Measurement Systems

The only use of a measurement system is communication, and communication is obviously easier when the measurement system is shared by all parties. Given that the metric system is already used by nearly all of humanity, and given that it is a much more elegant system than the imperial system, it is only logical that the metric system be adopted by the United States as early as possible.

In terms of measuring temperature perhaps the imperial system is more intuitive; humans typically live in the range of 0 to 100 F. Furthermore, the smallest temperature change detectable by humans is thought to be about 1F. The Celsius scale has water freezing at 0C and boiling at 100C, which is more convenient in academic contexts, but potentially less convenient in everyday life, which occurs over the range of roughly -20C to 40C.

Now that we've seen the success of the imperial system, let's examine its failings.

As far as measuring sizes the imperial system is woefully awkward. In length the four units - inch, foot, yard, and mile - are all based on obscure historical precedents and are all commonly used. Yet the conversion between inches and yards (how good are you at dividing by 36?), or between miles and anything else, is more or less impossible to do precisely without a calculator. The metric system deals only in factors of ten from the base unit, a meter, which comes from the size of the earth. Similarly for volume, one milliliter is the same as one cubic centimeter (and so on with powers of ten) while imperial units have the fluid ounce, the cup (8 ounces, half of a pint), the pint (the size of one pound of water), the quart (2 pints), and the gallon (4 quarts, 231 cubic inches).

When measuring mass and weight, the imperial system is not only awkward but lazy. The metric system distinguishes mass (the amount of stuff something is made of) from weight (how hard something is pulled down by gravity). In the imperial system both are measured in pounds. Gravity is very close to constant on Earth - varying by less than one percent between Mount Everest and the Dead Sea - but this is still inelegant, particularly in a scientific context. Similarly to length and volume we see that imperial weight is measured in several distinct units: the avoirdupois ounce (about the weight of one fluid ounce of water), the pound (16 ounces), and the ton (2000 pounds). On the other hand the metric system, predictably, uses powers of ten from the base units gram (or ton, which is exactly one million grams) and Newton (on Earth, gravity is about 10 m/s/s so you get ten Newtons for each gram).

Seconds are used by both metric and imperial systems, so of course changing them is not up for debate - though the system could obviously be more elegant.

For all of time humanity has had one constant time scale: the day. It's a length of time that is natural to anyone who has ever lived outside the arctic and antarctic circles. The year is next, as it comes with the passing of seasons. However, the time scales we use in our day to day lives - seconds, minutes, and hours - are all arbitrary. One second is 1/86400 day. That means that we could have easily decided to put ten "hours" to a day, one hundred "minutes" to an "hour," and one hundred "seconds" to a "minute." In that case a "second" and a second would have been nearly the same and a few "minutes" (aka a few millidays) would have been about a few minutes.

We run into more arbitrary units and inelegance when we look at days and months. For example, we have twelve months which can be 28, 29, 30, or 31 days long, and, as such, generally don't divide into an even number of weeks. The year also does not divide into an even number of weeks. And perhaps my favorite: the names September, October, November, and December come from the numbers 7, 8, 9, and 10 (but they're the 9th, 10th, 11th, and 12th months).

It takes just over 365 days for the Earth to go around the Sun. Unfortunately 365 factors into 5*73. Five months of 73 days each and vice versa both seem pretty awkward. If we knock off one day, however, we find that 364 factors to 13*7*2*2. That allows for 13 months of 28 days or 14 months of 26 days. A month of 28 days will allow a whole number of weeks per month (a 26 day month can be divided only into two weeks of 13 day), which seems nice. Furthermore, 28 days is pretty close to the lunar month.

We end up neglecting 1.24 days per year. There's a whole family of proposed reforms to the Gregorian calendar which in large part vary in how they aim to deal with this little amount. It's a mess. Some favor keeping the equinoxes on the same date while others want the same date to always fall on the same day of the week. I like the idea of having a leap month every twenty years, which allows significant drift of equinoxes. (For higher order accuracy a leap month would need to be skipped once every few centuries, just like leap days are now). This is by no means a provably best system, but I think it is clear that we can do better than the current system.