Dozenal

Why do we use the decimal system? Supposedly because most of us have ten fingers, and humans used this to count before the appearance of written numerals. This is known as base-ten. We go 1, 2, 3, 4, 5, 6, 7, 8, 9 and then we shift the 1 by one spot to give 10. But ten is a terrible number when it comes to division. If you wanted to equitably divide ten sweets and not deal with kids complaining that someone else got more than them, that’s difficult to do if the number of kids is not two, five or ten. Base-twelve works much better. Twelve sweets can be divided equally by two, three, four, six or twelve.

 

It's much easier to slice up a pizza for twelve people than ten. We divide our day into twelve hours and our night into twelve hours. (I grew up near the equator where sunrise and sunset times didn’t change very much.) The ancient Babylonians used base-sixty. We still use this to count minutes and seconds, and to measure angles. I learned that the Yuki of California used base-eight by “using the space between their fingers as markers”, while the Oksapmin of Papua New Guinea used based twenty-seven using body parts that included the nose. The Egyptians though used base-ten but had symbols to handle place-value. I learned this from reading Kit Yates’ The Math of Life & Death.

 

Does it matter? Apparently there is a Dozenal Society of Great Britain (Yates is British) and a counterpart here in the U.S. who think that base-twelve is superior. Yates writes that “advocates of the dozenal system claim it would reduce the necessity for rounding off and hence mitigate a number of common problems”. Yates provides real-life examples where rounding errors mattered in a national election and in a stock exchange index. And in real life we often divide things by the number three. A third. Two thirds. And then we have to deal with the annoying 3.333… and 6.666… Ugh.

 

When I was in elementary school, we were forced to memorize our times-table up to twelve. Why? I don’t know. Is it an unconscious relic of a dozenal base? Or is it simply because nine, ten, and eleven are easy, so kids need to be challenged to twelve? I don’t know, but my education was based on the British system. My spouse who grew up in the U.S. thinks she only had to memorize the times-table up to ten, but she can’t quite remember. I’ve heard that some countries require kids to get to sixteen. Ah, hexadecimal. I remember learning to read it when I first hacked into computer programs.

 

I don’t think the general public will ever shift to the dozenal or hexadecimal system. Decimal is too strongly baked in. But we, the general public, should learn to think more mathematically. And that’s what Yates’ book is about. Yates provides engaging examples in words and numbers. There are no equations for the math-phobic to worry about. Yates talks statistics, exponentials, probability, algorithms. His final chapter is devoted to thinking about disease spread in pandemics, aptly so since it was published in 2019 shortly before Covid-19. If only more people had read his book, they would have been less confused when talking heads mentioned herd immunity, patient zero, or R-nought.

 

I’ve read a number of “math is cool” books aimed at the general public. The Math of Life & Death is easy to read and has relevant examples that make you feel smarter after you figure out that math isn’t as hard as you thought, and it’s so useful! I’d been mulling an overhaul of my G-Chem classes to include a more significant data science and modeling component. Not sure yet if I’m ready to take the plunge but Yates is helping me move the needle.