Quipu

A quipu or khipu (from the Quechua word for a knot) is a record made of cords knotted into a pattern. The cords are cotton or the fiber of camelids such as the llama and alpaca, and the information is in the knots, in their positions, and in the colors, twist and attachment of the cords. The Inca state used khipus for its accounts and censuses, and it is not known to have used any other recording system. Several hundred survive in museums and collections.^[1]

The numbers in a khipu are read, and the rest is debated. In 2018 a convolutional neural network for nanopore signals was named for the device because its authors compared the bumps on a DNA molecule to the knots on an Inca string, and a viewer for its data set carries the name today; see QuipuNet.

The Spanish chroniclers wrote quipu, and the spelling stayed in English for centuries. Khipu follows the modern orthography of Quechua, in which kh is an aspirated k, and the studies cited here use it. A second Inca device for numbers, the yupana or counting board, is known from a drawing in the illustrated chronicle of Felipe Guaman Poma de Ayala of about 1615, and what the board was used for is still argued.^[2]

A khipu hangs from a primary cord, a thicker horizontal cord, with pendant cords falling from it like the strands of a mop. Smaller subsidiary cords can branch from a pendant. Each cord has a color or a pattern of colors, a direction of twist, and a way of being attached to the primary cord, tied from the front or from behind. Each of these is a choice made by the maker, and the choices can in principle carry information.

The knots on a pendant cord record a number in base ten. The position of a knot along the cord gives the power of ten, with the units nearest the free end. Single knots mark tens, hundreds, thousands and tens of thousands, a "long knot" of two to nine turns marks a digit from 2 to 9 in the units position, and a figure-eight knot marks 1 there. An empty stretch of cord marks a zero. A cord with three single knots in the hundreds place, nothing in the tens place and a long knot of four turns at the units reads 304.

The American mathematician L. Leland Locke showed in 1912 that the knots record numbers in this decimal system.^[3] Marcia and Robert Ascher then analyzed the structure of surviving khipus as a mathematical system.^[4] In 2005 Urton and Brezine analyzed 21 khipus from Puruchuco, an Inca administrative center on the central coast of Peru, by computer. They concluded that the archive shows how census and tribute data were combined, changed and passed between levels of accounting.^[5]

Numbers are a part of the content. Whether khipus recorded narrative and names is a question that the surviving evidence answers in a few cases and not in the rest.

In 2018 Medrano and Urton compared a group of six khipus said to have come from a burial in the Santa Valley of Peru with a Spanish census document of 1670 for settlements around San Pedro de Corongo. The census counted 132 tributaries in six ayllus, the clan-like units of Andean society. The khipus are organized into 133 color-coded groups of six cords. The knot values on the first cord of each group add up to the tribute assessed in the document, and the way the first cords are attached, from the front or from behind, divides the tributaries into two halves. The authors suggested that the names of the tributaries may be signed in the colors.^[6]

In 2017 Sabine Hyland of the University of St Andrews reported on two khipus kept by the residents of San Juan de Collata, a village in the Peruvian Andes, which were made in the eighteenth century as letters between local leaders during a revolt against Spanish authority. She counted 95 distinct signs, about the number expected of a logosyllabic system and more than the regional accounting khipus use, and proposed that the three cords at the end of each khipu spell a lineage name. Two names had been read when she published. Her university's announcement called the khipus "the first evidence that the Inkas possessed phonetic writing" and added that research to decipher the rest was continuing.^[7][8]

A different reading, in Gary Urton's book of 2003, treats the physical choices in making a khipu as a binary code, with each choice, such as the direction of spin or the way of attachment, a bit.^[9]

A khipu stores a number in positions along a one-dimensional fiber, and a DNA carrier does the same: a group of hairpins at the first position or the third is present or absent. Passing either one past a sensor in order, one position after another, reads it.

The paper that introduced QuipuNet, by Misiunas, Ermann and Keyser at the University of Cambridge, compares the reading of structures along a DNA carrier, as they pass through a nanopore and give spikes in the current, to "the knots on a string used in the Inca Quipu system", and cites the Aschers' book. The network classified the barcode and the protein bound to it, and raised the number of events that could be analyzed by a factor of five.^[10] The carriers were built by Bell and Keyser in 2016, each with a barcode of up to three bits, each bit a group of DNA hairpins that is present or absent; see DNA barcode (nanopore).^[11] A network trained on the same data in 2024 is called YupanaNet, after the yupana, a counting board of the Inca.^[12]

Molecular Reality Corporation uses the data set as a public test bed. In March 2026 its founder, Kent Kemmish, described a literal version of the idea, a nylon filament with knots tied in it, drawn through a hole about 2 mm wide while the current was recorded; the knots appeared as downward spikes. The demonstration is described in knot sequencing.^[13]

• QuipuNet
• Knot sequencing
• DNA barcode (nanopore)
• Sequence space