The absence of modern-day calculators did not stop ancient cultures from performing extraordinary feats of mathematics. The ancient Greeks kept count with abaci, frames with rods or grooves for moving beads that represent numbers. People living in Congo’s Ishango region 20,000 years ago etched notches into bones to keep track of lunar cycles, not unlike the tally sticks that remained popular in Europe well into the Middle Ages.
The most unusual manual counting device may well be the quipus used by various Andean communities in South America prior to the arrival of the Spanish and Portuguese conquistadors during the Age of Exploration. Derived from the Quechuan word for “knot,” quipus were collections of (usually cotton) strings that could be tied into knots, with each string marking a separate category of data, and different types of knots representing different numbers.
A quipu could be used to count a variety of things, from the number of people living in a particular village to the amount of taxes that village owed to their local overlords, not to mention calendar cycles. They were also used by a variety of cultures, from the Caral-Supe civilization, which thrived during the third millennium B.C.E., to the continent-spanning Inca Empire and its predecessors.
An Inca quipu attached to a wooden frame (1430-1532 B.C.E.). Photo: Werner Forman/Universal Images Group/Getty Images.
Although counting with knots may seem alien and impractical to people living in the 21st century, using a quipu isn’t as confusing as it appears. Because the strings are arranged vertically, numeric values were arranged from top to bottom, rather than right to left. The highest values appear at the top, and get smaller as one moves to the lower end of the string. Knots at the top represent values of 10, 100, 1,000, and 10,000, while knots in the middle of the strings represent values of two through nine. Lastly, knots at the bottom of the string represent a value of one.
The way in which these knots were tied, and the specific values they represented, varied from culture to culture. The Incas, for example, used a decimal counting system and relied on types of knots, the distance between knots, and the colors of the strings to help identify different categories of data recorded on a single quipu, including data pertaining to different jobs or genders.
Although the quipu was widely used in the pre-Columbian Andes, this did not mean that every member of society could read one. As anthropologist and documentary filmmaker Kim MacQuarrie explained, only a small group of learned, upper-class individuals knew how to read the information recorded on quipus, much less record information themselves. Among the Inca, these individuals were known as “quipucamayocs,” and they journeyed from village to village to collect the data requested by the governments they represented—a practice that allowed complex civilizations like the Inca to grow as large as they did.
Illustration of a Peruvian quipu. Photo: Getty Images.
As with many technologies left behind by pre-Columbian cultures, many aspects of the quipu’s origin and usage remain shrouded in mystery. There is, for example, heated debate among scholars about whether the knots constituted a semasiographic writing system (symbolic and disconnected from speech, like music notes or numerals) or a phonetic system (representative of speech, like ideograms). In 2015, anthropologist Sabine Hyland argued that quipus from modern-day Peru possessed a phonetic function, though her interpretation has yet to prove definitive.
The oldest-known quipus date back to more than 5,000 years ago. The devices remained in use until the arrival of the first Europeans, who pushed their own writing and numeral systems onto the continent’s native population. Quipus, like so many other age-old traditions, were seen as heretical by Christian missionaries and destroyed, though surviving specimens continue to be cherished—and, occasionally, used—by contemporary Indigenous groups.
Cecilia Vicuna, Brain Forest Quipu (2022). Courtesy Tate Modern.
Quipus continue to inspire contemporary Andean American art. Chilean poet and artist Cecilia Vicuña, for example, began creating quipus when she was still a teenager. Today, her art installations, often paired with archeological exhibitions, draw inspiration from traditional quipus to stage a dialogue between Chile’s present and its colonial past, including the disappearing language of her ancestors.
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