Essay by Johannes Iede Reckman
Glasgow School of Art 2012
For Core Research Skill Course “The Sociological Imagination” by William Clark


VISION ON DIVISION
On the distinction and origin of the imperial system and the metric system

When you grow up with a mathematical understanding directly related to the metric system it all seems so logical, counting your fingers, adding zeros when jumping from dozens to hundreds to thousands, just one ongoing line of numbers that could expand in infinity… Until suddenly you get to know this other system, called the imperial system. Ok, the units are different but convertible, but there is something else; how do they relate to each other? Why is there not an even relation between these imperial units? In order to try to answer these questions I will focus on the history and origin of measurement. And while doing so, other questions rise; how did the imperial system as well as the metric system develop and how do their differences relate to their cultural, social and scientific influences and contributions?


I. Prior Systems
Most sources state that the earliest known uniform systems of weights and measures were created around 4000 to 3000 BC (the beginning of the Bronze Age) among the ancient peoples of Egypt, Babylonia (roughly present Iraq)(NIST, ca. 1995: p.1; The story of maths, 2008) and the Indus Valley[1] (present Pakistan and North-West India). But it seems to me that one of the first known traces of measuring in human history appeared much earlier. Incised bone and clay counters have been found at Neolithic village sites in Turkey dating from the 9th millennium BC, more than 10.000 years ago (Linklater, 2002: p.4). Although this might not be reckoned as a rudimentary system, it is a way to secure amounts. This notion leads me to the realisation that interpreting the development of any early measurement system should not be separated from the development of mathematics and number systems. Therefore I will highlight where it can be of importance to illustrate the evolution of the imperial system and the metric system.

When, in the Bronze Age, the Egyptian, the Babylonian and the Indus Valley civilizations developed their first uniform systems, they used their bodies to measure the world, from which their units of measure evolved. The most common was the cubit; an arm length from elbow to fingertip. It was divided into the span; the length between the tip of the little finger to the tip of the thumb (half a cubit), the palm; the width of the hand (one sixth), and the digit; the width of the middle finger (one twenty-fourth). It is notable that the Egyptians used another second cubit when it came to constructing buildings and surveying. This cubit was enhanced by an extra palm leading to a total of 7 palms or 28 digits (Scott, 1959: p.24; Wikipedia, 2012a).
The Bible also mentions measurements, such as the cubit (Hebr. 'ammah, Lat. cubitus), that directly relate to the known records of Egypt and Babylonia. The available means of measurement of body related units could be directly applied when measuring someone’s height, the breadth of cloth or the thickness of a wall. Distances between points as distinct from measurements of the length of objects, were not expressed by large multiples of those units, but by expressions such as a bowshot (Gen. 21:16), a furrow’s length (1 Sam. 14:14), a day’s journey (1 Kings 19:4; Lk. 2:44), a three day’s journey (Gen. 30:36)(Scott, 1959: p.23-24).
For means of weight, seeds and stones were used as standards. The carat is derived from the carob seed and we still know it as the unit for gemstones. To compare the capacity of containers or vessels those were filled with seeds, grain or rice, which were then counted. Those foods were found to be ideal units because of their constant size and mass (NIST, ca. 1995: p.1; Wikipedia, 2012a; Zhengzhang, 1991: p.289).

Time was measured by the periods of the sun and moon and other heavenly bodies. Egyptians did record what was going on over periods of time in order to establish a calendar to register how many days elapsed between separate floods of the Nile. Recording the pattern of the seasons was essential, not only for the management of their land but also their religion. As their settlements grew larger it became necessary to administer them. The Pharaoh’s surveyors calculated the area of a farmers land so crop yields could be predicted and taxes could be charged. Although the Egyptians used a decimal system to count, they had no concept of a place-value.[2] Instead the Egyptians used different characters for ones, tens, hundreds etc. and they would multiply those characters if needed (The story of maths, 2008). Therefore to write bigger numbers it became more complex and it required inventive new characters.

Unlike the Egyptians the Babylonians did not use their fingers to count pairs of ten. Instead they counted pairs of sixty using the twelve knuckles on one hand and the five fingers on the other. It made it possible to count bigger numbers, but the number sixty had another powerful property; it could be divided in multiple arrangements: 2x30, 3x20, 4x15, 5x12 and 6x10. The base-sixty system (or sexagesimal system) was so successful that we still use elements of it today. We recognise units of sixty seconds in a minute, sixty minutes in an hour. The Babylonians also developed the system of angular measurement as we know it; 360 degrees in a full circle, each degree divided into sixty minutes and each minute into sixty seconds.
Babylonian digits from 1 to 59 represented with only two different marks.
But another important feature of the Babylonian number system was that it recognized place-value. They had a symbol for 1 and a symbol for 10, which were combined to make 59 different digits. The position of each digit records the pair of sixty (like the decimal figures count how many ones, tens, hundreds, thousands etc.).[3] In this way it became possible to create extremely large numbers. But to mark an empty place in the middle of a number, it would simply leave a blank spot, so they used a sign as a sort of breathing mark in the middle of a number to represent nothing. This was the first idea of a zero, but it was not considered a number, merely the lack of a number.

The Indians have been using the decimal place-value system since the 3rd century AD (The story of maths, 2008). They refined and perfected their number system and created the ancestors for the nine numerals that we use across the world today. But the zero as a number was still missing and the Indians introduced it. The earliest record of zero is only from the 9th century AD, although it was in practical use before. The Indians transformed zero from a mere placeholder to a number that made sense in its own right. How it came to be that the Indians invented the notion of zero, could be culturally related. The concepts of nothingness and eternity are deeply rooted in their religions. Now, with ten digits, it was possible to capture very large numbers in an efficient way.

This brief historical overview shows how counting and measuring without a notion of zero has not always been an obvious thing. It makes it more argumentative how different units developed by disproportional related divisions, as we do recognize in the imperial system. Because initially it was just not possible to use continuous larger or smaller sequences, by shifting a decimal point and adding zeros, people were obliged to pick a measurement unit suited for the subject they would measure.


II. The imperial system
The imperial system (or British Imperial System) was first officially defined in the British Weights and Measures Act of 1824 (Wikipedia, 2012c), but its units were in use long before throughout Europe. Its origin, for a great part, is directly related to the Roman Imperial influence in Europe. The Roman measurement system in turn has its origin from the Greek, who advanced their imperial reach (during the Hellenistic period, 4th century BC) also into Babylonia, Egypt and India.

Roman contributions to the imperial system include the use of 12 as a base number. The 12 divisions of the Roman libra (pound) and pes (pes is the Latin word for foot) were called unciae. The words ounce and inch are both derived from that Latin word (NIST, ca. 1995: p.2).
The yard, equal to 3 feet or 36 inches, in its early stage was divided into 2, 4, 8, and 16 parts called the half-yard, span, finger and nail, a sub-divisions still in general use for the inch. Some say that this early yard was derived from a double cubit (Wikipedia, 2012a).
These examples of units with their sub-divisional numbers show the convenience of dividing into halves, quarters and so on; all very suitable for daily use, commerce and trade. However because of limited exchange of goods and communication of ideas, different systems for the same purpose developed and became established in different parts of Europe and even in the same countries: “What was being measured was not a quantity but its local, subjective, human value”(Linklater, 2002: p. 22).

Through royal edict attempts were done to achieve consensus. The yard can be traced back to early Saxon kings. They wore a sash or girdle around the waist that could be used as a measuring device. The word yard comes from the Saxon word gird, meaning the circumference of a person’s waist (NIST, ca. 1995: p.2). It is said that King Henry I (who ruled from 1100 to 1135) declared that a yard should be the distance from the tip of his nose to the end of his outstretched thumb. Another ‘questionable’ unit was the perch, defined as “the total length of the left feet of the first 16 men to leave church on Sunday morning”(Kowalewski, 2002).
The length of a furlong (or furrow-long) was established by early Tudor rules as 220 yards. This led Queen Elizabeth I to declare in the 16th century, that henceforth the traditional Roman mile (The mille passus; 1000 paces or double steps) of 5000 feet would be replaced by one of 5280 feet, making the mile exactly eight furlongs and providing a convenient relationship between the furlong and the mile. Therefore, by the 18th century England had achieved a greater degree of standardization than other European countries (NIST, ca. 1995: p. 2;Wikipedia, 2012a).

In 1785 Thomas Hutchins, first Geographer of the United States, started to lay out a grid across the untamed land of America that would create a structure of landownership unique in history. Before this moment it was possible to own the use of land, but never to own the land itself. The idea that land might be treated as property belonging to an individual, to be traded and speculated on like any other commodity, required a shift in thinking. Before people figured that the span of one life was too brief to possess the earth that continued forever (Linklater, 2002: p. 5).
Measurement has probably never been a more powerful tool. Linklater (2002) states: “A map was a political document. It not only described territory but asserted ownership of it as well”(p. 9) and: “Since the Native Americans had nothing to show that they owned the land, the new Americans could take it freely, and New England, like the Old, would belong to those who could measure it and enclose it”(p. 23).
To survey, Hutchins, as well as landowners and farmers, used a chain with a distance of 22 yards, which was invented by the English mathematician Edmund Gunter by the 1620s. The 22 yards of “Gunter’s chain” measured 4 perches, also known as rods or poles. Originally the perch varied according to the quality of ground – a perch of poor soil was longer then a perch of fertile soil – but in the 16th century AD it was standardized at 16½ feet. This inconvenient length was derived from the area of agricultural land that could be worked by one person in one day, which amounted to 4 square perches. An acre amounted to 40 days work or one day if worked by a team of oxen.
The 22 yards were to become integral to the town planning of almost every major city in the United States (the lengths of most city blocks are multiples of it), but notable also to the game of cricket (it is the length of a pitch)(Linklater, 2002: p. 5). Like all other units of measurement then in use, the length of “Gunter’s chain” was ultimately derived from human activity and the dimension of the human body.
Gunter’s chain with its 100 links. The chain was marked
at every 10 links along its length by brass tags or tallies,
the number of points on the tag denoting its position on the chain.

In 1585 the Dutch engineer Simon Stevin was the first European to publish an account of decimals. Gunter grasped this concept. The chain has a decimal basis viz. 1/100th chain is 1 link. Measurements are made in chains and decimal parts, which are expressed in links. For example 4.25 chains equals 4 chains and 25 links. By using this system it was reasonably easy to work out acreage by multiplying together length times width of the chains and then dividing by ten to give the total acres. It made a synthesis of two incompatible systems (C J’s Metal Detecting Pages, 2002).
An overview of the units of Gunter’s chain
1 link          = 7.92 inches
25 links        = 1 perch or 16½ feet
100 links       = 1 chain or 66 feet/22 yards
10 chains       = 1 furlong or 220 yards
80 chains       = 1 mile or 5280 feet/1760 yards
10 square chains    = 1 acre


III. The metric system
Use of new measurements. Woodcut dated 1800.
Illustrating the new decimal units, which became the legal
norm across all France on 4 November 1800 (Wikipedia, 2012d).

In 1790, in the midst of the French Revolution, the National Assembly of France requested the French Academy of Sciences to "deduce an invariable standard for all the measures and all the weights"(NIST, ca. 1995: p.3). In use were still the old aristocratic unfixed measures, by which market traders exploited their customers and landlords their tenants.
The aim was to create a decimal system that was simple and scientific, but also democratic. Measures for capacity and mass would be based on cubes and were to be derived from the unit of length, therefore relating the basic units of the system to each other. Furthermore, larger and smaller multiples of each unit were to be created by multiplying or dividing the basic units by 10 and its powers.
The name metre (derived from the Greek metron, which means "a measure"). was assigned to the unit of length. The physical standard representing the metre, kept as a platinum bar in Paris, was to be constructed so that it would equal one ten-millionth of the distance from the North Pole to the equator.[4]
The gram was defined as the mass of one cubic centimetre of water at its temperature of maximum density. The fluid volume measurement for the cubic decimetre was given the name litre (NIST, ca. 1995: p.3).  

The simplicity of calculating in 10s should give the average citizen the opportunity to deal on equal terms with those who were more educated. Initially the decimalization was to be applied into the number of months in a year, days in a week, hours in a day etc. But what the people wanted was the old system made uniform. The metric system forced people to separate their measures from the related activities and deal with an abstract unit.
The reason that the metric system survived after all is mainly due to the effectiveness of centralized administration and government bureaucracy that spread across Europe. But when scientists started to use the metric system to communicate their results, and introduced, next to distance, mass, and time, four new elements – named; kelvin (temperature), mole (substance), candela (light intensity) and ampere (electric current) – it proved that the benefits of the new system accelerated scientific discoveries.
By the mid 20th century scientists were demanding a more accurate and reproducible standard than a prototype platinum bar could offer. Therefore the metre was re-defined in 1960 in terms of the wavelength of light from a krypton-86 atom and then again in 1983 as the length of the path travelled by light in a vacuum during 0.000000003335640952 second. A second, for its part, is the time in which a caesium-133 atom undergoes 9 192 631 770 vibrations. The only fundamental unit still based on an old-fashioned object is the kilogram. The international prototype kilogram is a platinum-iridium cylinder maintained at constant temperature at Sèvres in France (Cookson, 2002; Linklater, 2002). In 1960 the metric system was given the official name Le Système international d'unités (International System of Units or abbreviated SI).


IV. Conclusion
With the knowledge of measurement units derived from body parts, the theories of the philosopher Merleau-Ponty, who puts the emphasis on the body as a primary means of knowing the world, seems so literal and evident. In his phenomenology the body is a permanent condition for experience and is the instrument of understanding the perceived world.
How the units of the imperial system and the metric system came to their interrelation has been a process that evolved from ancient civilisations through the societies we live in today. Measurement transcended its sheer practical purpose and has primarily manifested and developed itself as an instrument to gain power and knowledge. As the surveyors had used measurement to create property from the wilderness, so had the 19th century physicists used it to create science from the natural world.
By measuring we can describe and understand the world, but the more we learn about this expanding world – from macro to micro – the more the system of measurement needs to be capable of accurately describing it. Eventually the discoveries accomplished by the virtue of its own features require re-defining and optimizing its own standards. Measurement became the tool to describe the world and at the same time measurement is searching the world for its own verification.
Although we could say that the imperial system is a more natural derivative, it is inevitable that the metric system will eventually overrule. In fact even the US is officially a metric nation. By Act of Congress in 1866, it became “lawful throughout the United States of America to employ the weights and measures of the metric system in all contracts, dealings or court proceedings”(NIST, ca. 1995: p.3). But the people rejected it and still hold on to the pound, the gallon and the mile, in contrast to the British who adapted most of its standards to the metric system.
There are many reasons for the US to change to the metric system, a good example is the foul-up that occurred when a British team working with NASA forwarded data to an American team in metric units, and the American team assumed the units were imperial. This resulted in the crash of the Mars Lander on the surface of Mars, destroying many millions of dollars worth of experiments and setting the Mars exploration program back many years (Kowalewski, 2002; Linklater, 2002).

While writing this essay another distinction chased me, it seems just linguistic, but there might be a relation with the distinction between the imperial and the metric. It is about how to consequently write down measurement symbols in combination with their value in numbers.
Officially a comma is used as a decimal separator. Only in the English language it is allowed to use a point. In most languages between the number and the unit symbol there is a space, though in English the number and unit symbol are written together.
Numbers can be separated by spaces in groups of three. Commas (or points in other than English notations) are not allowed (Wikipedia, 2012e).



Bibliography
Angela Ruskin University (2012), Harvard system, Angela Ruskin University, Cambridge & Chelmsford. Available at: http://libweb.anglia.ac.uk/referencing/harvard.htm (Accessed: 23 November 2012)

Bryson B. (2003), A short history of nearly everything, Transworld Publishers, London.

C J’s Metal Detecting Pages (2002), Gunter’s chain. [online image] Available at: http://www.ukdfd.co.uk/ceejays_site/pages/gunterschain.htm (Accessed: 12 November 2012)

Cookson C. (2000), “The Nature of Things”, Financial Times, 20 May, p. 2.

Kowalewski A. (2002), Why should you learn the metric system? Printed Circuit Design 19.5, May, p. 8-10.

Kwant Prof. Dr. R. C. (1968), De wijsbegeerte van Merleau-Ponty, 2nd edn, Aula, Antwerp.

Linklater A. (2002), Measuring America, Penguin Group, New York.

NIST (National Institute Of Standards And Technology)(ca. 1995), A brief history of measurement systems, Stock Number 003-003-03501-7.

Sample Harvard essay (n.d.), Language and learning online, Monash University. Available at: http://www.monash.edu.au/lls/llonline/writing/general/essay/analysing-citations/2.xml (Accessed: 21 November 2012)

Scott R. B. Y. (1959), “Weights and measures of the Bible”, The Biblical Archaeologist, Vol. 22, No. 2, p. 21-40, The American Schools of Oriental Research, Boston.

The story of maths (2008), television documentary series, BBC, London. Written by Marcus Du Sautoy.

University of Southern Queensland (2012), Harvard AGPS referencing guide, University of Southern Queensland, Brisbane. Available at: http://www.usq.edu.au/library/help/referencing/harvard (Accessed: 21 November 2012)

Wikipedia (2012a), History of measurement. Available at: http://en.wikipedia.org/wiki/History_of_measurement (Accessed: 20 October 2012)

Wikipedia (2012b), Babilonian numerals. [online image] Available at: http://en.wikipedia.org/wiki/Babylonian_numerals (Accessed: 4 November 2012)

Wikipedia (2012c), Imperial units. Available at: http://en.wikipedia.org/wiki/Imperial_units (Accessed: 3 December 2012)

Wikipedia (2012d), Usage des Nouvelles Mesures. [woodcut] Available at: http://en.wikipedia.org/wiki/File:Usage_des_Nouvelles_Mesures_1800.jpg (Accessed 13 November 2012)

Wikipedia (2012e), SI-stelsel. Available at: http://nl.wikipedia.org/wiki/SI-stelsel (Accessed: 21 November 2012)

Zhengzhang T. (1991), “On the origin of the carat as the unit of weight for gemstones”, Chinese Journal of Geochemistry, Vol. 10, No. 3, p. 288-293. Available at: http://link.springer.com/article/10.1007%2FBF02843332?LI=true#page-1 (Accessed: 20 November 2012)



[1] The measurements of the Indus Valley Civilization were extremely precise. Their smallest division of length is marked on an ivory scale, which was found in Lothal, India. It is approximately 1,704mm, the smallest division ever recorded on a scale of the Bronze Age (Wikipedia, 2012a).
[2] A place-value system is what we use nowadays, where the digits position within a number indicates its magnitude.
[3] In a Babylonian number with three digits the first digit would just represent itself, the second is the digit x60 and the third is the digit x60x60 (x3600).
[4] Although people became quite accurate in surveying and measuring the globe by angular measurement, the perfect definition of the meter was not that simple. In 1686 Newton proved with his laws of gravity that the Earth was not a perfect sphere, but due to its spinning was slightly dented at the poles (Bryson, 2003).