1491_ New Revelations of the Americas Before Columbus - Charles C. Mann [124]
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 12.19.13.12.18. (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