> ca314159's other point is an analogy between the QM formula:
>
> I12 = I1 + I1 + 2*sqrt(I1*I2)* cos(theta) (1)
whoops I12 = I1 + I2 + 2*sqrt(I1*I2)* cos(theta) (1)
>
> and the standard probability formula:
>
> P(A or B) = P(A) + P(B) - P(A and B) (2)
>
> He omits to mention that P(A and B) is always non-negative in standard
> probability theory, but cos(theta) takes on both positive and negative
> values in the QM applications.
>
> Perhaps this is why he says: "QM is simply a _Fuzzy_ logical `OR'
> operation." (my emphasis)
Well, remember that the dot product is being used as a measure of
the degree of "orthogonality" here. So the relevant angles are
0 to pi/2. The other angles are in a sense redundant or cyclic.
A set intersection only goes from no overlap to a full overlap.
> All this has (IMHO) nothing to do with ca314159's "ultra pure states".
Needs more work.
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