When the Yale University history lecturer Hiram Bingham III encountered the ruins of Machu Picchu in Peru 100 years ago, on July 24, 1911, archaeologists and explorers around the world (including Bingham himself) were stunned, having never come across a written reference to the imperial stone city. Of course, the absence of such historical records was in itself no great surprise. The Inca, a technologically sophisticated culture that assembled the largest empire in the Western Hemisphere, have long been considered the only major Bronze Age civilization that failed to develop a system of writing—a puzzling shortcoming that nowadays is called the "Inca Paradox."
The Incas never developed the arch, either—another common hallmark of civilization—yet the temples of Machu Picchu, built on a rainy mountain ridge atop two fault lines, still stand after more than 500 years while the nearby city of Cusco has been leveled twice by earthquakes. The Inca equivalent of the arch was a trapezoidal shape tailored to meet the engineering needs of their seismically unstable homeland. Likewise, the Incas developed a unique way to record information, a system of knotted cords called khipus (sometimes spelled quipus). In recent years, the question of whether these khipus were actually a method of three-dimensional writing that met the Incas' specific needs has become one of the great unsolved mysteries of the Andes.
No one disputes that the Incas were great collectors of information. When a battalion of Spanish conquistadors, led by the ruthless Francisco Pizarro, arrived in 1532, the invaders were awed by the Inca state's organization. Years' worth of food and textiles were carefully stockpiled in storehouses. To keep track of all this stuff, the empire employed khipucamayocs, a specially trained caste of khipu readers. The great 16th-century Spanish chronicler Pedro Cieza de León recalled that these men were so skilled that "not even a pair of sandals" escaped their annual tallies. The Spaniards, who were no slouches themselves in the bureaucracy department—Pizarro's landing party included 12 notaries—observed that the Incas were remarkably skilled with numbers. For many years during the 16th century, says Frank Salomon, a professor of anthropology at the University of Wisconsin, Inca khipucamayocs and Spanish accountants would square off in court during lawsuits, with the khipu numbers usually deemed more accurate.
Individual khipus seem to have varied widely in color and complexity; most of the surviving examples generally consist of a pencil-thick primary cord, from which hang multiple "pendant" cords. From those pendants hang ancillary cords called "subsidiaries." One khipu has more than a thousand subsidiary cords. Sixteenth-century eyewitness accounts describe khipucamayocs studying their khipus intensely to access whatever details had been recorded on them. According to Spanish chronicles of the 1560s and 1570s, some khipus appeared to contain information of the sort that other cultures have typically preserved in writing, such as genealogies and songs that praised the king. One Jesuit missionary told of a woman who brought him a khipu on which she had "written a confession of her whole life."
The Spaniards' institutional response to this singular accounting system, originally benign, shifted in 1583, when Peru's nascent Roman Catholic church decreed that khipus were the devil's work and ordered the destruction of every khipu in the former Inca empire. (This was the heyday of the Spanish Inquisition, and the church was making a major push to convert natives from their pantheistic state religion.) By the middle of the 17th century, Spanish accounts, the only historical sources available from that time, began to cast doubt on the idea that the khipus had ever been "read" like texts. Instead, the knots on khipus came to be viewed as mnemonic prompts analogous to the beads on Catholic rosaries, cues that supposedly had helped the khipucamayocs recall information that they had already memorized. Some scholars argued that a khipu could have only been understood by the same khipucamayoc who'd made it. Andean cultures secretly continued to use knotted cords to record information well into the 20th century, but the links between modern cords and Inca khipus aren't clear. What's certain is that no one in recent history has been able to fully interpret an Inca khipu.
The conquerors' mnemonic theory held sway for three centuries, and was buttressed in 1923, when the anthropologist L. Leland Locke analyzed 42 khipus at the American Museum of Natural History in New York City. Locke demonstrated how the knots represented the results of tabulations. These figures were grounded in the base-10 decimal system (tens, hundreds, thousands), and so were analogous to the beads on an abacus. Despite the evidence from 16th-century eyewitness accounts, the academic community accepted the hypothesis that the Inca, who had built the world's largest highway system and eradicated hunger in an empire of more than 10 million people, never managed to express their thoughts in written form.
In 1981, however, the husband-and-wife, archeologist-and-mathematician team of Robert and Marcia Ascher put the Inca Paradox into doubt. By closely analyzing the position, size, and color of the knots in 200 khipus, they demonstrated that about 20 percent of them showed "non-arithmetical" properties. These cords, the Aschers argued, seemed to have been encoded with numbers that might also represent other information—possibly some form of narrative.
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