One more facet

Adding A Filter

A new facet of size k multiplies the cells by k and the questions by k plus one. The largest edit, and the only one that changes the subject.

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

Home · One more facet · Reference

Adding a filter of k choices multiplies the resolution by k exactly. Not approximately, not on average: exactly, every time, whatever else the board carries.

The question count is multiplied by k plus one, for the same reason — the new filter can be set to any of its k values or left alone.

A data operation moving from estimates to observed effort can explore how the workflow is configured while preserving a clear process for correction and explanation. For a separate technical reference, see Elastic.

Before and after a new filter

one cell: one combination of values
the heavy outline with corner ticks: what the query returns

Four grids drawn; two set none, and so return everything.

The left pair is the board before; the right pair shows what a third facet of three would do to the same queries. The grids are drawn two facets at a time because a third axis cannot be drawn flat.

Computed from the two facet sizes. A query sets a facet to one value or leaves it unset: that is the convention, not a claim about how anybody searches.

The figures for each size

Starting from a board of four and six choices — twenty-four cells, thirty-five questions:

New facet	Cells	Questions
none	24	35
of two	48	105
of three	72	140
of four	96	175
of five	120	210
of six	144	245

A facet of six multiplies the resolution by six and the questions by seven. Nothing else in this record moves a board that far in one step.

Why it is the only edit that changes what a board is about

The other available edit — a new value in an existing facet — says there is one more kind of the thing already being sorted by. It refines a distinction the board already makes.

A new facet says something different: there is a dimension along which listings vary and this board has not been sorting by it at all. It is a claim about the field rather than about the options, and it is the only move that can make previously indistinguishable listings distinguishable.

Every listing that was merged with another because the board had no filter for their difference stays merged until a filter for that difference exists. No amount of refining the existing filters reaches them.

The cost nobody prices

Every listing already on the board needs a value for the new filter.

Listings posted last week can have their authors asked. Listings posted three years ago cannot. The usual outcomes are a default value for everything old, a classification pass by somebody, or two classes of listing — those with the new value and those without.

Of the three, the default is commonest and the most misleading, because the arithmetic says the resolution went up by a factor of k and the default means most listings are in one of the k values.

What the figures look like when the default dominates

Suppose a board of twenty-four cells adds a facet of six, and nine-tenths of its listings default to the first value.

The cell count is one hundred and forty-four, correctly. The queries setting the new filter to any of the other five values reach the tenth of listings classified since the change. The queries setting it to the default reach everything else, mixed exactly as before.

So the board now resolves one hundred and forty-four kinds of listing and sorts ninety per cent of its contents no better than it did. Both statements are true, the first is the one this record measures, and the second is the one that matters to a reader.

The one case where it is cheap

A board adding a filter before it has listings.

This is the sequence the section on the ceiling describes, and it is the reason that sequence matters: at the start, a new facet costs nothing to populate, and afterwards it costs more every week.

A board that expects to need a dimension later is better off carrying it from the beginning, even sparsely used, than adding it once ten thousand listings are in place. The arithmetic of the edit is identical in both cases; everything else about it is not.

The question count moves further

Resolution multiplies by the size; the question count multiplies by the size plus one. So the second figure always moves more.

Adding a facet of two multiplies the cells by two and the questions by three. Adding a facet of six multiplies the cells by six and the questions by seven.

That asymmetry is why a board can look much more capable after an edit than its resolution warrants, and it is sharpest for small facets: a toggle multiplies the question count by half again as much as it multiplies the resolution.

The summary figure

Multiply by the size. A new filter of four choices quadruples what a board can tell apart, which is a larger change than any number of refinements to existing filters can produce.

That is the whole of the arithmetic, and it is worth knowing before the conversation turns to whether the new filter is worth the work, because it establishes what is actually on the table.