Correlation does not imply causation. Everyone has heard that one. The less famous twist is that causation does not imply correlation either. A variable can directly drive an outcome and still produce a correlation coefficient near zero. The math and the mechanisms explain why. - Nonlinear relationships Pearson’s r only measures linear association. If y = x^2 and x is sampled symmetrically around zero, r comes out essentially zero. The dependence is perfect, yet the correlation vanishes. - Cancelling pathways Intense exercise can raise blood glucose through stress hormone release while also lowering it through increased glucose uptake by working muscle. Two causal paths with opposite signs can net to zero in the data. Statisticians call this a violation of faithfulness. - Control systems A thermostat is the classic example. The furnace clearly causes the house to warm, yet in a well-regulated home, furnace activity and indoor temperature look nearly uncorrelated, because the contro...