The ‘Argument of Twelves’ and the Metric System

The fact that we have 12 inches in a foot isn’t a good reason to reject the metric system. Image from arielrobin on Pixabay.

(Sorry for the long lag between posts. I had some things going on in my life that required my full attention. Things are pretty much back on track. Thanks for your patience.)

Awhile back I was fulfilling my role as a scientist ambassador at the Bradbury Science Museum here in Los Alamos, NM. (This mostly consists of setting up various measurement activities and chatting with visitors about the advantages of the metric system for a couple of hours on the occasional Saturday.)

One day I realized that a man was starting to pace back and forth in front of me. Even though I wasn’t yet done prepping and I sensed this gentleman was about to go on the attack, I went ahead and said, “People are dying in this country because we don’t use the metric system in this country.”

“I don’t believe you,” he replied.

Even the Centers for Disease Control recommends strict use of metric units for liquids. (Pills are measured in grams, or a fraction thereof, already.)

I then handed him the 2016 Top Ten Patient Safety Concerns for Healthcare Organizations report put out by ECRI [Emergency Care Research Institute]. Number seven on the list: “Medication Errors Related to Pounds and Kilograms.” It advocates for only using metric system units (i.e. kilograms for weight) to reduce dosing errors since most medications use weight to determine the correct dose. It’s reason is simple: There are about two pounds in a kilogram. Doctors and nurses are schooled in the metric system but have to bounce back and forth between metric and U.S. customary units to communicate with their American patients. If they mix up the two, they might give the patients half the dose they need (potentially rendering it ineffective) or twice the amount (read overdose).

Using metric system units for medicine has also been recommended by multiple health organizations including the Centers for Disease Control. (See the above image)

The gentleman reviewed the report and since—I assume—he could no longer argue on that particular point, he launched into what I’ve now dubbed “The argument of twelves.”

The Argument of Twelves

The argument goes something like this: If you are working with a group/set of 12s, then your factors are 1, 2, 3, 4, 6, and 12; but if you are working in the metric system, your factors are only 1, 2, 5, and 10.

I consider this to be a specious argument since (and please, but nicely correct me if I’m wrong) we don’t really measure a lot of things by twelves. Sure, a foot has twelve inches and there are twelve months in a year. (Apparently eggs are sold by the dozen—according to the New York Times—because eggs were a penny each and there are 12 pennies in a shilling. Selling eggs by the dozen meant, as a vendor, you didn’t have to make change.) However, there isn’t much else I can think of that comes in twelves except a gross of 144 items (which is 12 multiplied by 12). You can’t really cite time because military/Zulu time uses a 24-hour clock.

If we actually had 12 ounces in a cup and 12 cups to a gallon and 12 ounces in a pound and 12 yards to a mile, then I would understand that counter argument. (In reality, there are 8 ounces in a cup, 16 cups and 128 ounces in gallon, 16 ounces in a pound, and 1,760 yards in a mile…plus 36 inches or 3 feet in a yard and so on.)

But, when it comes to everyday measurement, we really only divide up inches, months, and eggs into twelves. I don’t think that’s enough reason to reject using the metric system.

However, I’ve found after seven years on this project (the anniversary of which was the day before yesterday), if people are threatened by the idea of changing to the metric system—for any number of reasons—they will latch onto whatever immediately comes to mind to reject it.

Around the time that the man was winding down his argument of twelves, some other—more open-minded people—approached me and I turned my attention to them.

I’ve said many times that, when it comes to this issue, there are probably 10-20 percent of people who already love the metric system and there’s about another 10-20 percent who are completely opposed to it.

It’s my plan to focus my attention on the 60 to 80 percent who don’t realize we have a problem in this country and are open to learning about it. Maybe action will eventually occur. That’s my hope. If you want to become more involved, let me know at

In a closing note: I realize that some people ascribe a historical and religious meaning to the number 12, but we don’t have to limit the number of members on a jury or the number of apostles due to the metric system so let’s not shoehorn that number into our measurement system unnecessarily.

Plan for another post in September.

Thanks for getting this far,


12 thoughts on “The ‘Argument of Twelves’ and the Metric System

  1. The “Rule of 12” is an extremely valid argument and was the first choice of the Académie des Sciences when they first sat in May 1790 to set up a strategy to standardise weights and measures. Joseph-Louis Lagrange, having arrived in Paris shortly before the outbreak of the French Revolution was a leading member of that committee. It was thanks to him that a base of 10 was chosen, his rationale being that people counted in 10s. He argued that a duodecimal system of measurement would only be useful if people counted in 12s and asthat was not going to happen the committee should settle for a decimal-based system.

    Thus, if one person writes that they 1.75 metres tall and another writes that they are 175 centimetres tall, one can see immediately that they are the same height. Compare this with one person saying that they are 5 ft 10 in tall and another saying that they are 70 inches tall – it takes a certain amount of mental work to compare the two. As Charles Dicken wrote “Let us measure as we count – in tens”.

  2. A related argument I keep running into is that you can’t divide a metre (or a litre or kilogram,) into thirds. This argument presupposes that everything metric measures exactly one metre or a multiple of a metre, and will need to be divided into three parts at some time.

    • This issue never comes up in countries using SI already as everyone knows you can use any number in SI. So, if you need to divide a dimension into thirds, make sure the original dimension is divisible wholly into thirds. 1200 mm instead of 1 m.

    • You can’t divide pounds into thirds either. 1 pound = 16 ounces, and 1 ounce = 16 drams. Despite the fact that the word “ounce” literally means “one-twelfth”.

      There’s also the problem that every nation of Europe has its own pound, whereas a kilogram is the same no matter where you go.

  3. There is a fantasy going around about SI especially by those who are poorly educated in SI that SI only works with factors of 1, 2, 5 & 10. There is no rule in SI that claims you can only use numbers that are integers of these factors. In fact SI leaves it up to the users to determine what factors work best for them.

    As an example, the construction industry works around the 100 mm module but produces products that are in increments of 300 mm, which is an integer factor of the 100 mm module. Thus you will encounter products that have dimensions of 300 mm, 600 mm, 900 mm, 1200 mm, 1800 mm, 2400 mm, 3600 mm and 4800 mm, etc, just to name a few. Why? Because all of these sizes can be divided into smaller parts all with whole number of millimetres. SI is more friendly to 12 than USC or imperial are.

    The only thing 10 based about SI is the increments of the prefixes. They are based on factors of 10. Units however are based on a factor of 1:1. One newton is equal to one kilogram times one metre divided by one second squared, One joule is equal to one newton times one metre. ETC.

    I blame the BIPM for this. They need to be more active in seeing how SI is taught in schools world wide. They need to work with the standards organizations of each country who would work with the national school systems to teach SI as it should be taught. Such as the units relating to each other 1:1 and how to use ALL of the prefixes, not just those that equate to older units. Otherwise SI will never have the advantages intended.

  4. > If they mix up the two, they might give the patients half the dose they need (potentially rendering it ineffective) or twice the amount (read overdose).

    In reality, it is even worse than that. When doing mental arithmetic, it’s easy to get the direction wrong and use the wrong operation.
    For example, converting from lbs to kg one should divide by 2 (approximately). If one gets the direction wrong and multiplies instead, one gets an answer that is four times too large. If one makes a mistake going in the other direction, one gets a result that is one quarter of what it should be.

  5. Pingback: The Argument of Twelves and the Metric System – INDIA NEWS

  6. The argument for 12s doesn’t really work unless we switch entirely to a duodecimal system of notation. So 12 would in fact be written 10, and we’d need new digits for 10 (X?) and 11 (E?).
    This would be extremely confusing when the decimal system was also still in use, so I think it would need to use entirely new digits for every number.
    A ‘heximal’ system (digits 0-5) might be better in that regard, with fewer new digits to learn, and it also gives you much smaller “times tables” etc.

  7. I worked as a carpenter for forty years, usually with Dutch and German tradesmen. We usually worked in Imperial, in spite of the fact that they had all been trained in Metric. There is a huge advantage in being able to recalculate the framing of a wall because you have just discovered that there is a drain pipe in way, or some other difficulty. In Imperial measurements you can do the necessary calculations on the spot with just a tape measure. You don’t even need a calculator because of the magic of proportions. It is easy because the ancient system, which is Babylonian, and at least 8,000 years old, (and probably much older than that,) because you can factor so many different ways in order to divide or multiply.
    The Roman number system, which was in use up until the French Revolution, used a system based on the finger joints of one hand. Using your thumb to count, there are four fingers with 3 bones in each finger = 12. Thus there are 12 inches in a foot, etc. This system would not have lasted for thousands of years if it was fundamentally unsound, it just works.
    However, I was in the first generation who were taught in primary school to use the metric system when Australia converted to metric money in 1966. It is a wonderful system for everything to do with science and engineering. I am so sick of having to use Imperial measurements when I am working on my car, it is just a silly, inappropriate way to measure drugs, air pressures, weights etc, in fact anything scientific. There is really no argument for the two different systems. They have appropriate uses. It is no coincidence that the scientific revolution happened after the French Revolution. Get over it! The French Revolution was quite a while ago. Can we just move on? (I’m lookin’ at you America. This is why you guys still can’t get over slavery.)
    I have lived and worked in India. There used to be a universal currency for many centuries, all around the world, based on ounces of silver. In India a rupee was an once ounce of silver, now it has been much devalued, just like an American silver dollar,) or a Maria Theresa Thaler, which was the standard of trade in Europe for centuries, in fact for millennia, the Romans and the Greeks did it.
    When I bought a basket of cabbages in the market for my restaurant, I would bargain with the market stall holders in Annas, which used to be a coin worth 1/16 of a Rupee. You can do it in sign language by holding up your fingers, even if you don’t speak each other’s language. We could understand each other perfectly. The Indian currency had been decimal for decades and there was no longer any such coin as an Anna, but in the market nobody cared. People did not own calculators, but every rickshaw driver could calculate the old fashioned way even though none of them had ever been to school. People still count on their fingers, and they probably always will.
    I support both sides in this argument, because each system has merit for particular uses.

  8. Multiplying and dividing by 10, 100, 1000 etc. is a HELL LOT easier. Americans should consider talking with the rest of the world to understand what they’re missing out on.

    When I buy a 10-pack of 330 ml beer cans, I get 3.3 liters of beverages in less than a split second. Buying a 6-pack of 12-oz beer cans? How much is that in gallons? Certainly requires a bit of mental arithmetic.

    SI units SAVE TIME. That is why they are popular in the rest of the world.

  9. Anybody that I know (American) that has had a mind open and flexible enough to take an objective look at why the metric system is so important and so much better has been wowed. I have a woodworker friend that I sent a rare (in the US) mm only tape measure and once he “got it”, he has vowed to never use the kings inch again. It is just a sad, sad shame that the voices of ignorance are the ones driving our metric stasis here. There is no need for the English “system” in the 21st century anymore. The US is literally the only place keeping it alive simply out of hubris and ignorance. They are defending ye olde English units with the same fury as Guadalcanal was defended in WWII. America, you’ve been partially using the metric system your entire lives. It’s your currency, which can directly be traced back to Jeffersons interaction with the French after our war with the Brits was over. Using the SI doesn’t make you a communist or a globalist or the “ist” du jour – It makes you smarter. It makes you not dependent on the rest of globe cater to your ignorance and special needs. It makes it so your doctor doesn’t have to describe that benign tumor to you in terms of various fruit or nut sizes. It makes it safer to dose that over the counter medication using the mL and not the ambiguous spoon of a 12th century prince. Grow up please, America. You’re hanging the rest of the globe up and nobody is impressed.

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