Origami & Folding
what one sheet can do
Concept

Identifiability — where it appears

Whether the evidence in hand can distinguish the answers a question allows. A record can support a statistic and still not support a third digit of it, and saying which of the two is the case is a different task from computing the number.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

what the outline and the thickness leave open, and what the order closesprofilesambiguousthe order settlesand does not3 creases on 12ths69166103 creases on 16ths1844712354 creases on 12ths23371692the last column is patterns that fold to the same object, so no better photograph reaches them

The order does not name it either

A photograph of a folded model carries an outline and a layer count, and that is not enough to recover the pattern. Hand the observer the layer order as well — everything the object physically is — and most of the ambiguity goes. Most. What is left are pairs of genuinely different crease patterns that fold to the same object, which no better photograph reaches.

flat-folding · Inverse problem 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.

history · Two traditions 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.

history · Two traditions 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.

history · Two traditions

Named alongside it

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

AttestationDocumentary recordExpected-valuePrimary sourceIndependent discoveryFolded stateIndependenceInverse problemLayer orderingProfileStacking

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