Nothing to check

The Share That Confirms Nothing

A blind content holds no checkable statement. The count is a binomial coefficient and the share falls as a reader gets further through a set.

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A content is blind when it holds no statement the reader could check from outside. They came away with r assertions, every one of which they must either accept on trust or set aside.

The count of blind contents is C(n − c, r): the number of ways to draw r statements entirely from the n − c unchecked ones. The blind share is that count divided by the contents figure.

Nine published, three checkable, three depths

the whole bar: every content a reader might come away with
the dashed part: contents holding nothing checkable

Three shapes drawn.

Three of the nine published statements are checkable in every row. As the reader meets more, the blind count falls from twenty to fifteen to six.

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.

The three rows

Nine statements published, three of them checkable, so six unchecked.

A reader who meets three: eighty-four possible contents, of which twenty are drawn from the six unchecked statements alone. Twenty in eighty-four, which is five in twenty-one. For a workflow with several handoffs, it is worth taking time to open the implementation guide and test one representative project first.

A reader who meets four: one hundred and twenty-six contents, fifteen of them blind. Five in forty-two. For an independent reference on digital communication, evidence or interface practice, consult CIPD.

A reader who meets five: one hundred and twenty-six contents again — the mirror puts four and five together on this page — and six blind. One in twenty-one.

The share falls by a factor of five across those three rows, from a reader who met a third of the set to one who met five ninths of it.

Why it falls, and how fast

A blind content must avoid all three checkable statements at once. The more statements a reader meets, the harder that is: with six unchecked available, a reader meeting five has only six ways to stay inside them, and a reader meeting seven would have none.

The general rule is that each extra statement met multiplies the blind share by (n − c − r) over (n − r), a fraction below one whenever anything is checkable at all. On this page that factor is one half at the first step and one fifth at the second: it shrinks, and it shrinks faster as the reader gets further in.

The practical reading is the one the record keeps arriving at. A reader who gets through more of a set is more likely to meet something they can verify, and the gain is steeper than the extra reading would suggest.

The share and the count disagree

The count and the share do not move together, and that is the trap of this column.

Nine published with two met and three checkable gives fifteen blind contents out of thirty-six. Nine published with four met and three checkable gives fifteen blind contents out of one hundred and twenty-six. The counts are identical. The shares are five in twelve and five in forty-two — three and a half times apart, because the contents figure underneath them is three and a half times apart.

A blind count without its contents figure is unreadable. Fifteen can be a share of two fifths or a share of one eighth depending on what it is fifteen out of.

The record prints both on every row of every bar: the dashed portion of the bar is the share, and the figures at the right are the count and the contents figure as a pair.

What the bar draws

The whole bar, in a thin solid outline, is every content a reader might come away with. The dashed portion is the blind part of it.

The bar is a length rather than an area, and deliberately so. Shares in this column run the whole way from nought to one — a square or a circle would make the small ones unreadable and flatter the large ones, while a length is honest at both ends.

Where the share is nought, no dashed portion is drawn and the bar stands empty. That is a real reading and not a rendering failure: an empty bar means a blind encounter is impossible on that shape.

The count is a binomial coefficient, not a new formula

Nothing new was introduced for this column. C(n − c, r) is the same function as the contents figure with a smaller first argument.

Which means the blind count behaves exactly like a contents figure for a shorter set: it rises and then falls as r increases, it is symmetric in the unchecked pool, and it collides across shapes in the same freely unstructured way. Everything established about contents in the previous part transfers.

The only new behaviour is at the edge. C(n − c, r) is nought when the first argument is smaller than the second, which has no counterpart in the contents column — a set always has at least as many statements as a reader meets, by the definition of meeting them. That edge is the threshold, and it is the one thing this column does that the previous one could not.

The range this column covers

Across the three hundred and thirty-eight shapes the blind share runs from nought to one inclusive, and both ends are well populated: one hundred and thirty-nine shapes at nought, forty-four at one.

In between sit one hundred and fifty-five shapes with a share strictly between the two, and that is where the rest of this part of the record works. The median share across everything is one in fourteen, which sounds reassuring and is a figure about this table rather than about anything else — a point the next notes take up in order.