Quantum Gravity 400.2: Probable Influence/Causation (PI) Game-Optimality vs Cause-Intersection Optimality
in [Physics]
|
Prev: JIM W. DEAN: FAKED ISRAELI FLOTILLA VIDEOS PROVIDE OPENING TO EXPOSE ISRAELI EXPIONAGE HERE
Next: expected spin measurement calculation
From: Osher Doctorow on 5 Jul 2010 12:38 From Osher Doctorow What I've been discussing in the last few subsections is Probable Influence/Causation (PI) Cause-Intersection Optimality, which roughly speaking optimizes the Influence of Cause A on Intersection AB of A with a particular or general set/event (Effect) B. In Section 399 early subsections, another type of PI Optimality was discussed, PI Game Theory Optimality, which maximizes P(A-->B) and/or P ' (A-->B), which turns out to occur iff P(A) = P(B), and roughly speaking yields Optimal Tracking (with applications far beyond spacecraft or missile tracking). PI Cause-Intersection Optimality occurs when: 1) P(AB) = 2P(A) - 1 (based on P(A-->B) = P(A)) or when: 2) P(B) = 2P(A) - 1 (based on P ' (A-->B) = P(A)) The two types of Optimality only coincide exactly using (2) if P(A) = 1, which is to say if A is the Universe, since from (2) we have P(B) = 2P(A) - 1 = P(A) iff P(A) = 1. So for most practical purposes other than for the Universe as a whole, they do not coincide, although (1) has not been thoroughly analyzed in comparison with PI Game Theory Optimality. Notice that both P(A) = P(B) and P(B) = 2P(A) - 1 are linear in P(A), since the first says P(B) = P(A), while the second says P(B) = 2P(A) - 1. Moreover, across varying (different) A or P(A), the second type has more rapid increase of P(B) with P(A) by ordinary differentiation.. Osher Doctorow |