SDN: A Basic Explanation

We've already seen in the SDN in brief article the basic principles of Systematic Dozenal Nomenclature. In other words, we already know how to count using SDN. This article means to go beyond that, to display some of the additional power of SDN. SDN is a system for counting, of course; but it is also a system for word-building, which allows words for any number to be constructed in a simple and regular way.

This article describe EE% (per gross) of the SDN system; just as SDN in brief is E6% of what anyone will ever need to know concerning SDN, this article is everything that EE% of people will need to know about it, and in fact is probably much more than most people will ever need.

Our current system (if we can call it that) for building words from numbers is irregular at best, and is often utterly chaotic. Forming words which involve "twenty" as a part is an excellent example of this linguistic anarchy. Names for two-dimensional shapes ("polygons") are formed with the word for the number attached to the suffix "-gon." So "pentagon" is a five-sided polygon, "hexagon" is a six-sided polygon, and so on. A twenty-sided polygon, on the other hand, is an "icosagon." Similarly, a twenty-sided three-dimensional shape is an "icosahedron."

It seems that "icosa," then, is the English particle which means "twenty" for forming words. But this has two problems:

1. It's not; or rather, it isn't always. When we're talking about numbers in base twenty, for example (a system that the ancient Mayans used extensively, and to great effect), we're not talking about icosa-anything, but rather about vigesimal. In other words, in some contexts we use the Greek root for "twenty," in others the Latin root, and there's no way to predict which will be employed other than memorization.
2. It's decimal. A twenty-four-sided polygon, for example, is an icosakaitera (don't even get me started on how that little gem is put together; even geometers don't get this system, and in practice call such shapes "24-gons"), when in dozenal this should be a very simple name, since twenty-four in dozenal is simply "20." We've already decided that twelve is the best base, so we can't be happy with this.

Systematic Dozenal Nomenclature makes sense of all this mess in two ways: it puts our words for numbers on a firm dozenal basis, and it makes our words for numbers regular and logical. And it does so, as we saw before, with only thirteen new words (most of which are already very familiar to us) and two particles. Here's the chart we'll need to go through this simple explanation:

The roots for zero through ten will already be familiar to most European-language speakers; the root for "nine," "enn," may be unfamiliar, but it's at least easily recognizable. The roots for 0-9 are, furthermore, internationally known, because they are the roots chosen by the International Union for Pure and Applied Chemistry (IUPAC) for naming new elements on the periodic table. As such, they should be easily recognizable all over the world.

But this is dozenal, so two new roots were necessary. The root for ten, "dec," is easy to derive; that for elv, "lev," equally so. And this rounds off twelve of the thirteen new words that we need to know for SDN. The thirteenth, "dit," is the word for the fractional marker in dozenal numbers, generally written with a semicolon like so: ";". It is useful when speaking about numbers, of course; but it is also useful in forming words about numbers in some circumstances which are beyond the scope of this basic introduction. For more information about that, readers are encouraged to go to the full explanation of SDN.

Our two particles, as again we've already seen, are "qua" and "cia," which make the roots positive or negative exponents. These provide our dozenal replacements for "hundred," "thousand," "million," and so forth.

When we form numbers with digits (like 1, 2, 3, and so forth), we simply put them together according to the rules of place notation; so we form "two dozen and three" by taking "2" and putting it in the dozens place and "3" and putting it in the ones place, like so: "23." This works for numbers as big or as small as we care to make them.

SDN makes number words in precisely the same manner: by putting them together according to the rules of place notation. So to form a word for "two dozen and three" (perhaps to come up with the name of a polygon with two dozen and three, or twoqua-three, sides), we take the word for "two," "bi," and put it in the dozens place, then the word for "three," "tri," and put it in the ones place, giving us "bitri." We can then attach this to the polygon suffix, "-gon," giving us "bitrigon." And that's all there is to it. This leaves in place such words as "bicycle" and "triceratops," but allows rarely-used words to follow the same rules as those we run into every day: "octagon" (an eight-sided polygon) is formed in precisely the same way as "bioctagon" (a twoqua-eight sided one).

We can form words in the same way with the positive power forms, as well. A polygon with 100 sides is a "biquagon," and a period of a triqua years (1000 years) is a "triquennium."

One will notice a column in the table above labeled "Multiplier." This column serves two purposes. One, it provides a form which goes well in some words that the root does not. A four-sided shape is difficult to say when it's "quadgon" but quite easy when it's "quadragon" (and sound much like already existing words using this root, like "quadruped"). Two, it allows us to mix power forms with roots to form words that are always difficult in our current mishmash of a system.

Take, for example, a "bicentennial." This much is easy; we all know that this refers to a two hundredth anniversary. But what about a two hundred and fiftieth? What about a fourtieth? SDN makes words for these easy, too, just as easy as writing down the numbers.

A two hundred and fiftieth anniversary: the dozenal analog of this is two biqua six zero, written in digits as "260." We form the word in precisely the same way that we form the number: two ("bi") six ("hex") zero ("nil"), and add "-ennial" since it's an anniversary. "Bihexnilennial." Easy.

We could also form it by using a power word. Consider, rather than "260," simply "200." It's two biqua, so the instinct is to say "bibiqua." We can't do that, though, because that means 10²², not 2 * 10², which is what we want. In this case, we must use the multiplier form, to show that what we want is two times biqua. In other words, "binabiqua." We then add "-ennial" since it's an anniversary and say "binabiquennial." Again, easy. Either this or "binilnilennial" will work just fine; whichever the speaker sees as more straightforward and logical can be selected.

One can freely choose between the roots and multiplier forms except when one is mixing roots and powers, when using the roots alone could be ambiguous. Then, power prefixes must be used.

And that concludes our discussion of basic SDN. Let's look at a few examples to solify our understanding; only a few should be more than enough.

1. Your friend's parents are celebrating their four dozenth anniversary. Other than just using "40th" (which, of course, you can do), what words can you put on their banner?

   SDN uses place notation. We write the number with a "4" and a "0," so we write the word with a "quad" and a "nil." This means that the honored guests are celebrating the "quadnilennial" of their marriage.

   We can also use exponents. In numbers we would write that as "4 x 10¹"; in SDN, we write it as "quadra" (remember to use the multiplier form, since we're mixing multiples and powers; this takes care of the "4 x"), and 10¹ is "unqua." This means that the honored guests are celebrated the quadraunquennial of their marriage.

2. Your town was fonded 350 years ago today. What is the word for that anniversary?

   Place notation. A "3" then a "5" then a "0"; in SDN, a "tri" then a "pent" then a "nil." It's the town's "tripentnilennial."

   Exponents; again, place notation. "3;5 x 10²." "3" is "tri"; ";" is "dit"; "times" means use a multiplier form; and "10²" is "biqua." So it's also the town's "triditpentabiquennial." Further, there's no reason we have to use the highest exponent, either, though that's the simplest choice; we could also called this 35 x 10¹, and call it the town's "tripentaunquennial."

Finally, SDN offers a more compact notation for what we currently call "scientific notation" (more accurate, it is called "exponential notation"). While currently we write long numbers in the form "2.9x10²³," putting a negative sign in front of the exponent when it is negative, SDN offers a more compact yet equally simply notation. Powers of the base and prefixed; positive powers are superscripted, negative powers are subscripted. So "2.9x10²³" becomes "²³2.9," and "2.9x10^-23" becomes "₂₃2.9." In ASCII, use "^" for a superscript and "_" for a subscript: 23^2.9, 23_2.9. And, of course, the old notation works equally well in dozenal if it is the only option.

You can now easily form words, according to a logical and consistent system, for any integer, and use them in compounds for shapes, base names, periods of time, anniversaries, or any other concept you can think of and care to express. That is the power of SDN.