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From: Osher Doctorow on 23 Jul 2010 17:21
From Osher Doctorow

I pointed out that although P(A<--B) and P(A-->B) respectively
represent the probabilities of Repulsion and Attraction or Expansion
and Contraction respectively, there are also other contextual factors
including stabilizing versus destabilizing structures that relate to
the above.

Another way of saying it is that P(A-->B) includes or generalizes to a
large number of Probable Causal variables or measures.

From the previous post, we have:

1) P(A-->B) = 1 + P(AB) - P(A)
2) P(A<--B) = -1 - P(AB) + P(A)
3) P(A-->B) + P(A<--B) = 0

Now we can see something more interesting about the second type of
Probable Causation/Influence discussed earlier in this thread:

4) P ' (A-->B) = 1 + P(B) - P(A), where P(B) < = P(A).

We already know that (as readers can verify):

5) P ' (A-->B) + P ' (B-->A) = 2 (formally - that is, dropping the
condition that P(B) < = P(A) or P(A) < = P(B) in context).

However, we can now define:

6) P ' (A<--B) = -(P ' (A-->B)) = -(1 + P(B) - P(A)) = -1 - P(B) +
P(A)

and therefore:

7) P ' (A-->B) + P ' (A<--B) = 0

Under the conditions when P(A-->B) = P ' (A-->B), which occurs iff
P(B) = P(AB) iff B is a subset of A with probability 1, (3) and (7)
are equivalent and can be derived from each other (the respective
terms are equal).

Notice that (7) does not imply that P(B-->A) is contraction while P(A--
>B) is expansion. The quantity P(B-->A) still remains 1 + P(B) - P(A)
for P(B) < = P(A), even though P(A<--B) = -P(B-->A).

So the physical interpretation of reversing Cause (A) and Effect (B)
has a certain formal resemblance to Expansion versus Contraction, or
Repulsion versus Attraction, using P ' , but they work physically
somewhat differently in general.

Osher Doctorow
From: Osher Doctorow on 23 Jul 2010 17:32
From Osher Doctorow

What is remarkable is that if you get 2 upon adding terms in the
previous contexts, then you are in the "domain" of reversing Cause
and Effect (using P ' ), while if you get 0 then you are in the
"domain" of repulsion versus attraction. Notice that 2 actually goes
outside the usual probability domain [0, 1], just as 0 is inside [0,
1] is generated by adding an ordinary probability to a "negative
probability" where the latter is automatically outside [0, 1] and is
in fact in [-1, 0].

We are arguing dealing with very deep properties of scales which
emerge especially when focusing on probabilities but may otherwise
not be obvious.

Osher Doctorow

From: Osher Doctorow on 23 Jul 2010 17:38
From Osher Doctorow

In the first paragraph, "is generated" should be "and 0 is generated".

Osher Doctorow
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