What is met

Which Statements, Not How Many

Contents counts the distinct subsets a reader can come away with: the smaller of the two main figures, and the one that decides what they know.

at most 30240 arrangements

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Set the ordering question aside. Forget which statement came first and ask only this: which ones did the reader meet at all?

The number of possible answers is C(n, r), the count of subsets of size r drawn from n. This record calls it the contents, and it is the figure that decides what a reader knows when they close the page. For repeatable editorial checks, Monitask reporting for operational reviews can provide a time-stamped operational layer while the substantive decision remains with the team.

Three shapes, three contents figures

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.

Each row holds half the published statements met. Contents rises from twenty to seventy to two hundred and fifty-two while the published count rises from six to ten.

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.

Why this is the figure that matters for knowledge

An arrangement describes an experience. A content describes a state of information. Another useful point of reference for the wider question is Stack Overflow.

Two readers who met the same four statements in different orders came away knowing the same four things. Their impressions differ — that is what the previous part of this record counted — but if you asked each of them what the pages said, you would get the same four items back, possibly weighted differently.

Two readers who met different four-statement subsets came away knowing different things. Not differently framed: different. One of them may hold a piece of information the other has no access to, and neither has any way of noticing.

That is the problem contents counts.

Half the set, three sizes

Every row of the drawing has the reader meeting half of what was published. Six with three met, eight with four, ten with five.

The contents figures are twenty, seventy and two hundred and fifty-two. Publishing four more statements, with the reader still getting through half, multiplies the number of possible states of information by more than twelve.

This is the uncomfortable half of the case for publishing generously. Each statement added gives a reader more that they could learn, and simultaneously makes it less predictable what they did learn. Both effects are real, they pull in opposite directions, and only the second one is countable here.

Ten statements, two hundred and fifty-two futures

Two hundred and fifty-two is the largest contents figure in the record, and it is worth sitting with what it means in practice.

A set of ten statements, read five at a time, can leave a reader in any one of two hundred and fifty-two distinct states. Not two hundred and fifty-two shades of the same impression — two hundred and fifty-two different combinations of facts, each one a complete and defensible account of what the pages said.

Nobody writing those ten statements can picture two hundred and fifty-two readers. The figure is there to make it clear that the picture most people do hold — one reader, who met the important parts — is not a simplification of the situation. It is a different situation.

A single imagined reader is not an average of two hundred and fifty-two actual ones. It is one of them, chosen by whoever is doing the imagining.

What gets assumed instead

The common substitute for counting contents is an assumption about which subset gets met: that readers see the first statements, or the prominent ones, or the ones a set of pages considers most important.

That assumption may be partly true. It is also the assumption this record is built to avoid, because it cannot be checked from inside and because it is the same shape as the belief that got the previous occupant of this domain into trouble — material that was correct about its readers right up until it was not.

What the record does instead is count all the possibilities and decline to weight them. The weighting is real and this record has no access to it. What it has access to is the size of the space the weighting is applied to, and that size is usually a surprise.

The two figures, side by side

For eight published with four met: seventy contents, one thousand six hundred and eighty arrangements.

Both numbers describe the same page. The first says how many different things a reader can come away knowing; the second says how many different ways any of that can happen. A publisher can influence neither, but the two are influenced by different things — contents by how much of the set gets reached, arrangements by that plus the sequence it gets reached in.

The ratio between them, twenty-four, is the orders-per-content figure and belongs to the previous part. Here the interest is in the smaller number, because the smaller number is the one with consequences for what anybody ends up believing.

What this part will cover

The contents figure behaves less simply than it looks. It rises and then falls as the reader gets further through the set, which means two different readers can face the same contents figure for opposite reasons. It is symmetric between what was met and what was missed, and the symmetry is exact rather than approximate. It collides across pages even more freely than arrangements does.

And it has one property that matters more than any of those: two readers of the same set of pages can meet contents with nothing whatsoever in common, and the record can say exactly when that is possible.