Number 12 and the Duodecimal System

by Liliana Usvat

The Duodecimal System

The duodecimal system (also known as base 12, dozenal, or, rarely, uncial) is a positional notation numeral system using twelve as its base.

Humans, for the most part, count in chunks of 10 — that's the foundation of the decimal system. Despite its near-universal adoption, however, it's a completely arbitrary numbering system that emerged for one very simple reason: We have five fingers on each hand.

In 1930, F. Emerson Andrews published a book, New Numbers: How Acceptance of a Duodecimal Base Would Simplify Mathematics, in which he cogently argued for the change. He noticed that, due to the myriad occurrences of 12 in many traditional units of weight and measures, many of the advantages claimed for the metric system could also be adopted by the dozenal system.

Indeed, examples of base-12 systems abound. A carpenter's ruler has 12 subdivisions, grocers deal in dozens and grosses (12 dozen equals a gross), pharmacists and jewelers use the 12 ounce pound, and minters divide shillings into 12 pence. Even our timing and dating system depends on it; there are 12 months in the year, and our day is measured in 2 sets of 12. Additionally, in geometry, a circle is replete with subsets and supersets of 12 — what's measured in degrees (a 360 degree circle consists of 30 sets of 12).

Three decades after Andrews's book, the brilliant mathematician A. C. Aitken made a similar case.

#### It's All About the Factors

First and foremost, 12 is a highly composite number — the smallest number with exactly four divisors: 2, 3, 4, and 6 (six if you count 1 and 12). As noted, 10 has only two. Consequently, 12 is much more practical when using fractions — it's easier to divide units of weights and measures into 12 parts, namely halves, thirds, and quarters.

Moreover, with base-12, we can use these three most common fractions without having to employ fractional notations. The numbers 6, 4, and 3 are all whole numbers. On the other hand, with base-10, we have to deal with unwieldy decimals, ½ = 0.5, ¼ = 0.25,

The number 12 has two factors that are prime numbers, 2 and 3. This means that the reciprocals of all smooth numbers (a number which factors completely into small prime numbers), such as 2, 3, 4, 6, 7, 8, have a terminating representation in duodecimal.

Critics of the dozenal system say that it would undermine the benefits of finger counting.

There are Dozenal Society of Great Britain, Dozenal Society of America, that promote teaching and using the Duodecimal System.

12 The Number of Perfection Refleccted in History and Religion

Twelve is a symbol of cosmic order. Twelve is the number of space and time.

The number 12 reflects to the ancient meaning of 12 being the number of perfection.

The number 12 is the result of 4×3, 4 elements – 4 corners of the earth – 4 cardinal points. When these are multiplied 4 x 3, three being the sacred number of God, the result is 12 – the perfect number.

In number symbolism: 12. The number 12 is strongly associated with the heavens—the 12 months, the 12 signs of the zodiac, and the 12 stations of the Moon and of the Sun. The ancients recognized 12 main northern stars and 12 main southern stars.

In early civilization, twelve became a very important number to mathematicians and astronomers. Twelve is a number that is divisible by 2,3,4 and 6 as well as by itself and 1. Astronomers divided a year, or the average time it takes the Earth to make a complete revolution around the Sun, into 12 months.

In Christian tradition there are twelve days of Christmas.

In many religions, such as the Greeks, the number 12 is considered holy and sacred for many generations. There are 12 main gods in Greek mythology, Odin had 12 sons in Norse mythology, 12 disicples of Christ in Christinaity, and 12 Imams in the Islam religion, 12 Sumerian Great Gods and 12 zodiac constellations.

• There are 12 months in a year.
• There are 12 hours in face of analogue clock.
• There are 12 inches in a foot.
• A dozen is a quantity that means twelve.
• A gross is twelve dozen.
• In astrology, there are 12 signs in the Zodiac.
• In the Bible, Jacob had 12 sons.