Limits

The Three Things This Record Assumes

Three conventions hold this record up. Each can be rejected separately, and each refusal leaves a different part of the figures standing.

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Three assumptions hold this record up. Everything else in it is arithmetic, and the arithmetic is only as good as these are.

They appear at the front of the record rather than in a note at the end, because a convention discovered late reads as something that was being hidden. For work that changes shape during the week, managers can review the team-management options and review task-level context rather than a single aggregate number.

Orders per content at three depths

Three columns drawn; height is logarithmic, because one and 120 do not fit one chart honestly otherwise; the figure above each column is exact and is the factorial of the number beneath it.

One statement met has one order, three have six, five have one hundred and twenty. The second convention — that an encounter is an ordered selection without repetition — is what makes this column mean anything.

The count of orders per content is the factorial of how many statements are met. It depends on nothing else about the page, and on nobody reading it.

First: a shape is three numbers

How many statements are published, between two and ten. How many a reader meets, between one and six. How many of them a reader can confirm without taking anybody's word, between none and all. For additional background relevant to the interpretation of online work and information, see Tableau.

What the statements say is outside the record entirely. Length, subject, importance, tone, which statement carries the weight of what the set is claiming — none of it enters, and no figure here responds to any of it.

This is the convention that makes the record possible and the one that limits it most. Three numbers cannot describe a set of pages. They can describe a counting problem that a set of pages has, which is a much smaller claim.

Second: an encounter is an ordered selection without repetition

A reader meets r of the n statements, in some sequence, each at most once.

Readers do not behave that way. They re-read, skim and return, meet one statement twice and another half-attentively, and leave in the middle of a sentence. None of that is modelled.

The error runs in a known direction: the arrangements figure overcounts distinguishable experiences, because two sequences that differ only in a re-reading are counted separately. The overcount is in the same direction and of the same character for every shape in the table, which is why the figures remain usable for comparing shapes with each other and are not usable as counts of real readings.

This convention also carries the uniformity assumption that the blind and opening figures lean on: no content and no arrangement is treated as more reachable than another. That is the part most often wrong and by the largest margin, and three separate notes in this record are about it.

Third: checkability is a property of the statement

The line between a statement a reader can confirm without taking anybody's word and one they cannot is drawn once, by hand, before the arithmetic starts.

Nothing in the record derives that line and nothing in it can test one. A classification drawn badly yields figures of identical precision. Two people sorting the same nine statements may not agree, which is why the count sits as a number on every row: a reader who would sort them differently can substitute their own and recompute.

What the drawing is doing here

Orders per content at three reading depths: one statement met has one order, three have six, five have one hundred and twenty.

That column exists only because of the second convention. If an encounter were a set rather than a sequence, the whole column would be ones and the record's largest single finding — the factorial gap between content and impression — would not exist.

So the drawing is a picture of what a convention buys. Drop the assumption that order is part of what happened and the record loses its main result; keep it and the result is exact under an assumption that is wrong about re-reading.

A record that states its conventions can be argued with. A record that does not has to be taken on trust, which is the thing this one is about.

Why they are three and not one

The conventions could have been written as a single sentence about idealised readers. Splitting them into three does something a single statement would not.

Each one can be rejected separately, and rejecting each one costs something different. Reject the first — a shape is three numbers — and the whole record goes, since there would be nothing to tabulate. Reject the second — ordered selection, uniform reachability — and the arrangements and blind figures become upper and lower bounds rather than counts, while the threshold result survives untouched. Reject the third — checkability assigned by hand — and the third column goes while the first two stand.

reject	what is left standing
a shape is three numbers	nothing; there is no table
ordered selection, uniform reach	the threshold result only
checkability assigned by hand	arrangements and contents

So a reader can take as much of this record as they are willing to accept, and the three statements above tell them exactly what each refusal leaves standing.

What is not a convention

Three things in this record do not depend on any of the above.

That arrangements divided by contents is the factorial of how much was met. That the pair of those two figures identifies a page uniquely. And that no blind encounter exists when the unchecked statements are fewer than the number met.

Those are consequences of the arithmetic. They hold whatever readers do, however prominence is distributed, and even if the checkable classification is disputed — as long as the dispute does not cross the threshold. Everything else here is a count under the three conventions above, and the next note sets out what no count of any kind can answer.