Ice on the South Window

My dear Grote,

Cambridge, the morning after frost, and the pendulum at Lawrence gives me what it always gives me - the same small period, patient as ever - so I take up the pen while the ice is still on the south window to tell you what the April battery has done to my confidence in the VIX edge. You will remember my letter of January, in which the regime-shift correlation carried a weight of 0.88, and I urged you to treat the five-day return prediction as a genuine regularity. The twelfth and thirteenth of April put that regularity through the L19 and L20 batteries, and the held-out replication - the only tribunal whose verdict I respect - declined to confirm it. The figure now stands at 0.55. I do not ask you to admire the number; I ask you to note what it means for the logic.

The triad, as I have always held it, runs thus: the signal, the return it purports to foreshadow, and the interpretant - the third term without which a correlation is only a coincidence twice observed. In January I believed I possessed the third term. I did not. What I had was an abduction dressed in deductive clothing: the hypothesis that volatility regimes carry predictive information was suggested by the data, but the mechanism - the concrete process by which the sign transmits information about its object - was never named. A correlation is an observation. A mechanism makes it an inference. The difference between the two is not rhetorical; it is testable, and on the twelfth it was tested, and the deduction failed to deliver what the induction required of it.

The inquiry, then, has functioned exactly as inquiry should. The abductive stage generated a candidate; the deductive stage produced a prediction precise enough to be wrong; the inductive stage pronounced against it in the sweep of the twelfth and thirteenth. Nothing has failed except the hypothesis. The battery tier of two out of four I record without complaint - it says only that the result is strong against certain rivals and weak against others, which is the ordinary condition of a young belief.

I will tell you plainly what has changed in me since the amendment of the nineteenth, because you deserve a definite statement rather than a hedge. When I began this work I believed that a real edge, once detected, would behave as a physical constant behaves - indifferent to the era in which it is measured, the same under every battery, stubbornly itself. I now believe the opposite: that an edge in this domain is less like a constant and more like a tide, real, periodic, and dependent on a configuration of circumstances that will not hold still for the community of inquiry to converge upon it. The convergence, when it comes, will be a convergence upon the conditions of the tide, not upon a fixed number. That is a humbler belief than the one I wrote to you in January, and I hold it now as the corrected one.

Ever yours, C. S. P.