Dividing We Fall: Base 12 and Resistance to Metric System Adoption

I’m not a math person, I’m a words person. That’s one of the reasons I find the metric system so appealing—it’s easy to learn, use and divide with. However, my readers should be aware that one of the metric counter arguments that will arise is the ease with which the foot and its 12 units can be divvied up as a reason to hold onto our current (if illogical) units.

Here’s the point that will be made: The foot—consisting of 12 inches—is superior to metric system units (of 10) because 12 is divisible in so many ways. The numbers 1, 2, 3, 4, 6 and 12 all go into it quite easily, while base 10 units are really only easily divisible by 1,2, 5 and 10.

That’s a crap argument and here’s why:

THE FOOT IS OUR ONLY POPULAR MEASUREMENT UNIT OF WHICH THAT IS TRUE.

Frankly, if all our measurement units were based on 12, I could almost see an argument that we should stay where we are. Not the best argument, mind you, but a stronger one. However, that is far from the case. Let’s take a look at a few of our other weights and measures and see where else the number 12 comes into play.

Teaspoons in a tablespoon = 3
Cups in a quart = 4
Pints in quart = 2
Quarts in a gallon = 4
Ounces in a pound = 16
Feet in a mile = 5,280
Pounds in a ton = 2,000

Hmmm, no luck so far. While I’m not saying there isn’t possibly another U.S. customary unit that uses 12 of something, it’s probably pretty obscure.

To interject some of my extensive research, in A History of Mathematics, Carl B. Boyer and Uta C. Merzbach point out (I used brackets below to include the numbers referenced in words to make it easier to follow):

A study of several hundred tribes among the of American Indians, for example, showed that almost one-third used a decimal system [10], and about another third had adopted a quinary [5] or quinary-decimal system [think abacus]; fewer than a third had a binary [2] scheme, and those using a ternary [3] system constituted less than 1 percent of the group. The vigesimal system, with the number 20 as the base, occurred in about 10 percent of the tribes.

As the book also points out:

As Aristotle had noted long ago, the widespread use today of the decimal system is but the result of the anatomical accident that most of us are born with ten fingers and ten toes.

And, according to the book, the number 10 even takes the upper hand when it comes to language:

The modern languages of today are built almost without exception around the base 10, so that the number 13, for example, is not described as 3 and 5 and 5, but as 3 and 10.

Given that we pretty much come with our own built-in decimal system it only makes sense (to me at least) that the metric system is the system that prevails around the world.

If those points aren’t enough, allow us to consider the Romans and their numerals. They were all about units of ten as you can see from the large number of “Xs.” (See chart from http://www.roman-numerals.org/chart100.html)

As a friend pointed out, there are other things that come in twelves, such as our months and recovery programs (as in 12 steps) but these are not numbers that we need to divide so go ahead and use a dozen of something where it makes sense, just not in our measurement system please.

Thanks,

Linda

10 thoughts on “Dividing We Fall: Base 12 and Resistance to Metric System Adoption

  1. There may be some advantage within numbering systems that 12 is divisable by 2, 3, and 4 while 10 is only divisable by 2 and 5 .. but not within measurement systems. People who are supporters of the base 12 numbering system, think that there would be the same advantages of the 12 numbering system, compared to the base 10 system, if measuring systems were structured on a base 12 system, but this is not true.
    Numbers are digits on paper, or computer screen. They are symbols, they do not divide. Its what the symbols represent that is divided. For example 6 could represent six apples. I can divide them into three parts consisting of 2 apples, 1 apple, and 3 apples. So most physical items can be didvided into 3 parts. But they are not equal parts. If I divided them into 3 parts of 2 apples, 2 apples, and 2 apples by the definition of the numbering system, they would be equal and EXACT, but they would NOT be equal and exact by the definition of a measurement system. Thats because a numbering system, and a measurement system, are two diffreent things. To divide the 6 apples into 3 equal parts with the measurement system, one has to weight the 6 apples and divide the total weight by 3. This would result in 1 apple being cut up.so that each of the 3 parts of the apples equaled a third of the weight. The numbering system gave an exact result, but the measurement system, metric or Imperial/USC, cannot give an exact result. It doesnt matter what measurement system we use, there is never any exact measurement, and there is always some tolerance and uncertainty in any measurement, and just as a meter or a kilometer cannot be exactly divided by 3, the same applies to a foot or mile which cannot be divided exactly by 3. It not possible for measurements to be exact and thats why all measurements are arbitrary.
    A third of a foot is 4 inches, a third of a meter is 333.3333 millimetres. These are not measurements, only numbers representing measurements. Numbers are exact but measurements are not. People who support a duodecimal measurement system, often overlook or ignore this fact. There is no advantage, to structuring a measurement system on base 12. However, there is an advantage, in structuring a measurement system on base 10 (the metric system), because base 10 is the standard, and default numbering system, used worldwide, and that’s something, that will not be changed.

  2. “one of the metric counter arguments that will arise is the ease with which the foot and its 12 units can be divvied up as a reason to hold onto our current units”

    In real-world use in metric countries one uses 300mm rather than 12 inches.

    The numbers 1, 2, 3, 4, 5, 6, 10 and 12 all divide into 300 quite easily.

  3. Linda: With respect, you need to do some personal research, primary sources, original research in a library, if you wish to make your own documentary, write your own articles and have them taken seriously.

    The reason for the INCH and Troy OUNCE (both corruptions of UNCIA, Latin for “twelfth”) is because the Romans were most definitely not base ten. For numbers greater than one they were, but for numbers smaller than one they used twelfths, one forty-fourths, seventeen twenty-eighths etc. in figuring amounts. This is a similar fractional system to that employed by the ancient Egyptians, reconning in fractions instead of base ten decimals.

    You should also know that the troy ounce is one twelfth of a troy pound for calculating precious metals, meaning there are two systems that use base twelve. Originally the inch was also sub-divided into twelfths, one forty-fourths and seventeen twenty-eighths as well. The apothecary and troy professional systems also contain factors of twenty-four. For any other trivia questions you have on Imperial and USC systems of measure, we’d be happy to help if you can’t find the information yourself, but there is a wealth of information available in many college libraries out there.

  4. The Romans used a base measurement system as well. The inch and the ounce are both from the Latin for balance or measure. There are a dozen ounces in a pound (not 16) and a dozen inches in a foot. (The page owner removed some name calling from this comment.)

  5. This is all fine and good, but you know what would be better than either system? And entirely new metric system, being entirely base 12.

    “THE FOOT IS OUR ONLY POPULAR MEASUREMENT UNIT OF WHICH THAT IS TRUE.”

    Other than time, you mean?

  6. I concur! Our highly advanced and scientific system should use base 10, because cavemen counted on their fingers!

    ——————–

    1. Why should the counting systems of primitive tribes dictate our modern systems? Humans not only can learn base-12, but are more efficient in it.

    2. At least make your non sequiturs accurate: the Romans used a base-10/base-5 system for whole numbers, and a non-decimal system for fractions. This information is irrelevant.

    3. Cups, pints, quarts, and gallons follow a base-2 system. This is commendable, but humans just aren’t great in base-2.

    4. English, a modern language, includes neither ‘twoteen’ or ‘tenty-two’. However, we do say ‘eleven’ and ‘twelve’. Choosing ’13’ was disingenuous.

    5. Now just a minute…. Nevermind, ‘minutes’ are not a metric unit, because they’re sexagesimal. Using metric time is just awful, because powers of 10 do not coincidentally fall into the lengths I want to use.

  7. “How many meters are there in a third of a kilometer?” This is a question that will never come up in life unless you’re doing a math test. So no, it doesn’t matter at all that it doesn’t divide neatly by 3.

    Also, it’s like the US never heard of fractions or something. God forbid they use something more than basic arithmetic.

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