Andean quipus: what we can read and what we cannot
From a quipu we can read the quantity with certainty, but not the subject. How the numerical reading of the knots was proved, and why a narrative reading is still unproven.
Los quipus andinos: lo que sabemos leer y lo que no
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An advanced Spanish reading text about quipus, the knotted cords of the Andes. It separates what is proved, that the knots encode figures in a base-ten positional system, from what is not, that they also record words. It covers how Leland Locke arrived at that reading and checked it against the sums on the top cords, the three knot types and the marking of zero, what is missing before a number can be said to be a number of anything, what sixteenth-century chroniclers report about the quipucamayos, and what happened after the Lima council of 1583 ordered quipus burned. It ends with questions for the reader.
Un quipu es un conjunto de cordeles anudados. De una cuerda principal, gruesa y dispuesta en horizontal, cuelgan decenas o centenares de cuerdas secundarias, y de estas pueden colgar otras. El material suele ser algodón o fibra de camélido. El color, el sentido en que está torcido el hilo y la forma en que cada cuerda se ata a la principal varían de una pieza a otra, y esa variación no parece casual.
Lo que hoy se lee con seguridad en ese objeto son cifras. A comienzos del siglo XX, el matemático estadounidense Leland Locke examinó los ejemplares del Museo Americano de Historia Natural de Nueva York y sostuvo que los nudos codifican dígitos en un sistema decimal posicional: el lugar que ocupa cada grupo de nudos a lo largo de la cuerda indica la potencia de diez, y el número de nudos o de vueltas indica la cifra. Publicó esa lectura en 1912 y la desarrolló en un libro de 1923.
La prueba de que la propuesta era correcta no vino de una teoría, sino de una suma. En muchos quipus hay cuerdas que no cuelgan hacia abajo, sino que salen hacia arriba desde la cuerda principal. Locke comprobó que el número anotado en una de esas cuerdas superiores coincidía con la suma de los números anotados en las que colgaban debajo. Una lectura equivocada no habría producido ese cuadre una y otra vez; la suya sí lo produjo.
Los tres tipos de nudo se distinguen a simple vista. El simple marca las decenas y las potencias mayores; el largo, formado por varias vueltas sobre sí mismo, marca las unidades del dos al nueve; el de ocho marca el uno. El cero no tiene nudo propio: se indica dejando vacío el lugar que le corresponde. Este último detalle es el más llamativo de todos, porque sugiere que quien anudaba manejaba la idea de un lugar vacío con valor.
Hasta aquí, todo son números. El problema es que un número solo no dice de qué. Cien, ¿de qué? ¿De llamas, de costales de maíz, de personas obligadas a tributar? Ese dato tenía que estar en alguna parte, y los candidatos son el color de la cuerda, la torsión del hilo y la forma en que cada cuerda se ata a la cuerda principal. Ninguno de ellos se ha descifrado de forma general, aunque en conjuntos concretos de piezas se han propuesto lecturas parciales.
Los cronistas del siglo XVI describen a los quipucamayos, los especialistas encargados de estos registros, recitando ante los funcionarios españoles genealogías, campañas y asuntos de gobierno con los cordeles en la mano. Ese testimonio es la principal razón para sospechar que en un quipu hay algo más que aritmética. Y es también la razón por la que conviene ser prudente:
About this article
What you'll learn
Cataphora with «es este:», the pair «la primera … la segunda», the article replacing a noun («el de ocho»), «ninguno de ellos», «este último» and lexical chains, plus academic and archival vocabulary.
An advanced Spanish reading text about quipus, the knotted cords of the Andes. It separates what is proved, that the knots encode figures in a base-ten positional system, from what is not, that they also record words. It covers how Leland Locke arrived at that reading and checked it against the sums on the top cords, the three knot types and the marking of zero, what is missing before a number can be said to be a number of anything, what sixteenth-century chroniclers report about the quipucamayos, and what happened after the Lima council of 1583 ordered quipus burned. It ends with questions for the reader.
After reading
Article learning block
Phrases, words, grammar, and quick practice from this text.
Phrases for training
Add useful phrases to SRS or mark them as already known.
a simple vista
newwith the naked eye, at a glance
`A simple vista` means without instruments and, by extension, plainly visible. Its opposites are `con lupa` and `al microscopio`. Keep it apart from `a primera vista`, which is closer to `at first sight` and often hints that the first impression may be wrong.
Constant in popular science writing and in museum labels.
dado con la clave
newto hit upon, to track down
`Dar con` means finding what you were looking for: dar con la clave, dar con la solución, dar con la casa. It is not the same as `dar a` (to look out onto: la ventana da al patio) or `darse cuenta` (to realise).
The natural way to say `find` when the finding is the result of a search.
El estado de la cuestión
newthe state of the question, the current state of knowledge
A set formula of academic writing: the section or paragraph that sums up what is already established and what is not. Near equivalents are `el estado del arte` and `el estado de la investigación`. It often opens an article or precedes a new hypothesis.
One of the load-bearing formulas of academic Spanish.
conviene ser prudente
newit is advisable to, it is worth
Impersonal `conviene` + infinitive gives advice without commanding: conviene ser prudente, conviene distinguir, conviene recordar. With a clause it takes the subjunctive: `conviene que sea prudente`. The tone is markedly softer than `hay que` or `se debe`.
A core way of softening a recommendation in academic and official prose.
Key words
Vocabulary that carries the school-day topic.
el cordel
el cordel
the cord, the thin rope
A `cordel` is a thin strong cord, thinner than a `cuerda` and thicker than a `hilo`. A `cordelería` is a ropemaker's shop. In descriptions of quipus, `cordel` names the thin cords that hang down, while the thick horizontal one is called `la cuerda principal`.
The series `hilo, cordel, cuerda, soga` ranks four very common terms by thickness and helps you pick the most exact one.
anudar
anudados
to knot, to tie in knots
The verb is built on `nudo` (knot) with the pattern a- + base + -ar, like `apuntar` (from punto) and `agrupar` (from grupo). `Cordeles anudados` are knotted cords. Figuratively, `anudarse la garganta` is for the throat to tighten.
The a-…-ar pattern is very productive, so recognising it lets you derive verbs from nouns.
el pleito
pleitos
the lawsuit, the legal dispute
A `pleito` is a legal case between parties, usually a civil one: ganar un pleito, perder un pleito, pleitos coloniales. Colloquially it also means a quarrel. Related forms are `pleitear`, to litigate, and `pleiteante`, a party to a case.
A key word in historical and legal writing in Spanish.
el cuadre
ese cuadre
the tally, the fact that figures agree
`Cuadre` is the result of `cuadrar`, used of figures that come out right: las cuentas cuadran, el cuadre de caja. When they do not, Spanish says `no cuadra` or `hay un descuadre`. In the text it is Locke's totals agreeing with the knots.
Basic vocabulary of accounting, statistics and any checking of data.
el costal
costales de maíz
the sack
A `costal` is a large sack of coarse cloth for grain, flour or potatoes. `Saco` is a close and slightly more general synonym. Hence `meter en el mismo saco`, a set phrase recorded in the dictionary that also circulates with `costal` in place of `saco`, meaning to lump everything together.
A frequent word in writing about farming, markets and storehouses.
el ejemplar
los ejemplares
the specimen, the copy (not `exemplary`)
As a noun, `ejemplar` is one item out of a series: a copy of a book, a specimen of a species, an object in a collection. As an adjective it means something quite different, `exemplary`: `una conducta ejemplar`. Same word, two jobs.
The noun appears constantly in museum, biological and publishing contexts.
Grammar in context
Patterns from the text worth noticing after reading.
`es este:`, a demonstrative that points forward
es este
the state of the question, put plainly, is this:
`Este` normally points back to something already said. Before a colon it does the opposite and announces what is coming: `El estado de la cuestión, dicho sin adornos, es este: de un quipu sabemos leer la cantidad...`. The colon is not incidental; it is the signal that the explanation follows.
A standard way of opening a thesis or a conclusion in academic prose.
`dos afirmaciones … La primera … La segunda`
La primera es que los quipus registran números
the first of those two claims is that quipus record numbers
The text first announces a number (`dos afirmaciones que suelen confundirse`) and then unpacks it with ordinals. These agree with the announced noun: `afirmaciones` is feminine, hence `la primera` and `la segunda` rather than `el primero`. The same machinery works with `dos hipótesis`, `tres motivos`, `cuatro fases`.
It lets you run a long argument without the reader losing count.
`el simple`, `el largo`, `el de ocho`: the article for the noun
el de ocho marca el uno
the figure-of-eight knot marks the one
Having named `los tres tipos de nudo`, the text stops repeating `nudo`: the masculine singular article is enough, plus whatever distinguishes each one, either an adjective (`el simple`, `el largo`) or a `de` phrase (`el de ocho`). The article takes its gender and number from the omitted noun.
It is what lets you list variants of one thing without naming it again on every line.
`ninguno de ellos`: negating after a list
Ninguno de ellos se ha descifrado
none of them has been deciphered
`Ninguno de` + pronoun or plural noun denies the members of a group already named, here the three possible carriers of information. The verb stays singular: `ninguno de ellos se ha descifrado`. Before a masculine singular noun phrase `ninguno` shortens to `ningún` (`ningún dato`, `ningún buen dato`), but it keeps its full form when it stands alone or before `de`.
A very frequent way of closing an enumeration by saying that no item qualifies.
`este último`: pointing at what was just mentioned
Este último detalle
this last detail
`Este último` singles out the item named last, rather than any other in the series. It agrees in gender and number with what it refers to: este último, esta última, estos últimos, estas últimas. Unlike a bare `este`, it makes clear that the most recent mention is meant.
It removes an ambiguity that is very common in the long lists of academic prose.
A lexical chain instead of repeating the term
estos registros
these records
Rather than repeating `quipu` in every paragraph, the text alternates names for the same object: `cordeles anudados`, `una pieza`, `ese objeto`, `estos registros`, `el cordel`. This is lexical cohesion: the chain holds the text together, but it only works if the reader recognises each term as the same referent. A synonym that is too distant breaks the chain instead of carrying it.
In long academic texts this is what keeps repetition of the technical term from smothering the prose.
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