From Osher Doctorow mdoctorow@comcast.net

I've introduced three probabilistic-statistics Attractor types in sci.stat.math, which readers can also access via Math Forum as keywords. As I mentioned last time, there is the type characterized by: 1) P(A-->B) = P(A), P(B/A) = P(A) where P(A-->B) = 1 + P(AB) - P(A) and P(B/A) = P(AB)/P(A) and where AB is the intersection of sets/events A, B. The slash / in P(AB)/P(A) is division if P(A) is not 0, but the slash in P(B/A) stands for "given", that is the prob- ability of B given A. P(A) is the probability of A. P(A-->B) is the Probable Influence of A on B. There are two other types, given fist by: 2) P(A-->B) > .95 and P(AB) > 0 3) P(A-->B) > .95 and P(AB) = 0 and their conditional probability analogs: 2') P(B/A) > .95 and P(AB) > 0 3') P(B/A) > .95 and P(AB) = 0 (impossible because P(B/A) = P(AB)/P(A)) By substituting for P(AB) into (2), (3), (2' ) it turns out that P(A) - P(AB) < .05 is equivalent to (2) and P(B) > .95P(A) is equivalent to (2'), while 3 is equiv- alent to P(A-->B) = 1 - P(A) > .95 or P(A) < .05 but in this last case only with the condition that P(AB) = 0. The second type, represented by (2) and/or (3), means that P(AB) is close to P(A), which turns out to mean that A and B intersect very highly (have very much in common) in the probability-statistics framework and that A is almost entirely inside B, that is A is almost entirely a subset of B. This could be designated as "A is an Internal Attractor of B", and makes intuitive sense. The third type says that A and B don't intersect, and is exemplified by equa- tion (3). Since A and B don't intersect, they have nothing in common, and so such Attractors can be called External Attractors - A is an External Attractor of B. An External Attractor could represent "action at a distance," where something influences something else without a physical connection or transmission from one to the other, or it could represent one alternative influencing another, or it could just represent two non-intersecting sets/events influencing each other or one representing the other. "Action at a distance" is difficult to confirm for physical events in our Universe, although theoretically it could occur in some alternative Universe or even in some "parallel universe" if those exist. Alternative choices influencing each other is an unusual concept. We usually think that if you can choose D or E, then D doesn't influence E or vice versa - only your choice influences anything, or D or E might be influenced by your choice, or conceivably D or E could affect your choice. But for D to affect E if they are completely alternative choices (like eating or not eating, or like buying 1 breads, 2 breads, or 3 breads) which exclude each other seems strange. Still, the fact that they exclude each other means that there is some type of influence going on - even if it is "exclusion" - although there is much research to be done in this area. Osher Doctorow