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Authors: Alex Bellos
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displayed its ‘revolutionary vision of time’ for a year or so before sheepishly removing them from its catalogue.
The French and Swiss, however, are not the only Western nations to have had barmy counting procedures in the not too distant past. The tally stick, which became outdated the moment the first Sumerian printed his first cuneiform tablet, was used as a form of British currency until 1826. The Bank of England used to issue souped-up tally sticks that were worth a monetary value based on the distance of a mark from the base. A document written in 1186 by the Lord Treasurer Richard Fitzneal set out the values as:
£1000
thickness of the palm of the hand
£100
breadth of a thumb
£20
breadth of a little finger
£1
width of a swollen barleycorn
The procedure the Treasury used was, in fact, a system of ‘double tallies’. A piece of wood was split down the middle, giving two parts – the stock and the foil. A value was marked – tallied – on the stock and was also marked on the foil, which acted like a receipt. If I lent some money to the Bank of England, I would be given a stock with a notch indicating the amount – which explains the origin of the words stockholder and stockbroker – while the bank kept the foil, which had a matching notch.
This practice was abandoned barely two centuries ago. In 1834, the Treasury decided to incinerate the obsolete pieces of wood in a furnace under the Palace of Westminster, the seat of British government. The fire, however, spread out of control. Charles Dickens wrote: ‘The stove, overgorged with these preposterous sticks, set fire to the panelling; the panelling set fire to the House of Commons; the two houses [of government] were reduced to ashes.’ Obscure financial instruments have often impacted on the work of government, but only the tally stick has brought down a parliament. When the palace was rebuilt it had a brand new clock tower, Big Ben, which quickly became the most recognizable landmark in London.
An argument often used in favour of the imperial system over metric is that the words sound better. A case in point is the measures for wine:
2 gills = 1 chopin
2 chopins = 1 pint
2 pints = 1 quart
2 quarts = 1 pottle
2 pottles = 1 gallon
2 gallons = 1 peck
2 pecks = 1 demibushel
2 demibushels = 1 bushel (or firkin)
2 firkins = 1 kilderkin
2 kilderkins = 1 barrel
2 barrels = 1 hogshead
2 hogsheads = 1 pipe
2 pipes = 1 tun
This system is base two, or binary, which is usually expressed using the digits 0 and 1. Numbers in binary are the numbers you would use in base ten when only 0 and 1 appear. In other words, the sequence that begins 0, 1, 10, 11, 100, 101, 110, 111, 1000. So, 10 is two, 100 is four, 1000 is eight and so on, with each extra 0 on the end representing multiplication by two. (Which is just like base ten – adding a 0 on the end of a number is multiplication by ten.) In the wine measures, the smallest unit is a gill. Two gills makes a chopin, 4 gills a pint, 8 gills a quart, 16 gills a pottle, etc. The measures replicate perfectly the binary numerals. If a gill is represented by 1, then a chopin is 10, a pint is 100, a quart is 1000 and this carried on all the way to a tun, which is 10,000,000,000,000.
Binary can claim as its cheerleader the greatest mathematician ever to have fallen in love with a non-standard base. Gottfried Leibniz was one of the most important thinkers of the late seventeenth century, a scientist, philosopher and statesman. One of his duties was as librarian to the court of the Duke of Brunswick in Hanover. Leibniz was so excited with base two that he once wrote a letter to the Duke urging him to cast a silver medallion inscribed with the words Imago Creationis – ‘in the image of the world’ – as a tribute to the binary system. For Leibniz, binary had practical and spiritual relevance. First, he thought that its capacity for describing every
The French and Swiss, however, are not the only Western nations to have had barmy counting procedures in the not too distant past. The tally stick, which became outdated the moment the first Sumerian printed his first cuneiform tablet, was used as a form of British currency until 1826. The Bank of England used to issue souped-up tally sticks that were worth a monetary value based on the distance of a mark from the base. A document written in 1186 by the Lord Treasurer Richard Fitzneal set out the values as:
£1000
thickness of the palm of the hand
£100
breadth of a thumb
£20
breadth of a little finger
£1
width of a swollen barleycorn
The procedure the Treasury used was, in fact, a system of ‘double tallies’. A piece of wood was split down the middle, giving two parts – the stock and the foil. A value was marked – tallied – on the stock and was also marked on the foil, which acted like a receipt. If I lent some money to the Bank of England, I would be given a stock with a notch indicating the amount – which explains the origin of the words stockholder and stockbroker – while the bank kept the foil, which had a matching notch.
This practice was abandoned barely two centuries ago. In 1834, the Treasury decided to incinerate the obsolete pieces of wood in a furnace under the Palace of Westminster, the seat of British government. The fire, however, spread out of control. Charles Dickens wrote: ‘The stove, overgorged with these preposterous sticks, set fire to the panelling; the panelling set fire to the House of Commons; the two houses [of government] were reduced to ashes.’ Obscure financial instruments have often impacted on the work of government, but only the tally stick has brought down a parliament. When the palace was rebuilt it had a brand new clock tower, Big Ben, which quickly became the most recognizable landmark in London.
An argument often used in favour of the imperial system over metric is that the words sound better. A case in point is the measures for wine:
2 gills = 1 chopin
2 chopins = 1 pint
2 pints = 1 quart
2 quarts = 1 pottle
2 pottles = 1 gallon
2 gallons = 1 peck
2 pecks = 1 demibushel
2 demibushels = 1 bushel (or firkin)
2 firkins = 1 kilderkin
2 kilderkins = 1 barrel
2 barrels = 1 hogshead
2 hogsheads = 1 pipe
2 pipes = 1 tun
This system is base two, or binary, which is usually expressed using the digits 0 and 1. Numbers in binary are the numbers you would use in base ten when only 0 and 1 appear. In other words, the sequence that begins 0, 1, 10, 11, 100, 101, 110, 111, 1000. So, 10 is two, 100 is four, 1000 is eight and so on, with each extra 0 on the end representing multiplication by two. (Which is just like base ten – adding a 0 on the end of a number is multiplication by ten.) In the wine measures, the smallest unit is a gill. Two gills makes a chopin, 4 gills a pint, 8 gills a quart, 16 gills a pottle, etc. The measures replicate perfectly the binary numerals. If a gill is represented by 1, then a chopin is 10, a pint is 100, a quart is 1000 and this carried on all the way to a tun, which is 10,000,000,000,000.
Binary can claim as its cheerleader the greatest mathematician ever to have fallen in love with a non-standard base. Gottfried Leibniz was one of the most important thinkers of the late seventeenth century, a scientist, philosopher and statesman. One of his duties was as librarian to the court of the Duke of Brunswick in Hanover. Leibniz was so excited with base two that he once wrote a letter to the Duke urging him to cast a silver medallion inscribed with the words Imago Creationis – ‘in the image of the world’ – as a tribute to the binary system. For Leibniz, binary had practical and spiritual relevance. First, he thought that its capacity for describing every
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