Tag Archives: numerals

Natlang Attestation of Ayeri’s Strategy of Forming Ordinals

I was actually reading one of the papers I was intending to read tonight and came across this, on (Classical) Tibetan:

The suffix -pa forms a noun from another noun, meaning ‘associated with N’ (e.g. rta ‘horse,’ rta-pa ‘horseman,’ yi-ge ‘letter,’ yi-ge-pa ‘one who holds a letter of office,’ cf. Beyer 1992: 117). When suffixed to cardinal numbers this suffix forms ordinals (e.g. gsum ‘three,’ gsum-pa ‘third’; bcu ‘ten,’ bcu-pa ‘tenth’). — Chung et al. 626

Ayeri does basically the same thing with -an, cf. First, at First, Once, First Time:

    1. rig- ‘draw’
    2. rigan ‘drawing’
    1. avan ‘soil, bottom’
    2. avanan ‘foundation, base’
    1. men ‘one’
    2. menan ‘first’
    1. ito ‘seven’
    2. itan ‘seventh’

Chung et al. don’t say whether Tibetan treats these derived forms as nouns or as numerals or whether it makes that distinction at all, unfortunately. In Ayeri, however, ordinals are basically nouns due to the derivational suffix -an forming nouns, typically from verbs and adjectives, but also from other nouns.

  • Beyer, S. The Classical Tibetan Language. New York: State U of New York P, 1992. Print.
  • Chung, Karen Steffen, Nathan W. Hill and Jackson T.-S. Sun. “Sino-Tibetan.” The Oxford Handbook of Derivational Morphology. Eds. Rochelle Lieber and Pavol Štekauer. Oxford: Oxford UP, 2014. 609–650. Print.

Ayeri number word converter in Python

Just a little something I started programming a while ago and elaborated on to make it useable today. It’s a little Python program which turns a base-10 number into its corresponding number word in Ayeri: Ayerinumbers.py on Github

  • The code is probably a bit unnecessarily complicated, because it tries to mimic Ayeri’s grammar rather than being mathematically straightforward. I may rewrite things in the future to make more sense from an engineer’s point of view.

Fractions

I was just wondering about the way Ayeri forms fractions. The Grammar (§ 4.2.2.1) currently says that:

Fractional numerals are formed from men ‘one’ plus the integer divided by.

A table with all the forms for the basic numerals from ja to tam is listed.1 It informs furthermore that in order to

give multiples of a fraction, the numerator is used as a modifier of the fraction word, which serves as the head of the phrase:

vadisān
bread
menkay
third [= one.three]
sam
two

‘two thirds of a loaf’

However, how about a competing (e.g. traditional/colloquial vs. mathematical) or regional alternative where the denominator is the genitive form of the respective cardinal number, like this:

  1. vadisān
    bread
    kay-ena
    three-GEN
    sam
    two

    ‘two thirds of a loaf’

Or, to pattern with other case-marked numerals and their special meanings,2 the numeral could also be nominalized first and then case-marked:

  1. vadisān
    bread
    kay-an-ena
    three-NMLZ-GEN
    sam
    two

    ‘two thirds of a loaf’

Although kayanena is strictly speaking a nominal form and thus might be expected to follow ordinals (kayan vadisānena ‘the third bread’, three-NMLZ bread-GEN), it makes sense to use it as a regular numeral anyway – a drop-in replacement for menkay – since noun phrases cannot usually be doubly case-marked in Ayeri:

  1. Ang
    AT
    konja
    eat-3SG.M.T
    vadisānena
    bread-GEN
    kayan-ena [= menkay]
    third-GEN
    sam.
    two

    ‘He ate two thirds of a loaf.’

  2. *​Ang
    AT
    konja
    eat-3SG.M.T
    kayan-ena-ley
    third-GEN-P
    sam
    sam
    vadisānena.
    vadisānena
  1. Cf. an earlier article on numerals on this blog.
  2. Cf. an earlier article on ordinals and multiplicative numerals on this blog.

Imperial Messages XI – “… nay viturongyāng …”

This is the eleventh posting in a series on the process of translating the short story “Eine kaiserliche Botschaft” by the Praguer writer Franz Kafka (*1883, †1924). The individual installments will go through the text mostly sentence by sentence, quoting from the German text as well as a translation of it into English. Following these quotations, I will discuss and comment on newly coined words and thoughts I had on grammar while doing the translation.

The text

This is again a rather long passage, so I’ve split this into four parts, still to be published semi-weekly to stay on schedule. This is the third part.

[…] und gelänge ihm dies, nichts wäre gewonnen; die Höfe wären zu durchmessen; und nach den Höfen der zweite umschließende Palast; und wieder Treppen und Höfe; und wieder ein Palast; und so weiter durch Jahrtausende; […] (Kafka 1994, 281:24–282:1)

[…]; and were he to succeed at this, nothing would be gained: he would have to cross the courtyard and, after the courtyard, the second enclosing outer palace, and again stairways and courtyards, and again a palace, and so on through thousands of years; […]. (Kafka 2011)

[…] – nay viturongyāng, le gamarongyāng ranya – sa rua lugongyāng mandayye – nay pang mandayēa, samanas mitanyena si midaytong – nay ehenyeley nay mandayjas sayling – nay mitanas menikaneng – nay edāre manga luga pericanyēa samang – […]

Interlinear glossing

[…]
[…]
nay
and
vitur-ong-yāng,
succeed-IRR-3SM,
le
PF.INAN
gamar-ong-yāng
manage-IRR-3SM.A
ranya
nothing
sa
PF
rua
must
luga-ong-yāng
pass_through-IRR-3SM.A
manday-ye
court-PL
nay
and
pang
behind
manday-ye-ea,
court-PL-LOC,
sam-an-as
two-NMLZ-P
mitan-ye-na
palace-PL-GEN
si
REL
miday-tong
surround-3PN.A
nay
and
ehen-ye-ley
stair-PL-P.INAN
nay
and
manday-jas
court-PL.P
sayling
further
nay
and
mitan-as
palace-P
menikaneng
another
nay
and
edāre
this_way
manga
MOT
luga
among
perican-ye-ea
year-PL-LOC
samang
myriad
[…]
[…]

‘[…]; and if he succeeded, he wouldn’t have managed anything; through the courtyards he would have to pass; and beyond the courtyards, two palaces which surround it; and further stairs and courts; and another palace; and thus for myriads of years; […]’

Notes on translation

Today’s passage is an admittedly rather large chunk compared to earlier passages, but most of it is just an enumeration, which is not terribly difficult to deal with. No words needed to be coined or extended here.

As far as syntax and grammar are concerned, I could have sworn that it should be mandayēa epang ‘court-PL-LOC after’, with a postposition, instead of (e)pang mandayēa ‘(after/)behind court-PL-LOC’ with a preposition, but even in my jumbled handwritten notes I could not find anything to that effect going as far back as 2007.

A grammatical intricacy that tripped me up was the last words of this passage, “durch Jahrtausende” (Kafka 1994, 282:1), respectively “through thousands of years” (Kafka 2011). For one, Ayeri counts in units of twelve, and the word for the third power of twelve is literally ‘ten-hundred’, which is rather uncatchy here. Since the next larger unit is the fourth power, or a myriad, I went for that term because ‘hundred’ felt too weak. In addition to this decision, Ayeri usually does not inflect nouns modified by numbers or measure adverbs for plural. Without plural inflection in “pericanyēa samang”, however, the noun phrase would simply mean “a myriad of years”, but not “myriads of years”, as is intended here. In order to take plural inflection, the numeral could be nominalized and then pluralized, so that you would get samanganyeley pericanyena ‘myriad-PL-P.INAN year-PL-GEN’, which is quite a mouthful and more similar to the construction used for ordinal numbers. Thus, I decided to keep the original order with the number as a modifier, but with the modified noun exceptionally pluralized.

  • Kafka, Franz. “Eine kaiserliche Botschaft.” Drucke zu Lebzeiten. By Franz Kafka. Eds. Wolf Kittler et al. Frankfurt a. M.: S. Fischer, 1994. 280–82. Print.
  • ———. “A Message from the Emperor.” Trans. by Mark Harman. NYRblog. The New York Review of Books, 1 Jul. 2011. Web. 9 Feb. 2012. ‹http://www.nybooks.com/blogs/nyrblog/2011/jul/01/message-emperor-new-translation›

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 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 menang2 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 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

  • Corrected the powers according to Ayeri’s equivalent of the “long” scale that I’m now using.
  1. Namely, 8,916,100,448,255 or BBB,BBB,BBB,BBB in base 12.
  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.
  3. The equivalent to English ‘-ty’ is now -lan, not *-la; malan-tam ‘tenty-three’ is also a coordinating compound.
  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.

First, at First, Once, First Time

This is another grammar musing on an issue I’ve been undecided about for quite some time now. If you look into the Grammar, you’ll find that ordinals and multiples are formed from cardinals like this:

men ‘one’ (one)
menan ‘first’ (one-NMLZ)
menanyam ‘once’ (one-NMLZ-DAT)

However, I came across situations where I wanted to say “at first” and “for the first time.” I wondered whether that could be covered as well by menanyam, literally ‘for first’, but somehow, I still wasn’t quite content, since doing something once isn’t always the same as doing it for the first time. Similarly, doing something at first is not necessarily doing it once or for the first time either. I came up with the following three alternate solutions for ‘at first’ some months ago:

?menya, lit. ‘at one’ (one-LOC)
menanya, lit. ‘at the first’ (one-NMLZ-LOC)
menanyam-ikan, lit. ‘very once/for the very first’ (one-NMLZ-DAT=very)

Now, through use, I somehow settled on menanya for ‘at first’ (English bias?), however, as of writing this, I think I could merge that with ‘for the first time’ and let context disambiguate: If there is a description of successive actions following, we know that the speaker probably means ‘at first’ (and then X, and then Y). Conversely, if context reveals that the action has never been done before, or that a person is new to something, we know that it is done ‘for the first time’. If there is no context, like in individual example sentences, things stay unclear, though I guess that this situation is kind of artificial, since sentences are rarely not embedded into context in real life, or even in texts.

If I didn’t want ambiguity, ?menanyam(an)ya could be possible, but I find that very unwieldy, as stacking case markers on top of each other is kind of avoided and renominalization with a case marker feels somewhat awkward, too, although I ran into situations where I wanted to do that with gerunds. Menanyam-ikan could be used as a very stern version of ‘once’, like ‘once and for all’.

Very much incongruent to this is ‘last’, which is now split between sarisa ‘former, previous’1 and pang-vā ‘back-most’. While sarisa is strictly used to mean ‘previous’, pang-vā2 can only be used to refer to the last item of a set.

  1. This looks like it’s derived from sara- ‘to leave’ + -isa ‘CAU’, so ‘made to leave’ literally, or ‘be left’, since causatives are used somewhat irregularly in Ayeri. I don’t usually keep track of how words are derived, which is kind of stupid sometimes.
  2. This appears to be somewhat in analogy to ban-vā ‘best’, although even that is strictly an irregularity …