002 – Go figure! – 4,000 BCE

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I know nothing except the fact of my ignorance.  Socrates

In October 1900 Captain Dimitrios Kondos and his crew, using the old-style canvas diving suits with brass helmets, were diving for sponges off the Greek island of Antikythera.  They discovered a wreck and with approval recovered a number of artefacts from it.

Antikythera mechanism

One find was the ‘Antikythera mechanism’, claimed to be a very early analogue computer dating from the 4th century BCE; some eighty-two fragments of it have been recovered.

It is an astronomical clock with up to thirty-seven gears used to forecast the celestial positions relative to Earth for a given date.  It showed the calculated positions of the Sun and Moon and the lunar phases and may have included the position of Mars and Venus.

It had forty-seven divisions with five rotations emulating the 235 months in the nineteen years of the Metonic cycle which is still a vital tool for defining calendars. 

The device was so sophisticated that there must have been predecessor devices although none have yet been discovered.  The engineering contradicts the belief that something like this was only possible from the Middle Ages when astrolabes and clocks emerged.  The Roman philosopher Cicero and others had mentioned such devices but had been dismissed as fanciful.

From the 13th century clocks and automata became popular. 

Prague’s Orloji

The Orloji in Prague’s Old Town Square built in 1410 was the third astronomical clock and is the oldest still in existence.

It plots the positions of the Sun and Moon. It has a calendar dial and shows the zodiac positions as a sort of planetarium.  There are figurines that march each hour, all twelve apostles are presented and four fixed figures represent vanity, greed, pleasure and death.

But these were really ephemera when it came to commerce where the abacus ruled supreme.  The name comes from the Greek word for calculating table.  The abacus was in use from 2,500 BCE before any system of writing of modern numerals had begun.

Abacus or Suanpan

The Chinese version of an abacus, the suanpan or counting tray, had a series of wires with the top section called ‘heaven’ and the bottom section called ‘earth’.  The Chinese developed techniques not just to add and subtract, they could also multiply and divide and work out square and cube roots.

Roman calculus

It was the Romans who moved the abacus to a system of 1s, 5s and 10s.  But their design used pebbles sliding within grooves which was slower and more open to error or fraud than the beads-fixed-on-wire version.  A pebble used with the Roman abacus was a ‘calculus’ and this is the origin of the term for that branch of mathematics.

The abacus was a very versatile piece of equipment and stayed stubbornly in use for a large period of the development of mankind’s commercial activity.

In Japan, Ryōichi Yazu was helping his father with his clerical work and was prompted to come up with a design for a mechanical automated abacus.  It was patented in 1902 and manufactured from 1903 but its high price meant it sold just two hundred units.

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