Suddenly the number twelve keeps popping up. It was Twelfth Night earlier in the week. I’ve been following the Wildlife Trusts Twelve Days Wild. My running calendar for the year now contains 12 10k races – one per month. There’s a fun article, I just read, about the 12 days of Christmas carol in the New Scientist. The Veg in one Bed book that I got as a Christmas present tells me ‘how to grow an abundance of food in one raised bed, month by month’. I’ve just got to the point in The Marriage Portrait, our book club book, when the main character, Lucrezia, is twelve years’ old.
And now I’m wondering what’s special about 12? Jogging my memory of twelve, I remembered the Grimms Fairy Tales I loved as a child. Several of them featured 12 – 12 brothers, 12 huntsmen, 12 dancing princesses. (Though they didn’t meet up in one story). And, of course, the 12 apostles. We had a tradition in our family of making an Easter Simnel Cake decorated with 11 marzipan balls. Judas – the 12th apostle not being represented.
Some other questions about twelve. Why is it called a dozen? Why is a baker’s dozen 13 items? Why are there 12 months in a year? Why are eggs packed in boxes of 12 (a dozen)? If I can find the answers to twelve questions about twelve, then I’ll be able to field questions about the number from my grandchildren – though they’ll probably come up with a question I haven’t thought of. Maybe I will find another seven questions and then I’ll have twelve questions about twelve. Meanwhile, I’ve now – thank you Google – got some answers to the five questions I’ve asked myself.
What’s special about 12? The encyclopaedia Britannica says, “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.” Well, this info gives me more things to investigate as I don’t know about the 12 stations of the moon and sun, nor about the main northern and southern stars. And it also raises the question why are there 12 signs of the Zodiac?
These aspects of twelve aren’t mentioned in the article Some fun facts about the number twelve which is written by a mathematician, Kevin Knudsen. Sadly, I understand very little of what he says:
“[Twelve] is a highly composite number, which means that it has more factors than any smaller positive integer (it has six of them: 1, 2, 3, 4, 6, and 12). The most famous such number is probably 5040, which Plato suggested as the ideal number of citizens in a city because of its large number of divisors. Twelve is a so-called sublime number, meaning it has a perfect number of divisors, the sum of which is also a perfect number. Recall that a perfect number is one that is the sum of its proper divisors. Six is such a number–6 = 1 + 2 + 3–and the sum of twelve’s divisors is 1+ 2 + 3 + 4 + 6 + 12 = 28, which is also a perfect number (28 = 1 + 2 + 4 + 7 + 14). We only know of two sublime numbers, 12 and 6086555670238378989670371734243169622657830773351885970528324860512791691264, so that makes 12 pretty special indeed.”
It’s fortunate I have registered to do a basic maths course but I don’t know if it will cover the terms that I am unfamiliar with in the para – ‘composite number’, ‘factors’, ‘positive integer’.
As an aside, last week some friends and I were discussing maths and numeracy. The discussion was sparked by one of us noting that there is confusion between the two and in their view, there is insufficient teaching of numeracy in English schools. National Numeracy notes “Numeracy is not always taught in the classroom: it means having the confidence and skills to use maths to solve problems in everyday life. Numeracy is as important as literacy – it’s sometimes called ‘mathematical literacy’ – and we need both to get on in life.”
Why is twelve called a dozen? The online etymology dictionary has a detailed explanation of the origin of the word dozen. A simple explanation is that it is from an old French word ‘dozeine’ (twelve) which was derived from the Latin word duodecim (meaning twelve)
Why is a baker’s dozen 13 items? According to Britannica There are a few theories as to how a baker’s dozen became thirteen. But the most widely accepted is that bakers would throw an extra loaf into orders of a dozen to avoid a flogging. In medieval England, there were strict laws controlling the price of bread. Bread had to be priced in relation to the price of the wheat used to bake it. If a baker was found to have cheated by shorting their loaves, things could go badly for them. … the big problem with these laws was that even careful bakers make mistakes. Variations in rising, baking, and air content could all change the size of a loaf and made it hard to be sure it was the planned weight. Afraid of accidentally coming up short, some bakers would just throw an extra loaf into lots of twelve. The extra made sure they were staying within the law–and avoiding a flogging.”
Why are eggs packed in boxes of 12? Because twelve divides by two, three, four, and six, and a gross (144 or 12 x 12) divides by two, three, four, six, eight, nine, twelve, sixteen, eighteen, twenty-four, thirty-six, forty-eight and seventy-two, traders (some say originating with the Romans) used to count in multiples and factors of twelve. Divisors and multiples of twelve are easier for packaging than packaging in divisors or multiples of 10s.
Why are there 12 months in a year? The system we use in the UK is the Gregorian calendar introduced in 1582. The introduction of the Gregorian calendar allowed for the realignment with events like the vernal equinox and winter solstice. (It was introduced to the US, UK and Canada in 1752). It is a solar calendar. However, although it is used in the international standard for representation of dates and times:, it is not the only calendar in use. An NY Times article gives info on multiple other calendars, noting “Each calendar reveals something about how the people who created it relate to the world around them while also preserving rich cultural identities and memories.”
Just for fun I looked up 12 in numerology (29 million hits) to see what the number represented there. There’s very little consistency. Among the attributes mentioned were: completion, harmony, unbridled creativity(!), individualistic self-expression, independence, new beginnings, the power of the mind, rapid expansion, nurture, physical strength, knowledge, optimism, imagination, efficient communication, inspiration, cooperation, and exploration. Shall I take a baker’s dozen of them and find meaning in why I’ve noticed the number twelve crop up several times this week?
Image: Twelve Drummers-drumming. The NariGunjan band of women drummers from a village in Bihar in Christmas themed sarees. Aparna Jain
One thought on “Twelve. It’s been popping up”
12 and 16 are both much better numbers for counting things than 10 is. In particular if you have a dozen items you can divide them equally between three people or four people or two people or six people. With 10 items you can divide them evenly between only 2 or 5. Same for carpentry etc. 12 inches is much more useful than 100 cm. Try dividing a meter into three! Note the smallest number divisible by 12345 and six is 60 which is the number of seconds in a minute and minutes in an hour. The Babylonians used to count to base 60. Why 13? The numerologists think that 13 is the right number for Jesus and the 12 apostles because when you pack spheres together, one sphere can be evenly encircled by 12, no more no less. 12 spheres all touching the center one which is the 13th.
Going back to 16, that is the number the computer scientists use as the base instead of 10. This is because it is a power of two. You can divide it in half and half again then half again and then in half again with no remainder each time.