## 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.

- X can too easily be mixed with a variable in computer or mathematical notation.
- X is a Latin number and doesn’t look like any Arabic number.
- X looks like the lowercase letter x, which is often used as a symbol for multiplication.
- X cannot be represented on seven-segment displays, (a display type commonly used for calculators and industrial equipment.)

**Ten as ‘T’**

- T is too recognizable as a letter.
- T as the first letter in ten shows a bias towards English.
- T doesn’t look like any Arabic number.
- T cannot be represented on seven-segment displays.

**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.

- A rotated 2 will look like a 2 on a rotated object, similar to 6 and 9. With 6 and 9, this can be resolved by underlining. From first glance, an underline on a 2 or rotated 2 might not be as obvious.
- There is no dedicated computer character for a rotated 2. The closest character would be the carrier “ᘔ” (which bears as much resemblance to 6 as it does 2.

**Eleven as ‘E’**

- Using letters are not practical for small numbers.
- E as the first letter in ten shows a bias towards English.

**Eleven as ‘B’**

- Using letters simply aren’t a good idea, and worse, B looks too similar to 8. Those who enter license keys into computers can share my pain on this one.

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

- A reversed 3 is still too similar to a 3. And identical to the “E” commonly used on seven segment displays.
- There is no dedicated computer character for a reversed 3. The closest character to my knowledge is the Greek letter “ξ”.
- Choosing a character because it looks like a capital “E” is biased towards English and otherwise arbitrary.

### Proposed Notations

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

- easy to read by anyone of any language.
- easy to write with the left or right hand.
- easy to distinguish from other numbers.
- easy to distinguish from Latin characters.
- easy to read in as many forms as possible.
- consistent in style to other Arabic-western numerals

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