Counting on the joints of the fingers
Most people who count on their hands use the fingers themselves, which leads naturally to five and ten. A second method uses the finger joints. Each of the four long fingers has three segments, and the thumb of the same hand can touch each one in turn. Running the thumb along the segments gives a count of four times three, which is twelve, using a single hand.
The other hand can then keep a tally of completed dozens, one finger raised for each. Five fingers allow up to five dozen, so two hands together can reach sixty. Methods of this kind have been reported in parts of South and West Asia, and some writers have suggested a link with the Mesopotamian sexagesimal system, which was built around sixty. That connection is plausible but speculative, because the evidence for how the ancient scribes first came to favour sixty is incomplete.
What a dozen-based system looks like
In base twelve, groups of twelve take the role that groups of ten play in everyday arithmetic. The numeral written “10” would mean twelve, and “100” would mean one hundred and forty-four. Two extra single-digit symbols are needed for ten and eleven; various proposals exist, including the letters X and E.
The attraction is divisibility. Twelve divides evenly by 2, 3, 4 and 6, while ten divides only by 2 and 5. As a result, many everyday fractions come out as short numerals in base twelve:
| Fraction | In base ten | In base twelve |
|---|---|---|
| one half | 0.5 | 0.6 |
| one third | 0.333… | 0.4 |
| one quarter | 0.25 | 0.3 |
| one sixth | 0.1666… | 0.2 |
Each entry can be checked: 6/12 is a half, 4/12 a third, 3/12 a quarter and 2/12 a sixth. One fifth is awkward in base twelve, just as one third is awkward in base ten, which is the usual reply to anyone who treats twelve as simply better.
Dozens in measures and trade
Twelve is unusually common in older measuring systems, even where the number words themselves are decimal. The best-known case is English-speaking trade, where a dozen is twelve, a gross is twelve dozen, or 144, and a great gross is twelve gross, or 1,728. Other examples of such traditional counting units survive in how goods were packed and sold.
British money before decimalisation in 1971 mixed bases: twelve pence made a shilling and twenty shillings made a pound. There are twelve inches in a foot, and twelve months in the year. The Romans divided their basic unit of weight and money into twelve parts, and the Latin word for one twelfth, uncia, is the source of both the English words inch and ounce. The Roman calendar also settled on twelve months, though its history is more tangled than a simple preference for twelve would suggest.
Societies that favoured twelve
It would be misleading to describe any large civilisation as counting in base twelve. Most languages with well-documented number words are decimal, or built on five or twenty. What the record shows is partial use of twelve alongside another base. In medieval Scandinavia and parts of the Germanic world, the word for a hundred could mean 120, often called the long hundred, which is ten times twelve. A few languages in Africa and Asia have been reported as counting in twelves or having strong traces of it, though these claims are thinly documented and vary in how well they hold up.
English itself does not count in twelves, despite the irregular look of its words for eleven and twelve. Those words are generally explained as meaning roughly “one left over” and “two left over” after ten, which is a decimal idea. They show nothing about a lost base twelve.
Astrological and calendrical twelves, such as the twelve signs and the lunar months, are a different matter. Twelve in astrology reflects beliefs about the sky and the year, not a counting base, even if the two may have reinforced each other in people’s minds.
The modern duodecimal movement
In the twentieth century, enthusiasts organised societies to promote counting and measuring in twelves. A Duodecimal Society of America was formed in the middle of the century, and later groups use the term dozenal. They argue for the divisibility advantages above and propose special symbols for ten and eleven. The movement has remained small. Changing a base that is built into money, language and schooling would be costly, and most of the benefit can be had by using dozens only where the divisibility actually helps.
For a reader, the lasting interest of twelve is how many human habits grew from a physical fact: the hand, counted by its joints, naturally holds a dozen.