Friday, June 10, 2011

The non-metric mind

I grew up in the US using English units.  I know my height in feet and inches, my weight in pounds, the distance to various places in miles, the area of my house in square feet, the area of my grandparents' property in acres, the capacity of my car's gas tank in gallons, the temperature in degrees Fahrenheit and so forth.

I've visited, and even lived in, places where it would be centimeters, kilos, kilometers, square meters, hectares, liters and Celsius, but never really got to the point where it felt natural to use metric units.  If I hear it's 86 degrees out, I know it's warm.  If I hear it's 30 on a summer day, I have to remind myself it's not below freezing and then think "30 ... that's warm, right? ... that's what, 80? 90?"

Non-metric units are still in use here and there outside the US, to be sure.  Even the English still use some English units, posting speed limits in miles per hour, quoting weights in stone (14 pounds) and quaffing beer by the pint (officially 568ml). All the same, the US is widely recognized as the world's least metricated nation.

Officially, this isn't supposed to have happened.  The US signed the Treaty of the Meter in 1875 and re-defined traditional measures such as the ounce and gallon in terms of metric units in 1893.  Then, for about a hundred years, the metric system was known to exist but largely ignored.

In 1975 Congress passed the metric conversion act, thereby establishing the US metric board.  The board was abolished as part of a round of spending cuts in 1982, so we tried again in 1988 with the Omnibus Trade and Competitiveness Act, which among other things required the federal government to go metric by 1992.  For all that the federal government is supposed to intrude into every aspect of Americans' lives and dictate the smallest details of behavior, I can't say I have any idea to whether it actually did.

The benefits of the metric system are well known, or at least widely touted.  Instead of a hodgepodge of arcane conversions from, say, teaspoons to tablespoons to ounces to cups to pints to quarts to gallons, you have (to continue the example) just liters, optionally with one of a standard set of prefixes should the numbers accumulate too many zeroes (in the case of cooking units, milliliters are fairly common).

Moreover, even if the metric system were based on multiples of random prime numbers rather than uniformly using base ten, it is the system that most of the world uses, giving a strong incentive for anyone interested in trading with the rest of the world to use it.  So why do we persist in going our own way? I don't know, but I can conjecture, can't I?

Two conjectures come to mind: The first is that standardization is by far the more pressing reason to use metric units, and that the US does just that when it matters.  US chemists and physicists do not insist on using Fahrenheit degrees or measuring liquids in gills and minims.  They use the same units as everyone else.  A US mechanic fixing a car and faced with 13mm bolt head reaches for a 13mm wrench.  For all that the US was supposed to have been faced with a crisis in competitiveness unless the metric system was made mandatory, market forces seem to have sorted this one out.

As far as I can tell the remaining differences in units matter mostly as an annoyance to travelers, and for better or worse, Americans in the aggregate don't spend much time traveling to foreign countries.  Even for those who do, metric units are just one more item on a long list of things to get used to: different languages, cultural customs, food, currency, traffic signs, line voltage and frequency, electrical socket designs, light switches, etc., etc..

It's also worth asking whether ease of conversion is all that important.  Advocating a single system of units, metric or otherwise, assumes that a single system is appreciably more convenient than having multiple systems.  This is a hypothesis to be verified, not an axiom.  In practice, people seem to tolerate quirks in measurement systems remarkably well.  The traditional profusion of units of measurement arose naturally, after all, which leads me to my second conjecture:  The hodgepodge of different units is in fact a reflection of how we think about measurement, even in ostensibly metricated environments.

For example, if I'm buying soda in the US, I can buy a two-liter bottle without caring that the gas in my car is measured in gallons.  Drinking soda and using gasoline are completely different experiences.  I'm not going to drink the gasoline or pour soda in my gas tank.  Two liters of soda is a lot of soda to drink. 17 gallons (about 64l) is way more soda than I even want to think about drinking.  Two liters of gas will just about get me to work in the morning.

From a practical point of view, soda could be sold by the ngogn and gasoline by the firkin so long as the numbers didn't get too out of hand (2 liters is about 172 ngogn; 17 gallons is about 1.6 firkins).  In fact, there are two prevalent units of soda in the US: 2-liter bottles and 12-ounce cans or bottles, generally packaged in multiples of six.  As it happens, a six-pack of 12-ounce cans is about two liters, but that's not exact and it doesn't matter much whether it is.

We learn to associate measures with the physical world on a case by case basis.  You learn how far a mile or kilometer is by traveling.  You learn how much a pound or kilogram is by handling things by the pound or kilo*.  Cognitively, there's not a lot of overlap.  I really don't need to know that a gallon of milk weighs about 8.3 pounds.  It weighs as much as a gallon of milk.  If I'm in the dairy business, I care how many gallons of milk I can load on my truck, but that's just another piece of specialized knowledge.

In general, there is either a natural or conventional unit for many things we deal with, and, because different things have different properties, that unit will vary.  It would be of little use to require, say, perfume to be sold only in liter sizes or to copper wire to be packaged in meter lengths.  Instead, perfumers have developed standard-sized bottles and wire comes in standard spools.  Whether these happen to measure a round number of ounces or liters or yards or meters is not particularly important.


Not only is it not a problem to use different units for different things, ad hoc units seem ubiquitous, once you look at the actual unit and not the number on the package.  Even in counting, where the unit is essentially the thing being counted, distinctions can be seen.  Many languages use different words for counting different sorts of things.  For example, in Japanese you would use ba in counting, say, copies of a newspaper but dai in counting, say, cars or bicycles.  English has signs of this as well.  Driving through the midwestern US, you might say you see five cows out in a field, but the owner of that field will almost certainly call them five head of cattle.




The metric system was designed for scientific use, and it's there that it really comes into its own.  In the physical sciences, there actually can be a need to deal with different orders of magnitude, for example, so it's very good to be able to shift decimal points instead of trying to figure out how many feet are in 1000 inches (83' 4").  In everyday life, shifting decimal points is not so important.  If you're doubling a recipe, it's actually not so bad to be using 1/2 teaspoons and 1/4 cups.

Even in the sciences, though, idiosyncratic units find their way in
  • How far away is Alpha Centauri?  To an astronomer, about 1.3 parsecs, not about 40Pm (petameters, not afternoon).  The parsec itself was originally defined in terms of the Astronomical Unit (about 150Gm) and the arc second (1/3600 of a degree, or about 4.8 microradians).
  • If you want to make sodium chloride (salt), you'll need about 23g of sodium and 35g of chlorine to make 58g of salt (a fume hood and other equipment will probably be a good idea).  Sodium atoms are less massive than chlorine atoms.  If you used the same mass of each you'd have sodium left over.  Chemists use a gram mole to represent the mass of Avogadro's number (about 600,000,000,000,000,000,000,000) of a given atom or molecule to account for this.  One gram mole of sodium plus one gram mole of chlorine makes one gram mole of salt.
  • In theoretical particle physics, Planck units (or "God's units") set five fundamental physical constants to 1, which simplifies a number of equations.  For example e = m when c is 1.  I'm not sure how often they're used, but they do turn up (for example here and here, to pick a couple more or less at random).
  • I previously remarked on compugeeks measuring data in units of K/kilo- (1024), M/mega- (1048576) and so forth.  That doesn't mean that a compugeek will think a kilowatt is 1024 watts (well, maybe, depending on how hardcore the geek).  It's only data that is measured this way.  The convention that K,M,G,T etc. refer to powers of two flows directly from addresses being represented in binary [Some folks prefer to say things like "Mebi" and use abbreviations like MiB in order to explicitly call out the distinction between a million and 1,048,576.  This can be a very good idea in some particular situations, but in everyday speech even geeks tend to ignore the difference and just say K, M, G, T etc.  --D.H.].
Even the plain vanilla metric system offers choices.  Strictly speaking, the liter is redundant.  We could just use cubic meters.  In practice, we choose the unit that fits best
  • Liters and cubic meters both act like basic units of volume.
  • Square meters and hectares both act like basic units of area
  • Grams and kilos both act like basic units of mass
That's leaving aside square and cubic centimeters.  Which units you use will depend on what you're doing.  A recipe might call for 15ml of oil but an olympic swimming pool will hold about 2500 cubic meters (2.5Gl) of water**.  Housing space is measured in square meters, but land is measured in hectares.


Finally, there is one area of common measurement that has universally and persistently resisted metrication: time.  Everybody uses days, years and some notion of months.  Hours comprising sixty minutes of sixty seconds are approximately as widespread as writing.  Even thoroughly metricated places use kilometers per hour instead of meters per second.  Outside very specialized contexts, long periods of time are measured in years, though which exact definition of the year may depend on context and most definitions vary over time.

There have been various efforts to "rationalize" time measurement, but none even close to successful.  The natural units are just too strong.  Only when dealing with very short periods of time, outside the realm of everyday experience, do we use "correct" units and talk about microseconds and such.


Measurement is not an abstraction.  It is a concrete action dealing with the physical world.  The experience of measurement depends on what is being measured, and our mental representations reflect this, making distinctions that appear illogical from an abstract point of view.




* No discussion of pounds and kilos would be complete without a pedantic comment that pounds measure weight, that is, force, while kilos measure mass.  In everyday life, we deal in force.  It takes careful observation to realize that there is a difference (for example, a diver at neutral buoyancy has little weight but just as much mass as on dry land).  Thus the pedantic distinction.  A kilo of something will normally weigh about 9.8 Newtons, which is what a scale "should" typically read if you put a kilo of something on it.

** I originally left out "of water" here.  After all, an olympic pool could just as well hold 2500 cubic meters of beer, or silly putty, or whatever.  But it's hard to think of a container without its expected contents.  Which more or less goes to prove my point.