Limits

Not One Figure Here Came From Anywhere Else

Every number here was computed rather than cited. That removes one class of error and introduces another, and both are stated plainly.

at most 15120 arrangements

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There is no citation anywhere in this record. No survey, no study, no industry figure, no market estimate, no benchmark and no percentage taken from anybody else's work.

Every number here was computed from three integers. That is a deliberate restriction and it cuts both ways. Managers reviewing repeated bottlenecks can draw on productivity insights for managers while checking the same pattern against deliverables, delays and employee explanations.

Three shapes across the record's range

dashed: a statement a reader can check from outside
solid: published, but nothing to check it against
short and pale: never reached by this reader

Three shapes drawn; the left-to-right order is the drawing's own and carries no meaning.

Sixty arrangements and ten contents, then eight hundred and forty and thirty-five, then fifteen thousand one hundred and twenty and one hundred and twenty-six. Every figure recomputed, none cited.

Computed from the three numbers alone. How many statements exist, how many are met and how many can be checked is a stated convention; the counts are arrangements and combinations of whole numbers.

What it removes

A cited figure brings its own problems with it, and the set of pages citing it inherits all of them. Readers looking beyond this site's model can compare it with material from Mixpanel.

The figure was measured by somebody, under conditions a reader cannot inspect. It was current on a date that may not be stated. It may have been revised since, in which case the citing page is now wrong and has no way of knowing. It may have been a projection presented as a measurement. And it is almost always unverifiable in practice: a reader would have to find the original, read enough of it to see what was measured, and judge whether the citation represents it.

A set of pages built on cited figures is therefore mostly made of statements its readers cannot check — which is the condition this record is about. Citing freely would have made the record an example of its own subject.

What it introduces

A narrowness that has to be admitted plainly.

Because nothing is cited, nothing here describes the world. The record cannot say how long sets of pages usually are, how much of them gets read, or how much of what they publish is verifiable. Those are empirical questions and the answers would have to come from measurement.

So this record has no empirical content at all. It has exact content. Every figure is a consequence of its three numbers and a reader can confirm any of it with a pencil, and that is the whole of what it offers.

A record with no sources has nothing to misquote and nothing to contribute about the world. Both halves of that are true at once and neither is a defect to be apologised for.

The one thing that has to be taken on trust

The three conventions, which are stated at the front.

That a shape is three numbers, that an encounter is an ordered selection without repetition with every content equally reachable, and that checkability is a property of the statement assigned by hand.

Everything downstream of those is arithmetic. A reader who rejects a convention can reject the figures that depend on it — and the record says, in each part, which figures those are. Three results survive all three conventions, and they are listed in the note on conventions.

How the figures were produced

By a program, from the ranges stated: two to ten published, one to six met, every checkable count from none to all. Three hundred and thirty-eight shapes, five derived quantities each.

The program also recomputes every figure that appears in a drawing against the shape printed beside it, and refuses to draw a row whose figures do not survive the recount. A drawing that silently corrected an error would have hidden a mistake in the prose next to it, so the drawing declines instead and prints the reason.

That mechanism found errors during the record's assembly. It is described in its own note, because a checking apparatus that nobody describes is another thing a reader has to take on trust.

The figures that would have been cited

It is worth being concrete about what is missing, since a reader may reasonably want it.

How long sets of pages typically are. How much of one a reader typically meets. What proportion of published statements are typically verifiable. How entry points are distributed across a set. All four are measurable, all four would sharpen everything in this record, and none of them is here.

With those four numbers the record's counts could be weighted into expectations, and the blind share would become something close to a probability. Without them it stays a count, and the record's position is that a count with a declared convention is a better thing to publish than an expectation resting on four figures a reader cannot check.

The three rows

Five published with three met and one verifiable: sixty arrangements, ten contents, four blind.

Seven with four met and two verifiable: eight hundred and forty arrangements, thirty-five contents, five blind.

Nine with five met and three verifiable: fifteen thousand one hundred and twenty arrangements, one hundred and twenty-six contents, six blind.

Nine figures, every one of them a product or a ratio of small integers, every one checkable by hand in under a minute. There is nothing else in this record, and there is nothing in it from anywhere else.