All My Base Are Belong To You

Numeric base, that is.

So far, for the most part, I have been handling this via Translation Convention, since exactitude has not been of crucial importance, and expecting people who care about such things to pick up that for a people who use duodecimal (base-12) notation, a century is naturally 144 years, a millennium 1,728, etc., etc.

This has been seeming to me increasingly inadequate, given potential and real confusion when I talk about lengths of time, etc., using my authorial voice rather than in-character, as well as differences between metaphorical and literal usages, and so on and so forth.

Where it has now broken down completely is in writing a piece involving people using two different number bases, in which an duodecimal millennium (1,728 years) and an octal millennium (512 years) aren’t even close to the same thing, and neither, for that matter, is particularly close to a decimal millennium. That’s stretching it even for metaphorical purposes.

And I would prefer not to just start dropping numbers in untranslated Eldraeic, etc., into the text, because that’s something that has no correspondence or roots at all for the English-speaking reader to figure out.

So I’m thinking of coining some new English words for use in an updated Translation Convention, such that things can be made clear. Or at least consistent.

Power Decimal Duodecimal Octal
x1 ten dodectave (12) octave (8)
x2 hundred dodecen (144) octcen (64)
x3 thousand dodeciad (1,728) octiad (512)
x6 million grand dodeciad (2,985,984) grand octiad (262,144)

(I’m not using “dozen” for 12 in duodecimal because I suspect that that would lead people to believe that they’re counting by twelves in base ten, which is misleading. Much the same reasoning applies to “gross” for 144, and also that “grossury” as a period of time sounds like a place you buy unpleasant food.

Instead, for time, we have the “dodecentury” and the “dodecennium”, which should parse better and are at least reasonably euphonious.)

Naturally, there’ll be footnotes and a numeric appendix in published works for those encountering these coinages for the first time.

Comments and thoughts, anyone?


Trope-a-Day: Alternative Number System

Alternative Number System: The eldrae, and thus the Empire, use base 12 – mostly because the common numeric base was agreed on by the same collective of the philosophically inclined that standardized the language, and they saw no particularly good reason why you should pick a number base just because that’s how many fingers you have when you can pick one based on something more useful, like its plethora of convenient factors.

There was a brief flirtation with base 16 (the Great Hexadecimal Reform) during the reign of the Online Emperor, but despite being more convenient for computational purposes (a base 16 digit converts into a whole number of bits, which a base 12 digit does not), it proved quite unpopular with the public and was later quietly dropped.

And, of course, other species have been known to use quite a large variety of numeric bases – 8, 10, and 16 being probably the most popular, but others far from unknown.  Base 16 is commonly used for interspecies communication (outside the Empire, in the Worlds), though, mostly because everyone who uses computers is at least somewhat comfortable with power-of-two bases.