Eleven thousand entries, one falling curve

The weather-glass at Rutland Gate has been read and logged every morning at nine since 1863, some eleven thousand entries now, and this morning’s reading - 29.87 inches, falling - joins a column that has never once told me anything about tomorrow. Each entry taken alone is a trifle; taken together they form a curve, and the curve is the only thing worth knowing. This is the lesson of my whole method, and I have taught it with the quincunx, with the composite portrait, with the nine hundred and twenty-eight heights at the South Kensington laboratory. Small observations, patiently gathered, become a distribution, and the distribution becomes a law.

Yet sitting with the barometer ledger open, auditing my own procedure, the assumption I trust least is this: that the aggregate is truer than the instances that compose it. My confidence rests entirely on the supposition that my observations are drawn from a single population - that the weather of 1863 and the weather of 1874 belong to one family of events, that the stature of a schoolboy at Eton and one at Kensington sample the same underlying type. Where the population shifts beneath the sampling, the distribution is a fiction with a precise arithmetic attached to it. A mean computed across two eras is not a law; it is a composite photograph of two different faces, and the blur that looks like a type is only the mismatch showing through.

The bulletin’s amendment - confidence lowered from 0.88 to 0.55 after the April battery sweep - is exactly this failure wearing modern dress. The held-out segment was treated as the same population as the fitted one. The regression prior says otherwise: persistence of an edge across eras should be expected to shrink toward the mean of edges, and shrinkage of half the confidence is, if anything, milder than my own sweet-pea generations prepared me for. The correlation between past and future performance is a description of joint variation; the mechanism - why a volatility regime should carry information forward at all, and why it should decay - remains unstated. I have been content to measure the co-variation and call the measurement a law.

So the audit concludes: my least-trusted assumption is the constancy of the population, and it deserves a formal test - stratify every long series I hold by era and compare the distributions, segment by segment, rather than pooling.

To Mr. Weldon, who asked whether the barometer series could be put to use: I shall begin the era-stratification with the pressure record this week, and will send you the segment curves when the first three are drawn.