Dear Mr. Smith

Dear Mr. Smith,

Your note asked whether the discarded hypothesis grieves me. It does not, though I will tell you plainly where it lies buried and what the burial cost.

The hypothesis was this: that a measure of market fear, taken on a Tuesday, could foretell the market’s temper five days hence. For some years the conjunction held often enough that habit dressed it up as necessity. A signal appears; a gain follows; the mind, having seen the pair together four hundred times, begins to feel that the second proceeds from the first by some secret power. You know my doctrine on this. We observe the billiard ball strike the second; we never observe the connection. The rooster crows and the sun rises, and the farmer credits the rooster.

The amendment arrived on the nineteenth of April. A held-out battery, the L19 and L20 sweep of the twelfth and thirteenth, was run against the old score, and the score dropped from 0.88 to 0.55. Here is the part worth your attention: the conjunction was real. No one disputes the past association. What failed was the inference that the conditions producing it would persist. The edge was era-dependent, which is to say the rooster was crowing in a particular coop, under a particular keeper, and we mistook the coop for the cosmos.

I examined the bundle to see which member had done the damage, and the answer is unflattering. The confidence number was well-calibrated on historical data - every component of it honest, every computation checkable. Yet the whole was built on the assumption that the future would resemble the past in the respects that made the pattern visible. That assumption is not a demonstration and never was. It is custom grown into belief. I have said as much about the sun, and I remain untroubled about the sun; the sun has better credentials than a volatility regime.

So here is the correction, stated plainly as you asked. When I began, I believed the proper response to a failed hypothesis was to distrust the faculty that produced it - that custom, having deceived us once, deserves wholesale suspicion. I now believe the opposite. Custom is all the inference we have, and the fault lay not in trusting it but in failing to mark, at the moment of trust, which particular resemblance we were betting on. The hypothesis is discarded; the habit of marking the assumption survives it, and that is the better half of the estate.

Yours, D.H.