The Mayan Zero Note: The Introduction Of Zero Allowed

The Mayan Zerosheadnotethe Introduction Of Zero Allowed The Average M

The Mayan zeros headnote the introduction of zero allowed the "average man" to do mathematical calculations. The introduction of the symbol for zero was one of the most significant events to occur in the history of civilization. Until zero was considered a number in its own right and given a symbol, performing more than simple calculations was impossible without a calculating device, such as an abacus. Only specialists knew how to use these devices. Tobias Dantzig says that the most important thing that the creation of the symbol for zero did was to allow the "average man" to do mathematical calculations (Dantzig, 1941, p. 35).

The Hindus of India created the symbol for zero in the form that most of the world uses today, but another culture far removed from the Hindus invented its own system of place value with the use of a zero. In fact, the Maya of Central America used more than one symbol for zero.

Multiple Symbols for Zero

We may never really know why the Maya used multiple symbols for zero because only a few records exist from the Mayan civilization, which began around the fifth century B.C. and declined around A.D. 900. Georges Ifrah explains that very few written records about the Maya remain because their civilization had waned by the time the Spanish arrived in the sixteenth century, and many of the records had deteriorated (Ifrah, 2000, p. 300). To make matters worse, the Franciscan monk Diego de Landa burned the written records left by the Mayan people, believing that doing so would make them more willing to convert to Roman Catholicism. However, later in his life, de Landa collected information from surviving Maya and transcribed what they remembered from their past. The remaining written records of the Maya include three codices housed in Madrid, Dresden, and Paris, as well as a few accounts from converts who learned to read and write Spanish. Only these survive today.

One reason the Maya may have used multiple symbols for zero is that they employed two types of numerals. The first type consists of glyphs called head variants, which show the head of a god, person, or animal. The second system evolved from these glyphs to facilitate calculation, using a dot or circle for units and a bar for fives. The head-variant numerals are illustrated in figure 1 (Closs, 1986, p. 335), where each glyph represented a unit of time used in specific contexts where the simpler dot, bar, and shell forms were inadequate. Additionally, a third, rarely used form depicted whole figures of gods, such as the "full-figure representation of '0 kins'" (days), shown in figure 2 (Ifrah, 2000, p. 320). Joseph (1992) demonstrates that the Mayan number for three was three dots, ten was two bars, and nine combined dots and a bar. A shell symbolized zero; for example, twenty was shown as one dot and one shell, illustrating the use of multiple symbols for zero depending on context (Joseph, 1992, p. 50).

The Mayan Long-Count System

The Maya developed their number system primarily for calendar purposes, known as the long-count system, which employed units of days and a calendar year of 360 days. When counting animate objects like people and animals, they used a strictly vigesimal (base-20) system. However, when counting time, they introduced an irregularity at the third order of units, where 18 x 20 (360) was used instead of 20 x 20 (400), to match the length of their year. This irregularity persisted through higher units such as katuns and baktuns, which represented longer cycles (Ifrah, 2000, p. 311). The sequence of units was measured in kins (days), uinals (20-day months), tuns (360-day years), katuns (20-year cycles), and baktuns (400-year cycles). Their calendars and numerical representations are often depicted on monuments known as stelae, where years were represented using glyphs assigned place values or the simple dot, bar, and shell symbols for zero (Ifrah, 2000, p. 316). The practice of varying the form of zero depending on its position in the calculation is unique to their system (Ifrah, 2000, p. 310).

The placement of glyphs vertically on stelae followed a specific order from bottom to top, with first-order units at the bottom and larger units above. When a particular unit was absent, the Maya used specific signs to indicate its absence, leading to the development of a sophisticated place-value numeration system with a genuine zero. For example, the number 1,087,200 is represented as the sum of multiples of 144,000, 7,200, 360, 20, and 1, with zeros used to fill in missing units, illustrating the system's comprehensive nature (Ifrah, 2000, p. 309).

Conclusion

Barrow (1992) explains that modern understanding of the Mayan use of zero is enhanced when recognizing that the Maya depicted periods of time as pictorial designs, with each element symbolizing a part of the whole. For example, representing 'one hour, one minute, and five seconds' involves distinct symbols for each component, and the absence of units—marked by zero glyphs—creates empty spaces that visually complete the picture (Barrow, 1992, p. 89). Despite their primarily calendar-focused application, the Mayan numeral system was fully functional for calculation, sharing the distinction with Hindu mathematicians of introducing the original symbol for zero. Tobias Dantzig highlights the profound significance of zero as one of humanity's greatest cultural achievements (Dantzig, 1941, p. 35).

References

• Barrow, J. D. (1992). Pi in the Sky: Counting, Thinking, and Being. Oxford: Clarendon Press.
• Closs, M. P. (1986). Native American Mathematics. Austin, TX: University of Texas Press.
• Dantzig, T. (1941). Number, the Language of Science (3rd ed.). New York: Macmillan Co.
• George Gheverghese Joseph. (1992). The Crest of the Peacock: Non-European Roots of Mathematics. London: Penguin Books.
• Georges Ifrah. (2000). The Universal History of Numbers: From Prehistory to the Invention of the Computer. New York: John Wiley & Sons.
• Sheila McNeill. (n.d.). Author’s biography and contributions.