[Math Lair] Measurement

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Weights and measures were among the earliest tools invented by man. Primitive societies needed rudimentary measures for many tasks: constructing dwellings of an appropriate size and shape, fashioning clothing and bartering food or raw materials. However, during prehistory, having standard units of measurement was not particularly important. The reason is that most measurement was performed by a single person completing one job at a time, so it didn't make much difference exactly how long a certain unit was, as long as the person used the same unit throughout the job.

With the dawn of civilization, however, standards became more important. For example, with thousands of workers working on building the pyramids in Egypt, it would be important that everyone means the same thing when referring to each unit of measurement. Measurements need to be standard so that they mean the same thing to everyone. Man understandably turned first to parts of his body and his natural surroundings for measuring instruments. Early Babylonian and Egyptian records, and the Bible, indicate that length was first measured with the forearm, hand, or finger and that time was measured by the periods of the sun, moon, and other heavenly bodies. When it was necessary to compare the capacities of containers such as gourds or clay or metal vessels, they were filled with plant seeds that were then counted to measure the volumes. With the development of scales as a means for weighing, seeds and stones served as standards. For instance, the "carat," still used as a mass unit for gems, is derived from the carob seed.

As societies became more complex, measurements also became more complex. The invention of numbering systems and the science of mathematics made it possible to create whole systems of measurement units suited to trade and commerce, land division, taxation, and scientific research. For these more sophisticated uses, it was necessary not only to weigh and measure more complex things it was also necessary to do it accurately time after time and in different places. However, with limited international exchange of goods and communication of ideas, different systems for the same purpose developed and became established in different parts of the world—even in different parts of the same country. As an example of this, you can read a newspaper article from 1907 on the curiosities of measurement.

The need for a single worldwide coordinated measurement system was recognized over 300 years ago. Gabriel Mouton, Vicar of St. Paul's Church in Lyons and an astronomer, proposed in 1670 a comprehensive decimal measurement system based on the length of one minute of arc of a great circle of the Earth. Mouton also proposed the swing length of a pendulum with a frequency of one beat per second as the unit of length. A pendulum with this beat would have been fairly easily reproducible, thus facilitating the widespread distribution of uniform standards. Other proposals were made, but more than a century elapsed before any action was taken.

In 1790, during 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." The Commission appointed by the Academy created a system that was, at once, simple and scientific. The unit of length was to be a portion of the Earth's circumference. Measures for capacity (volume) and mass were to be derived from the unit of length, thus relating the basic units of the system to each other and to nature. Furthermore, larger and smaller multiples of each unit were to be created by multiplying or dividing the basic units by 10 and its powers. This feature provided a great convenience to users of the system, by eliminating the need for such calculations as dividing by 16 (to convert ounces to pounds) or by 12 (to convert inches to feet). Similar calculations in the metric system could be performed simply by shifting the decimal point Thus, the metric system is a "base-10" or "decimal" system.

The Commission assigned the name metre to the unit of length. This name was derived from the Greek word metron, meaning "a measure." The physical standard representing the meter was to be constructed so that it would equal one ten-millionth of the distance from the North Pole to the equator along the meridian running near Dunkirk in France and Barcelona in Spain. The initial metric unit of mass, the "gram," was defined as the mass of one cubic centimeter (a cube that is 0.01 meter on each side) of water at its temperature of maximum density. The cubic decimeter (a cube 0.1 meter on each side) was chosen as the unit for capacity. The fluid volume measurement for the cubic decimeter was given the name "liter." In order to avoid a large number of zeroes to express very large or small measurements, the metric system uses Greek-derived prefixes to indicate multiples or submultiples.

Adoption of the metric system was slow but started occurring steadily after France made its use compulsory in 1840. The standardized structure and decimal features of the metric system made it well suited for scientific and engineering work. By the late 1860s, even better metric standards were needed to keep pace with scientific advances. In 1875, an international agreement, known as the Meter Convention, set up well-defined metric standards for length and mass and established permanent mechanisms to recommend and adopt further refinements in the metric system. This agreement, commonly called the "Treaty of the Meter" in the United States, was signed by 17 countries, including the United States. As a result of the Treaty, metric standards were constructed and distributed to each nation that ratified the Convention. By 1900 a total of 35 nations had officially accepted the metric system.

In 1960, the General Conference on Weights and Measures, the diplomatic organization made up of the signatory nations to the Meter Convention, adopted an extensive revision and simplification of the system. Seven units were established as the base units for the system:
Type of unitNameAbbreviation
Length metre m
Mass kilogram kg
Time second s
Electric current ampere A
Temperature kelvin K
Amount of substance mole mol
Luminous intensity candela cd
The name Systeme International d'Unites (International System of Units), with the international abbreviation SI, was adopted for this modern metric system.

On the Math Lair is a page that converts between pounds and kilograms, as well as between feet/inches and centimetres.