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From: Osher Doctorow on 10 Aug 2010 20:59
From Osher Doctorow

We return to the distinction discussed earlier between:

1) P ' (A-->B) = 1 + P(B) - P(A), where P(B) < = P(A)
2) P(A-->B) = 1 + P(AB) - P(A)

which together with elementary probability directly yield:

3) 0 < = P ' (A-->B) - P(A-->B) = P(B) - P(AB) = P(A ' B) < = both
P(B) and P(A ' )
4) 0 = P ' (A-->B) - P(A-->B) iff P(A ' B) = 0 iff B is a subset of A
with probability 1.
5) The maximum of P(A ' B) in (3) occurs for P(A ' B) = P(B) which
holds iff B is a subset of A ' with probability 1, and/or similarity
for P(A ' B) = P(A ' ).

6) From (4) and (5), P ' (A-->B) represents the "Outside Causation/
Influence of A on B", and P(A-->B) represents the "Inside Causation/
Influence of A on B," respectively PIO and PII.
7) Arguably, from (6), P ' (A-->B) represents Repulsion, and P(A-->B)
represents Attraction.
8) P(A-->B) = 1 iff P(AB) = P(A) (from (2)) iff A is a subset of B,
which says maximal Attraction for an object A on an object B occurs
for A a subset of B.
9) P ' (A-->B) = 1 iff P(B) = P(A), which says maximal Repulsion for
an object A on an object B occurs on PROBABILISTIC ORBITS (or roughly
speaking geometric orbits under proper conditions).

Based on (1) - (9), I conclude that Black Holes appear to be maximally
Gravitational objects and that Binary or Spiral Binary Black Hole
Systems (pairs) are both Gravitational (maximally) and Repulsive (via
Orbits).

Osher Doctorow
From: Osher Doctorow on 11 Aug 2010 04:33
From Osher Doctorow

Note that the machinery in which P(A-->A ' ) is Repulsion and P(A ' --
> A) is Attraction (or respectively Expansion and Contraction),
presented earlier, relates to the newer machinery of the previous post
if we recall that:

1) P(A-->A ' ) = P(A ' U A ' ) = P(A ' )
2) P(A ' --> A) = P{(A ' ) ' U A} = P(A U A) = P(A)

so that the appearance of A ' or P(A ' ) or expressions of that type
(when A is bounded and A ' unbounded in an unbounded Universe)
signifies Repulsion/Expansion, while the appearance of A or P(A) or
expressions of those types signifies Attraction/Contraction. Thus,
P(A ' B) is an expression of type P(A ' ) (in fact, A ' B is a subset
of A ' ), etc.

Osher Doctorow
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