Precise measurements are indispensable in science and technology. Belfast-born William Thomson – later Lord Kelvin – expressed their importance, stating: “When you can measure what you are speaking about, and express it in numbers, you know something about it. If you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.”
Many measurement systems were developed as civilisation evolved. The imperial system is nothing if not quirky. Readers may recall that a rod, pole or perch equals 5½ yards or 16½ feet, with 40 rods to a furlong and 320 to a mile.
Three barleycorns, making an inch, may serve for shoe sizes but are inadequate for astronomy or atomic physics. Something better is needed.
Today, the International Committee for Weights and Measures oversees the standardisation of measurements. The International System of Units (SI), popularly called the metric system, is based on the metre, kilogram and second as units of length, mass and time, and a range of other standard units.
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The need for standardisation was starkly revealed by the catastrophic failure of the Mars Climate Orbiter, launched by Nasa in December 1998 to study the Martian climate. The spacecraft reached Mars nine months later, on a trajectory that brought it disastrously close to the planet. This was due to a mismatch between two measurement systems, metric units used by Nasa and units derived from the imperial system by spacecraft builder Lockheed Martin.
When the Nasa engineers attempted to manoeuvre the spacecraft to a new orbit, their command used newton-seconds, but the thruster control software assumed the units were pound-force-seconds, more than four times greater. The probe descended too low and burned up in the Martian atmosphere.
In the 18th century, chaos reigned in France, with units of measurement varying from place to place and no standardisation. The French Revolution led to reform of the disparate systems of weights and measures then in use. The traditional units were replaced by consistent measures based on natural phenomena. The metre was defined as one 10-millionth of the distance from the North Pole to the equator, and the kilogram as the mass of one cubic decimetre (or litre) of water.
Today, the base units of metre, kilogram and second are defined by physical constants. Multiples and fractions are specified by prefixes: a kilometre is 1,000 metres and there are 1,000 milliseconds in a second.
As technology and science advance, a greater range of prefixes is required. These advance in steps of 1,000. The speed of computers has gone from megaflops, via gigaflops and teraflops, to petaflops and beyond. One petaflop means a million billion operations per second. As of 2022, the largest prefix is quetta, a factor of 10 to the power 30.
The SI system is now almost global (see illustration). Notable exceptions are the United States, Canada and the United Kingdom, where speed limit signs are misinterpreted by visiting drivers and numerous accidents have been caused by vehicles striking bridges with heights indicated in imperial units. For temperature, United States sticks stubbornly to the archaic Fahrenheit scale.
The International Bureau of Weights and Measures also determines the worldwide time of day. It combines the atomic time standards of member nations to define a single, official Co-ordinated Universal Time (UTC), closely related – but not equivalent – to Greenwich Mean Time.
Attempts to decimalise time never succeeded. During the French Revolution, a proposal was made to divide the day into 10 decimal hours, each hour into 100 decimal minutes and each minute into 100 decimal seconds, but the law in 1795 establishing the metric system repealed the mandatory use of decimal time.
- Peter Lynch is emeritus professor at the School of Mathematics & Statistics, University College Dublin. He blogs at thatsmaths.com
