if there's no corelation, there almost certainly isn't causation.

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.