Grain

The grain of a result

Subsets are many; their products are few.

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8 notes in this part

How Many Sizes Of Answer Exist

The size of a result is the product of the filters left alone. Count the distinct products for how many coarsenesses a board offers.

Reference

Sixty-Four Ways To Ask, Seven Answers

Six identical filters give sixty-four subsets and seven reachable result sizes, whatever the filters are. The collapse is caused by repetition, not by size.

Analysis

The Twenty-Seven That Do Not Collapse

In twenty-seven schemas every subset of filters produces a distinct result size. All of them have four facets or fewer, and most of them contain a five.

Reference

Two Rungs, Or Thirty-Nine

The ladder of reachable result sizes runs from two rungs to thirty-nine. The schema at the top does not look special from the sidebar.

Reference

Two Times Six, Three Times Four

Result sizes collide because the five facet sizes share factors. One of them shares nothing, and it is why any schema escapes at all.

Analysis

Same Resolution, Different Ladder

Seven schemas resolving one hundred and forty-four listings reach between six and fifteen result sizes. Grain is a third figure.

Reference

Choosing Sizes, Not Just Counts

Two boards with the same filters and the same resolution can differ fivefold in grain. The difference is free and nobody chooses it.

Analysis

Reading The Ladder From A Result

What the next step up or down will return, worked out before the click. The answer is always a facet size, printed on the page.

Reference