Concept

Denominator — where it appears

What a rate is divided by, which decides what the rate means and is rarely stated beside it. Two normalisations of one quantity induce different orderings on the same candidates, and one may preserve a property the other destroys.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

cost per column of the alignmentab / ba1.00 over 2 · 0.67 over 3kitten / sitting0.43 over 7 · 0.43 over 7intention / execution0.56 over 9 · 0.50 over 10gattaca / gactata0.29 over 7 · 0.29 over 7abracadabra / abrocadabro0.18 over 11 · 0.18 over 11unit cost, in edits per columnupper bar: the optimum, divided · lower bar: the best rate

A distance divided by a length is not a rate

Two substitutions turn "ab" into "ba", a distance of two over an alignment of two columns — a rate of 1.00. Deleting, matching and inserting also costs two, over three columns, for 0.67. Both are alignments of the same pair, the second has the better rate, and the optimal alignment is not the one that achieves it. Over every pair of strings up to three characters on three letters, 21% disagree.

tables · Cost
10×20×50×00.40.811.2skew of the join columnratio, logarithmicestimate off byregret, decided partregret, whole planR 4,000, S 40,000, T 2,000 rows, B = 64, M = 4,096 (M/B = 64)every order writes the same output

The join order is a guess

Three tables, two orders, and an estimate of the first intermediate result that assumes the join column is uniform. When the column is skewed the estimate is out by seventy-two times, and the plan chosen on it costs 1.49 times the better one — which sounds tolerable until the shared output is taken away, and the part of the cost the order actually decided turns out to be 43.9 times worse.

applied · Transfer
10⁴10⁵10⁶characters in the collectionshuffled ÷ real, phraseswhat the order is wortha million characters of prose · phrases per characterx1.37 over the sweep

The half of a fall that is the logarithm

Phrases per character on a real collection of essays fall by a factor of 2.34 as it grows. A shuffle of the same characters falls by 1.70. Nearly three quarters of the movement is arithmetic, and no definition of the measure says so.

wrong · Document

Named alongside it

The objects these essays reach for when they reach for this one.

AlignmentAlphabetBlock transferCardinality estimateControlCorpusCost modelDynamic programmingEdit distanceEntropyEstimatorHeavy hitter

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