12. Reading a Fact Box — The Procedure

Five questions for any number

First, ask what was actually measured, because the quantity in the headline is often not the quantity in the experiment — Cavendish measured a density and is credited with a constant. Second, ask in what units, and whether the unit was stable at the time; Eratosthenes' accuracy is unknowable because the stadion is not. Third, ask what the uncertainty is, and treat a number quoted without one as a number whose author did not want the question — G carries 22 parts per million and the second carries parts in 10¹⁸. Fourth, ask whether independent methods agree, since convergence from unrelated techniques is worth more than precision within a single one, which is what Perrin's work established. Fifth, ask what would change the answer, because a figure that nothing could overturn is not a measurement but a position. Any number that survives those five is worth carrying; most numbers in circulation fail at the third.

Where this book is weakest

The chapters here rest on secondary and tertiary accounts more than is ideal, and several traced their number back to a retelling rather than to the original paper. Two candidate facts were dropped in drafting because sources disagreed by an order of magnitude, and their absence is better than their inclusion would have been. The selection is also unbalanced by geography: these are overwhelmingly European and American measurements, which reflects whose apparatus and archives are easy to reach rather than who has measured the world. The Hubble tension in chapter 08 may well be resolved after this is written, and the chapter is deliberately dated so that a reader can tell.

What survives anyway

The procedure survives even where individual chapters age, because it is a way of reading rather than a set of results. It also inverts the usual relationship with a reference work: the entry stops being an authority to accept and becomes a claim to interrogate, which is more respectful of the people who made it. Those people were mostly working with insufficient equipment against a background of noise, and they got the numbers anyway — that is the part worth taking from a childhood spent reading encyclopedias.

Example: A museum label tells you what the object is; the conservator's notes tell you how anyone knows, and only one of them can be argued with.

Verdict. A number is worth carrying when its quantity, its unit, its uncertainty, its independent confirmations and its refutation conditions can all be stated, and most published figures fail on uncertainty.

Overturned if: the five questions are applied to a well-established measurement and fail to distinguish it from a fabricated one, which would mean the procedure discriminates nothing.

Sources. 2022 · CODATA, "Recommended Values of the Fundamental Physical Constants" — NIST · 2019 · "2019 revision of the SI" — Wikipedia