It was in the second grade when I came across measurement and units for the first time. Our science teacher told us that we could measure things. Until then I did not need units. It seemed a bit awkward to define such concepts. Numbers were just good enough. And what did it have to do with science anyway? I hoped it would be over soon.

It wasn’t…

Worse than that, in the third grade we had to learn about “conversion of units.” I figured it was good source of test problems. So I couldn’t escape from learning it. I admit it was difficult in the beginning. “The strange rule” said if we are to measure with a bigger scale, then we had to divide the number by ten and vice versa. Why was 120 cm equal to 1.2 m? If we knew that it was 120 already why did we bother to say it was also 1.2 in another unit? I got confused whether I should multiply the number by ten or divide by ten? (At least it was easy to multiply or divide by ten instead of another number, so I kept silent.)

In time, I realized that people used the unit to measure almost anything. Length is measured in meters, mass is in kilograms, time is in seconds. Wherever there was quantity, there was also a base-unit associated with it. Of course I never asked what a “second” was, because our teacher said everyone accepted this unit of time. Since it was a world-accepted “standard measure,” I subconsciously got the impression that the universe had a clock* and that people calibrated their time accordingly. In the same way, one kilogram was an absolute quantity in my mind by which every other mass can be measured.

As we grew up, more and more types of measures and units entered our lives: Volt, Joule, Ampere, Newton, and many others. Dealing with the “old” units of length and time was a piece of cake then. However, my faith in “standard measures” as universal remained unchanged until high school.

I was quite surprised in high school when our chemistry teacher told us that our very fundamental units of measures were actually not absolute. They were not fundamental in the sense that they, too, were defined in terms of other quantities. In fact, there is a history of “what to define as a unit” and “how to measure it.”

Let’s take time, for instance. We measure years by days and days by hours. Have we ever thought about why a year is 365 days and one day is 24 hours? Can’t we divide a year into 400 days or a day into 25 hours? Is this an artificial choice or a natural timing? It all depends on how we define a year and a day. We can identify a year by a full rotation of the earth around the sun. Also we can distinguish the beginning of day and night clearly. These are definite intervals of time dictated through our observations, and so there is not much choice other than setting one year at 365 days. Is there a similar fact behind the relation of day to hours? Not at all! It was in ancient Egypt, around 2000 BC, that days for the first time were sliced into 24 pieces of time. In the age of Babylonians, however, a day was designed to be 60 hours. Perhaps the reason for such division of the day (into 24 or 60) hours was that 24 or 60 are nice numbers which are divisible by many integers; the same reason why a full-angle is 360 degrees instead of 2π.

In the Middle Ages, for Muslims, measurement of astronomical phenomena was a very serious affair. They were very concerned about accurate timing. Determining the changing time of the five daily prayers and the beginning and ending of the month of Ramadan was more than a custom, it was a religious duty. And such calculations required high precision. This precision was exemplified in year 1000 AD by the Muslim scholar al-Biruni who gave the times of the new moons in terms of days, hours, minutes, seconds, thirds, and fourths after noon Sunday.

In the West, the first accurate time measurements were made by Roger Bacon in thirteenth century. In 1657, Christian Huygens invented the pendulum clock, which uses swinging weights to keep time. Later, Hyugens and William Clement refined the design so that clocks were accurate up to seconds. Another problem with older clocks was that although they worked fine in the local region, they lost accuracy at different parts of the globe and were thus unsuitable for navigation. The reason for the lack of accuracy was that earth’s rotation around the sun on its axis (which definitely affects the period of the pendulums) was not uniform. Several adjustments were made in the nineteenth century for better accuracy by improving the design to compensate for thermal expansion of the metal rods and air drag, which globalized the measurement of time. In 1956, the “second” was redefined in terms of the earth’s revolution around the sun, according to data gathered in year 1900. As the scientists were not completely satisfied, they re-defined the second (as the atomic second) a decade later. In 1967, the Thirteenth General Conference on Weights and Measures defined a second of atomic time in the International System of Units as:

The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

Measuring the length was another important task for ancient peoples. Among the earlier civilizations, the most accurate system was developed by Indus Valley Civilization. While their contemporaries were using parts of the body for measurement, as early as 2600 BC, the Indus civilization had a much finer unit system that accounted even for millimeters. Most societies continued to use their own length scale until eighteenth century.

As early as seventeenth century, with the advances in the accurate measurement of time, pendulum motion was suggested to measure standard length. In the eighteenth century, there were two main approaches for measuring the standard unit of length. One suggested defining the meter as the length of a pendulum with a half-period of one second. The other suggested defining the meter as one ten-millionth of the length of the Earth’s meridian along a quadrant, which is the distance from the equator to the North Pole. In 1791, the French Academy of Sciences selected the choice based on the meridian. After several changes in the definition in 1960, the International Bureau of Weight and Measure organized the 11th CGPM (General Conference on Weights and Measure), during which the meter was redefined as 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum. The final decision came from the 17th CGPM as: “a meter is defined as 1/299,792,458 of a light-second.”

Figure 1. Historical International Prototype Meter bar, made of an alloy of platinum and iridium, was the standard from 1889 to 1960.

As for the measurement of mass, the situation is even more complicated since scientists cannot even agree on what mass is. There are mainly two different understandings of mass based on its features. One is called inertial mass (related to the quantity of a material); the other is gravitational mass (related to gravitational pull and acceleration). Whether these two concepts are equivalent or not is still in debate though in modern theories like Einstein’s general relativity, these two definitions are equivalent. We can, therefore, leave these philosophical discussions about the concept of mass to the scientists and go back to its measurement.

Just like the measurement of time and length, scientific mass measurement gained a boost after the French Revolution. At first, a gram, defined as the absolute mass of 1 cm3 of water at 0o C, was chosen as the standard. In 1799, scientists made a slight modification to the unit of mass by re-setting the definition at 4oC since it is the temperature at which water is most stable. Later, officials noticed that this unit was too small to be a standard of everyday commercial materials, which usually appear in large amounts. In 1889, the International Prototype Kilogram (IPK), made of an alloy of 90% platinum and 10% iridium (by weight), was designed to define the standard mass (Figure 2). After the first production, several more stable replicas of IPK have been produced to replace the older ones. Today every government who subscribes to this standard must have an exact copy of IPK, and these replicas must be returned to Paris periodically as they may get rusted or dirty with time.

Figure 2. Shown above is a computer-generated image of the International Prototype Kilogram (IPK). The IPK is made of a platinum-iridium alloy and is stored in a vault at the BIPM in Sèvres, France.

These facts may sound very odd to some, as it did to me when I first heard of them. I asked myself: If all these measures are defined in terms of something else, what is the point of defining them in the first place? For example, if we can agree to use the second as some interval of time, why do we bother to count the number of oscillations of Cesium. The answer is: We cannot agree unless we use a reference time which is geography-free, climate-free, and politics-free. Only then we will be sure that I, here in Western Pennsylvania, a person on the top of Everest, or a person in a submarine under the Pacific Ocean will call the same interval of time a “second.” In other words, the oscillation of the cesium isotope was believed to be free from all possible deficiencies that are results of physical location (Australia or America), environmental change (the Amazon Forests or the Sahara Desert), and politics.

In short, sand-clocks for measuring time (think of what kind of sand in what shape of glass tube) or the arm of a king as a length unit (imagine a king who seized the throne at 13 and died at 60), or weighing with iron cylinders (common in small grocery stores in some countries) is too unreliable, too unstable, too local, and of course, inaccurate to create a standard. Especially in this age of globalization, a consensus on measurement is absolutely necessary.

It seems a bit ironic that a simple-looking concept of science, measurement, could cause such controversy. A simple way to keep track of numbers that belong to different kind of quantities evolved into an area of serious research through time. Perhaps then, I should have not worried that much about my bad math grades on a subject which troubled the scientist themselves. After all, my grades were just my teacher’s own measurement.**

O. S. Caglayan has a PhD in mathematics. He is a freelance writer. He lives in Pittsburgh, Pennsylvania.

* This famous quotation attributed to Newton was opposed by Leibnizian view of time: “The universe is the clock.” The scientist as philosopher, Friedel Weinert, Springer; 1 edition (May 27, 2004)

** The author is indebted to his dear elementary school teacher Muazzez Ozalp for instilling in him the love of science.

References

1. G. J. Toomer. Ptolemey's Almagest (Princeton, New Jersey: Princeton University Press, 1998)
2. The History of Time (Leofranc Holfrod-Strevens).
3. al-Biruni (1879). The chronology of ancient nations: an English version of the Arabic text "Vestiges of the Past". London: W.H. Allen, 147-149. OCLC 9986841.
4. Matthew Bennett, Michael F. Schatz, Heidi Rockwood and Kurt Wiesenfeld, Proc. R. Soc. Lond. A 2002 458, 563-579.
5. Ian Whitelaw. A Measure of All Things: The Story of Man and Measurement, St. Martin’s Press, 2007.
6. http://physics.nist.gov/cuu/Units/meter.html
7. www.bipm.org/eng/home