+++ title = "What the Tablet Was For" description = "Plimpton 322 is dated to a thirty-eight-year window and its purpose has been contested for a century. The field prints both facts at their own confidence, which is an apparatus, and the reason it can is that the loss of context has a date." date = 2026-08-22 draft = false [taxonomies] topics = ["history-of-mathematics"] kinds = ["stated-purpose", "provenance", "institutional-memory"] [extra] tier = "public" schema_type = "Article" canonical = "" hero = "articles/what-the-tablet-was-for/hero.webp" hero_alt = "Old Babylonian clay mathematical tablet in a later conservation sleeve" podcast = "" mechanism = "The question a record was made to answer determines what can be inferred from it, is not recoverable from the record's contents, and is lost by a process that leaves the record itself intact and in use." apparatus = "History of mathematics, which dates an undated artifact by comparative formatting to a narrow window, states its purpose as an open question after a century of argument, and refuses to average the two confidences together." discriminating_test = "Name the purpose being assumed, then look for something outside the record that is consistent with it. Where the only evidence for the purpose is the record itself, the purpose is an interpretation and the inferences resting on it inherit that status." false_friend = "A data-quality defect. Missing values, broken lineage and revision gaps are visible, owned and fixable. A record whose purpose has been lost passes every quality check, because nothing in it is wrong." test = "For each series a decision depends on, try to locate a document written at collection time stating what question it was for. Record what fraction can be sourced to a contemporaneous statement rather than to current usage." symptoms = [ "A field collected for regulatory reporting is used as an economic indicator", "Two teams use the same series and disagree about what a value means", "The definition of a metric is reconstructed from how it currently behaves", "A series has complete lineage, full revision history, and nobody who can say why the threshold in it is where it is", "An inference is defended on the grounds that the data has been used this way for years", ] sources_verified = false [[extra.faq]] q = "How do historians date an object that has no date written on it?" a = "By comparison to objects that do. Plimpton 322 carries no date line, and historians place it between 1822 and 1784 BCE by comparing its scribal formatting against dated tablets from the city of Larsa. That is a thirty-eight-year window derived entirely from how the thing is laid out. The same field, working on the same object, cannot say what it was for." [[extra.faq]] q = "Why does it matter what a dataset was originally collected for?" a = "Because the collection question decides which inferences the numbers support, and it is not visible in the numbers. Plimpton 322's fifteen rows are genuinely compatible with a trigonometric table, a reference list of Pythagorean triples, a teacher's exercise set and a surveying aid. The rows do not choose between them. A series collected to satisfy a regulator and a series collected to measure an economy can be numerically identical and support different claims." [[extra.faq]] q = "How do you test a claim about what a record was for?" a = "Eleanor Robson's argument is the model. She rejects the trigonometric reading of Plimpton 322 not on grounds of unlikelihood but because it depends on ideas absent from the rest of the Old Babylonian mathematical record. The test looks outside the object: is anything else from the same setting consistent with the proposed use? Where the only support for a purpose is the object itself, the purpose is an interpretation." [[extra.faq]] q = "Is this the same as a data quality problem?" a = "No, and the difference is why it survives audits. A quality defect is visible — missing values, a broken join, a revision that did not propagate — and something in the system reports it. A record whose purpose has been lost is complete, consistent and correctly typed. Every check passes. What is missing was never a field. Plimpton 322 is undamaged, correctly dated and fully legible, and nobody knows what it was for." [[extra.faq]] q = "Why is provenance treated separately from authenticity here?" a = "Because both of these objects are genuine. Plimpton 322 reached Columbia through a private collection with no recorded excavation context, and the Rhind Papyrus was bought in the Luxor market around 1858. Neither is in doubt as an object. What the purchases destroyed is findspot, layer and association — the external evidence that would otherwise constrain interpretation — leaving two of the most cited artifacts in the field to be read almost entirely from the inside." +++ Plimpton 322 was written between 1822 and 1784 BCE. That is a thirty-eight-year window on a clay tablet carrying no date at all. Historians reached it by comparing the tablet's scribal formatting against other tablets from the city of Larsa that do carry dates, and the window is narrow enough to name a generation of scribes. Nobody knows what the tablet is for. It has fifteen rows of Pythagorean-triple data, and those rows have been read as a trigonometric table, a reference list, a teacher's set of exercises and a surveying aid. Eleanor Robson's analysis, which won the Mathematical Association of America's Lester R. Ford Award in 2003, argues for the teacher's exercises and against the trigonometric reading. It is an argument with a leading candidate answer. After more than a century of study, it is not a closed question. ## Date and purpose are separate columns Date and purpose do not get averaged into a single statement about how well the tablet is understood. The date is published to a forty-year window because comparative formatting supports that. The purpose is published as contested because the evidence does not choose among the readings. Both appear, at their own strength, in the same paragraph. That separation is the apparatus, and it is the whole of what transfers. ## Robson's argument looks outside the object Her case against the trigonometric reading is not that it is improbable. It is that the reading depends on ideas absent from the rest of the Old Babylonian mathematical record. The move is worth isolating. The fifteen rows fit several purposes, which is the problem rather than the evidence — an object compatible with four uses discriminates between none of them. So the test of a proposed purpose runs outside the record. Is anything else from the same setting consistent with this use? Where the only support for a purpose is the object it is being read from, the purpose is an interpretation, and every inference resting on it carries that status forward. ## A purchase destroyed the context Plimpton 322 entered the record through a private collector's holdings before its bequest to Columbia in the 1930s. There is no recorded excavation context of any kind. The Rhind Mathematical Papyrus was bought by Alexander Henry Rhind in the Luxor market around 1858, and it is the instructive contrast, because that one talks about itself. Its scribe, Ahmes, records that he is copying it in Year 33 of the Hyksos king Apophis, and states that his source was writings made in the time of a 12th Dynasty king some three centuries earlier. So the Rhind Papyrus supplies its own date, its own status as a copy, and the provenance of the material in it. The document it names does not survive. Neither object's authenticity is in question. What the market route removed is findspot, stratigraphic layer and associated objects — the external evidence that would ordinarily constrain what the thing was doing and who was using it. Two of the most cited artifacts in the history of mathematics are therefore dated and interpreted almost entirely from the inside: script, format, content. The corroboration archaeology would normally supply was gone before either reached a museum. ## Every series was built for a question The question a dataset was built for decides what the numbers can be used to claim, and it is almost never recorded anywhere. A field populated to satisfy a regulatory return gets read as an economic indicator. An internal metric specified to trip a limit gets used as a research variable. A customer classification whose boundaries were set to survive an audit becomes a segmentation. In each case the numbers are correct. The schema is documented, the lineage is complete, the revision history is intact, and every automated check passes, because nothing in the record is wrong. What is missing was never a field. The reading survives on usage. A series is treated as measuring what the people currently using it take it to measure, and that reading is reinforced every quarter it produces a plausible number, which is the same evidence a wrong reading produces. ## One loss has a date Archaeology's version of this is legible from a distance. A purchase happened, the context went with it, and the gap is visible to everyone downstream because the acquisition history travels attached to the object. The caveat is part of the citation. The institutional version has no event to point at. The people who specified the field move on. Nothing was written down because it was obvious to everyone in the room at the time. The series continues to arrive on schedule, correctly formed, and arriving on schedule is what a working system looks like. So no moment ever comes when somebody attaches the caveat. The record does not degrade, and the thing that has been lost is not the kind of thing a monitor watches for. By the time two teams disagree about what a value means, the reconstruction has to be done the way Robson does it, from the surrounding record, and most institutions have not kept a surrounding record either. Columbia can date the tablet to within forty years and cannot say what it was for, and the field publishes both facts at their own confidence. A daily file has a timestamp accurate to the millisecond and exactly the same open question. The timestamp is the part that gets audited.