Methods: Where the Numbers Come From

Every number on The Yardstick Almanac should be traceable to a document you could open yourself, and every calculation should come out the same if you redo it. This page sets out how that works: which sources come first, what the tags after numbers mean, and how dates, conversions, estimates, charts and maps are checked.

Which sources come first

Sources are ranked in this order:

1. Standard documents now in force and official resolutions, such as the SI Brochure and the resolutions of the General Conference on Weights and Measures (CGPM).
2. Publications of standards bodies, such as NIST handbooks and special publications.
3. Journal articles that have passed peer review.
4. Authoritative reference books.
5. Everything else.

When two sources disagree, the higher one does not quietly win. Both figures appear in the text, each with its source, and the claim is tagged [contested]. We can think of a primary document as a benchmark, the fixed mark every later reading is tied to; when two benchmarks fail to agree, that closure error is reported, not smoothed over.

Some sources can only be reached as a catalog record, with the full text out of reach. In that case the Sources list says “bibliographic record only,” and the article reports only who said what, in softer terms. A source that could not be read is never presented as if it had been.

This site works only from documents that are open to read. ISO and DIN standards are not quoted. Where a point depends on what a standard says, the figure comes from openly published material, and if none exists the point is left out.

What the tags after numbers mean

Major numbers carry one of four tags, in the text and in the Calibration card alike. The wording follows the two international guides on measurement, the GUM (JCGM 100) and the VIM (JCGM 200). In particular, “tolerance” is used only for the range a law or specification allows, never for measurement uncertainty or for the range of an estimate.

[exact by definition] means the value is fixed by a definition and has no measurement uncertainty. Since 1959, 1 inch has been 25.4 mm [exact by definition].

[measured, u = …] gives a standard uncertainty, at a coverage factor of k = 1. [measured, ±… (k=2)] gives an expanded uncertainty, with its coverage factor stated. [bounds …–…] is used when a source gives only an upper and a lower limit. These three are copied from the source as the source gives them; one kind is never converted into another, and a bare “±” with no explanation is not used. When a source gives a measured value with no uncertainty, the tag says so: [measured, source gives no uncertainty].

[estimate, range …–…] marks an estimate. The same paragraph or the Calibration card states the inputs and how they were combined, with a link to the full working. The range shows how far the answer moves when the inputs move; it is not a statistical confidence interval.

[contested] means sources disagree and the disagreement is unresolved. The competing figures are given side by side, each with its source.

Dates

Every date, weekday, leap-year call and count of days between dates is computed two independent ways, and the two results must agree before the number is published. Nothing is reckoned by eye. A Julian date is worked out with Julian rules; the Gregorian rules are never run backward over it.

Units and conversions

Unit conversions are done in exact fractions, so no rounding creeps in partway through. The results are compared with the exact values published by NIST. Where a definition changed, the article gives the year and the document that changed it.

Estimates

An estimate shows its working. Each input has a source and a range. The result is given as a central figure and a band. Where an estimate rests on an assumption, the assumption is written out in plain words next to the number.

Charts and data files

Every chart is redrawn from a data file you can download beside it, and the numbers quoted in the text are read from that same file. If the chart and the sentence disagree, one of them is wrong, and that is a correction. Each data file comes with a short notes file naming its sources, its date and its license.

Figures that go out of date, such as population counts, carry the date of their data. Charts and maps built on such statistics are rechecked every 12 months, and any older than 24 months are redrawn or marked [data as of YYYY].

Some pages change when the record changes. When the International Earth Rotation and Reference Systems Service (IERS) announces a leap second, the CGPM passes a resolution that changes a definition, or NIST or BIPM revises a document an article relies on, the affected pages are rechecked within 30 days.

Maps

Each map states the version of the data it uses and the parameters of its projection. The projection is a setting for the base map, written out so the map can be rebuilt. Where a disputed area cannot be left off a base map, the map uses the default boundary layers of its data source and says that the boundaries shown are not an endorsement.

Pictures

Photographs and scans of real objects, historical maps and documents come with their source and license in the credit line. Illustrations are labeled “Illustration” and are there to set a scene. They carry no evidence, and they never stand in for a real instrument, document, person, map or chart. Anything with a scale, a measured shape or a date on it is drawn from data instead.

Corrections

Mistakes get fixed in the open. A substantive correction updates every place the same claim appears, moves the revision date shown in Cite this page, and is logged both at the end of the article and on the corrections log. To report an error, see Write in.