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SilasBarta comments on Causality does not imply correlation - Less Wrong
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As per my comment here, there is no statistical correlation between the PRNG and the seed value, but there is mutual information.
When someone says "no correlation" to mean "no statistical correlation", people hear "no correlation", which invokes that clump of conceptspace in their minds which implies "no mutual information". But that isn't true. There are other ways for variables to be related than statistical correlation, and mutual information is one way, and this is an important distinction to make before you get all giddy!
Ah, yes, this clears things up... correlation and mutual information are the kind of things that can get confused easily.