How to Make the Metric System Useful by the Dozen
I rather like the letter R for representing 12, it rather looks like a 12, but it can be written in one stroke, helping keep it from being seen as 10+2. I rather dislike referring to R as 12, for much the same reason I don’t like referring to ten as 1010. Describing numbers that you’re trying to work with in terms of an inferior base tends to be needlessly complicated, and I try to avoid it whenever possible.
Base X(previously written as 10) is kind of an awful thing to base math on. The only things it makes easy are dividing by even numbers, 5s, and Xs. If something ends in 5 or 0, you know instantly it’s divisible by 5 … and … that’s about it. Everything else is weird random tricks we figure out and memorization so we can remember things like how to add 9 to any number, or how to multiply by 6.
It is pretty awesome for dividing by 5 and X though, you can probably tell just by looking at 150 how many times 25 goes into it. Remember that, because in base R(previously written as 12), what it’s like to divide by 5s and Xs gets switched to 3, 4, 6, 8, and 12(10, or R; from here on out). For the most part, it doesn’t really change our most basic math at all. 4 + 5 is still 9, 100 / 10 is still 10. 10 to the sixth power is still 1,000,000. It’s just that now when we want to switch from one digit to the next, there are two more numbers between 9 and 0. To make things more comfortable, I’m mostly going to avoid them, they don’t come up much when multiplying and dividing anyway. Though it may be helpful to remember that now there’s the same distance between 6 and 9 as there is between 9 and 10. For the symbols to use in between, I like X and E, when writing I usually loop the top of the x and make the E look more like a backwards 3, to avoid getting it confused with other symbols.
I also like putting a number line on the paper to act as an ambassador of sorts, sometimes with lines showing how easily divisible everything is.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | X | E | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 1X | 1E | 20 |
|
1*2 |
2*2 |
3*2 |
4*2 |
5*2 |
6*2 |
7*2 |
8*2 |
9*2 |
X*2 |
E*2 |
10*2 |
||||||||||||
|
1*3 |
2*3 |
3*3 |
4*3 |
5*3 |
6*3 |
7*3 |
8*3 |
||||||||||||||||
|
1*4 |
2*4 |
3*4 |
4*4 |
5*4 |
6*4 |
||||||||||||||||||
|
1*6 |
2*6 |
3*6 |
4*6 |
||||||||||||||||||||
| 1/6 | 1/4 | 1/3 | 1/2 | 2/3 | 3/4 | 5/6 | 1010 | 7/6 | 5/4 | 4/3 | 3/2 | 5/3 | 7/4 | 11/6 | 2010 |
Note that anywhere I’ve filled in the table with something, that’s always true, whenever the digit at the end is the same. Just like anything that ends in 5 or 0 is always divisible by 5 in base X, anything that ends in 3, 6, 9, or 0 is divisible by 3, and anything that ends in 4, 8, or 0 is divisible by 4. Every time. And when you see 6, think of it like the decimal 5, it’s halfway to 10, and anything you could do with 5 before you can do with 6.
The fact that we use base X is really the main reason why no one ever wants to convert to the metric system. All other measuring systems we’ve ever developed have been based on numbers like 4, 6, 8, 12, and 16. Numbers you can easily cut into manageable fractions, NONE of which go into X evenly. This makes the metric system is awkward, and has dividing into it to get manageable units a pain. But it does make it so anytime we want to switch down or up, we get to keep the same numbers, only multiplying or dividing by factors of 10. No conversions required, ever, just move the decimal point and change the prefix.
So, let’s fix it, all of it, in one fell swoop, with one change. 10 is now R, 100 is still 10^2, only now it means 144(d) in decimal, and 1000 is 144*12(d), or 1728(d). Don’t worry about how scary that number looks, it’s just 1000 to you from now on, only now it’s divisible by any digit except 5, 7, x, and e, to get a perfectly normal looking number ending in zeroes.
We developed the metric system specifically to make our math and conversions easier, so we can represent the same measurement in whatever way is most convenient without ever having to change our actual numbers, and all those benefits still exist in base R, but with the added benefits that keep us from switching from our good old imperial standards, far more useful factors to split things into.
So, now that we’ve switched to base R, let’s convert the metric system to it. We’ll be keeping the liter, kilogram and meter, and keeping all our prefixes the same, 1/1000 of a Liter is still a milliliter, only now a milliliter is a bit smaller, and all our units can be broken into 12 parts.
Looking at a 12 oz can of soda, we could always have put that into 1/3 a liter, we just could never write it before. Now 1/3 a liter is 40cL(400mL), incidentally, that also means an ounce is 4cL, or 40mL. Can you believe it used to be 28? I didn’t even change the liter, only how it’s divided. In case you’re curious, a 16th of an ounce is 2 and a half mL, but you’ll probably just divide it into Zenths anyway, or 3rds, or 4ths, or 6ths, or 8ths, or whatever you need. When you’re used to it, all those divisions will come as naturally as if you were dividing by 2 or 5 in base X. If you’re curious, those numbers into 40mL would come out to 14, 10, 8, and 6, perfectly evenly. You can do the same thing with any number ending in 0. And you can always make a number end in zero by dropping down a unit in metric.
For distance, a mile would be just about x0(d/120) meters short of a km, instead of d/1.609km to the mile, Going smaller, a centimeter is a quarter inch, so 3 mm is d(1/16) an inch. if you want d(7/16) of an inch, you want 24 mm. How about a third of an inch? Well, that’s 14mm. No conversions, no ‘Well I suppose it’s about…’, everything is exactly measurable and calculable, and all of this being just as easy as dividing by 2 and 5 is for you now, but with all the benefits of having an inch ruler with with clear and evenly divisible marks
For weighing things, kilograms are going to be a more useful unit of measure than pounds are, since you can’t cut a pound into ounces of thirds, or sixths, or dozens, or ninths. Ok, wanting 9ths is a bit extreme, but a ninth a kilogram is totally 140 grams now. Think of all we’re missing at not being able to make these conversions at will? Want a quarter pound hamburger? 160 grams, or 16 dag, is a quarter of half a kilogram, (remember, when you see six, think 1/2, like decimal 5, so that number should be looking about like 150 used to). Or 2 hg(20 dag, 200 grams) would give you a third a pound(1/6 a kg).
Most people who talk about using base R seem to be trying to separate it from the decimal system everyone else uses as much as possible, making it some independent thing that gives some advantages if you happen to see the merit in it, but I find some issue with that. We already have a perfectly good understanding and long history with measurements, time, math, and representing and manipulating numbers, and for the most part, every single thing we’ve learned from them is transferable to base R entirely, with the only real disadvantage being that any numbers you happen to have memorized will change, and most of them will now be easier to work with. The only thing we really need to mess with is what we’re going to call X(2*5), E(5+6), and R(3*4). Personally, I’m partial of converting X to “dec”, E becoming “El” or “Elv”, and R becoming “Zen”. With every other number being mercilessly and wholly converted over to dozenal. 1X becomes “desteen”, 1E becomes “Elteen”, X5 is “Desty five” and E0 is “Elty”. And 1EX3 is “one thousand, elhundred desty 3”
In short, base X needs to go the way of the roman numeral and make way for a far more reasonable standard, if only so we might finally be able to get some good use out of the metric system.
Links
The Dozenal Society of America
– Z Calculator – Used to get and confirm most of the numbers for this article 🙂
The Dozenal Society of Great Britain
Youtube
The Eternal Melody of Pi Base 12 by Jim Zamersky – Chromatic
Tags: Base R, dozenal, Math, metric system
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