An Open Letter to Supporters of a Dozenal System

Currently proposed numerals are too arbitrary and impractical in too many situations. To be practical as possible, the dozenal system should be looked at from every potential user’s point of view and made as generally accessible as possible.

Proposed Names

Before discussing the meat and potatoes of this topic, I would like to cover the bread and butter. For those reading this that are lost, Numberphile made a great video here not only explaining the dozenal counting system, but using the proposed names for ten, eleven, and twelve. My counterpoint to these names is that English already has names for base-12 counting.
Using a dozen as a grouping for measurements of length and time are far older than English itself, which is why English even has the standalone number names ten through twelve. Ten is just a name with no reliance on a ten-base system. As long as you remember there are no teens then it is fine. We don’t need to use the Latin words “dec” or “decem” any more than Koreans need to use the Spanish word “diez”. Names are language specific. Same goes with eleven and “el”. (Besides, if we were going for universal names, wouldn’t “el” be easily confused with the Spanish word “el”?).

Previously Proposed Notations

None of the notations for ten and eleven hold much from a practical or aesthetic perspective. I imagine they were all hastily inserted by mathematicians with no regard to their use by other humans.

Ten as ‘X’ – Proposed adoption from the Roman numeral for ten, it’s easily recognized by westerners and easily accessible digitally, being a common English letter.

Ten as ‘T’

Ten as ‘A’ – Works great for bases larger than twelve, such as hexadecimal.
Unlike hexadecimal, dozenal numbers are meant to be read by humans. Alphadecimal notation can cause confusion to many readers, especially in small number situations. Imagine apartment number “1-A” being confused with a dozenal “1A” (22 in decimal).

Ten as a rotated ‘2’ – Of the popular proposals, this is possibly the easiest to read and mentally process.

Eleven as ‘E’

Eleven as ‘B’

Eleven as a reversed ‘3’ – Another one proposed by Sir Isaac Pitman, containing the same qualities of the rotated 2.

Proposed Notations

In order of things I think are important, numerals should be…

There are no numerals that perfectly meet this guideline. You could do away with Arabic numerals and start from scratch, but for the sake of being humanly practical I won’t delve into that (right now). Here are a few suggestions I made for personal use:

You can quickly see that this is essentially a 5 numeral reversed and missing the stave. Reversing would not have made it look dissimilar enough from the 5 numeral, and removing the stave makes it easier to write or print. This could be used to represent either ten or eleven, but I personally prefer to use this to represent a ten as my brain subconsciously connects this as a multiple of 5.

This is a vertically mirrored, (or mirrored and rotated,) derivation of 7. This can be rotated without being mistaken for a 7. This could be used to represent either ten or eleven, but I personally use this to represent an eleven as my brain makes a strong connection between 7 and 11 (like the store chain 7-11). It can also look similar to a reversed, upper-case “L” depending how you write it, which could be associated with “el” in “eleven” if you are primarily an English speaker.

Not quite as easy to write or read as the other two, this still follows my guidelines better than other notations I have been suggested. I do not use it myself as I think the other two notations are better suited. The only apparent downside I can see to using this is the possibility of a handwritten variant being mistaken for a plus “+” sign or a reversed, lower-case “h”.

0 1 2 3 4 5 6 7 8 9 X E

Of course there are no digital characters made for these numbers, but that’s really the point. Make your own numerals from scratch, write them out, teach them to your kids, spread the ideas out there and expand other minds. Make people think differently. Great ideas stick only if you stick to them, and perhaps one of these numerals will appear in one of the Unicode character maps if enough people use them.

Posted 2013-08-03 01:16:21 -0400