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One Content, Many Impressions

Fifty notes on how many impressions one set of statements allows

What is met

What Both Figures Are Blind To

Three shapes on one page, identical in both main figures, where the count of readings that confirm nothing runs from all seventy to none.

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Eight statements published, four met. Seventy contents, one thousand six hundred and eighty arrangements, twenty-four orders per content.

Those figures are fixed for the whole of this page and the drawing holds them still while the one thing they cannot see moves from one extreme to the other. A final check is to review the current service description, verify the current terms and test exports, corrections and access controls with real users.

With nothing checkable published, all seventy contents are blind. With four checkable, one is. With six or more checkable, none is. A broader source for checking the surrounding technical or organisational context is Associated Press.

One page, the blind count from all to none

share of contents with nothing checkable4 of 8 met, 0 checkable70/704 of 8 met, 4 checkable1/704 of 8 met, 8 checkable0/70
  • the whole bar: every content a reader might come away with
  • the dashed part: contents holding nothing checkable

Three shapes drawn; one of them leaves no blind content at all; one is blind whatever the reader meets.

Eight published with four met in every row. The bars are the same length because the contents figure is the same; the dashed part is the share of contents holding nothing a reader could check.

Computed from the three numbers. A blind content is one holding no checkable statement: that is a property of the page, not a prediction about any reader.

Three readers who are not in the same position

Consider three sets of pages, each publishing eight statements, each read four at a time. By everything counted in this part of the record they are indistinguishable: identical contents figure, identical arrangements figure, identical orders per content.

In the first, no published statement can be checked from outside. Every reader, on every path, comes away with four assertions and no means of confirming any of them.

In the second, four can be checked. Sixty-nine of the seventy possible contents include at least one of those four. The one exception is the content made entirely of the four unchecked statements.

In the third, six can be checked. There are only two unchecked statements, a reader meets four, so a checkable statement is unavoidable.

Nothing in the first two parts of this record separates these three. A report of contents and arrangements, however carefully worded, says the same thing about all of them.

Two figures that are identical across the entire range of a third are not measuring the third badly. They are not measuring it at all.

Why the third number was not folded in

It would be possible to build a single composite figure — some product or weighted sum of the three numbers — and report one value per shape. The record does not, deliberately.

A composite figure can be moved by any of its inputs, which means a reader of the figure cannot tell which input moved. A page that publishes more and verifies less would look the same as one that publishes less and verifies more. The whole use of a record like this is to separate what has been conflated, and a composite would re-conflate it in one step.

So the record carries three numbers per shape and five derived quantities, and refuses to summarise. The cost is that nothing here can be put in a single column. That cost is the point.

What this part established

Contents counts the distinct states of information a reader can end up in, and it is the smaller and more consequential of the two main figures.

It peaks in the middle rather than rising, so the half-read reader is the least predictable one. It is exactly symmetric between met and missed, which makes mirrored shapes agree on one number and nothing else. It is more crowded than arrangements — twenty-four values for three hundred and thirty-eight shapes — so it identifies a page only on nine of the twenty-four values.

And on twenty-five of the forty-four pages, two readers can come away with contents that do not overlap at a single statement.

Why this page is eight published and four met

The shape used throughout this record as its standing example is eight published, four met, three checkable, and the choice was made for one reason.

Its blind share is five in seventy, which reduces to one in fourteen, and that is the median blind share across all three hundred and thirty-eight shapes. The example sits at the middle of the table rather than at an end of it.

Everything else about the shape is unremarkable, which is the point. Seventy contents and one thousand six hundred and eighty arrangements are large enough to be awkward and small enough to be checked by hand: eight times seven times six times five, divided by twenty-four. A reader who wants to verify the record's arithmetic has a worked version of this shape in the last part.

The composite that was not built

One more reason for keeping the columns apart, stated here because this is where the temptation is strongest.

A composite would have to decide how much a blind content is worth against an extra possible content, and that exchange rate does not exist. One is a count of states a reader might be in; the other is a count of states in which they can confirm nothing. They are not denominated in the same thing, and any rate chosen would be an opinion wearing a decimal point.

So the record prints three numbers and five derived quantities per shape and offers no total. A reader who wants a single figure has to choose the exchange rate themselves, in the open, which is the only honest place for it.

What comes next

Everything so far has treated the published statements as interchangeable. They are not, in one respect the record can count: a reader can confirm some of them without taking anybody's word, and cannot confirm the others.

That distinction does not touch either figure discussed so far. It changes only whether an encounter leaves the reader with anything they could check, and the next part of this record counts how many statements that applies to, what the count does, and what it fails to do.

The drawings change with it. A dashed stroke has stood for a checkable statement throughout the record without being explained; from here on, how that line is drawn and why the meaning is carried by the type of line rather than by its colour becomes part of the subject.

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