Actually, there is a theorem which states that two variables X and Y are independent if and only if f(X) and g(Y) are uncorrelated for any two functions f,g. That means that you cannot bring things into correlation by any independent transformations whatsoever exactly when the variables are independent. Specifically regarding affine transformations, you would have to add some multiple of X to Y in order to get a correlation, which is obviously silly.
Thanks for the link to RCCP, I hadn’t seen the history of d-sep before. You should definitely check out the causality section of Highly Advanced Epistemology 101 for Beginners and possibly Judea Pearl’s book Causality, which contain a more up-to-date discussion and address many of your concerns much better than I could.
I like your outside view of insight. That was part of the reason I pointed out that this is not a new insight, and has been found many times by other people before.
Edit after reading pragmatist’s comment: Knowing your background, I’ll add some technical meat.
First, regarding correlation versus dependence, consider any functions f(T) and g(e). The exact same argument made in the post still applies: without time, there is no ordering of the points, so we cannot establish any correlation. Since there is no correlation for any functions f,g the variables are independent. The argument could be made that the correlation is undefined rather than zero, but if we take a Bayesian approach then we should probably be summing over all permutations (since there is no reason to prefer any particular permutation). Intuitively, that seems like it ought to go to zero given enough data, but I’m not sure if it’s identically zero for smaller data sets.
Regarding quantum, RCCP works under the MWI which everyone seems to love around here (the world-branch becomes a hidden common cause). But setting that argument aside, we can happily restrict ourselves to non-chaotic macroscopic situations.
You should definitely check out the causality section of Highly Advanced Epistemology 101 for Beginners and possibly Judea Pearl’s book Causality, which contain a more up-to-date discussion and address many of your concerns much better than I could.
Just a heads up, in case Ilya considers it indelicate to mention this himself: He’s an expert in this area, and definitely familiar with Judea Pearl’s work (Pearl was his Ph.D. supervisor).
Actually, there is a theorem which states that two variables X and Y are independent if and only if f(X) and g(Y) are uncorrelated for any two functions f,g. That means that you cannot bring things into correlation by any independent transformations whatsoever exactly when the variables are independent. Specifically regarding affine transformations, you would have to add some multiple of X to Y in order to get a correlation, which is obviously silly.
Thanks for the link to RCCP, I hadn’t seen the history of d-sep before. You should definitely check out the causality section of Highly Advanced Epistemology 101 for Beginners and possibly Judea Pearl’s book Causality, which contain a more up-to-date discussion and address many of your concerns much better than I could.
I like your outside view of insight. That was part of the reason I pointed out that this is not a new insight, and has been found many times by other people before.
Edit after reading pragmatist’s comment: Knowing your background, I’ll add some technical meat.
First, regarding correlation versus dependence, consider any functions f(T) and g(e). The exact same argument made in the post still applies: without time, there is no ordering of the points, so we cannot establish any correlation. Since there is no correlation for any functions f,g the variables are independent. The argument could be made that the correlation is undefined rather than zero, but if we take a Bayesian approach then we should probably be summing over all permutations (since there is no reason to prefer any particular permutation). Intuitively, that seems like it ought to go to zero given enough data, but I’m not sure if it’s identically zero for smaller data sets.
Regarding quantum, RCCP works under the MWI which everyone seems to love around here (the world-branch becomes a hidden common cause). But setting that argument aside, we can happily restrict ourselves to non-chaotic macroscopic situations.
Just a heads up, in case Ilya considers it indelicate to mention this himself: He’s an expert in this area, and definitely familiar with Judea Pearl’s work (Pearl was his Ph.D. supervisor).
Really? I’m impressed. I guess he assumed that I was unfamiliar with it (not an unreasonable assumption).