Algorithms & Data Structures
the bound is a claim, and it is checkable
Concept

Logarithm — where it appears

The factor that appears inside a measure without being part of its definition. Where a quantity is the length divided by a logarithm of the length, a per-character rate falls as the object grows for reasons of counting rather than of content, and a control is what separates the two.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

① prose144,617 chars12 docs · median 12,335① code106,283 chars8 docs · median 13,150① revisions75,658 chars10 docs · median 7,774② essays1,004,822 chars82 docs · median 12,335② captions549,210 chars2,214 docs · median 230② history174,282 chars14 docs · median 12,963① the first freeze · ② the second6 parts

A million characters of the same thing

Every measurement this collection has published about real text was taken on twenty-four thousand characters, because the phrase count was quadratic. It is linear now, so here is the same corpus at forty times the size — and what forty times does to its own numbers.

text · Document 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.

AlphabetControlCorpusEntropyPhrase countRepetitionRun countScaleDenominatorDocument collectionIndex sizeShuffle

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