[linhchi]

Correlation has a formula, it detects the linear relation between two variables. So the quadratic relation is actually having zero correlation.

Second, in academic research, we mean 'correlation doesnt imply direct causation'. Because we're talking science (what's significant) not astrology (as above, so below).

For example, the octopus predicts the results of football match correctly most of the time. But as a scientific person, would you say that there is any conceivable causation?

The important word is conceivable.