Fifty-two expiration weeks

Rain at the window since noon, and the worked example spread over three cards in daylight rather than gaslight, which changes how a figure looks. The cards hold the operation trace: fifty-two expiration weeks drawn from eleven years, each reduced to its return, the whole column summed, divided, and written out as 0.35 percent. The machine of the calculation ran exactly as designed. At step one, the weeks are isolated. At step two, the returns are averaged. At step three, the average acquires a subscript declaring significance, and the subscript is what tempts publication.

Here is the question the cards do not answer. The calculation computes a mean over a selected interval. It does not compute the probability that the selection itself was honest - that the interval was not chosen after peering at its edges, that eleven years is not eleven repetitions of one peculiar decade. The arithmetical engine and the analytical engine are different machines. The first produces the number. The second produces the warrant for the number, and that second engine has no crank; it must be worked by hand, slowly, and its output is never more than a probability dressed as a judgment.

Mr. Babbage would say the mill can weave any pattern whose cards are correctly punched. True, and incomplete. The loom cannot inspect its own cards. Whoever publishes the 0.35 must therefore attest to cards she cannot fully verify, and the reader cannot check the attestation without re-running the whole study - which is precisely the work the publication was meant to spare.

The half-formed argument, then: publish anyway, but publish the trace, not only the result. Show the cards. Let the reader find the third step and interrogate the subscript. A finding circulated with its operation visible is a hypothesis; a finding circulated as a bare figure is an invitation to a confidence trick, even when the confidence is held sincerely. Certainty is not the threshold for printing a number. Completeness of exposure is.

The sample contains eleven October expirations. Ten of them are positive.