A Brief Overview of SDN

Counting in dozenal can sometimes present some difficulties. English, as an example, has lots of words for various multiples of ten, most of which we're quite familiar with: ten, hundred, thousand, million, and so forth. It does not, however, have many words for multiples of twelve. There is twelve, or the dozen, of course; and a dozen dozen is traditionally called a gross. There is the word great-gross for a dozen gross; but it's an old word that is rarely, if ever, used or recognized anymore.

SDN provides the solution to this problem. (It solves other problems, and offers other abilities, as well; but this brief introduction is designed simply to show how to count in SDN.) SDN, or Systematic Dozenal Nomenclature, is a simple system of words that allows easy counting in dozenal. By learning only thirteen new words (most of which are already familiar) and two particles, we can easily name any number we wish.

This article, and the chart below, describes E6% (per gross, or per biqua) of what the vast majority of people need to know about SDN.

As the above chart shows, our current decimal system leaves many gaps, requiring us to fill in those gaps by multiplying by some of the lower multiples. E.g., there is no decimal word for X⁴ or X⁵, so we have to take the word for X³ ("thousand") and multiply it by our word for X¹ ("ten") or X² ("hundred"), forming our "ten thousand" or "hundred thousand."

SDN solves this problem. Each power of twelve has an easily-recognized number root (such as "un" for one, "bi" for two, and so on), with "qua" added on it to show that it is an exponent. This makes it easy to express any number up to 10^E.

Higher than 10^E, SDN provides an equally easy way to describe numbers. Using the standard rules of place notation, we simply put together the number with words rather than digits. So just as we write "one dozen two" by putting "1" in the dozens digit place and "2" in the ones digit place, making "12," we put words together to make the number when using SDN. For 10¹² (twelve to the one-dozen-two power), we combine "un" for one, "bi" for two, and "qua" to show that we're describing the exponent, making "unbiqua." It's that simple.

SDN also provides names for the negative powers of twelve, as well. In decimal, we add "th" to words to make them negative powers; so while X³ is a "thousand," X^-3 is a "thousandth." However, the same gaps in the chart exist for negative powers as for positives; and the workarounds, such as "hundred thousandths," are even more cumbersome than before.

For SDN, simply change "qua" to "cia," and one has words for negative powers of twelve. So while 10³ is a triqua, 10^-3 is a tricia. This is the difference between 1000 and 0;001.

One may notice that this is the same as counting the zeroes in the number. Simply count those zeroes, select the root corresponding to that number (in our example, "tri" for three), and then add the "qua" or "cia" depending on whether it is a positive or negative exponent.

SDN promised unlimited counting with only thirteen words and two particles. We've met twelve words and the particles already; where's the thirteenth? This is the fractional point, which in dozenal we write as ";". This is pronounced "dit"; so, for example, "0;7834" or "zero dit seven eight three four." "Dit," therefore, is the thirteenth word of SDN.

So let's count a little using SDN, just to give an idea of how powerful yet how simple the system is:

We can only count so far on a chart, so let's look at a few other numbers and see how easy it is to read them and refer to them using the SDN system. Only a few examples should suffice:

• 56: Five unqua six, or, for short, fivequa six.
• 5678: Five triqua six seven eight. It's often easiest to name the highest power (in this case, triqua), and then simply list the digits in order.
• 824 7643: Eight hexqua two four seven six four three.
• 84;56: Eightqua four dit five six.
• 378;9872: Three biqua seven eight dit nine eight seven two.

These roots and prefixes can be combined with other words the same way that many decimal words can be. For example, the word mille means "thousand," and the word ennium means "year," and we combine these into millennium to mean "a period of one thousand years." A similar construction allows century to be built, though it does not use the ennium root.

SDN allows the same types of word coinages, but in a regular and consistent manner. So ennium can be combined with any of these words in any way. E.g., bi and ennium make biennium, a period of two years; biqua and ennium form "biquennium," a period of one biqua (100) years.

Finally, SDN offers a simpler way of writing out these multiples of twelve. Rather than formatting long numbers in the length and cumbersome manner we are accustomed to in decimal, we have a compact and consistent notation. Decimal utilizes so-called "scientific notation," more accurately called "exponential notation," of this form: "3.4x10²³." This allows lengthy numbers to be expressed in a reasonable way; however, it is still lengthier than it has to be.

SDN instead prefixes the power of twelve; a superscripted numeral indicates a positive power, while a subscripted numeral indicates a negative power. So "²³3.4" is equivalent to "3.4x10²³," and "₂₃3.4" is equivalent to "3.4x10^-23." In plain text, use "^" for superscripts and "_" for subscripts: "23^3.4," "23_3.4." This notation is at once more compact yet equally easy to read; and, of course, the old notation works equally well in dozenal if it is really necessary.

And that is the essential core of the SDN system.