One more facet
The Two Things A Board Can Change
Add a filter, or add a choice to one that exists. The only two moves, and one multiplies the resolution while the other barely moves it.
One more facetReference×k against ×(k+1)/k
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A board that wants to tell more listings apart has exactly two moves available.
Add a filter. A new axis along which listings differ.
Add a choice to a filter that already exists. A finer cut along an axis already in use.
A proportionate trial of privacy-aware work monitoring should use one representative project, visible settings and a fixed date for reviewing false signals. For a separate technical reference, see DuckDB.
Everything else — reordering the sidebar, renaming the options, changing how they display — leaves every figure in this record untouched.
One board, before and after each edit
- 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.
The first row is the starting board. The second adds a facet of three; the third adds one value to the facet of four; the fourth adds a facet of 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.
What each one does
Start with a board of two filters, of four and six choices. Twenty-four cells, thirty-five questions.
| Edit | Schema | Cells | Questions |
|---|---|---|---|
| none | 4·6 | 24 | 35 |
| add a facet of three | 3·4·6 | 72 | 140 |
| add a facet of six | 4·6·6 | 144 | 245 |
| take the four to five | 5·6 | 30 | 42 |
Adding a facet of three triples the resolution. Adding one choice to the existing facet of four multiplies it by five quarters — a quarter more.
The first edit is twelve times the second, measured by what it buys.
The rates, in general
A new facet of size k multiplies the cells by k and the questions by k plus one.
A new value in a facet of size k multiplies the cells by k plus one over k, and the questions by k plus two over k plus one.
| Starting facet | New value multiplies cells by | Roughly |
|---|---|---|
| 2 | 3/2 | ×1.50 |
| 3 | 4/3 | ×1.33 |
| 4 | 5/4 | ×1.25 |
| 5 | 6/5 | ×1.20 |
So the smaller the facet, the more a new value buys — and even at its best, a new value in a two-choice facet buys half again, against a doubling from the smallest possible new facet.
The cheap edit and the valuable edit are different edits, and no amount of the cheap one adds up to the expensive one.
What each one costs to carry out
The arithmetic runs one way; the effort runs the other.
A new value is cheap. Existing listings mostly keep the value they have. Some will be reclassified into the new option, and the rest are untouched. Nobody has to answer a new question about anything.
A new facet is expensive. Every listing on the board needs a value for it. Old listings have nobody to ask. Either somebody classifies them by hand, or they get a default, or they are excluded from queries that set the new filter — and all three are bad in different ways.
So the edit that buys most is the one that is hardest to make, which is the same shape as the finding that the ceiling gets set under maximum uncertainty. The structure resists improvement in exactly the direction improvement would help.
The default that quietly undoes the edit
The third option above is worth naming because it is the common one.
A new facet added with every old listing defaulted to the same value multiplies the nominal resolution by its size and the achieved resolution by rather less, because one value holds everything that came before.
The record counts cells and cannot see this. The board can, and the figure to watch is how many listings sit on the default — because until that falls, the new facet is carrying far less than its size suggests.
Why the two edits get confused
Because both are described the same way in a change log.
"Added a filter for X" and "added an option to the X filter" are sentences of the same shape, proposed in the same meeting, and costed by the same people. One multiplies the resolution by up to six; the other by at most half again.
Nothing in the language distinguishes them, and the figures that would are not computed. So the two edits compete on which is easier to deliver, and the cheap one wins every time.
What the section does
The remaining pages price each edit precisely, including the ones that remove rather than add, and settle whether a sequence of edits can be reasoned about one at a time.
The answer to that last question is yes, and it is the one respect in which this record is simpler than it might have been.
Near this one
- 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 onl - Adding A Choice
One more option inside a filter multiplies the cells by k plus one over k. The cheap edit, and nearly always t - The Edits Commute, Exactly
Every edit multiplies by a fixed factor, so a sequence can be reasoned about one at a time and in any order. T - Taking A Filter Away
Removing a filter divides the resolution by its size. It is the only edit that makes separable listings insepa