[From Bill Powers (2006.12.18.1145 MST)]
Rick Marken (2006.12.18.0900) --
So Martin's formula is correct: the minimum correlation between d and o is 1-1/CD^2
assuming CR is var(d)/var(p)
I don't see how he could mean "variance" when he specifically says "CR is an amplitude ratio that has a potential range of between 1 and infinity, and you know the derivation of it quite precisely, since you've been criticizing the same derivation with some authority over the last couple of days." That derivation had no random variables in it. Also, he said "Are you OK with the result that "the absolute value of the minimum correlation between d and o must be sqrt(1 - 1/CR^2)?" if there's no loop transport delay, no noise, and the output function is a pure integrator?" That, too, implies that there are no random variables. If nothing is random, the correlations all have to be 1.0 if there is any variation at all. All relations are completely systematic, with no uncertainties.
I'm sure Martin will explain.