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jimrandomh comments on Causality does not imply correlation - Less Wrong
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Type error! Causal relationships between booleans imply correlation between them. Causal relationships between numbers imply correlation only if the relation is monotonic. Other types, such as strings, need not even have a meaningful definition of correlation, but they can nevertheless be causally related to eachother.
That is true, but not relevant. These numbers have, I think, as strong an independence as bit strings can have: no bit that can be extracted from A is correlated with a bit that is extracted from B.