One more facet

Splitting One Filter Into Two

Replacing a facet of six with facets of two and three leaves the resolution alone and multiplies the questions by twelve sevenths.

One more facetAnalysis×k against ×(k+1)/k

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Take a facet of six choices and replace it with two facets, of two and three. The listings are classified the same way — each one still lands in one of six combinations — and the resolution does not move, because six is two times three.

The question count does move. Seven becomes three times four, which is twelve. So the board permits twelve sevenths as many questions as before, around seventy per cent more, with no change in what it can distinguish.

Where a board hides handoffs between specialists, project time reporting software can add project-time context while quality remains a separate editorial and technical assessment. For a separate technical reference, see OpenSearch.

One resolution, split further each time

one bar is one facet; the divisions are its values
cells: how many listings the schema can tell apart
queries: how many different questions it lets anybody ask
sizes: how many different result sizes are reachable

Four schemas drawn; all of them tell the same 144 listings apart, across four different facet counts.

Each row splits a facet of the row above. The resolution stays at one hundred and forty-four throughout; the questions rise from two hundred and forty-five to one thousand two hundred and ninety-six.

Computed from the schema alone. How many facets and how many values in each is a stated convention; the three figures are products of whole numbers.

The sequence

Start with four, six and six: one hundred and forty-four cells, two hundred and forty-five questions.

Split	Schema	Cells	Questions
none	4·6·6	144	245
one six	2·3·4·6	144	420
both sixes	2·2·3·3·4	144	720
the four too	2·2·2·2·3·3	144	1296

The first column never moves. The second rises by a factor of more than five across four rows.

This is the class of seven, generated. The seven schemas that resolve one hundred and forty-four listings are reachable from one another by splitting and joining, and that is why they form a class.

What splitting gives a reader

More ways to express a partial idea.

On a single facet of six, a reader either picks one of the six or leaves it alone. On facets of two and three, they can pick the two and leave the three, or the reverse, or both, or neither. Four positions where there were two.

The underlying six categories are identical. What changed is that they have been given a structure — a coarse distinction and a fine one — and a reader can use either half on its own.

Splitting does not add categories. It adds a way of talking about the categories that were already there.

What it costs

Nothing in the listings, which is unusual for an edit in this section.

Every listing already has a value in the six-way facet, and that value determines its values in the two new ones mechanically. No reclassification, no defaults, no gap between old listings and new.

What it costs is a control. The sidebar gains a row, and the reader has one more thing to read and decide about. On a board already carrying five filters that is a real cost; on one carrying two it is nearly free.

What it does to the grain

It usually improves it, and sometimes badly.

Splitting six into two and three gives subset products that include two and three separately, where before only six was available. More distinct products, more rungs on the ladder.

But splitting into sizes already present makes things worse. Splitting a six into two and three on a board that already has a two and a three creates repeated sizes, and repetition is the heaviest cause of grain collapse there is.

Board	After splitting the six	Grain
4·6·6	2·3·4·6	13
2·3·4·6	2·2·3·3·4	15
2·2·3·3·4	2·2·2·2·3·3	15

The first split gains seven rungs. The second gains two. The third gains none at all — the schema has become four twos and two threes, and the repetition has absorbed everything the split might have offered.

What it does to the share

It lowers it, and the amount is computable.

Replacing a facet of six with facets of two and three replaces one fraction of six sevenths with two fractions, two thirds and three quarters, whose product is one half.

So the share falls from six sevenths of its previous value to one half of it — a drop of about forty per cent on that facet's contribution. The board has gained questions and lost precision in the same edit.

That is the trade splitting makes, and it is the same trade as anywhere else in this record: more controls, more ways to ask, less chance that any given way reaches a single kind of listing.

When to do it

When readers want to use half a distinction.

If a six-way category is really a coarse choice crossed with a fine one — and people regularly want one without the other — splitting gives them that for the price of a control. The arithmetic says the resolution is safe and the questions improve.

If those six options are genuinely six unrelated things, splitting them into two and three means inventing a grouping that does not exist, and the new controls will be confusing in a way the figures cannot see.