A record is not a proof

This site has a habit and the habit is the whole of its method. Every claim is given a test it could fail, every figure is generated from a stated rule, and a generator whose picture would contradict its caption stops the build. The crease patterns are run past four theorems before they are allowed onto a page. The stamp-folding counts are computed rather than quoted, and checked against a published table they never consult.

None of that is available here. A date is not derivable from anything. No figure settles who folded what, and no amount of care in the drawing changes that.

What the checker actually checks #

The record’s checker is a gate, and it is a gate on shape, which is a much weaker thing than a gate on truth. It is worth spelling out exactly what it enforces, because the temptation to let it stand in for more is strong.

Every entry must carry the date the claim is popularly given; the year of the oldest surviving source; the name of that source; what kind of thing that source is, from a closed list running from a surviving artefact down to an inference; and a count of how many independent sources survive. An entry missing any of those is refused. A source of a kind not on the list is refused.

And one substantive refusal: an entry whose popular date is earlier than its own evidence, with nothing said about the gap, is refused — on the grounds that either the gap is the essay’s point and should be stated, or nobody has looked at the entry.

The check fired, which is why it is worth having #

An assertion that has never rejected anything proves nothing, and this site says so often enough that it would be embarrassing not to report the first run.

The check refused two entries. One was the Spanish pajarita, popularly given a Moorish origin around 1500 with the earliest thing anybody can point at being an engraving of 1793 — a gap of nearly three centuries that the entry had simply not mentioned. The other was Froebel, at one year, which is a rounding rather than a dispute and is kept in the table precisely so the check has a case where the answer is that nothing is wrong.

Both are now marked. Neither was wrong before; both were unexamined, which is the failure mode the gate exists for.

Survival is not a fair sample #

The deepest problem with the table is not any entry in it. It is the assumption the whole table rests on, which is that what has come down is representative of what existed.

It is not, and the bias has a direction. Print survives better than manuscript. Court and temple survive better than village. A wealthy patron’s commission survives better than a child’s toy. A practice with a written tradition leaves a written trace and one without leaves nothing whatever, regardless of how widespread it was.

Every one of those pushes the same way: toward over-representing formal, wealthy, documented practice and under-representing ordinary practice. So every date in the record is a lower bound on the practice and an upper bound on nothing, and no amount of care with the sources changes that, because the missing evidence is missing.

The two biases point opposite ways #

There is a consequence of the survival argument that the essay sets up and does not draw, and it bears directly on the field’s headline finding.

Survival is biased toward the formal and the documented, so the record’s dates are systematically late relative to the practice. The popular dates, by the incentive argument, are systematically early relative to the practice. The gap between them is therefore the sum of two errors pulling in opposite directions, and nothing in the table separates one from the other.

So the median overrun of two centuries is not an estimate of how much the folklore over-dates. It is an upper bound on it, inflated by however much the record under-dates — and that second quantity is exactly the one nothing can measure, because it is made of documents that did not survive.

What survives the qualification #

That is a real weakening and it does not touch the direction, which is worth saying because the direction is the finding.

A claim cannot be attested earlier than its earliest surviving source. That is true whatever the survival bias is, so a popular date earlier than the record is a claim with nothing behind it, and the eight forward bars are eight claims in that position regardless of how late the record runs.

What the bias removes is the size. “Recreational folding is attested from 1680 and popularly dated to the tenth century” is a statement about evidence and survives intact. “The folklore over-dates it by seven hundred years” is a statement about the practice and does not, because part of that seven hundred is the record’s own lateness.

So the field’s honest claim is about the record and not about the past, which is the position the essay reaches by argument and which this makes exact: every bar’s left end is a claim, every bar’s right end is a source, and the length between them is not an error bar on anything.

That also says which entries would move most if the bias were quantified. The claims resting on print — the 1797 book, Froebel’s curriculum — sit near the low-bias end, because printing is what survives. The claims resting on a poem or an inference sit at the high-bias end, and those are exactly the two the age essay is load-bearing on.

The comparison that makes this concrete #

This site already has an essay about the limits of a checker, and holding the two side by side is the clearest way to see what is different here.

assertFlatFoldable runs four local conditions and passing all four proves nothing — a pattern can satisfy every vertex test and still fail globally, and closing that gap would decide an NP-hard problem. That is a known, characterised limitation. The checker is a necessary condition, the gap has a name, and the essay can exhibit a pattern that lives in it.

The history checker has no such story. It is not a necessary condition for a date being right, because a well-formed entry with a dated source can be simply mistaken, and there is no example that can be constructed to exhibit the gap. The two look superficially alike and are epistemically nothing alike.

Two kinds of not knowing #

There is a distinction buried in the table that is worth pulling out, because conflating the two is how a reader over-trusts the whole thing.

The first is uncertainty about a date: the source says 1797, and the practice it describes may be older. That kind is bounded and well behaved. It has a direction — earlier, never later — it has a floor at the source, and the essays can and do say so.

The second is uncertainty about the sample: there may be a whole practice, in a whole region, over a whole century, of which nothing at all survives. That kind is unbounded and badly behaved. It has no direction, no floor, and no way to be reasoned about from inside the table, because the table is made of the things that survived.

Every entry here carries the first kind and is silent about the second. The silence is not an oversight; there is nothing to say. But a reader who takes the marked gaps as the full extent of the uncertainty is reading only the tractable half.

Which claims here are weakest #

Naming them is more useful than a general disclaimer, and the figure does it by construction.

Five entries rest on a single surviving source: the arrival of paper in Japan, folding for amusement, the thousand cranes, Beloch’s fold, and the one-cut star. Of those, two are the load-bearing dates in the essay about the age of the subject — Saikaku’s poem of 1680, and the 1797 book.

That is an uncomfortable dependency and it should be uncomfortable. The claim that recreational folding is not attested before the late seventeenth century rests on a poem. If a manuscript turns up tomorrow, the claim moves, and nothing in this repository would notice.

A single source is not a weak source #

The five single-source entries deserve one qualification, because “resting on one source” is often read as “shaky” and that is not quite the claim.

A single source can be excellent. A printed book with a date, a publisher and surviving copies is strong evidence for what it says, whether or not a second one exists. What a single source cannot do is corroborate: there is no independent check on it, so an error, an invention or a copyist’s slip in that one document propagates into everything downstream with nothing to catch it.

So the count in the figure is not a quality score. It is a measure of how much of the claim would move if one document turned out to be unreliable — which is the question that matters when a chronology is being assembled out of a dozen documents and used to date a subject.

The one that is secondary #

Worth separating out is the one-cut star, because it is the only entry whose source is a secondary account and the difference matters.

The Betsy Ross story — that a five-pointed star was cut from a folded sheet in a Philadelphia workshop in 1776 — has as its earliest source an account given in 1873 by a descendant of the family, ninety-seven years after the event. That is not a primary source; it is somebody reporting what they were told.

The generator marks it as such and the record’s kind field exists for exactly this. A ninety-seven-year gap between event and first telling, from an interested party, is a specific and well-understood kind of weak evidence, and filing it beside a printed book with a publication date would flatten a distinction that is the whole point.

What would change a date here #

A useful discipline, and one this site applies to its computational claims as a matter of routine, is to state in advance what would falsify a thing. It is harder here and it is not impossible.

The recreational-folding entry would move on any dated Japanese source before 1680 describing folding for amusement — a diary, an inventory, an illustration. The senbazuru entry would move on any surviving copy or reference to an earlier printing. The pajarita entry would move on a dated European depiction before 1793. The Beloch entry would move on any earlier publication connecting a folded line to a common tangent.

Each of those is a specific object that could exist. None of them is checkable by anything in this repository, and all of them are the sort of thing that turns up in archives every year.

What a computable field looks like beside this one #

There is a version of the history field that would have been easy to write and would have been dishonest, and it is worth naming so the difference is visible.

It would have been a timeline. Dated events, arranged along an axis, drawn attractively, and completely unfalsifiable — every claim on it looking exactly as solid as every other, with no way for a reader to tell the 1797 printing date from the 1776 anecdote. It would have passed every gate this site has, because nothing here checks prose against reality.

What was built instead is narrower and the narrowness is the point: the figures plot the structure of the evidence rather than the events. A bar runs between two dated sources. A dot count is a count of surviving documents. A kind is a classification of what sort of object is being relied on. None of that asserts what happened, and all of it is checkable.

The one thing this field can genuinely settle #

There is a class of historical claim this site can dispose of completely, and it is worth being clear about it because the essay is otherwise unrelieved.

When a claim is about what a construction does, rather than about who did it, it is fully checkable and the checking is exact. Whether the traditional five-fold star comes out regular is not a question about 1776; it is a question about geometry, and it has an answer to a part in a million million. Whether Haga’s fold gives exact thirds is not a question about a classroom in Japan; it is arithmetic. Whether the pattern in a buckled cylinder satisfies the flat-folding theorems is not a question about who noticed first.

So the field splits cleanly. Claims about what are as solid as anything on this site. Claims about who and when are as good as their sources, and the sources are named so a reader can tell which kind they are reading.

The rule the field runs under #

Out of that comes the rule the field was built to, and it is the one thing here that transfers to any other site attempting the same thing.

A history figure draws something that is computed, or it does not get drawn. Three kinds qualify: the shape of the evidence, as above; a historical construction re-run, where the arithmetic is exact and modern — Haga’s thirds, Beloch’s tangency, the star’s regularity; and a claim about the mathematics that happens to be historical in framing, like the buckling pattern being the same pattern somebody later designed, which is settled by building both.

A date on an axis with nothing computed about it does not qualify. That is a stricter rule than the field needs and it was adopted because the alternative has no floor.

Why the honest version is still worth building #

Given all of that, the reasonable question is whether the field should exist.

It should, for a reason that has nothing to do with completeness. A reader arriving at this subject has already been told a history, and that history is wrong in specific, repeated, checkable ways — dated too early, attributed to the wrong people, and merging separate traditions into one. Saying nothing leaves the wrong version in place, and the wrong version does damage: it makes the subject look older and more settled than it is, and it hides the fact that almost everything mathematical here happened within living memory.

Correcting that does not require certainty about what happened. It requires only showing that the confident version is not supported, which is a much weaker claim and one the evidence can carry.

What this costs #

The rule has a price and the price is real: there are things worth saying about this subject’s history that cannot be said in a figure, and they either go in the prose unillustrated or they do not go in at all.

The essays here carry more unillustrated argument than anywhere else on this site for that reason. That is a departure from the site’s founding invariant, which is that an essay exists because a figure explains something better than prose can, and it is a deliberate one. A history field that manufactured figures to meet the quota would be worse than one that admits the medium is a poor fit.

The honest summary #

Put plainly, so that a reader can calibrate: the claims in this field are as good as the sources named and no better, the sources are named on every entry, five of the fifteen are single-source, one is a secondary account from a partisan ninety-seven years late, and the whole table sits on top of a survival process that is biased in a known direction and by an unknown amount.

Everything else on this site is re-derived on every build. This is not, and no future phase will change that, because there is nothing to change it to.

Where this goes next #

This closes the attribution ladder. Below it, nothing here is as old as it sounds is the record read as a whole, the name is not the date is the same compression inside the mathematics, and fifty years in the wrong language is the one case where a result was neither lost nor rediscovered but simply unread.

The generalisation worth carrying out of the field: a check on the form of a claim is not a check on the claim, and the two are easy to confuse precisely because the first one feels like diligence. Every table on this site that validates its own schema is in the same position, and this is the field where the difference is impossible to hide.