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paulfchristiano comments on The best 15 words - Less Wrong
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Judea Pearl, Causality:
If two things are correlated, there is causation. Either A causes B, B causes A, they have common cause, or they have a common effect you're conditioning on.
Edit: If two variables are correlated, there is causation. Either A causes B, B causes A, they have common cause, or they have a common effect you're conditioning on.
That doesn't seem to be strictly true. Of all the things that are correlated it would seem that there would be some that have none of the listed causal relationships. It is merely highly probable that one of those is the case.
To the mathematicians, correlation is a statement about random variables, and not the same as empirical correlation (which is a statement about samples, and might be spurious).
Of course the world isn't made of random variables, but only in the same sense that the world isn't made of causal models. They are models, and "correlation" and "causation" are features of the model which don't exist in the real world. In a causal model, correlation implies causation (somewhere).
But then this "true correlation" is unobservable, is it not? Except for trivial cases we can never know what it is and can only rely on estimates, aka empirical correlations.
Well, that makes Pearl's statement an uninteresting tautology. Correlation implies causation because we construct models this way...
Emphasizing random variables sounds pretty frequentist to me, while the source being summarized is bayesian. But, yes, models are made of random variables.
thanks, this is exactly the case. a better objection is, it's not strictly true because things can be some complex net of the above cases, and it doesn't always break down into one of the four, but that doesn't fit in "15" words, and it's less important
edit: also it's possible in rare cases for things to be uncorrelated but causally connected