Origami & Folding
what one sheet can do
Series

Two traditions — the series

6 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Folded paper is used ceremonially in Japan400 yrPaper is folded for amusement in Japan980 yrThe thousand cranes897 yrThe pajarita is folded in Spain293 yrPaper folding is taught as geometryyear of the source500100015002000the date generally giventhe oldest source that says somedian overrun 400 years

    Two traditions and a merge

    Ceremonial wrapping, recreational folding and the kindergarten syllabus are three separate lineages with three separate purposes, and they were independent until the late nineteenth century. Told as one continuous tradition, the oldest date in any of them becomes the age of all three.

    part 1 · history
  2. the year the record can put two lineages in the same worldthe later of two surviving sources, which is what a joint claim rests onFolded paper is used ceremoniawith paper is folded for amusement 1680Folded paper is used ceremoniawith the pajarita is folded in spai1793Paper is folded for amusement with the pajarita is folded in spai1793Folded paper is used ceremoniawith the thousand cranes1797Paper is folded for amusement with the thousand cranes1797The thousand craneswith the pajarita is folded in spai1797Folded paper is used ceremoniawith paper folding is taught as geo1838Paper is folded for amusement with paper folding is taught as geo1838The thousand craneswith paper folding is taught as geo1838The pajarita is folded in Spaiwith paper folding is taught as geo1838all 5 are jointly attested only from 1838 — every earlier joint claim is a claim about at most 4 of themeach row is the later of two surviving sources · Paper folding is taught as geometry at 1838 is what the whole set waits for

    When two of them are first attested together

    Every single date in this field is argued about by centuries, and a pairwise one is not. The earliest year at which two claims are both attested is simply the later of their two surviving sources, so it inherits the better-attested half of each pair rather than the worse — and the year at which all five lineages of practice are jointly on the record is 1838, one year from where the same claims are popularly dated together.

    part 2 · history
  3. how many witnesses each claim has5 of 15 have one, and a loss removes them from the record rather than weakening themclaimsurviving sourcesafter one lossPaper is made in China21 leftPaper reaches Japan1nothing attests itPaper is made in Europe32 leftFolded paper is used ceremonially in Japan43 leftPaper is folded for amusement in Japan1nothing attests itThe thousand cranes1nothing attests itThe pajarita is folded in Spain21 leftPaper folding is taught as geometry43 leftOne fold solves a cubic1nothing attests itThe diamond pattern in a crushed cylinder21 leftThe conditions at a flat-foldable vertex32 leftThe dashed-and-dotted diagram notation21 leftThe Miura fold32 leftA five-pointed star from one straight cut1nothing attests itAny straight-line drawing, from one straight cut21 leftby kind of source: artefact 2 · manuscript 2 (1 single) · printed 9 (3 single) · secondary 2 (1 single)the average overrun falls from 357 years to 193 without them, and the median from 201.5 to 184.5 — the effect is two rows, not a tendencywitnesses counted from the record itself · Paper is folded for amusement in Japan and The thousand cranes are the two largest overruns and have one document each

    One lost source and the story changes

    Five of the record's fifteen claims rest on exactly one surviving document. Take those away and the field's most-quoted statistic — how far ahead of its evidence a popular date runs — falls from three hundred and fifty-seven years to a hundred and ninety-three, while the median hardly moves at all. The effect is not a tendency spread through the record; it is two documents, and both of them are single-witness.

    part 3 · history
  4. 200400600800100002004006008001000120014001600mean years ahead of the evidenceresamplingsquoted: 3575%: 15095%: 591spread 13320,000 resamplings of the fifteen entries · five per cent of them fall below 150 and five per cent above 591

    The interval is wider than the number

    The field's most-quoted statistic — how far ahead of its evidence a popular date runs — is the mean of eight positive gaps, and it is quoted as three hundred and fifty-seven years. Resampling the fifteen entries puts ninety per cent of its weight between a hundred and fifty and five hundred and ninety-one. The interval is wider than the number, the middle gap's interval is a fifth as wide, and the difference is the same two documents the leave-one-out found.

    part 4 · history
  5. how many independent sources survive for each claimthe record states this per entry and nothing has ever read the column as a distribution1 source5paper-japan, recreational-folding, senbazuru, beloch, one-cut-star2 sources5paper-china, pajarita, yoshimura, yoshizawa-notation, fold-and-cut3 sources3paper-europe, vertex-conditions, miura-ori4 sources2ceremonial-wrapping, froebela claim resting on one source is one document away from disappearing; five of the fifteen are in that position

    A question the record is too small to answer

    Five of the fifteen claims rest on one surviving source and five on two, and those two counts are exactly what an estimate of the claims that left no source at all is made of. Applied, it says two and a half are missing. Its ninety-five per cent interval runs from fifteen to thirty-one, re-reading a single entry's source count moves it by a fifth, and its independence assumption is false in the one way documents actually fail — which is what makes computing it worth more than declining to.

    part 5 · history
  6. what one document would dono date is invented here — each row asks what the arithmetic would say if one turned upclaimdatedevidenceits gapif a source 200 years earlier turned upceremonial-wrapping12001600400357 → 332 (-25)recreational-folding7001680980357 → 332 (-25)senbazuru9001797897357 → 332 (-25)pajarita15001793293357 → 332 (-25)paper-china1051050nothing changespaper-europe11501056-94nothing changesbeloch19911936-55nothing changesyoshimura19691951-18nothing changesvertex-conditions19891979-10nothing changesyoshizawa-notation19611954-7nothing changesmiura-ori19951970-25nothing changespaper-japan610720110357 → 392 (+35)one-cut-star1776187397357 → 394 (+37)fold-and-cut1922199876357 → 397 (+40)froebel183718381357 → 408 (+51)the statistic is 357 as the record stands; a positive number in the last column is a discovery that makes the field look worse

    Some discoveries would make it worse

    The field's headline statistic averages the claims dated ahead of their evidence. So a document found for a claim that was nearly right removes a small number from a mean of large ones and the average overrun goes up: finding a source two centuries earlier for the kindergarten entry would take the figure from 357 to 408. The four claims where a discovery helps can take twenty-five years off each, and no single document at any date can bring the number to 250.

    part 6 · history

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