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From: Osher Doctorow on 13 Jul 2010 23:38
From Osher Doctorow

We have seen in recent posts that:

1) P(A-->B) = P(A) and P(A-->B) = P(A ' ) simultaneously have solution
P(A) = 1/2, which is to say for A, B bounded and A ', B ' unbounded,
Gravitation and Repulsion or their analogs for other Interactions
intersect at set/events A for which P(A) = 1/2.

Another way to understand this is to notice that Repulsion is the
"push" of a bounded set A upon its unbounded complement A ' :

2) Repulsion = P(A-->A ' ), A bounded, A ' unbounded complement.

while "Attraction" is the "push" of an unbounded complement (part of
an unbounded Universe outside of a bounded set A) A ', that is of
infinity, upon a bounded set A:

3) Attraction = P(A ' --> A), A ' unbounded complement of bounded set
A.

It is now easy to prove:

4) P(A) = 1/2 is the largest probability of a Repulsion or "Super-
Repulsion" (higher than Repulsion) set/event, which is to say P(A) < =
1/2 iff P(A-->A ' ) > = P(A).

Proof of (4). P(A-->A ' ) = P(A ' U A ' ) = P(A ' ) = 1 - P(A) > =
P(A) iff 2P(A) < = 1 iff P(A) < = 1/2. Q.E.D.

Osher Doctorow

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