Duodecimal System
The duodecimal system is a mathematical plan that uses a base of twelve rather than the standard base ten. Under base twelve, the place value changes from 10 to 12. Quantities are explained in terms of twelves, such as dozens, grosses, and great-grosses, rather than tens, hundreds, and thousands. In the duodecimal system, there are new symbols for 10 (X or dek) and 11 (E or el). Dozen is called dodo, and dozenal is a synonym for duodecimal.
The rationale for base twelve lies in many duodecimal models. Some of the best known examples include 12 months in a year, 12 hours on a clock face, 12 items to a dozen, and 12 inches to a foot. The system of 12 hours in a day came from the Egyptians. Shopkeepers favored selling by the dozen because it was easy to store goods on a shelf in three rows of four. The world calendar, easily divided into 12 months and four quarters, is already suited for duodecimal use.
Supporters of the duodecimal system point out the limitations of base ten: it can only be evenly divided by 2 and 5. However, base twelve offers many more options, as it is evenly divisible by 2, 3, 4, and 6. Supporters of base twelve say fractions are much easier to work with, since there are more divisors. Thus, fractions can readily be reduced to their simplest form.
To indicate temperature in base twelve, a Do-Metric system is used, with the boiling and freezing points of water separated by 100 degrees. The duodecimal abacus has 11 or 12 beads, as opposed to nine or 10 beads on a base ten abacus. Zero is used the same way in duodecimal and decimal systems, as a placeholder.
Other mathematical bases have been considered: two, eight, and sixteen. These numbers are easily divisible by 2 but they are not divisible by 3, so they do not hold much of an advantage over base ten. However, there are some remnants of base sixteen in the system of 16 ounces to a pound.
The duodecimal system was first introduced by Babylonians around 2400 B.C., but they ended up working with several different bases. The Babylonian sexagesimal system was based on 60 units, but they found they needed a smaller unit for counting and they chose base ten. Many observers trace the popularity of base ten to ten human fingers.
The Romans spread the duodecimal system in the second century B.C.. The term duodecimal is based on the Latin duodecim for 12. The Latin word for one-twelfth, unus, means unit. The English words ounce and inch are both derived from this root. The Latin pes means foot. The popularity of the Latin terminology is borne out in the system of 12 inches to a foot that is still widely used.
Napoleon reiterated the acceptance of the foot as a unit of measurement when the decimal system was first introduced in France. In Napoleon's view, base twelve was more logical because he could understand one-twelfth of a foot, but he found it hard to grasp the concept of one-thousandth of a meter. John Quincy Adams declared his preference for base twelve in 1821. He criticized the decimal system as being unnatural, commenting that there was no model for base ten in nature. At the end of the nineteenth century, some countries tried to change from a system using a base of 12 hours to a system using a base of 10 hours, so the hours of the day would be consistent with other metric systems already in use. However, 12-hour timekeeping was very firmly ingrained. The British tried to incorporate base ten and base twelve in their monetary system. Until 1971, the British used a duodecimal system combined with a vigesimal system (base twenty, for 10 fingers and 10 toes). The British pound sterling was divided into 20 shillings of 10 pence each.
During the 1950s, there was renewed enthusiasm for base twelve and a Duodecimal Society was formed in the United States. The society published one of the few books devoted to base ten and devised tables for logarithms and trigonometry. Musicians and artists have proposed base twelve systems for musical notation and color values, but these have never been widely used. Despite the vestiges of base twelve in many activities of daily life, the duodecimal system has consistently been overshadowed by the success of the decimal system.
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