There is correlation without causation, but there is also causation without correlation. Why, when is the latter? Is there one reason or more and if so how can they be structured and by what? If one of the observables does not change, because there is a controlling observer (prediction+feedback), there is no way to establish correlation. I am displeased by bayesian probability combined with graphs (DAG), it so obviously lacks the nonlinear activation function. If two random binary streams feed into a XOR gate, the output is uncorrelated with anyone of the streams even though there is plenty of change to observe and perfect causality.

"parabola" That would be a third category then: No correlation observed because the aggregated observation cancels out the effect working both ways.