This is a question that often arises during discussions on the merits of the metric system. Martin Vlietstra, one of our regular readers, provides some thoughts on the matter, coincidentally on 10 October.
Critics of the metric system of cite the difficulty of dividing ten by three or four, something which would be easy in a duo-decimal system. This note examines why the original developers of the metric system used ten and not twelve.
Mankind has developed various counting systems over the ages. The Babylonians inherited a sexagesimal (base 60) system of counting from the Sumerian civilisation. They did not however have 60 different symbols, but 14 symbols: symbols for 1 to 9 and symbols for 10, 20, 30, 40 and 50, implicitly defining 60 as 6×10 rather than 5×12. Although the Hebrews, Greeks and Romans used a decimal system of counting, the sexagesimal system still used when telling the time or measuring angles while the IT world often uses hexadecimal (base-16) as a shorthand for grouping set of binary numbers.
A few civilisations have used the duodecimal (base-12) system of counting, but their influence in western scientific and philosophical thinking has been minimal.
The duodecimal system has however been widely used in measurements. The French royal system of measurement of length user the pied or foot (324.8 mm) which had twelve pouces or inches (27.07 mm). The pouce had 12 lignes or lines (2.25 mm) and the ligne had 12 points (0.188 mm).
The duodecimal system was not extended to units greater than one pied, though the toise or fathom was six pieds. The French did not use a duodecimal system weight or volume, though many European countries had a “light pound” of 12 ounces (as opposed to a “heavy pound”). In Britain, the “light pound” was the troy pound made up of 12 ounces each of 31.1 g while the “heavy pound”, more correctly known as the avoirdupois pound, has 16 ounces, each of 28.35 g. As is rightly pointed out by supporters of the duodecimal system, 12 can easily be divided by 3 and 4 – a boon to those who do not have calculators.
Simon Stevin, who in 1585 published the basis of what we today know as decimal fractions, forecast that one day units of measure would one day be divided decimally. In 1620 Edmund Gunter developed Gunter’s chain which was 22 yards in length and which had 100 links, each of 7.82 inches (782 inches = 66 feet = 22 yards). This chain enabled him to measure the lengths of fields in decimals of a chain and so facilitate the calculation of the area of the field (one square chain had an area of 0.1 acres). In practice, when using Gunter’s chain, the area of the field was measured in acres and decimals of an acre and then, to keep the lawyers happy, the decimal part was converted into rood, perches and square yards.
In 1668 John Wilkins published a proposal that was remarkably similar to the metric system as we know it. He proposed that the base unit of length should be a “seconds pendulum” (which turned out to be about 993 mm in length) and that multiples and sub-multiples of this base unit should be integer powers of 10. He made similar proposals for area, volume and weight, defining one unit of weight as being equal to the weight of one cubic volume of rainwater (this compares with a litre of water at 4°C having a mass of one kilogram). Unlike the modern metric system, he reused names of units that were already in use.
One of the most forward-looking European rules of the pre-revolutionary era was Peter the Great (1672 – 1728), Czar of Russia. He dragged Russia from being a medieval state to being an equal of other European states. In 1698 he reformed the Russian system of weights and measures and took the English foot as the new Russian fut. In 1704 he reformed the Russian currency, introducing a “new” rouble which was divided into 100 kopecks, probably the first decimal currency in the world.
One of the eighteenth century’s biggest projects, as least insofar and the amount of computation that was involved, was the survey of France undertaken between 1756 and 1789 by César-François Cassini and his son Jean-Domenica Cassini. The Cassinis enlisted the help of the British establishment to extend the map to the Greenwich Observatory thus providing a correlation between British and French maps. The theodolites used were able to measure angles down to about one second of arc, an accuracy that would have required seven-figure trigonometric tables.
When the French Revolution broke out (1789), the royal system of measure was not mandatory (except possibly for assessing the king’s taxes). Merchants could (and did) define their own systems of units which resulted in a wholesale exploitation of the peasants. In 1790 the French Assemblée set up a new committee under the auspices of the Académie de Sciences to investigate weights and measures. The members were five of the most able scientists of the day: Jean-Charles de Borda, Joseph-Louis Lagrange, Pierre-Simon Laplace, Gaspard Monge and the Marquis de Condorcet.
The Committee quickly agreed that the system of weights and measures needed to be overhauled rather than be “fine-tuned” and that there should be a universal multiplier for units of the same quantity. There was a debate as to whether the universal multiplier should be 10 or 12. Those connected with trade and commerce favoured a duodecimal system of weights and measures but those who were connected with astronomy and surveying, especially Monge, an associate of the Cassinis, favoured a decimal system. They argued that nice as the duodecimal system was for simple calculations, it impractical in the fields of heavy computation and would remain so unless the decimal system of counting was replaced by a duodecimal system of counting. Eventually the decimal argument won the day as the introduction of a duodecimal system of counting was totally impracticable.
In 1792 the United States introduced a decimal-based currency as have most, if not all the countries in the world, thereby eschewing the “divisibility” argument of a decimal-based system.