SDN: The Full System

This document is designed to give a full and exhaustive treatment of the Systematic Dozenal Nomenclature (SDN). Most people will not need to know SDN in this depth; however, SDN aims to cater to all possible expressions of numbers in words. For simpler explanations of the system, please see the Summary, Brief, and Basic pages.

SDN consists of a basic set of roots, to which can be attached two particles, "qua" and "cia," which indicate that the preceeding roots are positive or negative exponents respectively. Each root can also take a multiplier suffix, either "a" or "i," to provide separation between roots which are performing different functions. These suffixes are called "multiplier" because they indicate that the succeeding roots, if any, are multiplied by the preceeding roots in order to formulate the final number.

A full table of roots, multiplier forms, positive power forms, and negative power forms appears below.

Note that the columns for positive and negative powers are strictly unnecessary, as they are completely regular, formed simply by affixing "qua" for positive powers and "cia" for negative.

There is considerable flexibility in the multiplier forms in terms of the terminating vowel. Through practice these examples have proven to be easiest and most convenient; however, any vowel sound between roots (or following the "n" affixed to "bi" and "tri") will serve the purpose unambiguously.

Roots can be combined without addition to create strings of numbers according to the standard rules of place notation. The final root will typically be the multiplier form, though this is sometimes left out (as in words like "bicycle"). So, for example, to create a word for the number "7482," simply combine the roots: "septquadoctbina."

Multiplier forms can be used to separate groups of roots which are performing different functions. So, for example, "7400" could be expressed by place notation as simply "septquadnilnil"; however, it could also be expressed as "septquadrabiqua." The multiplier form "quadra," rather than the bare root "quad," is necessary here to show that "septquad" are a unit separate from "biqua"; otherwise, the word could be parsed as either "74 * 100" (septquad times biqua) or "10⁷⁴²." Requiring the multiplier prefix resolves this ambiguity; the latter would have to be "septquadbiqua," using "quad," the bare root, rather than "quadra," the multiplier form.

These allow the unambiguous creation of words for any integer. There are two additional particles which allow the creation of any number whatsoever. The first is "dit," the particle indicating the fractional point. "Dit" is used not only in dozenal counting, but also as a particle helping form words in SDN. For example, to form a word meaning "one half," the uncial fractional particle (as "dit" is called) can be employed quite easily, using the same standard rules of place notation. "Dithexa" means "half"; a quarter is "dittrina," and an eighth is "ditunhexa."

For those fractions which do not give themselves to short, manageable uncial representations, such as the seventh, SDN offers the "per" particle. "Per" indicates that the root groups surrounding it are parts of a fraction, which subsequent parts of the words are multiplied by. The root group preceeding "per" is the numerator of the fraction; the root group following it is the denominator. If the numerator is "one," then it may be omitted. "Per" does not span multiplier forms; when a multiplier form is encountered, "per" stops. So, for example, a seventh is simply "persepta," and four sevenths is simply "quadpersepta." One can express four and three sevenths as "quadratripersepta." The last is unambiguous because "quadra," the multiplier form, is used; if "quad," the bare root, were used (as in "quadtripersepta"), the fraction expressed would be "43/7," while with "quadratripersepta" it can only be "4 * (3/7)."

Note that these rules mean that many numbers can be made into words in multiple ways. "7400," for example, can be expressed in a word as "septaditquadratriqua," "septquadrabiqua," "septquadniliunqua," or "septquadnilnil." "One half" could be "dithexa" or "perbina." One of SDN's strengths is that it offers so many ways to express things; the one most appropriate to a given situation can be selected.

This allows the creation of words for any integer or fraction, a power offered by no other existing system of referring to numbers.