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