From Osher Doctorow
If gravitation is in a sense an inverse to the Strong/Color Force,
let's look at the Probable Influence/Causation (PI) subtractive
"inverse".
1) P(A-->B) = P(B-->A) - [P(A) - P(B)] for P(B) < = P(A)
which has the rather surprising form:
2) P(A-->B) = P(B-->A) - z, z = P(A) - P(B) > = 0
It is rather easy to prove that P(A-->B), P(B-->A), and z are not
linearly dependent, and so we can regard them as involving 3
dimensions, with z the third dimension.
Equations (1) and (2) do refer to "inverses" because P(A-->B) and P(B--
A) work in opposite directions, namely the Probable Influence/
Causation of A on B and B on A respectively. They also are related by
subtraction, but not the usual way as with a + (-a) = 0 for arbitrary
additive inverses of elements "a".
For physics, the significance of (1) and (2) especially relates to the
fact that gravitation must have a PI "inverse", so that the Strong/
Color Force is certainly a candidate. Notice carefully, however,
that (1) and (2) are not quite symmetric, that is to say, whichever
one of gravity and the Strong force is higher in probability must be
designated by A, and the other one by B, so that the "inverse" is in a
sense one-sided. Assuming that gravity has a higher probability that
the Strong Force, everything is fine; otherwise, the Strong Force has
gravity as an "inverse" but not vice versa. We could, of course,
refer to "left inverse" or "right inverse" but not both.
There is one case in which P(A-->B) has an inverse P(B-->A) regardless
of whether P(A) > P(B) or not, namely if P(A) = P(B). This is an
important case, but most scenarios don't involve it.
Osher Doctorow
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