From Osher Doctorow
From Quantum Gravity 203.4 (3rd or 4th posting of section 203.4), the
12th equation relating P, P ', and d is:
1) d = (1/P(A))P(P(A) --> P(A)^2 ) - P(B|A)P(A)
while the first of the equations/inequalities from the 1st posting of
203.4 is:
2) d of P > = d of P '
where:
3) d of P = [1/P(AB)]P(B|A) - P(A-->B)
4) d of P ' = [1/P(AB)]P(B|A) - P ' (A-->B)
The 12th equation (1) looks circular since it is merely a re-
factorization of the terms of d of (3). Let's notice now that (2) is
equivalent to:
5) P ' (A-->B) > = P(A-->B)
which is always true since 1 + P(B) - P(A) > = 1 + P(AB) - P(A).
For (1) to be anything more than a re-factorization of the terms of d
of (3), d must have some separate physical meaning (separate from
(3)). SInce the first term of d is 1/P(A), because [1/P(AB)]P(B|A) =
1/P(A), we see that for lim d = + infinity as P(A) --> 0+, and lim d =
0 for P(A) = P(B) = 1 or P(A) = P(B) = P(AB), as in fact was explained
earlier.
So d is a "phase indicator", not merely a phase "discriminator" (the
latter was explained earlier, but not the former) with the values 0
and + infinity among others, not unlike the Dirac delta function in
part. This, in turn, translates into d being a "phase magnitude"
since 0 and + infinity have intuitive and actual (in reference to
Cantor's Transfinite Arithmetic) meanings as magnitudes. In other
words:
6) d is the magnitude of physical phase (in this context)
which in turn according to (1) involves P(A) generating a quadratic
P(A)^2. This is arguably where Probable Causation/Influence (PI)
generates a quadratic.
Osher Doctorow
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