The Genesis of Ayeri’s Numerals

In my last posting I said something about how Ayeri’s way of dealing with numbers is still a little difficult to work with for me. The Grammar already has a chapter explaining numerals, though I don’t know how intelligible that is. For the reason of explaining this issue to myself and also to potentially puzzled readers of the grammar, I will try to elaborate by explaining the development of Ayeri’s number system from a metafictional point of view.

Ayeri has gone through a number of changes in its system of counting. One thing that was established from the beginning on is that it would use a duodecimal system (base 12), just because I found it somehow pretty, as you can conveniently divide things by 2 and 3 without running into continued fractions, which is maybe more useful than the division by 2 and 5 that base 10 offers. Because I was taking French at school at the time I thought it was cool to have unique words for a couple numbers over 12, and I didn’t yet know about the history of treize, quatorze, quinze and seize, thinking that they would be just as unanalyzable as the numerals from 1 to 10. The following table gives an overview of my original draft (with the numerals fitted to current spelling):

0 — ja
1 — men
2 — sam
3 — kay
4 — yo
5 — iri
6 — miye
7 — ito
8 — hen
9 — veya
A — mal
B — tam
10 — malan
11 — malem
12 — mesang
13 — manay
14 — magos

I found this design stupid after a while, especially because you would get malan and malanan as ordinals from mal and malan (spot the point of confusion …), so I got rid of the individual words for numbers over 12 (or 10₁₂, i.e. those from malan on). I don’t want to go into the development of ordinals and multiples, except let me note that the system of deriving multiples by putting nominalized cardinal numbers (= ordinals) into the dative case which I’m using now is less messy than the system I used before.

A thing I’ve long pondered about and which also saw a fair number of changes was the way in which to form higher numbers. According to the notes I have, up until late 2007 the (duo)decadic numerals greater than 10₁₂ (like 20, 30, 40 etc.) were derived with the suffix -la, hundreds were derived with -sing, thousands were derived with -ya, and hundred thousands were irregularly derived with -sinya < -singya. In order to derive (short-scale) millions, billions, trillions etc. the first syllable of the thousand-numeral was reduplicated, e.g. memenya ‘million’ < menya ‘thousand’, sasamya ‘billion’ < samya ‘two thousand’ etc., and for milliards, billiards, trilliards etc. those million-numerals had a -kan < -ikan ‘much, many’ appended additionally, so e.g. memenyakan ‘milliard’, sasamyakan ‘billiard’ etc. However, I’ve never figured out what would happen if you were to arrive at 12¹². I was somehow uncomfortable with just counting on like mamalan-menyakan, mamalan-samyakan etc.

When I got to the chapter in the Grammar that deals with numerals, however, I scrapped the previous system as described above because I didn’t like it anymore. Its regularity seemed boring and the reduplication seemed inelegant. Because I’ve never decided about the 12¹² problem, I just assumed the old system was finite also, although the highest number, 12¹²-1, is still larger than you’ll probably ever need in day-to-day life.[1. Namely, 8,916,100,448,255 or BBB,BBB,BBB,BBB in base 12.] I still wanted to be able to form higher numbers, though, just because.

Now, the thing English does (and French, and German) is to borrow its terms for large numbers from Latin: billion < bi(s)- ‘twice’, trillion < tri- ‘three’, quadrillion < quadri- ‘four’, etc. However, there’s no such accompanying language that could donate these terms (yet). Of course, I could just have made up a neighboring language to take the numbers from 1 to 10 from, but all too obviously and unreflectedly copying English and European languages in general is often regarded as lame among conlangers, and in this case it felt lame to me as well. However, I found reusing the ‘small numbers’ to derive ‘large number’ units still appealing because it seemed practical and potentially open-ended because the system would be self-referential, and this time no awkward reduplication should be involved.

Just to be different from European languages, I made the step to the next unit 100₁₂ wide at first, so that menang[2. I’m afraid I don’t know anymore where I got that -(n)ang as a derivative suffix from, though it might be related to nake ‘large, tall’. The final /ə/ would have been dropped, and phonotactics demand a change of a terminal plosive to a nasal, so /k/ > /ŋ/, which results in nake > nang.] would be 12², or 100₁₂, samang would be 12⁴ or 10,000₁₂, kaynang would be 12⁸ or 1,000,000₁₂ etc. Bunches of 100₁₂ seemed a little inelegant to use after some time, though, so that I decided to skip every other unit and bundle numerals as units of 10,000₁₂ – a myriad, essentially, except based on units of 12 instead of 10 of course. Instead of using every single item of the progression men, sam, kay, yo, iri, miye etc. only men and then sam, yo, miye etc. would be used thus, i.e. ‘one’ and after that only the even numerals. I left it this way instead of refitting the width of steps as a little additional twist. After another while I decided to go back to using every step in the progression of numerals 1, 2, 3, …, n again instead of every other, so now we are back to 12² menang, 12⁴ samang, 12⁸ kaynang, 12¹² yonang, 12¹⁶ irinang, etc. at long last.

The vicious thing with forming the words now is that Ayeri likes to put heads first, especially as far as adjectives and other modifiers are concerned: the modifier follows the modified. And of course this applies to numerals as well, so that the unit word always goes first, which causes some nesting. Hence, to reuse the example I gave in the Grammar, though breaking it down a bit more:

If we consider the number 24AB,A523₁₂ we see that there are two bundles of myriads, so we know that we’ll have to start at samang (1,0000₁₂). So first of all, there are 24AB samang to break down into smaller units: 24,AB₁₂, or 24₁₂ menang and a rest of AB₁₂. This gives us menang samlan-yo malan-tam – literally ‘hundred twenty-four tenty-eleven’.[3. The equivalent to English ‘-ty’ is now -lan, not *-la; malan-tam ‘tenty-three’ is also a coordinating compound.] You can see here (or are supposed to) that samlan-yo is used as a modifier to menang in analogy to a phrase like ayon kay ‘three men’ (man three) where the numeral modifies the noun it follows. This greater unit of menang samlan-yo malan-tam is again used as a modifier to samang, giving samang₁ [menang₂ [samlan-yo]₂ [malan-tam]]₁ for 24AB,0000₁₂. For the other half of the original number we proceed in the same way, except now we need to start only at menang, of which there are A5₁₂ and a remaining 23₁₂: thus we get menang₁ [malan-iri]₁ [samlan-kay]. The whole number word assembled thus is samang menang samlan-yo malan-tam, menang malan-iri samlan-kay where it used to be memenya samla-yo, malsinya tamla-mal, irising samla-kay.

What is the procedure in the case of skipping units, though? Given a number like 1002,0030,0004₁₂ this would be pronounced as kaynang menang menlan nay sam, samang kaylan, nay yo. In this case, nay ‘and’ is used to indicate a blank where there could be confusion, since menlan-sam means ‘tenty-two’ (12₁₂), but in this case it’s 10₁₂ units of menang and a remainder of 2 single units that we want. Similarly, we don’t have kaylan-yo ‘thirty-four’ (34₁₂) units of samang in this example, but 30₁₂ samang and 4 single units at the very end. A number like 502₁₂ then would be menang iri sam, since there is no confusion between what belongs together here, although in practice you might still actually say menang iri nay sam so as to avoid having two single-digit units after another.

To be honest, no simplicity has been gained with the new system, quite the opposite: the old system was in fact more straightforward, but I like the quirkiness of the new system better just for the system itself. And in fact I’ve still not thought about whether to allow menlan-menang as a valid way to express 12⁴⁸.[4. 6,319,748,715,279,270,675,921,934,218,987,893,281,199,411,530,039,296 or 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 in base 12. That’s awfully huge.]

  • Corrected the powers according to Ayeri’s equivalent of the “long” scale that I’m now using.