Stephen P. King (stephenk1@home.com)
Mon, 25 Oct 1999 13:12:28 -0400
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.)"
I naively see this as Leibnitz anticipating the notion of Bisimulation,
were the "influences of one Monad upon another is only ideal, and it can
have its effect only through the mediation of God" is the key phrase.
The only problem that I see is that Leibnitz' notion of "God's
mediation" must not be considered as being "in time".
I would like your comment on the later part of the quote; it seems to
be an attempt to explain this "mediation". BTW, the statement: "one
created Monad cannot have any physical influence upon the inner being of
another" is identical to Hitoshi's statement of how LSs are independent
of each other!
On another note, is anyone familiar with "Alexandrov's Theorem", viz:
"...one to one mappings \phi : R^4 -> R^4 preserving the
Lorentz-Minkowski distance for light [rays]
0 = c^2(t_x - t_y)^2 - (x - y)^2 = c^2(t'_x - t'_y)^2 - (x' -y')^2,
x = (t_x, x), y = (t_y, y) \subset R^4 are Lorentz transformations
x' = \phi(x) = \alpha L x + a
up to an affine scale factor \alpha."
[page 4 of http://tph.tuwien.ac.at/~svozil/publ/relrel.htm]
Could someone explain what "affine scale factor" means?
Kindest regards,
Stephen
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