The Study: It All Adds Up

I've moved some books onto the shelves. Here's how they look now. I'll move them about and get them in order later, but I'm tired now and my back hurts.

Talking of numbers and counting, and hexidecimals, I've been thinking about other counting systems and base units. As humans, we find the decimal system easy - we have ten fingers, so allotting a number to a digit makes sense. But wait a tick - we have ten toes as well - why not use them too? A double decimal, if you will, or vigesimal system. Not as rare as you might initially imagine. The French use a variant for numbers from 70 to 99 - 70 is soixante-dix (sixty-ten), 80 is quatre-vingts ( four-twenties), 90 is quatre-vingt-dix (four-twenty-ten). The Bretons use ugent as their base, so daou-ugent (two-twenty) is 40, pevar-ugent (four-twenty) is 80. Old Welsh uses ugain (same root word as Breton), so deugain (two-twenty) is 40, trigain (three-twenty) is 60. The Imperial system, used in the UK prior to the partial decimalisation in 1971, used twenty as a base for some measurements - 20 fluid ounces make one pint, or twenty hundredweights make one ton, for example. In the old currency, twenty shillings made one pound sterling.

One Pound Note - from 1984

Reverse of same - Portrait of Isaac Newton

The 'score' is a measure of twenty - I have often bought a score of screws in old-fashioned ironmongery shops - and the biblical measure of 'three score years and ten' is used for the usual expectation of the 70 years of a lifetime; Abraham Lincoln's Gettyburg Address opens with the words," Four score and seven years ago ...", meaning 87 years. It comes from the Old Norse skor - a scratch or notch cut onto a tally stick.

I find the Greenland Inupik counting method is one of the most interesting. It's a vigesimal system with an added twist - it breaks it into four quinary (base-5) units. So, counting on the fingers of your first hand, we have :

0 = nuulu

1 = atuseq

2 = mardluk

3 = pingasut

4 = sisamat

5 = tatdlimat

then, it's onto the other hand, giving

6 = arfineq (second hand one)

7 = arfineq-mardluk (second hand two)

8 = arfineq-pingasut (second hand three)

9 = arfineq-sisamat (second hand four)

10 = arfineq-tatdlimat (second hand five) also called qulit

so then it's off with your socks, and

11 = arfaneq (first foot one)

12 = arfaneq-mardluk (first foot two)

13 = arfaneq-pingasut (first foot three)

14 = arfaneq-sisamat (first foot four)

15 = arfaneq-tatdlimat (first foot five)

switching to the other foot, we have

16 = arfersaneq (second foot one)

17 = arfersaneq-mardluk (second foot two)

18 = arfensaneq-pingasut (second foot three)

19 = arfensaneq-sisamat (second foot four)

20 = arfensaneq-tatdlimat (second foot five)

So, that's it. 20 is also called inuk navdlugo - 'man counted out' or 'complete human'. Anything above 20 means grabbing your pal(s) and it's off we go again

21 = inup aipagssane atuseq (second person first hand one)

32 = inup aipagssane arfaneq-mardluk (second person first foot two)

49 = inup pingajugssane arfineq-sisamet (third person second hand four)

and so on, adding another person when each becomes 'counted out'. Qujanaq.

Another fascinating counting system is the old fashioned way of counting sheep, used by shepherds across the UK, but mainly now lingering in the North. Based on the very ancient Brythonic Celtic tongue, this is another vigesimal system. As each twenty was reached, the shepherd would move a stone or coin from one pocket to another, or move his hand up or down the notches on his crook, (remember skor mentioned above) . In Lancashire, where I live, we would count Yain, tain, eddera, peddera, pit, tayter, layter, overa, covera, dix, yain-a-dix, tain-a-dix, eddera-dix, peddera-dix, bumfit, yain-a-bumfit, tain-a-bumfit, eddera-bumfit, peddera-bumfit, jiggit.

Sheep Shears - as used before electric clippers.

The words vary every so slightly according to accent and local tradition, but the method is most commonly called 'Yan Tan Tethera', from the first three digits. The late, great, sainted Jake Thackray introduced his song Old Molly Metcalfe with this explanation : -

"In Swaledale, North Riding of Yorkshire, sheep farmers used to, and some of them still do, count their sheep in a curious fashion. Not in the English way - “one, two three, four five,” but thus:

“Yan, Tan, Tether, Mether, Pip
Azar, Sazar, Akka, Cotta, Dik
Yanadik, Tannadik, Thetheradik, Metheradik, Bumfit
Yanabum, Tanabum, Thetherabum, Metherabum, Jiggit.”

Having thus reached twenty they then take a stone in the hand, representing the sheep that’s counted and if they have more than twenty sheep to count they begin again.

Yan, Tan, Tether, Mether, Pip
Azar, Sazar, Akka, Cotta, Dik.

Another twenty, another stone and again

Yan, Tan, Tether, Mether, Pip.

Another twenty again a stone and so they go.

Yan, Tan, Tether, Mether, Pip.

Not a right long time ago there was a shepherdess on a moor in Swaledale. Well, not a shepherdess - “shepherdess” is a word for a woman with a pretty pinafore with frilly petticoats, with a complexion and a cleavage. No this woman was a sheep minder. She was sent to mind sheep up upon the moor as soon as she was able — at the age of seven. She scarcely left the cruel place and was found rotting with her ghastly sheep at about the age of twenty-eight. Here is a song for her."