Q-reeus wrote:Xray wrote:
1. Let A and B be correlated events under condition X. Then, per (little-known) Watson's Law*, a law supported by many experiments and (so far) never refuted:
P(AB|X) = P(A|X)P(B|XA) = P(B|X)P(A|XB). (1)
Commutativity thus reciprocity? Assuming a product formula universally applies and is meaningful, (1) seems trivial given all P's are reals - right?
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Hi Xray. Regret ever wading into this swampland, having never really studied Bell's theorem beyond a cursory inspection. Seems certain accepted notions of 'correlations' and 'joint probability' are quite foreign to my thinking. Back to the sidelines for me!
Hi Q-reeus,
Many of us here are seeking to understand the swamp; to explain it, not drain it. So, please, no retreat to the sideline just yet; we need all the help that we can get.
Or, please, no retreat until you are clear about the critical importance of equation (1) in all walks of life! For example, via the link to that famous Professor Meadow and his blundering.
Which brings me to this, by you: "Commutativity thus reciprocity? Assuming a product formula universally applies and is meaningful, (1) seems trivial given all P's are reals - right?"
1. I do not understand the relevance of this: "Commutativity thus reciprocity?".
2. To me, there is nothing trivial about (1): eg, see that Prof. Meadow example! Then the next:
3. Why not have a go at deriving (1) from simpler first principles? This might help you to understand why (1) will be very useful for the rest of your days.
4. In my terms: All Ps are in the interval [0,1].
HTH; cheers,
Xray