• Choose a category
• All
• Classic-Fiction

Arguably their greatest intellectual feat was the invention of zero. In his classic account Number: The Language of Science, the mathematician Tobias Dantzig called the discovery of zero “one of the greatest single accomplishments of the human race,” a “turning point” in mathematics, science, and technology. The first whisper of zero in the Middle East occurred about 600 B.C. When tallying numbers, the Babylonians arranged them into columns, as children learn to do today. To distinguish between their equivalents to 11 and 101, they placed two triangular marks between the digits: 11, so to speak. (Because Babylonian mathematics was based on 60, rather than 10, the example is correct only in principle.) Curiously, though, they did not use the symbol to distinguish among their versions of 1, 10, and 100. Nor could the Babylonians add or subtract with zero, let alone use zero to enter the realm of negative numbers. Mathematicians in India first used zero in its contemporary sense—a number, not a placeholder—sometime in the first few centuries A.D. It didn’t appear in Europe until the twelfth century, when it came in with the Arabic numerals we use today (fearing fraud, some European governments banned the new numbers). Meanwhile, the first recorded zero in the Americas occurred in a Maya carving from 357 A.D., possibly before the Sanskrit. And there are monuments from before the birth of Christ that do not bear zeroes themselves but are inscribed with dates in a calendrical system based on the existence of zero.

Does this mean that the Maya were then more advanced than their counterparts in, say, Europe? Social scientists flinch at this question, and with good reason. The Olmec, Maya, and other Mesoamerican societies were world pioneers in mathematics and astronomy—but they did not use the wheel. Amazingly, they had invented the wheel but did not employ it for any purpose other than children’s toys. Those looking for a tale of cultural superiority can find it in zero; those looking for failure can find it in the wheel. Neither line of argument is useful, though. What is most important is that by 1000 A.D. Indians had expanded their Neolithic revolutions to create a panoply of diverse civilizations across the hemisphere.

Five hundred years later, when Columbus sailed into the Caribbean, the descendants of the world’s Neolithic Revolutions collided, with overwhelming consequences for all.

A GUIDED TOUR

Imagine, for a moment, an impossible journey: taking off in a plane from eastern Bolivia as I did, but doing so in 1000 A.D. and flying a surveillance mission over the rest of the Western Hemisphere. What would be visible from the windows? Fifty years ago, most historians would have given a simple answer to this question: two continents of wilderness, populated by scattered bands whose ways of life had changed little since the Ice Age. The sole exceptions would have been Mexico and Peru, where the Maya and the ancestors of the Inka were crawling toward the foothills of Civilization.

Today our understanding is different in almost every perspective. Picture the millennial plane flying west, from the lowlands of the Beni to the heights of the Andes. On the ground beneath as the journey begins are the causeways and canals one sees today, except that they are now in good repair and full of people. (Fifty years ago, the earthworks were almost completely unknown, even to those living nearby.) After a few hundred miles the plane ascends to the mountains—and again the historical picture has changed. Until recently, researchers would have said the highlands in 1000 A.D. were occupied by scattered small villages and one or two big towns with some nice stonework. But recent archaeological investigations have revealed that at this time the Andes housed two mountain states, each much larger than previously appreciated.

The state closest to the Beni was based around Lake Titicaca, the 120-mile-long alpine lake that crosses the Peru-Bolivia border. Most of this region has an altitude