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From: OsherD on 28 Dec 2009 00:41
From Osher Doctorow

In 349/92, I proved:

1) P(A-->B) = P(B-->A) and P(A<-->B) = 0 iff P(A-->B) = 1/2.

We have now seen, however, that P(C) = 1/2 for any event C in an
unbounded Universe is the borderline between bounded and unbounded
sets/events.

Thus, (1) becomes especially interesting, because although we know
that P(A<-->B) = 0 means that we are concerned with Memory rather than
Memoryless events, P(A-->B) = P(B-->A) is the boundary of P(A-->B) > =
P(B-->A) which is required for Memory Events (actually, > is required
for Memory Events speaking strictly). And P(A-->B) = 1/2 is the very
boundary between bounded and unbounded P(A-->B), recalling that
probability is always between 0 and 1.

The part of (1) that says P(A-->B) = 1/2 thus tells us that the
boundary between bounded and unbounded Probable Causation events has
an important relationship to the boundary between Memory and
Memoryless events.

Osher Doctorow
From: OsherD on 28 Dec 2009 01:01
From Osher Doctorow

I meant 349.92, not 349/92.

Osher Doctorow
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