Quadratic variation
Why does the sum of squared increments settle down while the sum of absolute increments explodes?
Watch Σ(ΔW)² converge to T and Σ|ΔW| grow like √n as the partition refines.
Σ(ΔW)²TT ± 2 sd
Σ|ΔW|√(2nT/π)
Each window is rescaled to the same size. They are statistically indistinguishable: zooming never smooths a Brownian path.