Positional decimal in knots
verified
Quipus encode numbers positionally in base ten. A pendant cord carries clusters of knots at levels corresponding to units, tens, hundreds and so on, with position along the cord giving the power of ten. The reading was established by L. Leland Locke in a 1912 paper, extended in his 1923 American Museum of Natural History volume, and confirmed repeatedly since — including by checking that subsidiary cords sum to their totals. It remains the only undisputed decipherment of any part of the quipu record.
verified
Three knot types carry the encoding: a long knot with turns equal to the digit for units, a figure-eight knot for the digit one, and simple knots elsewhere. Absence of a knot at a level is a zero — a genuine positional zero, expressed as empty space.
That last point deserves emphasis. A positional system needs a way to say “nothing in this place”, and the Inca solution — leave the position bare — is both elegant and unambiguous, because position on a cord is physically fixed. Compare the Maya, who invented a written zero glyph independently. Two American civilisations, two solutions to the same problem, neither derived from the Old World.
What quipus were for
verified
The great majority of surviving quipus are administrative: census figures, tribute and storehouse accounts, labour obligations. Spanish colonial sources describe quipu-keepers (quipucamayocs) reading such records aloud, and in some cases their testimony was accepted in colonial courts.
verified
Inca administration was itself organised decimally, in units nominally of 10, 100, 1,000 and 10,000 households with officials at each level. The notation and the bureaucracy share a base, which is what one would expect of a system built for administration.
This is a sharp contrast with most traditions on this site. Quipu numeracy is not symbolic or liturgical; it is an instrument of state. It belongs here because it demonstrates something the rest of the corpus can obscure: a sophisticated numerical system need have no mystical dimension at all.
Do some quipus encode language?
disputed
A minority of quipus do not parse as numbers. Whether these encode narrative, names or language in some non-numeric way is an active and genuinely unresolved research question. Colonial sources refer to quipus recording histories and songs, which is suggestive but not decisive, since a mnemonic aid to a memorised text is not the same as a script.
exploratory
Specific decipherments of narrative quipus have been proposed and none has been generally accepted. The corpus is small, provenance is often poor, and there is no bilingual. This is an open problem, not a solved one, and it should be reported that way.
The site grades this as genuinely open rather than as a failed claim — the same treatment given to the 432,000 convergence. Not every unresolved question is a bad one.
The yupana
verified
The yupana, a compartmented counting board, is depicted in Guaman Poma's early seventeenth-century chronicle and survives archaeologically. That it was a calculating device is not in doubt.
disputed
How it worked is. Several reconstructions have been proposed — decimal, and Fibonacci-based schemes among them — and none is established. The Fibonacci proposals in particular are modern reconstructions fitted to the compartment layout, not readings of any source.
The pattern is familiar from sacred geometry: an artefact survives, its documentation does not, and reconstructions multiply. The honest position is that the Inca certainly calculated, that the yupana was certainly used for it, and that the method is not recoverable from what survives.
Maya Numerics
The other American positional system, with an independently invented written zero.
Aztec & Mexica Numerics
Mesoamerican calendrical mathematics for comparison.
Numeral Systems
How the world’s traditions encode number in physical media.
Claims That Fail
Why the Fibonacci yupana reconstructions are graded as they are.
Cite this page
Formatted references for this page. The evidence grade is part of the claim — when quoting a graded statement, carry the grade with it.