2.1 Earliest measures
Experts theorize that the earliest units of length were derived from parts of the body. Units of capacity probably also had the same beginning. The problems with this are obvious. Different size people result in different size measurements. Man realized early that a standard system of weights and measures was necessary. Officials, either government or religious, became the setters and keepers of the standardization for different societies. Still the diversities continued. Both the Greek and Roman civilizations made attempts at standardization and yet neither were entirely successful with dual systems resulting in both empires. None of the systems that developed were entirely logical. Some weights were derived from natural sources such as grain, others from the weight of water in a particular cube. Another weakness of logic in some areas was the tendency to mix two or more systems of numbers in one system of weights and measures.
Then, as now, there were four systems of numbers at use in different places and for various purposes; the decimal system of units subdivided by tenths, the duo-decimal system in which twelve and its factors are dividers, the binary system of halves, quarters etc. and the sexagesimal system of division by 60, as in time and angles. The decimal system supposedly came from the Chinese and Egyptians, the duo-decimal from the Romans, the binary from the Hindus and the sexagesimal from the Sumarians and Babylonians.
2.2 How and why metrics came about
Confusion in the European system of weights and measures was well established by the time the Roman Empire collapsed. The Dark Ages probably caused the regression from any semblance of standardization that existed. By the Middle Ages the number of local units of weights and measures had become almost limitless. The crude systems of the Middle Ages continued throughout the world without much question until the 16th or 17th century when scientists started demanding something better. Traders and travelers could convert from one system to another but the work of scientists was becoming international and science could not progress without an exact and uniform system of weights and measures.
At the end of the 18th century, scientists created the metric system. While there was sentiment in both England and America for standardization, it was the political climate of France that allowed it to happen. The basic concept of the metric system was not new in the 1790’s. Scientists such as France’s Mouton, England’s Tallyrand, and America’s Franklin had developed theories based on the decimal system. The main holdup seemed to be agreement on a fundamental unit. In the end, the lineal system was to be one ten millionth of the meridian distance between the pole and the equator as determined by survey. In 1795 in France an act was passed legalizing the metric system. The names, it was agreed, would be polysyllabic in which Greek prefixes would be affixed to denote multiples of it and Roman prefixes to denote subdivisions.
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Myriameter
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—
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10,000
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meters
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-
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Kilometer
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—
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1,000
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meters
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Hectometer
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—
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100
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meters
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Dekameter
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—
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10
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meters
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Meter
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—
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1
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meter
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Decimeter
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—
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0.1
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meter
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Centimeter
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—
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0.01
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meter
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Similar prefixes were applied to units of weight and capacity.
There were two important points of simplicity. Its basic units of weight and capacity were directly related to the fundamental linear unit; the liter was a cubic decimeter and the gram, the weight of a cubic centimeter of water. And, all of its secondary units were multiples or divisions by ten of the basic units. All that it is needed to know is the size of a meter, the relationship between meters and units of capacity and mass, and the meaning of the prefixes. The memorizing of the mass of arbitrary and unrelated units such as miles, feet, and acres was unnecessary. The original basis for the meter, the ten millionth of a meridian, proved to be both inaccurate and continuously changing, but that is unimportant. What is important is that most any length would do as long as it was basic to all aspects of the system and was divided and multiplied decimally.
2.3 Progress once developed
Although it was official, the real acceptance was gradual. The acceptance of the system in other European countries has taken even longer. A conference in France in 1870 attended by 15 nations including the United States, led to the signing in 1875 of the “Metric Convention”, a treaty under which an International Bureau of Weights and Measures was established. The bureau resides in suburban Paris and is still the world center of metrology. The fault of any physical material standard, or a linear measure is that its length remains fixed only under certain controlled conditions. Thus, a meter is now defined as 1,650,763.73 wavelengths of the orange-red radiation of Krypton 86, and this is only the semi-scientific definition. During the twentieth century most of the other nations of the world have officially adopted the metric system. The United States is the only remaining major nation not officially converted to the metric system. It must be said that there is no country in the world in which the pure metric system is used for all transactions in weights and measures. The most common variation is the continued use of old names for metric units. Another departure from the true metric system is the application of the binary number system to metric units. For example, the equivalent of a pint of milk is called a half-liter. In most metric countries nonmetric units continue to be used in some industries, sometimes side by side with metric units, sometimes independent of them. In general this is true in industries that have a close association with the United States. Japan’s bicycle industry still does much business on an inch basis.
In countries that have been on the metric system for any length of time, the nonmetric instances are minor. Most people live by the metric system, and the young people know no other. The exceptions may comfort people who fear that quarts and pounds will disappear from supermarket shelves or roadsigns will change from miles to kilometers overnight.
Since the establishment of the International Conference on Weights and Measures, some changes have been made in the metric system, most of them of interest primarily to scientists and engineers. The Standard of the second has been redefined and prefixes have been added for both multiples and subdivisions to extend the scale of measurement. The prefix “tera” before meter or gram means one trillion, “giga” one billion, and “mega” one million. “Micro” means one millionth, “nano” one billionth, and “pico” one trillionth. At its 1960 meeting, the International Convention, which meets every six years, interpreted the metric system in the System International d’Unites, for which the abbreviation is S.I. in all languages. For all purposes other than scientific and advanced technical work this is merely a change in name. Actually, it is a purification and extension of the metric system to make it truly universal.
Through the years, several systems had developed which were all metric but differed in detail in various parts of the world. The S. I. also formalized the extension of the metric system to seven base units. The basic units of the complete S. I. system are:
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Quantity Measured
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Name of Unit
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Symbol
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-
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Length
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—
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Meter
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(m)
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Mass
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—
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Kilogram
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(kg)
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Time
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—
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Second
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(s)
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Electric Current
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—
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Ampere
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(A)
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Temperature
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—
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Kelvin
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(K)
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Luminous Intensity
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—
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Candela
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(cd)
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Amount of Substance
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—
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Mole
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(mol)
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In addition to base units the S. I. system includes a number of derived units for measurement of such things as force energy and power. The unit of force is the “newton” (N) which is defined as the amount of force that, acting for one second on one kilogram of matter, will increase its speed by one meter per second. Named for the English formulator of the law of mechanics, it is,appropriately, just about the gravitational force acting on an average falling apple.
Energy has many forms, but all energy is basically the product of force and distance and is convertible form one form to another. Thus, the S. I. system uses one unit for all kinds of energy; the “joule” (J) which is the amount of energy needed to push a distance of one meter against a force of one newton.
When Watt perfected the steam engine it replaced the horse so people wanted to know its capabilities in terms of the horse. So engines were rated in horsepower. When the electric motor was invented, its power was named after Watt. No matter what form power takes, it is a rate of generation or dissipation of energy, so the only unit of power in the S. I. system is called the Watt (W) which represents one joule of energy per second. One horsepower is roughly equivalent to 746 Watts.
2.4 Conclusion
These derived units, as well as the ampere, the kelvin, the candela, and the mole are of use to scientists and engineers, but not of much concern to most people. Measures of length, weight, and capacity are the commonly used ones. The most commonly used metric units of length in everyday life are millimeter (mm) for small dimensions, the centimeter Ccm) for daily practical use, the meter (m) for expressing dimensions of larger objects and short distances, and the kilometer (km) for longer distances.
The most convenient unit of volume for everyday use is the liter (1), although it is part of the S. I. system only in that it is recognized as a name for the cubic decimeter.
There is no international standard liter. One liter is slightly larger than the U.S. quart. Precise measurements of volume in science are expressed in cubic centimeters (cm
3
) or cubic millimeters (mm
3
).
The most common unit of mass or weight is the kilogram (kg) which equals about 2.2 pounds. Grams (g) and metric tons (t) are also used.
To the general public, most of the history and all but the more basic units of the metric system are unnecessary. Some background and at least a basic awareness of all the components of the metric system are useful for those of us who will teach it.
What does all this mean to teachers of math? First of all, like it or not, this country will eventually join the rest of the world in using the metric system. Thus, we would be doing our students a disservice by not equipping them with the tools necessary to compete in the world. And even though they would learn the metric system without us, by teaching them in a manner in which they can see the usefulness of it, we can go a long way in eliminating the unfavorable way that our students compare in math with students in the rest of the world.
Besides, it’s easier. Not only does the aforementioned simplicity make it easier to teach, but also, the areas of the present curriculum which could be eliminated or at least deemphasized would also simplify our jobs. For example, the customary measures as they are now taught could be relegated to the status of simple mention as a historical footnote, or better, eliminated completely. Also, with the system of fractions and the operations using them, reduction to the introduction of the most basic such as halves, thirds, and quarters with a few simple calculations would be sufficient. Who among us hasn’t sighed at the frustration of trying to impart the concept of “inverse” when teaching the division of fractions. Time spent on these areas would be greatly reduced allowing more time for concentration on more useful areas.
Certainly, there would also be drawbacks. The major one, of course, is monetary. The expense of converting all packaging, signs, much machinery, etc. would be astronomical. Along with the cost would be the inconvenience. Most of the population has not grown up learning metrics and therefore might find conversion annoying at best. An argument could certainly be made for just allowing the “creeping conversion” now going on to simply continue. At some future time conversion would be complete with far less disruption and cost.
I am of the opinion that compromise is probably the best route to go. Immediate, legislated conversion would not be practical. Yet, by concentrated education of our youth in the metric system, the next generation would hasten and complete the conversion as they assumed roles of responsibility. That brings us back to our unit.
