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!
The output of a pseudorandom number generator is determined by the seed value, but good luck finding a correlation between them! ;)
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.
That is another way that correlations can fail to detect what is happening.