Jokes about Units

One of the “joys” of moving from the US to just about any other country is the need to get used to SI, or metric, units.  Food is sold by grams, kilograms, and liters; street signs are marked in kilometers and kilometers per hour.  An attendant joy is that periodically, someone will mock the fact that the US still uses the old English units to your face.  As an American physicist, I have lived and worked with both, and also as a physicist, I can be annoyingly focused on the use of units past the attention span of those cracking the original joke.  So let’s discuss the metric system, shall we?

The metric system was introduced in 1799 in France an attempt to move beyond older and regional systems of units to something more logical and universal.  Today, the metric system has been replaced by le Système international d'unités, often abbreviated SI units.  The idea was to have units that related to each other in a logical way, that could be derived from a set of basic units, and (a bit more modern priority) that could be derived from natural phenomena.  The original basic metric units were the meter (m), the second (s), and the kilogram (kg); the SI system currently has seven fundamental units, adding the Kelvin, the candela, the mole, and the ampere to the original three.  All other units within the system can be derived from simple combinations of this basic group.  For example, the unit for force, the Newton, is defined as the force needed to accelerate 1 kg of material to a speed of 1 m/s in 1 s. 

The part of the SI typically cited to me as its greatest benefit is that the basic units can be converted to something more convenient for a specific task by adding prefixes.  While the meter is a perfectly good unit for measuring all distances, mankind finds it cumbersome to measure things like the distance between the sun and Jupiter or between carbon atoms in a lattice in meters, as those distances work out to be very large or very small numbers that are difficult for us to remember.  To make things easier, the metric system has a set of prefixes that let one define whatever unit one wants.  The prefixes are based on powers of ten, so that “centi” always means “one-hundredth” and “kilo” always means “one thousand.”  Hence a kilogram is one thousand grams, a kilometer is one thousand meters, a kilowatt is one thousand watts, and so on.  This is much easier to remember than the similar conversions in the English system, where sixteen ounces make a pound and 5,280 feet make a mile.

Now, allow me to point out a few things that the metric system is not.

It is not a decimal system.  At least, it isn’t any more or less a decimal system than English units are, despite the comments I’ve received to the contrary.  One can deal with either set of units using either decimal or fractional numbers, because they are equivalent. In my experience, people tend to find it easier to add and subtract with decimals (preferring 0.33333 – 0.090909 to 1/3 – 1/11) but to multiply and divide with fractions (preferring (1/7)/(1/49) to 0.14285/0.020408).  Stereotypically, long division of decimals is held to be the hardest portion of basic math, not division of fractions.  The metric unit prefixes merely make the math easier by needing to multiple or divide by a multiple of ten to convert a unit within a family.

Historically, the reliance on fractions probably made things much easier in the days before good measuring devices.  Consider needing to split some quantity of grain between people when you only have a balance to measure it with.  Would you rather divide that quantity into five equal portions or eight?  I personally rather split it up into eight, because I could produce two portions that have equal weights using the balance, then split each of those halves in half, and then split each of the resulting fourths in half again.  To get five equal portions using a balance, I would need to make my best guess, and then repeatedly balance each of the five portions against each other, adjusting as I went, until I got all of the variations sorted out.  So while dividing things into eighths and sixteenths seems needlessly difficult now, it was probably easier to implement before calculators; conversely, dividing things by tens and fives would have introduced difficulty.  Hence having sixteen ounces in a pound, as odd as that seems today, probably made good sense when it came into use a few centuries ago.    

It is not perfectly logical.  The SI has its own traditional holdouts.  I have yet to hear anyone use dekaseconds instead of hours to divide up their day.  The kilogram, not the gram, is the basic unit of mass, even though that is contrary to the intended use of the base units and their prefixes.  The Celsius system, by the way, is not technically part of the SI, having been replaced by the Kelvin. 

It is not natural.  Nature doesn’t come in SI units.  There is a trend now to define the basic SI units based on natural phenomena, which allows users to rederive the base units wherever they may be.  This leads to some rather esoteric definitions.  The second is now technically defined as the time it takes a cesium atom to make 9192631770 transitions between two hyperfine levels in the ground state.  One meter is the distance traveled by light in vacuum in 1/299792458 s.  I don’t find either of these particularly memorable.  (The kilogram is still defined as whatever is equal in mass to a cylinder of platinum-iridium kept by the International Bureau of Weights and Measures in a vault outside of Paris, despite efforts to find something in nature to use instead.)  In fact, in some ways nature provides units that don’t fit into the SI well at all.  Take the Coulomb, the SI unit of electric charge.  In keeping with the general philosophy of SI units, it is defined as the amount of charge transported by a current of 1 amp in 1s.  But electric charge in nature already comes in nice little packets.  Every electron has exactly the same magnitude of charge as every proton.  If electric charge is exchanged, it is by this amount or by an integer multiple of this amount.  The quarks each have exactly one-third or two-thirds of this amount.  Using the electron charge itself as the basic unit, the math in calculating electrical interactions would only involve integers with some basic fractions.  But in SI units?  The electron charge is 1.602e-19 C.

So, yes, I agree that the unit conversions within the SI are much easier to remember than those of the older systems.  I agree that many fields, mine included, would be somewhat simplified if everyone stuck with one system and didn’t report anything in units outside that system.  But as I see it, the benefits end there.  In my particular corner of my field, we prefer to use what we call “natural units,” based on nature’s fundamental constants, because using SI units would make things needlessly complicated.