We all know that correlation isn’t causation, but correlation isn’t always indicative of a relationship at all. You can construct a map of cancer incidence where the incidence is positively correlated with the 1/r distance to literally every point on the map! This holds for at least Pearson correlation.
I don’t claim to have an explanation of why actual cancer incidence would have this properly (I constructed my example by having an AI chug the linear programming problem given some constraints I made up so I could see what it looked like).
It is, therefore, absolutely not the case that the average correlation to distance from a random point is zero.
See my other comment:
https://news.ycombinator.com/item?id=49946244