. The guiding principle is "all things are monads or "parts" of a monad. The "parts" here is a perspective issue that occurs when one monad has only a partial simulation of another... In more theological terms we might say that the Godhead is immanent in all monads as it is all of its aspects.


Now Man, being near the top of the Great Chain of Being, and the
"perceptions" of each monad are being constantly and instantly
updated to reflect the perceptions all of the other monads in the universe,

Yes, exactly, but this "being constantly and instantly updated" is not a communication scheme as we think in classical terms with signals traveling to and fro; it is the moving in and out of synchrony of monads. The key is that there is no exact and finitely representable orchestration of this movement (Bohm's implicate order was an attempt to capture this idea, but Bohm missed the non-archemedean aspect and thus misunderstood the mereology problem!!), there is only finite and inexact approximations.

So, to the degree of their logical distance from one another,
their intelligence, and  clarity of vision, each monad is
omniscient.

Yes, and this "omniscience", I believe, is captured by the superposition aspect of a QM wavefuction. I use the Net of Indra concept to illustrate this. Each monad, like the jewels in Indra's net, is a reflection (simulation!) of all others but never exactly as exact reflection would be identity (exact bisimilarity).

Personally  I use the analogy of the holograph,
each part contining the whole, but with limited resolution.

Yes exactly (pun!), this does a good job representing the phase angle canonical form of this idea. It must be understood that there is no one "true picture" of this. We have to consider all of the versions of it as we see the properties of objects are dependent on the means with which we observe them. This is the implication of the saying: Nature (God) does not have a preferred observational basis. What we need to define this mathematically is to find the canonical form <http://en.wikipedia.org/wiki/Canonical_form>.

Roger , rclo...@verizon.net <mailto:rclo...@verizon.net>
8/20/2012
Leibniz would say, "If there's no God, we'd have to invent him so everything could function."

    ----- Receiving the following content -----
    *From:* Stephen P. King <mailto:stephe...@charter.net>
    *Receiver:* everything-list <mailto:everything-list@googlegroups.com>
    *Time:* 2012-08-18, 17:34:30
    *Subject:* Re: Monads as computing elements

    Dear Roger,

        From what I have studied of Leibniz' Monadology and commentary
    by many authors, it seems to me that all appearances of
    interactions is given purely in terms of synchronizations of the
    internal action of the monads. This synchronization or
    co-ordination seems very similar to Bruno's Bp&p idea but for an
    apriori given plurality of Monads. I identify the computational
    aspect of the Monad with a unitary evolution transformation (in a
    linear algebra on topological spaces).
        I have been investigating whether or not it might be possible
    to define the mereology of monads in terms of the way that QM
    systems become and unbecome entangled with each other. Have you
    seen any similar references to this latter idea?


    On 8/18/2012 11:58 AM, Roger wrote:
    Hi Stephen P. King
    In the end, as Leibniz puts it,  you couldn't tell the
    difference, they would
    "seem" to have windows, but actually, since substances,
    being logical entities, cannot actually interact,
    they all must communicate instead through the supreme monad,
    (the CPU) which presumably reads and writes on them.
    I think they are like subprograms, with storage files,
    which can't do anything by themselves, but must be
     operated on by the CPU according to their
    current perceptions (stored state data) which
    reflect all of the other stored state date in
    the universe of monads.
    Roger , rclo...@verizon.net <mailto:rclo...@verizon.net>


-- Onward!

    Stephen

    "Nature, to be commanded, must be obeyed."
    ~ Francis Bacon

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Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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