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Elements · Proposition II of VI

Nothing moves without a cause.

IIWhy it holds

A signal is admitted only with its mechanism: who is on the other side of the trade, why they accept the price, and what would make the effect disappear. If we cannot say what causes it, we cannot say when it will stop.

We look for causes, not just correlations — and we write down, in advance, the condition whose absence should end the edge.

∎Proof

corr⁡(Xt, Yt)≫0butcorr⁡(ΔXt, ΔYt)≈0\operatorname{corr}(X_t,\,Y_t) \gg 0 \quad\text{but}\quad \operatorname{corr}(\Delta X_t,\,\Delta Y_t) \approx 0
Proof · correlation without a causeIllustrative · seed 35
corr(X, Y) = 0.81corr(ΔX, ΔY) = −0.01— X— Y400 steps · independent by construction
Two random walks generated independently — by construction, neither causes the other. Their levels correlate at 0.81; their daily changes at −0.01. A relationship you cannot explain by its conditions is not yet a relationship.

Q.E.D.