if we have longer pipes with more junctions, like this: A ← B ← C → D ← E → F → G ← H → I → J? The answer is very simple: if a single junction is blocked, then J cannot “find out” about A through this path. So we have many options to block communication between A and J: control for B, control for C, don’t control for D (because it’s a collider), control for E, and so forth. Any one of these is sufficient. This is why the usual statistical procedure of controlling for everything that we can measure is so misguided. In fact, this particular path is blocked if we don’t control for anything!
