In Mesoamerica, timekeeping provided the stimulus that accounting gave to the Middle East. Like contemporary astrologers, the Olmec, Maya, and Zapotec believed that celestial phenomena like the phases of the moon and Venus affect daily life. To measure and predict these portents requires careful sky watching and a calendar. Strikingly, Mesoamerican societies developed three calendars: a 365-day secular calendar like the contemporary calendar; a 260-day sacred calendar that was like no other calendar on earth; and the equally unique Long Count, a one-by-one tally of the days since a fixed starting point thousands of years ago. Establishing these three calendars required advances in astronomy; synchronizing them required ventures into mathematics.

  The 260-day ritual calendar may have been linked to the orbit of Venus; the 365-day calendar, of course, tracked the earth’s orbit around the sun. Dates were typically given in both notations. For example, October 12, 2004, is 2 Lamat 11 Yax, where 2 Lamat is the date in the ritual calendar and 11 Yax the date in the secular calendar. Because the two calendars do not have the same number of days, they are not synchronized; the next time 2 Lamat occurs in the sacred calendar, it will be paired with a different day in the secular calendar. After October 12, 2004, in fact, 2 Lamat and 11 Yax will not coincide again for another 18,980 days, about fifty-two years.

  Mesoamerican cultures understood all this, and realized that by citing dates with both calendars they were able to identify every day in this fifty-two-year period uniquely. What they couldn’t do was distinguish one fifty-two-year period from another. It was as if the Christian calendar referred to the year only as, say, ’04—one would then be unable to distinguish between 1904, 2004, and 2104. To prevent confusion, Mesoamerican societies created the third calendar, the Long Count. The Long Count tracks time from a starting point, much as the Christian calendar begins with the purported birth date of Christ. The starting point is generally calculated to have been August 11, 3114, B.C., though some archaeologists put the proper date at August 10 or 13, or even September 6. Either way, Long Count dates consisted of the number of days, 20-day “months,” 360-day “years,” 7,200-day “decades,” and 144,000-day “millennia” since the starting point. Archaeologists generally render these as a series of five numbers separated by dots, in the manner of Internet Protocol addresses. Using the August 11 starting date, October 12, 2011, would be written in the Long Count as 12.19.18.14.4. (For a more complete explanation, see Appendix D.)

  Because it runs directly from 1 B.C. to 1 A.D., the Christian calendar was long a headache for astronomers. Scientists tracking supernovae, cometary orbits, and other celestial phenomena would still have to add or subtract a year manually when they crossed the A.D.-B.C. barrier if a sixteenth-century astronomer named Joseph Scaliger hadn’t got sick of the whole business and devised a calendar for astronomers that doesn’t skip a year. The Julian calendar, which Scaliger named after his father, counts the days since Day 0. Scaliger chose Day 0 as January 1, 4713, B.C.; Day 1 was January 2. In this system, October 12, 2011, is Julian Day 2,455,847.

  The Long Count calendar began with the date 0.0.0.0.0.* Mathematically, what is most striking about this date is that the zeroes are true zeroes. Zero has two functions. It is a number, manipulated like other numbers, which means that it is differentiated from nothing. And it is a placeholder in a positional notation system, such as our base-10 system, in which a number like 1 can signify a single unit if it is in the digits column or ten units if it is in the adjacent column.

  That zero is not the same as nothing is a concept that baffled Europeans as late as the Renaissance. How can you calculate with nothing? they asked. Fearing that Hindu-Arabic numerals—the 0 through 9 used today—would promote confusion and fraud, some European authorities banned them until the fourteenth century. A classic demonstration of zero’s status as a number, according to science historian Dick Teresi, is grade point average:

  In a four-point system, an A equals 4, B equals 3, and so on, down to E, which equals 0. If a student takes four courses and gets A’s in two but fails the other two, he receives a GPA of 2.0, or a C average. The two zeroes drag down the two A’s. If zero were nothing, the student could claim that the grades for the courses he failed did not exist, and demand a 4.0 average. His dean would laugh at such logic.

  Without a positional notation system, arithmetic is tedious and hard, as schoolchildren learn when teachers force them to multiply or subtract with Roman numerals. In Roman numerals, CLIV is 154, whereas XLII is 42. Maddeningly, both numbers have L (50) as the second symbol, but the two L’s aren’t equivalent, because the second is modified by the preceding X, which subtracts ten from it to make forty. Even though both CLIV and XLII are four-digit numbers, the left-hand symbol in the first number (C) cannot be directly compared with the left-hand symbol in the second (X). Positional notation symbols take the aggravation out of arithmetic.

  Stirling’s stela in Tres Zapotes bore a Long Count date of 7.16.6.16.18. The implication is that by 32 B.C. the Olmec already had all three calendars and zero to boot. One can’t be sure, because the date does not include a zero or a reference to the other calendars. But it is hard to imagine how one could have a Long Count without them. Tentatively, therefore, archaeologists assign the invention of zero to sometime before 32 B.C., centuries ahead of its invention in India.

  Discovered in 1975, this prone, disemboweled man was carved onto the stone threshold of a temple in San José Mogote, near the city of Oaxaca. Between the corpse’s feet is the oldest certainly dated writing in the Americas: two glyphs (shaded in drawing) that probably represent his name, 1-Earthquake. The ornate scroll issuing from his side is blood. According to Joyce Marcus, the first archaeologist to examine this bas-relief, the Zapotec words for “flower” and “sacrificial object” are similar enough that the flowery blood may be a visual pun.

  (Illustration Credit 7.2)

  How long before 32 B.C.? The carved cadaver in San José Mogote may give a hint. In Mesoamerican cultures, the date of one’s birth was such an important augury of the future that people often acquired that day as their name. It was as if coming into the world on New Year’s Day were such a sign of good fortune that children born on that day would be named “January 1.” This seems to have been the case for the man whose death was celebrated in the San José Mogote temple. Between his feet are two glyphs, one resembling a stovepipe hat with a U painted across the front, the other looking vaguely like a smiling pet monster from a Japanese cartoon. According to Marcus, the Michigan anthropologist, the glyphs correspond to 1-Earthquake, the Zapotec name for the seventeenth day of the 260-day sacred calendar. Because the carving depicts a man instead of an event, the date is generally thought to be the dead man’s name. If so, 1-Earthquake is the first named person in the history of the Americas. Even if the date is not a name, the two glyphs indicate that by 750 B.C., when the slab was carved, the Zapotec were not only on the way to some form of writing, but had also assembled some of the astronomical and mathematical knowledge necessary for a calendar.

  To judge by the archaeological record, this development took place in an astonishingly compressed period; what took the Sumerians six thousand years apparently occurred in Mesoamerica in fewer than a thousand. Indeed, Mesoamerican societies during that time created more than a dozen systems of writing, some of which are known only from a single brief text. The exact chronology of their evolution remains unknown, but could be resolved by the next object that a farmer discovers in a field. The earliest known Olmec writing, for example, is on a potsherd from Chiapas that dates from about 300 B.C. For a long time nobody could read it. In 1986 a workcrew building a dock on the Acula River in Veracruz pulled out a seven-foot stela covered with Olmec symbols. Thought to have been written in 159 A.D., the twenty-one columns of glyphs were the first Olmec text long enough to permit linguists to decipher the language. Two linguists did just that in 1993. The stela recounted the rise of a warrior-king named Harvest Mountain Lord who celebrated his ascension to the t
hrone by decapitating his main rival during the coronation. This information in hand, the linguists went back to the writing on the potsherd. Disappointingly, it turned out to be some banal utterances about dying and cutting cloth.

  FROM 1-EARTHQUAKE TO 8-DEER

  The development of writing in Zapotec society went hand-in-hand with growing urbanization. In about 500 B.C., San José Mogote seems to have transplanted itself to Monte Albán, in the middle of the buffer zone. About half an hour by bus from Oaxaca City, Monte Albán is today a decorous sprawl of walls and pyramids enveloped by a lush lawn (this last is an import from Europe; lawn grass did not exist in the Americas prior to Columbus). Arriving tourists are hailed by “guides” with backpacks full of phony ancient figurines and ethnically incorrect souvenirs of Mexica drawings. Their ministrations do not diminish the lonely dignity of the ruins. Monte Albán is atop a steep, 1,500-foot hill that overlooks the valley of Oaxaca. The Zapotec reconfigured the entire hill to build the city, slicing out terraces and platforms. By leveling the entire summit, they created a fifty-five-acre terrace half the size of the Vatican. At its zenith, Monte Albán housed seventeen thousand people and was by a considerable margin the biggest and most powerful population center in Mesoamerica.

  The rationale for its construction is the subject of yet another lengthy archaeological dispute. One side proposes that Monte Albán formed because maize agriculture allowed the Oaxaca Valley’s population to grow so much that the rural villages naturally clustered into something resembling cities. For most of its history Monte Albán was thus a huge village, not a true city, and certainly not a hierarchical state. Others argue that warfare had grown so devastating, as shown by the destruction of San José Mogote, that the main valley chiefdoms formed a defensive confederation headquartered at Monte Albán. Yet a third theory is that the Zapotec of Monte Albán—not the Olmec of La Venta—consolidated to form North America’s first imperialist power, an aggressive state that subjugated dozens of other villages.

  Among the strongest evidence for the last view are the nearly three hundred carved stone slabs at Monte Albán that depict slain, mutilated enemies: the rulers, Marcus believes, of communities conquered by Monte Albán. Some of the stones are labeled with enemy names, as with the unfortunate 1-Earthquake. These may commemorate victories in Monte Albán’s grinding battle for supremacy with its local rival, San Martín Tilcajete, in the southern arm of the Central Valley. When San José Mogote founded Monte Albán, Tilcajete responded by gathering people from its surrounding villages, doubling in size, and erecting its own ceremonial buildings. War was the inevitable result. Monte Albán sacked Tilcajete in about 375 B.C. Undiscouraged, Tilcajete rebuilt itself on a better defensive position and acquired larger armies. When it again became a threat, Monte Albán attacked for the second time in 120 B.C. This time its forces finished the job. They burned the king’s palace to the ground and emptied the rest of Tilcajete, leaving Monte Albán firmly in control of the entire valley.

  With nothing to impede it, Monte Albán swept out and established a domain of almost ten thousand square miles. For centuries it stood on equal ground with its neighbors, the rising Maya states to the east and Teotihuacan to the north. It enjoyed relatively peaceful relations with both but had continual trouble with the Ñudzahui (pronounced “nu-sa-wi”—Spaniards called them the Mixtec), a constellation of petty principalities immediately to the west. By contrast with Monte Albán, these were minuscule entities; most were clusters of rustic villages covering ten to twenty square miles. Yet they were amazingly troublesome. Monte Albán repeatedly overran the Ñudzahui statelets, but never managed to eliminate them. These tiny, fractious domains endured for more than a thousand years. Meanwhile the much stronger and more centralized Zapotec empire collapsed completely in about 800 A.D.

  Ñudzahui writing survives in eight codices, the deerskin or bark “books” whose painted pages could be folded like screens or hung on the wall like a mural. (The Spaniards destroyed all the rest.) More purely pictorial than Zapotec or Maya script, the texts were arranged almost randomly on the page; red lines directed the reader’s eye from image to image. The symbols included drawings of events, portraits labeled by name (the king 4-Wind, for example, being shown by symbolic wind and four little bubbles in a line), and even punning rebuses. Enough writing has survived to give, when coupled with archaeological studies, a vivid picture of Ñudzahui life.

  Like medieval Italian city-states, Ñudzahui principalities were rigidly stratified, with the king and a small group of kinspeople and noble advisers gobbling up much of the wealth and land. They constantly shifted configuration, some expanding by swarming over their neighbors, others imploding when their constituent villages seceded and joined other polities. More commonly, two states joined when their rulers married. Alliance through royal marriage was as common in eleventh-century Mixteca as it was in seventeenth-century Europe. In both, royal family trees formed an intricate network across national boundaries, but in Mixteca the queen’s lands stayed in her line—the king’s heir wasn’t necessarily the queen’s heir. Another difference: primogeniture was not expected. If the queen did not think her eldest son was fit for the crown, she could pass it to another child, or even to a nephew or cousin.

  No fewer than four of the codices treat the story of 8-Deer Jaguar Claw, a wily priest-general-politician with a tragic love for the wife of his greatest enemy. Born in 1063 A.D., 8-Deer was a shirttail cousin to the ruling family of Tilantongo, which had been engaged for decades in a dynastic struggle with the kingdom of Red and White Bundle. (The name, a modern invention, comes from its name-glyph, which pictures the cloth wrapping used by the Ñudzahui to wrap holy objects; its exact location is still not nailed down.) Like his father, a high cleric, 8-Deer was trained for the priesthood, but political events and his own overweening ambition stopped him from following that path.

  After an unprovoked attack on Red and White Bundle by Tilantongo raised hostilities to a fever, the warring parties agreed to meet in a sacred mountain cave with the Priestess of the Dead, a powerful oracle who had stripped away the flesh from her jaw, giving her a terrifying, skull-like appearance. Tilantongo’s representative was 8-Deer, who attended the meeting in place of his recently deceased father. To his dismay, the priestess sided with Tilantongo’s enemies and ordered 8-Deer, Tilantongo’s champion, to exile himself a hundred miles away, in a jerkwater town on the Pacific called Tututepec.

  Tucked away in Tututepec, 8-Deer assembled a private army, staffed it with many relatives, and in a series of swift campaigns seized dozens of neighboring villages and city-states. In addition to assembling the greatest empire ever seen in the region, the conquests managed to kill off most of the siblings and cousins above him in the line of royal succession. After six years of war he returned home to Tilantongo. During this visit, according to John M. D. Pohl, the archaeologist whose interpretations I am mostly following here, 8-Deer accidentally encountered 6-Monkey, the young wife of the much older king of Red and White Bundle. Despite the long enmity between the two kingdoms, 8-Deer and 6-Monkey secretly became lovers.

  In 1096 Tilantongo’s sovereign died in mysterious circumstances. The Priestess of the Dead selected 8-Deer’s beloved elder half brother to be the regent—that is, the half brother became the last person between 8-Deer and the throne of Tilantongo. Three years later, unknown assailants stabbed the half brother to death in a sweatbath. The inconsolable 8-Deer took the throne of Tilantongo and declared war on Red and White Bundle, which he claimed had orchestrated the murder.

  In this fragment from a Ñudzahui codex, the jaguar-cowled Lord 8-Deer (right) captures 4-Wind, son of his former lover, by the hair. As in other Ñudzahui codices, the characters’ names are indicated by the accompanying circles-plus-head symbols.

  (Illustration Credit 7.3)

  Red and White Bundle’s royal palace was built on a cliff over a bend in the river. Guarded by sheer walls on three sides, its soldiers had only to watch the fourth side, a
cross which was an earthen berm. Leading an army of a thousand, 8-Deer threw up ladders, swarmed over the berm with his men, and entered the palace. As befit a conqueror, 8-Deer was wearing elaborate cotton armor, a ceremonial beard wig, and a cowl made from the head of a jaguar. Gold-and-jade necklaces dangled across his naked chest. In the palace he found 6-Monkey and her husband, the king of Red and White Bundle. Both were mortally wounded. In Pohl’s account, 8-Deer held 6-Monkey as she died.

  Captured with the royal couple were their two sons, the elder of whom, 4-Wind, was heir to the throne. Seizing him by the hair, 8-Deer forced the teenager to grovel before him. But he also made what seems to have been a sentimental decision: he spared the life of his lover’s son. The folly of this action became apparent when 4-Wind and his brother escaped from confinement.

  Seeking revenge, 4-Wind approached the Zapotec empire for help. With Zapotec backing, he linked rebels in Red and White Bundle and a host of other cities defeated by 8-Deer. They besieged Tilantongo in 1115. The battle lasted six months and ended in total defeat for Tilantongo. In a mirror image of the past, the captured 8-Deer was forced to bow to 4-Wind. He was fifty-five years old and had six official kingships and dozens of petty states under his control. Victorious and vengeful, 4-Wind personally disemboweled him. Then he married 8-Deer’s daughter.