The Inca Empire (1400–1532) is one of few ancient civilizations that speaks to us in multiple dimensions. Instead of words or pictograms, the Incas used khipus—knotted string devices—to communicate extraordinarily complex mathematical and narrative information. But, after more than a century of study, we remain unable to fully crack the code of the khipus. The challenge rests not in a lack of artifacts—over 1,000 khipus are known to us today—but in their variety and complexity. We confront tens of thousands of knots tied by different people, for different purposes, and in different regions of the empire. Cracking the code amounts to finding a pattern in history’s knotted haystack.

Using locally available materials such as camelid fleece and cotton, the khipukamayuqs (Quechua for “knot-makers/animators”) encoded administrative data such as census figures and tax allocation in the twisted strings of these ancient spreadsheets. The Inca bureaucrats used these data to keep tabs on the largest empire in the pre-Columbian Americas. We have known for about a century that the accounting khipus follow a base-10 knot scheme (imagine an abacus made out of string). However, these quantitative khipus account for only about two-thirds of the samples remaining today. The remaining third of these devices—the so-called narrative khipus—appear to contain encoded nonnumerical, narrative information, including names, stories, and even ancient philosophies. For those who love puzzles, the narrative khipus are a godsend.

What is so radical about wrapping numbers in knots? Consider how we typically learn to count. In school, counting begins with objects—wooden blocks, Lego pieces, or other toys. Addition and subtraction involve making piles of these objects or tallying with our fingers. Then fingers and blocks turn into two-dimensional formulas, as students are taught a series of mathematical figures, commonly called “ciphers.” As a result, we can lose our ability to appreciate numbers as being represented by anything other than these abstract written symbols. Think about it: Is there anything about the symbol “7” that communicates the meaning of seven? By contrast, the Inca khipu code for seven was a special type of knot, made by wrapping the string around itself to make a series of loops—seven, to be exact.

Then there are the narrative khipus. These might have used numbers as qualitative identifiers for people or ideas—consider how we are each identified by a phone number, social security number, or street address. This raises an important question: When numbers can signify quantities, identities, or some combination of both, how do we know what category of number we are looking at? In other words, might a knot that signals the number “3” reflect a count of 3 pesos, an identifier of a local villager, or perhaps an emerging postal-code system? Some scholars have even suggested that the knots themselves encoded syllabic language.

The search for a narrative “Rosetta khipu” amounts to finding a match between the text of a Spanish document and the knots of twisted strings. Given these complexities, how confident can we be in our ability to learn about the narrative khipus, when they are so radically different from our understandings of communication? We are trained from an early age that mathematics and language are two discrete worlds. The Incas, however, collapsed them into a three-dimensional construct—an achievement of civilizational complexity in the form of narrative cords.