to hold? The answer, on the assumption that causality flows to the right, and on the other assumptions previously given, is no.
True if we’re sure we’re perfectly reading L1/L2 and perfectly interpreting them to predict M2. But if not then I think the answer’s yes because M1 provides additional implicit evidence about L1/L2 than we get from an imperfect reading or interpretation of L1/L2 alone.
Then again, you still get evidence about the direction of causality by how much P(M2|L1,L2) and P(M2|M1,L1,L2) tend to approximately equality in each direction, so even very imperfect knowledge could be got around with statistical analysis. I haven’t read Judea Pearl’s book yet so sorry if I this is naive or already discussed.
Dynamically Linked, that’s cheating because M1 always equals M2. It’s like those division by zero proofs.
Regardless, Eliezer’s point here is utterly beautiful and blew my mind, but I just want to check it’s applicability in practice:
That is, will we observe the conditional dependence
to hold? The answer, on the assumption that causality flows to the right, and on the other assumptions previously given, is no.
True if we’re sure we’re perfectly reading L1/L2 and perfectly interpreting them to predict M2. But if not then I think the answer’s yes because M1 provides additional implicit evidence about L1/L2 than we get from an imperfect reading or interpretation of L1/L2 alone.
Then again, you still get evidence about the direction of causality by how much P(M2|L1,L2) and P(M2|M1,L1,L2) tend to approximately equality in each direction, so even very imperfect knowledge could be got around with statistical analysis. I haven’t read Judea Pearl’s book yet so sorry if I this is naive or already discussed.