[time 955] Re: [time 954] Liebnitz's monadic interaction


Stephen P. King (stephenk1@home.com)
Mon, 25 Oct 1999 17:34:53 -0400


Dear Lance and Friends,

        Refocusing!

"Stephen P. King" wrote:
>
> Dear Lance and Friends,
>
> I have been scanning over Alexander Zenkin's various sites, which I
> find fascinating once I got past the EGO, and I found this:
> http://www.mi.sanu.ac.yu/vismath/zen/zen9.htm
>
> The selected quotes from Leibnitz strongly remind me of Hitoshi's Local
> Systems!
>
> There is one part that I would like to ask your comment on:
> "51. But in simple substances the influence of one Monad upon another is
> only ideal, and it can have its effect only through the mediation of
> God, in so far as in the ideas of God any Monad rightly claims that God,
> in regulating the others from the beginning of things, should have
> regard to it. For since one created Monad cannot have any physical
> influence upon the inner being of another, it is only by this means that
> the one can be dependent upon the other. (Theod. 9, 54, 65, 66, 201.
> Abrege, Object. 3.)"

        Thinking about Leibnitz' explanation of monadic interaction:

        The segment: "...it can have its effect only through the mediation of
God, in so far as in the ideas of God any Monad rightly claims that God,
in regulating the others from the beginning of things, should have
regard to it." is the key phrase

        This is what Pratt calls a "preordained synchronization" between the
monads in http://boole.stanford.edu/chuguide.html#ratmech. Unless we are
careful and consider that there is _no_ absolute beginning of things
definable by any constructive procedure (I am appealing to Brouwer and
Goedel!) we will not escape the trap of initiality that so many others
(like Barbour!) are caught in!
        I am appealing, one again, for us to consider the ideas that are
described for us in Peter Wegner's papers, specifically the concept of
co-induction. Notice the notions of the Iteration and Maximality:

"Iteration condition: if t is a stream over an alphabet a, and a \subset
A, then (a, t) is a stream over A consisting of an element a followed by
a stream t of elements

Maximality condition: the set of streams over A is the maximal set
satisfying the iteration condition."

from: http://www.cs.brown.edu/people/pw/papers/math1.ps

        Note that there is no "minimality condition" as there is in the
ordinary induction, this relates to our thinking here as there can not
be defined by any finite constructive procedure a proof that an
arbitrary event is the unique initial event. I am reminded of the Stuart
Kauffman and Lee Smolin paper that Hitoshi and Lance co-authored. The
concept of constructability is the key!
(http://www.kitada.com/time_V.html)
        We see this notion explicit in the ordinary thinking about the Big
Bang. It is assumed that a unique singularity "exploded" and from such
the totality of existence (space, time and matter, etc.) This thinking
is "not even wrong"! The Universe in it-self (The Totality) can have no
beginning or end! It is our observations, or as I conjecture, our
bisimulations of each other (and thus the Universe) are finite and thus
bounded.
        If we model the clocking of LSs in terms of co-inductive Heraclitian
streams (a nice pun ;^) ) following the outline given to us by Peter
perhaps we can make some headway. :-)

Kindest regards,
 
Stephen



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