Base 12 is better!

By Bobby Neal Winters

Let’s talk about feet.  Not the ones on your legs, but the feet that you measure with.  We could dive into a discussion that the foot was defined to be the length of some king’s foot, but I don’t know the king and I don’t even know if that is true.  What I do know is that we use a foot to measure with and that we divide a foot into twelve inches.  So when I said let’s talk about feet, I really meant to say, let’s talk about inches and feet.

Twelve is a lovely number.  We can think of twelve as 2 times six like we do in the standard egg carton that holds a dozen eggs in two rows of six.  We can also think of it as 3 times 4.

Mathematically speaking, when we measure length in inches and feet, we are operating in base 12.  When you take out your tape measure and measure off a length of 100 inches, you don’t say that, at least not for long. What you do is say 8 times 12 is 96, so the measurement is 8 feet and 4 inches.  You’d write that out as 8’4’’, using the single apostrophe as an indicator of feet and the double as an indicator of inches. 

Using feet is a convenient way of keeping track of a large number of inches.  It helps our human minds by keeping the numbers small.

Working in base 12 gives us an advantage if we want to divide our woodwork into equal pieces.  Say you have a board that is 7’ long and you want 3 equal pieces. One-third of one foot is 4 inches.  Four times seven is 28.  So you only need to cut the board into three pieces, each of which is 28 inches (2’4’’) long. There is no need to convert the 7’ to inches first. The system is set up to do the math for you.  

You can do the same thing if you want to cut the board into 6 pieces.  One-sixth of twelve is two.  Two times seven is 14. You can cut the board into six 14-inch (1’2’’) long pieces. 

This is the advantage of using a base that works according to your needs.

The question arises, however, of what happens when you need to do work where a whole inch is just too coarse a measure.

At this point, we abandon base twelve and have to shift to a variety of bases.  When I said a variety of bases, I made it sound scary, but now I am going to make it scarier still by telling you the bases: Two, Four, Eight, and Sixteen.  That does sound scary, but it’s just a fancy-pants mathematical way of saying what everyone who works with wood knows: You work with half-inches, quarter-inches, eighth-inches, and sixteenth-inches.  There are some who will refer to 32nd inches, but I always roll my eyes, and ask who the heck are they trying to impress?

The fact that we use these bases for lengths less than an inch gives testimony to the fact that when you get to lengths this small it is really easy to divide in half by eye.  You can take whatever length you have in front of you and whatever marking tool you might have, and find the middle.  It is easy to check that the length on one side of your pencil is the same as the length on the other.  If you doubt your own eyeball, you can check it with a pair of dividers or use a multisquare. 

Using base two is all about cutting things in half.  If something is 17 inches long and you want to cut it in half, you say half of one inch is a half-inch, so half of 17 inches is 17 half-inches.  Now 8 times 2 is 16, so half of 17 inches is 8 and one half-inch.

You can do the same thing by using base 4 to cut into fourth, base 8 into eights, and so on.  

I will be the first to admit that this gets a bit awkward and a bit more like algebra than arithmetic. What is more, you can’t use this to divide into thirds, which you can with a foot.

This will be a spot where those who are constantly trying to push the metric system will come in and make their pitch.

“Switch to metric,” a voice like Gollum’s hisses. “Use base ten, my preciousssss.”

It does have a point, but at the same time, I will say it outloud for all: 10 is a lousy number to use as a base.  It is only divisible by 2 and 5. 

Do I have anything better?

Yes, and if you’ve read this far you’ve seen it: 12.

When the French Revolution adopted the metric system, they didn’t go quite far enough. As long as they were lopping off heads, they should’ve just gone ahead (see what I did there) and gone to base 12. As you’ve seen up to this point, 12 is evenly divisible by 2, 3, and 4.

We can’t change now.  There is too much literature done with the other system. 

The changeover would be a nightmare too.  I can just see all of the crying as grade school students start learning duodecimal arithmetic, and that’s just the parents and teachers.

We are stuck with base ten.  I will continue to use feet and inches in my woodshop, as much as ever measure anything.  The Scientific-Fascists who are the heirs of the French Revolution will continue to force metric in wherever they can.

And we will ignore the elephant in the room: Base 12 is best!