Mathematics of the Incas: Code of the Quipu by Marcia AscherThe Incas of ancient Peru possessed no writing. Instead, they developed a unique system expressed on spatial arrays of colored knotted cords called quipus to record and transmit information throughout their vast empire. The present book is based on a firsthand study of actual quipus that survived the destruction of the Inca civilization. Written by a mathematician and an anthropologist, this book acquaints the reader with the cultural context of the quipus, the problem of interpreting artifacts from another culture, and the place of the quipu-maker in Inca culture. Although no previous mathematical knowledge is assumed, the reader is introduced to the mathematical ideas embedded in the quipus and learns how to make a quipu.
Enhanced with over 125 illustrations, this unusual and thought-provoking study will interest mathematicians, historians, anthropologists, archeologists, and students of folk art with its unique perspective on the way in which pieces of colored string serve to embody a rich, logical, numerical tradition and are, ultimately, a metaphor for the civilization that created them. Preface. Exercises and answers within chapters.
Mathematics of the Incas
By Daniel Cossins. THE Incas left no doubt that theirs was a sophisticated, technologically savvy civilisation. At its height in the 15th century, it was the largest empire in the Americas, extending almost kilometres from modern-day Ecuador to Chile. These were the people who built Machu Picchu, a royal estate perched in the clouds, and an extensive network of paved roads complete with suspension bridges crafted from woven grass. But the paradox of the Incas is that despite all this sophistication they never learned to write.
The motorcycle taxi driver had my number immediately. Every time I stepped out of my hotel in Mancora, there he was offering me a ride. It took longer for me to figure out what he was doing with the colorful cords tied to the handlebars of his machine. He knotted one cord whenever I paid him. Another cord seemed to be unraveling each time. It was a form of double entry accounting; he tied one knot to record payments. The other cord recorded his expenses; a knot was untied for each tank of gas he purchased.
Over the subsequent decades, however, the plate turned out to be the key in decoding ancient Egyptian hieroglyphics, which had for ages persisted as a mystery among scholars. In a perfect world, more artifacts like the Rosetta Stone would be found to help decipher other mysterious and mind-boggling writing systems. When tablets with Olmec writing were unveiled in , nobody had a clue what any of the 62 strange symbols might mean. And these just might be the oldest writing samples found in the Western part of the planet. Another perplexing writing system lurks in Easter Island. When missionaries arrived there in the latter part of the 19th century, they came across several wooden tablets carved with mysterious symbols.
Quipu also spelled khipu , or talking knots ,  are recording devices fashioned from strings historically used by a number of cultures in the region of Andean South America. A quipu usually consisted of cotton or camelid fiber strings. The Inca people used them for collecting data and keeping records, monitoring tax obligations, properly collecting census records, calendrical information, and for military organization. A quipu could have only a few or thousands of cords. Objects that can be identified unambiguously as quipus first appear in the archaeological record in the first millennium AD. They subsequently played a key part in the administration of the Kingdom of Cusco and later Tawantinsuyu , the empire controlled by the Inca ethnic group, flourishing across the Andes from c.
The pendant cords may also have cords known as subsidiaries attached. The type of knot tied and its position on the pendant relative to the top cord records a numeric value. The numeric value of a cluster of single knots is determined by counting the number of knots in the cluster and multiplying it by The quipu were created and maintained as historical records and were kept not only by high officials at the capital of Cuzco —judges, commanders, and important heads of extended families—but also by regional commanders and village headmen—that is, at every level of Inca bureaucracy. About examples of quipu have been discovered.