Friday, 11 May 2012

Counting Out Time

                I've varnished the shelves. What can you say? Nowt, really. Here's what they look like now, waiting for the varnish to dry. Then I need to sort the top out and it's job done.
And there's nothing else to say for now, so I'll write about something else instead. 
One of the oldest technological inventions is the counting frame. I’d argue that it is the first true computer – it can be ‘programmed’, it is not ‘dedicated’ (it can be used for a variety of tasks), input is made through an interface, and it can be re-set and different data sets entered into the same hardware. The most familiar counting frame is the abacus – which are still found in almost every nursery school. The abacus derives its name from the Greek word abakos, coming to us through the Latin, and originally meant a sand- or dust-box used for counting or drawing geometrical figures. The Romans used a tray of sand, with pebbles sitting in shallow troughs or grooves in the sand. The pebbles were called in Latin calculi – from which we get our word calculate (and calculus). The problem with Roman mathematics was the notation they used – just try multiplying LVI by XXIV in your head, and without converting them into Arabic numbers. Tough, eh?  
My suanpan with black beads ...
There is some argument about whether the Chinese developed the abacus independently (I think they did), or if there was a crossover with the West. The Chinese abacus is called the suanpan, and has a minimum of thirteen rods, which are divided by a horizontal bar, with two beads on the rods in the top section, and five beads per rod in the bottom section. The suanpan can be used for decimal calculations or hexadecimal (base 16) calculations, (in Chinese weighing 16 liang make one jen - just as 16 ounces make one pound in our Imperial system). A suanpen can be used for addition, subtraction, multiplication, division, and square- and cube-root calculations, and a skilled operator can work at astonishingly high speed, commonly outpacing someone with an electronic calculator.
... and my suanpan with red beads.
The suanpan is more versatile than the Japanese soroban, which has only a single bead in the top section and four beads in the bottom one. The Russian schoty has a single, usually bowed frame, with ten beads on each wire (the 5th and 6th beads are usually differently coloured) with, sometimes, a single four-bead wire (for calculating quarters).
'Neper's' or 'Napier's' Bones
Another interesting calculating device is Napier’s Bones. Invented by John Napier in c. 1617, the bones are numbered rods, which can be used to calculate products and quotients by using a variation on the Arabic lattice method of calculation. Napier was an interesting character – he was interested in mathematics, physics, astronomy, and astrology, and was in contact with Tycho Brahe (more of whom at a later date). He used his sombre appearance to suggest his occult credentials (not perhaps the best move in the early 17th century), and travelled everywhere with a black cockerel.

Frontispiece to Napier's Memoirs
"It is not improbable that our philosopher made a pet of some jetty chanticleer, which he cherished as the badge of his office … There can be little doubt that in those days it would pass for a spirit. A story was once abroad of this animal, which has since reappeared in some popular drama or nursery tale. It is said that Napier adopted the policy of Mahomet to control his own domestics, and impressed them with a belief that he and chanticleer together could detect them in their most secret doings. Having missed some property, and suspecting his servants, he ordered them one by one into a dark room, where his favourite was confined, and declared that the cock would crow when the guilty one stroked his back, as each was required to do. The cock remained silent during all the ceremony; but the hands of one of the servants were found to be entirely free from the soot with which the feathers of the mysterious bird had been anointed."
  Memoirs of John Napier of Merchiston Mark Napier Esq. London (1834) p. 214
So, the innocents, having nothing to hide, were not afraid to touch this ‘jetty chanticleer’ and all emerged with sooty fingers, but the guilty person was revealed when they only pretended to touch the bird – and so didn’t get soot on their hands. Very clever, Mr Napier, very clever.


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