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. 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 *men**ang* would be 12², or 100₁₂, *sam**ang* would be 12⁴ or 10,000₁₂, *kay**nang* 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’. 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**]**ₓ**]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**]**ₓ*. 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.

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