Counting sheep

Sadly I can’t, I presume, reproduce in its entirety the delightful and serendipitous poem Counting Sheep by Linda Pastan which is today’s poem at Poetry Daily. However I strongly recommend heading that way to read it. Here is an excerpt:

At a thousand fifty
I notice a ram
pushing up against
a soft and curly female,
and for a moment
I’m distracted by errant
images of sex.
It is difficult
to keep so many sheep
in line for counting—
they are not a parade
but more like a roiling
sea of whitecaps…

Counting and sheep go together like, er, probably like a shepherd and a sheepdog (dogs were the first animal species to be domesticated by humans, sheep the second). There are special words for counting sheep which derive from the language spoken in Britain in the Iron Age. Which is cool. In base 20. Which is cool. And with a sub-base 5 element. Which is cool. And three cools make freaking awesome. And the fact that you can use the system to count up to 399 using only two hands makes it mind-blowing.

Like most Celtic numbering systems, they tend to be vigesimal (based on the number twenty), but they usually lack words to describe quantities larger than twenty; though this is not a limitation of either modernised decimal Celtic counting systems or the older ones. To count a large number of sheep, a shepherd would repeatedly count to twenty, placing a mark on the ground, or move his hand to another mark on his crook, or drop a pebble into his pocket to represent each score (e.g. 5 score sheep = 100 sheep).

It is also worth noting the number theory behind the scheme. Although decimal up to 10, in most dialects the scheme then changes to counting in(sub-)base 5. It is possible to carry out limited arithmetic in base 5 on numbers up to 30 (decimal) using your fingers as a rudimentary abacus. It is pure speculation, but there may be a connection between the two facts, and the shepherds of England may have carried out limited accounting on their fingers.

In particular, the names of the numbers fit a pattern in which the index finger and forefinger each represent 0 when retracted, 1 when bent, and 2 when straight, while the other three fingers each represent 5 when extended. The rhyming transitions occur with the straightening of a finger, and the pattern repeats at intervals of 5. Thus, with two hands, a person can count up to 399. In the similar but simpler system, discernible in Roman numerals, in which the thumb is 5 and the other fingers 1 each, a person can only count up to 99 on two hands. The Yan Tan Tethera system was thus advantageous until writing made the limitation of two hands less important.

Another reason for the use of base five is suggested by the design of the shepherds crook which has grooves, nobbles, nicks or other impressions on it which enable the shepherd to note the number of fives counted on the other hand. Using base five counting in this way allows the shepherd to total as many sheep as the markings on the crook will allow, each mark representing five sheep.

But why waste an excellent counting system on just one use. It was employed by stitch-counting knitters too, as recently as 1863:

Notes and queries September 12 1863

So which of the small selection given on Wikipedia of the more than 100 variants of the system shall I reproduce here? Since there are strong family ties to Kirkby Lonsdale, it is the Kirkby Lonsdale variant, divided into fives for ease of reading:

Yaan, tyaan, taed’ere, mead’ere, mimp;
Haites, saites, hoves, daoves, dik;
Yaan’edik, tyaan’edik, tead’eredik, mead’eredik, boon;
Yaan’eboon, tyaan’eboon, tead’ereboon, mead’ereboon, buom’fit.

I remember going to see Harrison Birtwistle‘s opera Yan Tan Tethera and being very excited by recognising Michael Nyman in the audience. Oh heady days. In fact the main reason I wanted to see/hear it was because the libretto was by one of my heroes, Tony Harrion. He, unfortunately, was not in the audience (that I saw).

Needless to say Language Hat has a post on the counting systems. Be sure to read the comments too. His is prompted by poet Basil Bunting. Unfortunately all I can find of poet James Crowden’s radio programme about counting sheep is this rather perfunctory summary. If anyone ever comes across the now-unobtainable audio I’d love to hear it.

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