We all harbor one particular prejudice. We are each and every one of us irrevocably focused on and devoted to our number system in base ten. Our languages, our engineering discussions, our methods, our metrology, our mental visualizations, are all tied to that one single thing, our decimal system in base ten. Therefore, this note will, of linguistic necessity, condescend to that prejudice.

The hysterical foolishness of introducing "the new math" to our school systems, in the aftermath (no pun intended) of the launch of Sputnik in 1957, led to a demand that students be facile with arithmetic systems in multiple bases. We had to beat the Russians, you see.

That educational goal was resoundingly done in by our prejudice for base ten with the result that a whole generation of young people was left with many individuals unable do arithmetic at all, never mind in what base.

I believe that we can trace our prejudice for base ten to our anatomy. I once read that in the evolution of early land-living vertebrates, there were many animals with different numbers of toes on each foot. Some animals had five toes on each foot, some had six, some had seven, and all of them were crawling quadrupeds with legs that were splayed outward. There was/is a gap in the fossil record of those eras, following which most land living vertebrate species had come to have only five toes, our present day human condition, and further, that they had developed the ankle which allowed their legs to work in the vertical and raise their bodies off of the ground for more efficient locomotion.

Did having exactly five toes make the ankle possible? I don't think that paleontologists have yet been able to answer that question.

Setting aside all of the modern day animals having hooves, a very much later development, if those post-gap vertebrates had evolved six toes on each foot instead of five and if that trait had been carried through to us in our modern times, I submit that we would today be prejudiced in favor of duodecimal arithmetic in base twelve instead of decimal arithmetic in base ten.

We would be using twelve numerals (having two additional names) instead of only ten numerals, our elementary school children would have a somewhat larger multiplication table to memorize and our component color codes would have two additional colors. How do pink and teal strike you?

Our clocks would probably be the same except of course, for the numerals.

Duodecimal clock

It would all seem perfectly natural.

My mother was a math teacher. One day, she and I were discussing numerical bases when I discovered that she had never understood base two, binary arithmetic. As I explained it to her and as she came to understand it, my father overheard us. He got very upset and I do mean VERY upset indeed.

"WHAT'S MORE BASIC THAN TEN???" he said holding both of his hands fully open in front of me. "TWO!!!" was my reply as I held up both of my hands closed. I thought I was gonna be dead right then and there but instead he turned around and strode away. I was really sorry to have upset him so badly, but you can see how intensely he himself was prejudiced in favor of base ten.

Today, I know many people with that same propensity. Et tu?

John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).

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