From Osher Doctorow
I proved earlier in this thread that:
1) P' (A-->B) - P(A-->B) = P(A' B)
But we also can easily prove that:
2) P(A' B) = P{(B-->A)' } = 1 - P(B-->A)
since (B-->A)' = (B' U A)' = BA' = A' B. We therefore get:
3) P' (A-->B) = P(A-->B) + P{(B-->A)' }
Thus, P' (A-->B) is maximum with respect to P(A-->B) when P{(B-->A)' }
= 1, which is to say when P(B-->A) = 0, and P' (A-->B) is minimum with
respect to P(A-->B) when it equals P(A-->B), which occurs when P{(B--
A)' } = 0, in which case P(B-->A) = 1.
Therefore, P' (A-->B) represents a phase beyond that of P(A-->B) in
which P(B-->A) is less than 1 except at the intersection of the two
phases, and in which the P' (A-->B) phase becomes more different from
that of P(A-->B) insofar as P(B-->A) gets closer to 0.
In ordinary language, P' (A-->B) represents the "increasingly
noncommunicating phase" in the sense of both P(A-->B) and P(B-->A)
not being high in P' (A-->B) although the former can be but not the
latter as we go deeper into the phase.
The idea that (Probable) Causation P(A-->B) may change phase when it
ceases to be reciprocated by a high P(B-->A) in turn relates to
several physical scenarios. In the very early Universe, arguably
Causation was reciprocated between two events A and B, analogously to
the 4 Fundamental Forces being unified and "reciprocal". So P(A-->B)
described that phase. Then in response to being "relatively
alone" (the "problem of 0") which is a challenge to reciprocation of
Causation, the Universe responded by Inflation. After Inflation, it
found itself "gigantic" or with what appeared as an over-abundance of
reciprocal Causation, and it responded by slowing down its rate of
expansion or even possibly reversing it to contraction.
Expansion is in a sense a search for reciprocal communication, while
contraction is in a sense a search for one-way or anti-reciprocal
communication. From this viewpoint, the recent acceleration of the
Universe a few billion years ago (somewhere between 3 and 5 billion
years ago) was an attempt to find reciprocal communication in
(Probable) Causation and may have arguably generated the seeds of
life, since life is highly interactive or reciprocally communicating
with feedback in Causation. Interestingly, life tends to be both
contractive and expansive locally, so that we may have in life a
literal communication or feedback between the two phases P(A-->B) and
P' (A-->B) or the phases which they represent.
From this viewpoint also, gravitation is contractive and represented
by P' (A-->B), while the Cosmological Constant or whatever drives
acceleration of the Universe is expansive and is represented by P (A--
B). This is arguably an "opposite" force from gravitation. At the
very heart of Quantum Gravity and indeed Unified Gravity is (Probable)
Causation and its phases.
Osher Doctorow
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