COUNTING AND WRITING
Writing begins with counting. When a culture grows big enough, it acquires an elite, which needs to monitor things it considers important: money, stored goods, births and deaths, the progression of time. In the Fertile Crescent, village accountants began keeping records with clay tokens around 8000 B.C. As the need for precision grew, they scratched marks on the tokens as mnemonic devices. For example, they might have distinguished a count of sheep from one of wheat by drawing a sheep on one and a wheat stalk on the other. Gradually the information on each record increased. The bureaucrats were not intending to create writing. Instead they were simply adding useful features as they became necessary. By 3200 B.C. Sumerian scribes had progressed to inscribing on clay tablets with sharpened reeds. A tablet might contain, say, two hash marks, a box, a circle with a cross in the middle, an asterisk-like shape, and an arrangement of three triangles. Scribes would know that the hash marks meant “two,” the box was a “temple,” the circle stood for “cattle,” an asterisk meant “goddess,” and the triangles were “Inanna”—two cattle owned by the goddess Inanna’s temple. (Here I am lifting an example from Gary Urton, a Harvard anthropologist.) They had no way to indicate verbs or adjectives, no way to distinguish subject from object, and only a limited vocabulary. Nonetheless, Sumerians were moving toward something like writing.
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 13, 3114, B.C., though some archaeologists put the proper date at August 10 or 11, 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 13 starting date, October 12, 2006, would be written in the Long Count as 18.104.22.168.18. (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, 2006, is Julian Day 2,454,021.
The Long Count calendar began with the date 0.0.0.0.0. *22 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 22.214.171.124.18. 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.
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.
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.
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 throne 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.