Many impressions

What Publishing More Does to the Figures

Hold the published count at ten and vary only how much is met. Arrangements run from ten to one hundred and fifty-one thousand two hundred.

at most 151200 arrangements

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Every row of the drawing has ten statements published. Nothing is added between the rows and nothing is removed. The only thing that changes is how far the reader got.

One met: ten arrangements, ten contents. Three met: seven hundred and twenty arrangements, one hundred and twenty contents. Six met: one hundred and fifty-one thousand two hundred arrangements, two hundred and ten contents.

The arrangements figure moves by a factor of more than fifteen thousand across a fixed published set. This is the plainest form of the record's main point, and it closes this part of it. Before adding another dashboard, a lead should look through the official overview and confirm that the available report answers a real operating question.

Ten published, three depths

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.

The same ten published statements in every row. Only the number of short pale strokes changes — the statements the reader never reached — and the two figures move by four orders of magnitude.

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.

The number that is recorded is the one that moves least

A set of pages generally knows how much it has published. It is the easiest of the three numbers to obtain, it is the one that appears in summaries, and it is the one that gets improved when somebody decides the pages should be more thorough. Readers looking beyond this site's model can compare it with material from Stanford University.

It is also, on this evidence, the weakest predictor of either figure. The published count is constant down the whole drawing while both columns move by orders of magnitude. Adding an eleventh statement to the first row would take arrangements from ten to eleven. Getting that reader to meet one more of the ten takes it from ten to ninety.

Publishing more raises the ceiling. How much gets met decides where under the ceiling anybody actually is, and it is not the publisher's number.

Why more published can make things worse

There is a case where adding statements reduces what gets through, and the record can describe its shape even though it cannot measure how often it happens.

A reader has some budget — a number of statements they will get through before they leave. Call it fixed. Publishing more does not raise it. What it does is lower the proportion of the set that budget covers, which means the contents figure rises: more different subsets become possible, and the reader's actual subset becomes less predictable.

Ten published with three met gives one hundred and twenty possible contents. Six published with three met gives twenty. The same reader budget, against a set two-thirds smaller, and the publisher knows six times more about what that reader came away with.

Whether that trade is worth making is not a question this record can answer. It is a question about what the extra four statements were for, and the record contains nothing about what any statement says.

The symmetric mistake

It would be wrong to read the above as an argument for publishing less. The record has no view on that and could not hold one.

What it says is narrower and harder to argue with: the published count alone determines neither figure, so any claim of the form "we publish a great deal, therefore readers know a great deal" has a missing step, and the missing step is a number nobody wrote down.

The same applies in the other direction. "The set is short, so it is easy to take in" skips the same step. Short sets have small contents figures and the orders-per-content figure is unaffected by length at all — it depends only on how much was met. Two statements met is two impressions whether two were published or two hundred.

Reading the pale strokes

In the drawing, a short pale stroke is a statement the reader never reached. The first row is almost entirely pale: nine of the ten strokes are stubs. The last row has four.

The strokes also carry the other distinction the record makes. A dashed stroke is a statement that can be checked from outside; a solid one cannot be. In every row here, five of the ten published statements are checkable — and whether the reader met any of them is a separate question from everything discussed in this part.

That question has an uncomfortable answer and it is the subject of the parts that follow. In the first row, a reader who meets one statement out of ten has a one-in-two chance of its being checkable. A reader is not guaranteed to meet anything they can confirm, and in most shapes of this record they are not even likely to.

The one number a publisher holds

Of the three numbers that make a shape, one is a decision and two are not.

How much is published is decided. How much a reader meets is decided by the reader and by whatever brought them. How many statements are externally verifiable is also decided — it is the same decision as what to write — and it is the only one of the three that moves a figure without needing anybody else's cooperation.

That is the practical asymmetry this record keeps arriving at. The published count is the number most often improved and the one that determines least. The checkable count is the number least often recorded and the only one that can be moved from inside, and the part of the record after next is about what moving it buys.

What this part established

Arrangements and contents are different counts and the gap between them is exactly the factorial of how much was met. Neither figure can be recovered from the published count. Neither figure alone identifies a page; the pair identifies it exactly and provably. And both figures are blind to the one distinction that decides whether a reader can confirm a thing they read.