the impossibility of arriving at A-->B<-->C for this example from any existing algorithms for deriving causal structure from statistical information.
Correct me if I’m wrong, but I think I already know the insight behind what you’re going to say.
It’s this: there is no fully general way to detect all mutual information between variables, because that would be equivalent to being able to compute Kolmogorov complexity (minimum length to output a string), which would in turn be equivalent to solving the Halting problem.
Correct me if I’m wrong, but I think I already know the insight behind what you’re going to say.
It’s this: there is no fully general way to detect all mutual information between variables, because that would be equivalent to being able to compute Kolmogorov complexity (minimum length to output a string), which would in turn be equivalent to solving the Halting problem.
You’re wrong. :-)
Kolmogorov complexity will play no part in the exposition.
Check my comment: I was only guessing the underlying insight behind your future post, not its content.
I obviously leave room for the possibility that you’ll present a more limited or more poorly-defended version of what I just stated. ;-)