## Measures and Metrics

It was a day at the races for two young boys in Gimli, Manitoba. As crowds gathered to watch cars flick back and forth on the track, they took their bikes a few hundred metres away to re-enact the races on a derelict runway. Unbeknownst to them, a giant silently bore down upon them. Air Canada’s flight 143 had run out of fuel and was attempting to glide to a safe landing. We can’t imagine their terror. We can’t imagine what it was like to see their short lives flash before their eyes as they turned to see the jet nearly upon them. They stood still in shock for a moment then raced down the runway as fast as they could. They made it. Barely.

This crash was no tragedy. But it could have been. Hundreds of people could have been injured or killed. And for what? For a conversion error. The ground crew thought that they were adding fuel in kilograms but were actually adding pounds. Hence only about half the fuel was added than intended. That is, the Gimli Glider was a casualty of Canada’s metrication process. There were others, though much less severe. And yet, metrication is worth it. The metric system is the best measurement system we have available to us.

This is a weird claim. All measurement systems are arbitrary. Rulers and thermometers were not the gifts of Heaven like those law tables carved in stone. Humans have always used what was available to them to keep track of weights and measures. Humans have used stones and feet and thumbs and brines and cups and so on. The metric system is just one more in this long list of arbitrary measures.

But arbitrary things can also be more and less apt to accomplish what it was designed for. For metrics, there are at least three primary criteria we use to evaluate aptness: ease of use, ease of conversion, and its ability to represent real difference.

Most metrics throughout history were designed with ease of use in mind. Weights and measures needed to be compared to some standard, and that standard had to be readily available. The cubit is the gold standard in ease of use: what is more available to a carpenter than her own forearm? If she wishes to measure out a board, she need only count how many of her forearms it is long, and she has some measure. And since her forearm does not change in size, everything she measures with it will be bound to the same standard.

Now, the problem with a cubit is that it isn’t easily convertible into other measures. How many thumbs go into a cubit? How many feet? It isn’t obvious, and the carpenter must determine that for herself. If another carpenter were to use her measurements, he might find that his cubits are of a different size, and the ratios of his feet to his cubits might be different altogether. People solved this long ago by standardising their previously variable measures into formal units. The foot no longer corresponded to the carpenter’s own foot but to some arbitrary standard foot, say the king’s. And so too with thumbs and all the rest. And once this is established, the ratios between different measures remain static. There are twelve thumbs in a foot. There are sixteen ounces in a pound. There are two pints in a quart. And so on. This may slightly reduce the ease of use for these measures, but it vastly improves the overall utility of the measurement system.

Finally, the ultimate purpose of any measurement system is to record real differences in the world. We want to know whether two boards are the same size or different. We want to know whether our apple-only diet is helping us lose weight. We want to know whether it is warmer or cooler outside than it was yesterday. And this is the hardest part about any measurement system: some of those differences are more important to us than others, and our measurement system must recognise this.

So given all this, why metrication? There are of course practical questions. Metric is the international standard; US manufacturers lose millions of dollars every year because they have to convert quantities into metric for export, a phenomenon that does not plague manufacturers elsewhere. This also puts American students behind their peers from other countries. Metric is the official measurement system of science, and so students in American schools must not only learn the imperial system, but also the metric system. However, these pragmatic questions say nothing about metrication. The US could without too much difficulty exert its influence to motivate other countries to switch back to imperial. If we want to justify metrication, we need to do this internal to a theory of measurement alone.

So why is metric the gold standard? In no uncertain terms, it unambiguously meets the measurement criteria better than any other measurement system. Metric is no more difficult to use than any other measurement alternative. Both imperial and metric require standardised instruments, and both are equally available. But metric makes conversion easier than any other measurement system. Imperial maintains constant ratios between different units, but these ratios are not uniform. There are twelve inches in a foot, three feet in a yard, and 1280 yards in a mile. A person needs to remember each one of those ratios, or at least look them up in some rule book, before one can complete even the simplest conversions. Metric dispenses with this difficulty. The conversion ratios in metric are not only constant, but also uniform. Every unit is distinguished from the others as multiples of ten. And when in doubt, the conversion ratio is included in the name of the unit. A kilometre is a kilo-metre, or a thousand metres. Easy.

Perhaps the most impressive benefit is the metric system’s ability to represent real difference. The metric system employs a greater diversity of units, in part due to its uniform conversion ratios, than any other measurement system. Objects as small as atoms and molecules or as large as stars and galaxies can be easily and coherently represented in metric units without ambiguity. And while the very small and very large do not affect ordinary people very often, the metric system does a better job with ordinary measures as well. The best example of this is temperature. The Fahrenheit scale is pinned to three different benchmarks: ice and salt brine, the freezing point of pure water, and human body temperature. These correspond to 0, 32, and 96 degrees respectively. These choices are arbitrary, of course. But they are also meaningless. There is no firm relationship between these standards that ties their temperatures nicely to a single scale. And moreover, they tell us nothing about what the temperature of a thing is like. The Celsius system is very different. It is pinned only to the phase changes of water. 0^{0} is freezing. 100^{0} is boiling. This too is arbitrary, but it does tell us quite a lot about the world we live in. Water is fundamental to Earthly life, and its properties determine life’s conditions. It is plain that negative temperatures represent a different kind of weather than positive temperatures. Negative temperatures are associated with snow and ice. Positive with rain and warmth. Fahrenheit never gives us that clean divide. It could be snowing at 30^{0} but raining at 35^{0}. Those five degrees are far more important than the scale lets on.

This is the reason the world has adopted the metric system. This is worth all the troubles metrication caused. The metric system is completely and unambiguously the superior measurement system. Now we need only for the most powerful country on Earth to catch up.