Systems of measurement

• SUMMARY: Various systems of measurement have been used and debated throughout history, with accuracy and precision becoming increasingly important.

Some define measurement as the process of determining the magnitude of a quantity. The word comes from the ancient Greek metron, meaning “proportion,” but the process itself is as old as humankind. Long before humans used calculus or algebra, they were measuring length, area, volume, time, and mass. Measures were needed to make furniture, buildings, and ritual places, as well as landscaping, timekeeping, and making sky charts and calendars. Evidence of standardized systems of weights and measures dating back to approximately 3000 BCE has been found, showing that, though measurement systems have become more refined over centuries, the concept is ancient. By 1600 BCE, people offered silver and gold sticks in exchange for products, and in this manner, money became a way to measure value.

Mathematicians generalized the notion of measurement in several ways, such as in length spaces, metric spaces, and the field of measurement theory. Numerous mathematicians have measures named after them, like the Lebesgue measure, named for Henri Lebesgue, who pioneered the theory of integration, and the Borel measure, named for Émile Borel, who is known for his work in measurement theory and probability. Other notable minds in the development of modern measurement systems include Nikolai Luzin (descriptive set theory), Johann Radon (Radon–Nikodym theorem), Constantin Carathéodory (the calculus of variations and measurement theory), and Maurice Fréchet (defined metric spaces). These scientists and mathematicians developed systems of measurement to quantify objects that were once thought impossible to measure. For instance, they have developed measurements for infinite sets, ways to measure π that are accurate to huge numbers of decimals, measures for hyperbolic geometry in which the Pythagorean theorem no longer holds, tiny-scale measurements on the quantum level or in nanotechnology, large-scale measurements of the universe, and even measurements of political opinion. Some of these measurements remain controversial, such as how to assess educational achievement or human intelligence. Mathematicians and statisticians continue to design, refine, and improve measurements. In twenty-first-century mathematics classrooms, students in pre-kindergarten through college investigate measurable attributes, including formulas, models, and processes, as well as units and systems of measurement.

Early Measurement Systems

Historical records indicate that the concept of measurement was vital for ancient civilizations, as humans needed to build dwellings, make clothing, and barter for goods. Historical study has indicated that the people of ancient Egypt, Mesopotamia, and the Indus Valley all developed systems of measurement, some of which were remarkably precise. For example, the people of the Indus Valley used measurements of length where the smallest division was approximately equal to 1/16 inch, as well as “yardsticks” that were exactly 33 inches in length. These measurements, while ancient in origin, were used in traditional Indian architecture and remain in use in the twenty-first century. Ancient humans typically used body parts as instruments for measuring length. The most standard unit of length that developed from ancient cultures is the cubit. The cubit was commonly defined as the length of the forearm from the elbow to the tip of the middle finger.

However, ancient Egyptian culture also defined the Sacred Cubit as a common cubit plus an extra hand span. The Sacred Cubit was used to construct buildings and monuments in ancient Egypt and to survey the land. As ancient civilizations progressed and trade became more vital, standardization of measurement systems became more of a concern. Ancient peoples attempted to solve this problem by creating a rod or bar of a given length (usually a cubit) designated as the standard unit of measure. The rod was usually normed on a ruler’s dimensions. The original rod was typically kept in a temple or other safe place, and other identical rods were created and distributed throughout the community. The number of seeds that filled a clay jar or gourd served as a measure of volume. Some civilizations also used water instead of grain. Later, stones or sometimes lumps of metal of a certain weight were used for larger units. Like the rods used for length, these stones or lumps of metal were typically kept in temples or other safe places as the official weight standard. However, duplicating the weight provided opportunities for the deception of customers, as it was fairly easy for merchants to remove weight from a lump of metal. Therefore, inspections of weight measures became common practice, and this practice still continues through the twenty-first century. Some modern measurement forms, such as the carat, were developed from this ancient tradition.

Standardized Measurement Systems

The English system of measurement was developed from the systems of a variety of cultures, including Babylonian, Egyptian, and Roman. From the Roman culture came the use of the base 12 system (for example, 12 inches in one foot); studies in the etymology of the English measurement units show strong Roman influence. The English system was widely used through the nineteenth century because of royal edicts that helped standardize measurements. For example, King Henry I issued a decree that the distance from the tip of his nose to the end of his outstretched thumb should be designated as one yard. This standardization made the English system very popular in various parts of the world. However, not all areas recognized and utilized the English system, which motivated some to call for a single global standardized measurement system.

The idea of a single worldwide system of measurement is generally credited to Gabriel Mouton (1670). While several proposals of how such a system might be established were presented at the time, Mouton’s proposal used a decimal system based on the length of one minute of the arc of a great circle of the Earth. Gottfried Leibniz proposed a similar system in 1673, leading to the concept of a seconds pendulum. However, little was done for more than 100 years to further establish this system of measurement.

The metric system known in the twenty-first century originates in the French Revolution, as the National Assembly of France commissioned the French Academy of Sciences to develop a standard of measures and weights. The system created was based on establishing a portion of the Earth’s circumference as the unit of length. This unit of length was designated a “meter,” derived from the Greek word for “a measure.” Units of volume and mass were derived from the basic unit of length. The unit of mass, the gram, was found by examining the mass of one cubic centimeter of water at its temperature of maximum density. The unit of volume, the liter, was designated as the amount of water in a cubic decimeter (a cube 10 centimeters on each side). The integral relationship between units of length, mass, and volume made the metric system unique. Additionally, the metric system was based on the concept that smaller and larger increments were created by multiplying or dividing the basic units by powers of 10. Working with a base-10 system made the metric system easy to use, as previous measurement systems had used base-12 or base-16 systems.

The first countries that used the new system were Belgium, the Netherlands, and Luxembourg around 1820. France made its use mandatory in 1840. Additionally, the metric system quickly became the standard for scientific and engineering work, which increased its global use as nations developed technologically. In 1875, seventeen countries signed the “Treaty of the Meter,” which officially established metric length and mass standards. In addition, this agreement established mechanisms for recommending and adopting refinements to the system. The metric system was officially accepted by thirty-five nations by 1900 and was the standard system of measurement in most nations at the start of the twenty-first century. However, traditional units are still used worldwide, and conversion tables and programs ensure successful calculation. Confusion between the two systems can lead to devastating consequences, such as the 1999 crash of the Mars Climate Orbiter, which NASA attributed to the failure to convert from English to metric values.

Modern-day developments in measurement have focused on developing more precise measurement units within the metric system. In 1960, the original nations of the “Treaty of the Meter” convened as the General Conference on Weights and Measures to develop a revision and simplification of the system. From this convention, seven units of measure were established as the base units of the system: meter for length, kilogram for mass, second for time, ampere for electric current, Kelvin for thermodynamic temperature, mole for substance, and candela for luminous intensity. Also, from this convention came the name of Système International d’Unitès (SI), or International Systems of Units, prompting the international abbreviation of SI for the metric system.

Since then, the General Conference on Weights and Measures has continued developing more precise and more easily reproducible definitions of measurement units. For instance, the meter was originally a fraction of the distance from the equator to the North Pole, but this measurement was complicated because the Earth is not a perfect sphere. The late-eighteenth-century expedition of mathematician and astronomer Jean-Baptiste-Joseph Delambre and surveyor Pierre Méchain to calculate the geodesic measurement was fraught with difficulties. Later, a standardized platinum and iridium meter bar was used. In 1983, the meter was redefined to relate to the speed of light, and it became defined as the distance light travels in a vacuum in 1/299,792,458 seconds. Improvements to the metric system have been ratified by the General Conference eight times since the 1960s, with the most recent taking place in 1995.

Modern Measurement

The International System of Units (SI) is commonly used in the twenty-first century. The British Imperial system and the United States customary system are also used in their respective countries. The International Bureau of Weights and Measures (BIPM) and the International Bureau of Legal Metrology (BIML) are regulating bodies that attempt to evaluate and standardize measurement systems. Several other organizations have been established for this purpose. In the United States, the National Institute of Standards and Technology’s Office of Weights and Measures (OWM) ensures the uniformity of measures and weights and their alignment with the International Committee for Weights and Measures (CIPM) requirements. Regular evaluations of measurements and their appropriate application occur at several conferences, including the General Conference on Weights and Measures and the National Conference on Weights and Measures.

Bibliography

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"History of Measurements." Vitrek, vitrek.com/mti-instruments/knowledge-center/history-of-measurements. Accessed 1 Oct. 2024.

"Office of Weights and Measures." National Institute of Standards and Technology, www.nist.gov/pml/owm. Accessed 1 Oct. 2024.

Robinson, Andrew. The Story of Measurement. Thames & Hudson, 2007.

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