In 1866, the US government made it legal to employ weights and measurements of the metric system (e.g. kilometers, liters, grams) in addition to standard US measurements (e.g. miles, gallons, pounds). A hundred years later, the system wasn’t really catching on in America as quickly as it had throughout most of the world, so in 1975, the US government adopted the metric system for all government weights and measures. Ten years later, the metric system became the preferred system for trade and commerce. After another decade had passed, the metric system became not just preferred, but mandatory on all consumer commodities, though US standard measurements were, and are, still allowed.

Another decade has passed since, but the metric system still hasn’t really caught on in America. If you look closely at nutritional labels, you can see how many grams of fat your food contains, and you can even see how many liters are in your gallon of milk. But you’re unlikely to get a ticket for driving too many kilometers per hour. And you certainly won’t get a ticket for driving too many kilometers per kilosecond. (The decimalisation of time hasn’t really begun to catch on anywhere outside of Swatch.)

But as with universal health care, America is far behind the curve on the decimalization of weights and measurements. Liberia and Myanmar are the only other two countries in the world not using the metric system for nearly everything. And those two have just been distracted from the task of metrication, both going through civil wars while the rest of the world was converting speeding tickets to be easily divisible by ten.

America, on the other hand, has had plenty of time to do the metrication, but has steadfastly resisted the idea. The state of Kentucky even went so far as to reverse the national government’s mandate to use the metric system within government agencies. The process of converting the nation to the metric system has generally stalled in the past ten years and shows no signs of restarting any time soon.

While decimalisation has almost spanned the globe in weights and measurements, and hasn’t really begun in time, decimalisation has actually been completed in every country of the world in one area: currency. Decimalised currency is so ubiquitous that it’s hard to imagine that there was ever a country that had non-decimal currency.

But prior to 1710, no currency was decimalised. In that year, Russia was the first country to decimalise currency. Peter ("the Great") I is most well-known for the westernization of Russia, including oddities such as changing from the Russian calendar to the Julian calendar just as Europe was changing from the Julian to the Gregorian calendar, and taxing men who wore beards. And at the time, currency decimalisation probably seemed odd as well.

I didn’t find any record of the relative value between rubels and kopeks prior to 1710, but assuming it was something other than 100, Peter’s declaration that it was to be 100 henceforth probably sounded as crazy as someone declaring that a gallon of milk will always cost $5. After all, money back then had actual value based in scarcity, not just the agreed upon value money has today.

It wasn’t until eighty years later that America, under the progressive leadership of Thomas Jefferson (who would have carried out full metrication at the time were it up to him) became the second country with decimalised currency. The Coinage Act of 1792 defined the dollar as being worth the still-standard 10 dimes and 100 cents, but it also defined an "eagle" as being worth 10 dollars, in the form of a gold coin that was minted until 1933. The Coinage Act also took the seemingly ridiculous step of declaring the relative value between gold and silver, with gold worth fifteen times the equivalent weight in silver. Currently, gold is worth about sixty times silver, so that obviously didn’t stick.

Currency decimalisation did stick, however, and has since been adopted by every country in the world. There are two countries that still formally have non-decimal currency, but not in practice. In Mauritania, one ouguiya has the same value as five khoums, but that value is so low that no one uses khoums at all. The same is true of Madagascar’s currency, where one ariary has the value of five iraimbilanjas.

Neither of these currencies would be difficult to use today if they were in circulation (except perhaps pronouncing "iraimbilanja"). Because ten is easily divisible by five, we can use decimal math to make calculations on these currencies. If I had thirteen khoums, and I wanted to deposit them in a bank that recorded money in ouguiya, they could divide thirteen by five and record that I had deposited 2.6 ouguiyas. Similarly, it’s easy for us to exchange any number of quarters for the equivalent amount of dollars. When doing the math, we don’t actually consider four quarters to a dollar; we consider one quarter to 0.25 dollars.

Where non-decimal currency becomes a problem is with relative values that don’t work cleanly in decimal math. For example, one thaler in Hamburg was once worth three marks. If I took four marks into a Hamburg bank that recorded money in thalers, they would need to record that I deposited 1.333333333... thalers, with the three extending forever. Non-decimal currency works fine under a similarly non-decimal number system. But the prevalence of decimal math in the world has encouraged a gradual decimalisation of the world.

This raises the question of when and how decimal math conquered all other number systems throughout the world. The common assumption is that ten-digit math came from ten-digit appendages, i.e. the ten fingers on our hands. But this certainly wasn’t the only option. Several languages still indicate base numbers of twenty, a vigesimal number system, presumably based on the number of fingers plus toes. The Danish word for sixty, for example, is literally "three times twenty," though it is now written in the conventional "60" or "six times ten."

The twelve months on our calendars, twelve hours on our clocks, and twelve inches to a foot all suggest a duodecimal (base twelve) number system, possibly derived from the twelve knuckles on the fingers of one hand (not counting the thumb). Duodecimal math is actually simpler than decimal math because twelve has more factors than ten. Those four marks I took to the hypothetical Hamburg bank, for example, could be easily recorded as 1.4 thalers in duodecimal notation.

In 1935, F. Emerson Andrews wrote a book titled New Numbers: How Acceptance of a Duodecimal Base Would Simplify Mathematics. And if you’re interested, there are still people promoting duodecimal numbers today. The Dozenal Society of America is next meeting on October 6, 2007 at 10am, location to be announced. But as they declare Today is day 24; of month 1; of year 11#3, I would double-check that date and time (and, of course, get a location) before you head to the meeting.

Dozenal societies and Kentucky notwithstanding, the decimalisation of all things numeric appears to be slowly crawling forward. It will be interesting to see which American politician will next join the ranks of Peter the Great and Thomas Jefferson, declaring America decimalised, and if we’ll be doing so before or after Liberia takes the plunge.

 

I’ve added a simple math question to the comments. I don’t like inconveniencing innocent people to stop the guilty, just in principle, but I was getting really tired of deleting all the spam from my moderation queue. If you can’t figure out the correct answer to the math question, your comment doesn’t even make it into the queue now. But when you fail, it will tell you the correct answer, so it’s really more of a literacy test than a math test. If you’re able to read, you should have no trouble submitting a comment. And if you’re not able to read, well, you should go learn instead of submitting comments here.