Another monthly installment of the rationality quotes thread. The usual rules apply:
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This is completely wrong, though not many people seem to understand that yet.
For example, the voltage across a capacitor is uncorrelated with the current through it; and another poster has pointed out the example of the thermostat, a topic I've also written about on occasion.
It's a fundamental principle of causal inference that you cannot get causal conclusions from wholly acausal premises and data. (See Judea Pearl, passim.) This applies just as much to negative conclusions as positive. Absence of correlation cannot on its own be taken as evidence of absence of causation.
It depends. While true when the signal is periodic, it is not so in general. A spike of current through the capacitor results in a voltage change. Trivially, if voltage is an exponent (V=V0exp(-at), then so is current (I=C dV/dt=-aCV0 exp(-at)), with 100% correlation between the two on a given interval.
As for the Milton's thermostat, only the perfect one is uncorrelated (the better the control system, the less the correlation), and no control system without complete future knowled... (read more)