Andean knotted-cord records · the number in the knot

The Knot Says How Many, the Space How Much

An Inka khipu records a number in two separate acts. The shape of a knot fixes a digit; a person's eye never has to guess it. The position of that knot along the cord fixes its power of ten, and reading that means seeing columns, and empty columns, in the spacing. Here is a real cord, decoded straight from the knots. Then the whole open corpus, 110,677 knots, asked how strongly each act actually holds.

Every column but the last is a little bundle of single knots; you just count them. The last column, nearest the free end, is the units, and it is tied differently: a long knot whose turns you count, or, for a lone 1, a figure-eight. That difference is not decoration. It is the one rule that makes the reading start in the right place.

1Why a long knot can never say “one”

A long knot is made by wrapping the cord through a loop several times before pulling it tight; the digit is how many turns you can see. But you cannot wrap once and get a long knot. One turn is just an overhand knot, a different thing. So the code has a built-in hole exactly at the digit 1, which is why the units place needs a second sign, the figure-eight, to fill it.¹ This is not a story about how khipus should work. It is a prediction, and the corpus can be asked whether it is true.

2The units knot really does sit at the far end

If the position of a knot fixes its place value, then the one knot that marks the units, the long knot or figure-eight, should sit at the end of the cord farthest from the top, below all the higher-place bundles. Take every cord that carries at least two knot-columns and exactly one units-type knot, read only the knot shapes and their order down the cord, and check where that units knot lands. Against a null world where the units knot could sit in any of the cord's columns with equal chance, here is what the cords do.

3The digit is objective; the zero is a judgment

Read each digit off the knot shapes, lay the columns out one place after another, and you get a number. Compare it to the number the trained recorders wrote down for the same cord. They agree exactly on most cords. Nearly all of the rest differ for one reason only: the recorder saw an empty column, a place with no knots, and read it as a zero, where the naive left-to-right reading has no way to know a column was skipped.² That gap is the whole interpretive act. The knot's shape is on the cord; the zero is in the spacing, and only a reader who trusts the columns can see it.

4What is not a plain number

Not every cord is a tidy decimal number, and an honest reading has to say how many are not. Of the knotted cords in this corpus, most parse cleanly as a run of decimal digit-columns. The remainder do not: cords with more than one units-type knot, mixed clusters, knots the code has no digit for. Some are damage or recording gaps; some may be the part of the khipu that was never counting at all.³ The decimal reading is strong and it is partial, and the size of the part is itself a fact worth stating.

Honest apparatus

1. The decimal reading, single knots for the higher places and a long knot for the units, with no more than nine to a place, was published by L. Leland Locke (“The Ancient Quipu, a Peruvian Knot Record,” American Anthropologist 14, 1912, elaborated in his 1923 monograph of the almost-same name). Locke states the physical fact directly: a long knot is an overhand knot with the free end passed through the loop once per unit, so a “long knot of one turn” is just an overhand knot, and cannot be a long knot at all. The figure-eight sign reserved for the units digit 1 is the standard modern statement of the convention (Marcia and Robert Ascher, Code of the Quipu, 1981; Manuel Medrano, 2021); it is not named in Locke's 1912 text, and this page treats it as the received reading, not a claim of its own. This page does not argue the convention; it measures how well the corpus obeys it. The 5 long knots recorded with a single turn out of 21,893 are almost certainly recording slips or unusual ties, not counterexamples to the physical fact.

2. The “naive” reader lays columns out contiguously and cannot infer a skipped place, so it reads 5 004 as “54”. That is the point: the difference between the two is exactly the set of numbers whose value depends on reading an empty column as a zero from spacing. The recorders' place assignment (from cluster alignment across the whole khipu) is a trained interpretation, not a mechanical fact, and the residual few per cent that differ for other reasons are cords where the clusters are not simple place-columns at all. None of this is read from the value field for the digit itself.

3. “Clean decimal number” here means every cluster on the cord is a well-formed digit-column (single knots 1–9, a long knot of 2–9 turns, or one figure-eight). Bare cords with no knots are excluded from the clean/not-clean split. The khipu remains, as a whole, undeciphered: the numbers are readable, but what they count, and whatever the many non-numerical khipus record, is not settled. Knot direction (Z vs S) is recorded in the data and has been argued to carry further, binary information; this page reports its raw split () and makes no claim about it.

What is new here, carefully. That khipus are decimal, and that most of them carry readable numbers, is a century old and not in question. What two research passes could not find measured and published in a checkable form is this page's finding 2 and finding 3: the corpus-wide rate at which the units-marking knot actually occupies the units position, set against an explicit chance baseline, and the split of a khipu number into the part the knot's shape fixes and the part the reader's eye must supply. The nearest published figures are consistent with what is measured here. The Khipu Field Guide reports that non-Lockean knot typologies appear on about 12% of all cords (in roughly 80% of khipus), close to the 13.6% of knotted cords that do not read as clean decimal numbers in finding 4; Sabine Hyland (“Knot Anomalies on Inka Khipus,” 2024) finds “nether knots” below the units position on at least one pendant in over 20% of khipus. A 2026 preprint (ALBA Project) reports that 5.4% of knotted cords are incompatible with decimal encoding; it is not peer-reviewed and its derivation is not published in a form I could check, so it is noted, not relied on. Corpus-scale work on khipu sums (Medrano and Khosla, ~74% of khipus; the Khipu Field Guide) is a separate, occupied question, and one this page does not enter.

Source: Open Khipu Repository, born as the Harvard Khipu Database Project and now maintained by the Open Khipu Research Laboratory; see the repository at github.com/khipulab/open-khipu-repository and cite DOI 10.5281/zenodo.18025748. The exact file this page reads is pinned by hash and holds 619 khipus (the snapshot Contreras 2026 also analysed); a later Zenodo release adds more. The data reflect decades of fieldwork by many scholars and, as the repository's own README states plainly, the uneven history of the discipline that produced it. Recording conventions vary between investigators and about a fifth of cords are broken, so a real rate of ambiguous or incomplete cords is expected and is part of what finding 4 measures.