Unique, thought-provoking study discusses quipu, an accounting system employing knotted, colored cords, used by Incas. Cultural context, mathematics involved, and even how to make a quipu. Over 125 illustrations.

In an age when computers process immense amounts of information by the manipulation of sequences of 1s and 0s, it remains a frustrating mystery how prehistoric Inka recordkeepers encoded a tremendous variety and quantity of data using only knotted and dyed strings. Yet the comparison between computers and khipu may hold an important clue to deciphering the Inka records. In this book, Gary Urton sets forth a pathbreaking theory that the manipulation of fibers in the construction of khipu created physical features that constitute binary-coded sequences which store units of information in a system of binary recordkeeping that was used throughout the Inka empire. Urton begins his theory with the making of khipu, showing how at each step of the process binary, either/or choices were made. He then investigates the symbolic components of the binary coding system, the amount of information that could have been encoded, procedures that may have been used for reading the khipu, the nature of the khipu signs, and, finally, the nature of the khipu recording system itself—emphasizing relations of markedness and semantic coupling. This research constitutes a major step forward in building a unified theory of the khipu system of information storage and communication based on the sum total of construction features making up these extraordinary objects.

Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is an open textbook; it can be read free online at http://www.opentextbookstore.com/mathinsociety/. Editable versions of the chapters are available as well.

Inka khipus--spun and plied cords that record information through intricate patterns of knots and colors--constitute the only available primary sources on the Inka empire not mediated by the hands, minds, and motives of the conquering Europeans. As such, they offer direct insight into the worldview of the Inka--a view that differs from European thought as much as khipus differ from alphabetic writing, which the Inka did not possess. Scholars have spent decades attempting to decipher the Inka khipus, and Gary Urton has become the world's leading authority on these artifacts. In Inka History in Knots, Urton marshals a lifetime of study to offer a grand overview of the types of quantative information recorded in khipus and to show how these records can be used as primary sources for an Inka history of the empire that focuses on statistics, demography, and the "longue durée" social processes that characterize a civilization continuously adapting to and exploiting its environment. Whether the Inka khipu keepers were registering census data, recording tribute, or performing many other administrative tasks, Urton asserts that they were key players in the organization and control of subject populations throughout the empire and that khipu record-keeping vitally contributed to the emergence of political complexity in the Andes. This new view of the importance of khipus promises to fundamentally reorient our understanding of the development of the Inka state and the possibilities for writing its history.

Documents the epic conquest of the Inca Empire as well as the decades-long insurgency waged by the Incas against the Conquistadors, in a narrative history that is partially drawn from the storytelling traditions of the Peruvian Amazon Yora people. Reprint. 20,000 first printing.

In this exhilarating celebration of human ingenuity and perseverance—published all around the world—a trailblazing Italian scholar sifts through our cultural and social behavior in search of the origins of our greatest invention: writing. The L where a tabletop meets the legs, the T between double doors, the D of an armchair’s oval backrest—all around us is an alphabet in things. But how did these shapes make it onto the page, never mind form complex structures such as this sentence? In The Greatest Invention, Silvia Ferrara takes a profound look at how—and how many times—human beings have managed to produce the miracle of written language, traveling back and forth in time and all across the globe to Mesopotamia, Crete, China, Egypt, Central America, Easter Island, and beyond. With Ferrara as our guide, we examine the enigmas of undeciphered scripts, including famous cases like the Phaistos Disk and the Voynich Manuscript; we touch the knotted, colored strings of the Inca quipu; we study the turtle shells and ox scapulae that bear the earliest Chinese inscriptions; we watch in awe as Sequoyah single-handedly invents a script for the Cherokee language; and we venture to the cutting edge of decipherment, in which high-powered laser scanners bring tears to an engineer’s eye. A code-cracking tour around the globe, The Greatest Invention chronicles a previously uncharted journey, one filled with past flashes of brilliance, present-day scientific research, and a faint, fleeting glimpse of writing’s future.

This book begins by proposing a theoretical model that reconciles orality-literacy studies and media theory in order to avoid the specious dichotomization of societies into those with and those without writing. The more relevant issue is the way in which a given society distributes semiotic functions among the various media that it employs and the forms of economic and political integration within which such media function. This theoretical model then informs a history of the Andean khipu from pre-Columbian times through the first 120 years of the colonial period. The first half of the book examines early Andean media and their socioeconomic and political contexts, culminating with the emergence of Wari and subsequently Inca khipu. The second half of the book documents and analyzes the continued use of khipu by indigenous individuals and communities in their interactions with Spanish officials, chroniclers, and priests. The study corrects many common misconceptions, such as the alleged mass destruction of khipu in the late sixteenth century. Even more importantly, it highlights the dialogue that occurred in the colonial period between the administrative and historiographic discourses of alphabetic Spanish and those of native Andean khipu genres.

Unraveling all the mysteries of the khipu--the knotted string device used by the Inka to record both statistical data and narrative accounts of myths, histories, and genealogies--will require an understanding of how number values and relations may have been used to encode information on social, familial, and political relationships and structures. This is the problem Gary Urton tackles in his pathfinding study of the origin, meaning, and significance of numbers and the philosophical principles underlying the practice of arithmetic among Quechua-speaking peoples of the Andes. Based on fieldwork in communities around Sucre, in south-central Bolivia, Urton argues that the origin and meaning of numbers were and are conceived of by Quechua-speaking peoples in ways similar to their ideas about, and formulations of, gender, age, and social relations. He also demonstrates that their practice of arithmetic is based on a well-articulated body of philosophical principles and values that reflects a continuous attempt to maintain balance, harmony, and equilibrium in the material, social, and moral spheres of community life.