Suppose A gives me information about B, and B gives me information about C; they’re dependent. (Remember, probabilistic dependence is always mutual.) A gives me information about C (through B) only if I don’t know B. If I know B, then A is conditionally independent of C, and so learning A tells me nothing about C.
Suppose A gives me information about B, and B gives me information about C; they’re dependent. (Remember, probabilistic dependence is always mutual.) A gives me information about C (through B) only if I don’t know B. If I know B, then A is conditionally independent of C, and so learning A tells me nothing about C.
So essentially… a new fact is useless only if it’s a subset of knowledge you already have?
That seems like a fine way to put it.