Twelve

It’s that day of the year again. It seems to come around faster every time. On this day twelve years ago The Renaissance Mathematics first entered cyberspace. What does the word, twelve, actually mean? In the Germanic languages twelve and its equivalents means two left that is after counting to ten:

Old English twelf “twelve,” literally “two left” (over ten), from Proto-Germanic *twa-lif-, a compound of *twa- (from PIE root *dwo- “two”) + *lif- (from PIE root *leikw- “to leave”). Cognate with Old Saxon twelif, Old Norse tolf, Old Frisian twelef, Middle Dutch twalef, Dutch twaalf, Old High German zwelif, German zwölf, Gothic twalif. 

Online Etymological Dictionary

Twelve features widely in culture, religion, science, and society in general. There were twelve apostles, twelve days of Christmas, the twelve Olympians (the major ancient Greek deities), The Twelve Tribes of Israel, jury of twelve good men and true, somehow twelve has always been a favoured number for humans. But this is a history of science blog and here we meet many instances of the number twelve.

The Romans used a base twelve or duodecimal number system, the only fraction that they used were twelfths. The remnants of this system are present in many countries that were once parts of the Roman Empire.

Table of units from a base of 12
Relative value	French unit of length	English unit of length	English (Troy) unit of weight	Roman unit of weight	English unit of mass
120	pied	foot	pound	libra
12−1	pouce	inch	ounce	uncia	slinch
12−2	ligne	line	2 scruples	2 scrupula	slug
12−3	point	point	seed	siliqua

Table taken from Wikipedia

Also, in English we still have the term dozen for twelve and gross for twelve squared, which reflect a twelve based number system.

There are modern societies in both the UK and the US that wish to replace our decimal system with a duodecimal one or as they prefer to call it Dozenal to avoid the decimal in duodecimal. They argue that because twelve has more factors than ten, a Dozenal system would be arithmetically preferable to a decimal one.

Our twelve-hour day has a different source. To tell the time at night Egyptian astronomers used the so-called decans, a set of thirty stars or groups of stars, which rise consecutively on the horizon throughout each earth rotation. In any given night twelve decans rose successively over the horizon dividing the night into twelve.

Astronomical Ceiling of Senemut tomb showing various decans, as well as the personified representations of stars and constellations Source: Wikimedia Commons

Gradually they developed the habit of also dividing the day into twelve units, our twelve-hour day. Originally, twelve seasonal hours, the length of which, varied throughout the year. In the early modern period these became our equinoctial hours of equal length. Hours are divided into sixty minutes and minutes into sixty seconds, sixty is a multiple of twelve.  

Astronomy and astrology deliver up a two-significant-twelves. Twelve months in the year and twelve signs of the zodiac that are in fact related. The word month has the same etymological root and the word moon and originally referred to the lunar moon, which is about twenty-nine and a half days long. Early calendars were lunar calendars, but the solar year is about eleven days longer that twelve lunar months, so if you want to keep your calendar aligned with the solar year you have to add an extra lunar month about once every three years.  The Greeks adopted the Metonic cycle, named after a Greek, but conceived by the Babylonians, in which seven extra months are added in nineteen solar years.

The Romans used a more random method in which an extra month was added by a political official when it was thought necessary. Because the dates for elections were determined by the calendar, this led to political corruptions with manipulation of the calendar. Julius Caesar solved the problem by introduction a solar calendar borrowed from the Egyptians with three hundred and sixty-five days divided up into twelve months. Nothing says there should be twelve months in a solar year, the French Revolutionary Calendar only had ten months, but by analogy to the lunar calendar twelve was chosen. Now, the solar year is closer to three hundred and sixty-five and a quarter days, which was known to the Egyptians and Caesar’s astronomical advisors, so you have to add an extra day approximately every four years. Caesar’s astronomical advisors got this slightly wrong leading to the whole Julian Calendar/Gregorian Calendar reform, which we won’t go into here. 

That the ecliptic is divided into twelve thirty-degree signs of the zodiac, also goes back to the Egyptian solar calendar. The Egyptians divided the year into twelve thirty-day months, with five non-days between the beginning and the end of the year, making a total of three hundred and sixty-five days. These twelve thirty-day months became the twelve thirty-degree signs of the zodiac.

A 6th century mosaic zodiac wheel in a synagogue, incorporating Greek-Byzantine elements, Beit Alpha, Israel Source: Wikimedia Commons

And so, the Renaissance Mathematicus enters its thirteenth year expectantly looking forward to what its Gemini horoscope will deliver. We wish all of our readers, commentators and supporters, both active and passive, all the best for our next circuit of the Sun and hope you enjoy the future blog posts.