Finding Zero Read Online Free PDF

We talked quietly about it for almost half an hour, standing mesmerized by this mysterious stone carved by mathematically inclined people centuries ago. A nearby display explained that the Aztec Stone was likely made in the fifteenth century and had been discovered right in the center of Mexico City.
    Some years earlier, I was surprised to learn from an anthropologist friend that much scientific research is actually done inside museums—not just in the field, as one might expect. Museums present collections of artifacts that have been cleaned and prepared for display and are usually shown within the context of similar items that are related to them by date or type or location of discovery, or all of these. This practice facilitates analysis by expertsas much as admiration by the general public. Recently, many great museums around the world have begun enhancing their exhibits with video presentations about topics related to their displays, which serve an important public-education need.
    And when Debra and I went upstairs from the Aztec Stone, we serendipitously found an ongoing video presentation on Mesoamerican mathematics. I was fascinated to learn that two millennia ago, the Mayans had devised a sophisticated calendar using glyphs for numbers—including a zero. The Maya numerals go back to 37 BCE, and they are simple to write. The numbers 1 through 4 are dots, 5 is a bar, and 10 is two bars one on top of the other; and for zero there is a crescent-moon glyph.
    In fact, the Maya invented four kinds of calendars. One was the Long Count calendar, which represented days from a starting point that corresponds, in our modern calendar, to August 11, 3114 BCE—the date of the creation of the universe, according to Mayan mythology. The counting of days from creation used a mixed base-20 and base-18 number system. One of the digits in this calendar would reset to zero after reaching 18; otherwise the calendar used the vigesimal (base 20) numbers. Surprisingly, the ancient Maya, who inhabited the Yucatan Peninsula in Mexico and parts of Central America, apparently understood the concept of zero as early as the first century BCE.
    The Maya also had a Short Count, a cyclical calendar with 260 days (20 times 13 days), which was their sacred calendar. At the end of the cycle, monuments were erected to commemorate the fulfillment of the period. A third Mayan calendar had 360days—close to the usual solar year of 365.24 days. It was for the construction of this calendar that the usual base-20 Mayan number system was adjusted to also employ a base of 18, because 360 equals 20 times 18. Had they used only multiples of 20, their year would have been forced to have 400 (20 × 20) days. 1
    Yet a fourth calendar used by the Maya was based on cycles of the planet Venus. The Mayans were astute observers of the sky and had long ago noticed that Venus would rise with the sun (we call this a heliacal rising) every 584 days—so the calendar based on Venus reset itself to zero after 584 days. The Mayan calendars, and the predominantly vigesimal Mayan number system with zero, are some of the most intriguing discoveries in the history of science. In 2012 there was worldwide panic in some circles of society fearing the end of the world because one of the Mayan calendars reset itself to zero. Of course, nothing happened; our planet continued to revolve around the sun, and this fear turned out to be as unfounded as the similar Y2K worry of a dozen years earlier.
    But the Mayan system was isolated from the rest of the world, and it used glyphs—written or carved symbolic signs—that were not suitable for economy of notation. Their signs grew in number as the numbers they represented got larger, in a manner similar to that of the Roman system. The zero was not a perfect positional element as in our numbers, and the base changed, depending on need, from 20 to 18. Georges Ifrah calls the Mayan numbers “a failed