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Wednesday, October 18, 2006

Multiplicative vs. Additive

I don't recall if I ever used the terms on here, but in a recent e-mail I sent to my grandpa (a professional linguistic) telling him about Caia, I mentioned that I specifically wanted it to have additive complexity rather than multiplicative. I cited a couple example languages that fall into these categories (the same ones I'm going to talk about here), but I didn't really explain what I meant by them. His response did not particularly indicate or suggest whether he understood what I meant.

My knowledge of world languages is nowhere near sufficient to know whether there exist any purely additive or purely multiplicative natural languages, so I'll use some particular instances from two languages as examples. Latin is kind of the classic multiplicative-complexity language (although some parts of it have additive complexity); we are going to talk about the Latin close demonstrative pronoun ("this/these" in English).

As I mentioned quite some time ago, Latin inflects nouns based on gender (masculine, feminine, and neuter), number (singular and plural), and case (nominative, genitive, dative, accusative, and ablative). This results in their being 30 different "this/these" pronouns (!), as shown (I'm gonna do my best to make this look okay without FrontPage - what I usually use when doing complex formatting):
        Nom     Gen     Dat     Acc     Abl
Masc. hic huius huic hunc hoc
Fem. haec huius huic hanc hac
Neut. hoe huius huic hoc hoc
Masc. hi horum his hos his
Fem. hae harum his has his
Neut. haec horum his haec his

Ugh. That's disgusting. As you can see, there is some degree of regularity, but enough exceptions that you really need to memorize about 18 of the 30. This is what I mean by multiplicative: the number of different forms of a given thing that must be memorized are roughly equal to the multiplicative total of all the different ways in which the thing can be inflected (3 * 2 * 5 - gender, number, case - in this example).

English is a bit better than Latin, although that's partly due to the fact that, compared to Latin, English inflects very few of its words, and those it does inflect have few variations. Japanese, however, has an example of additive complexity that's just beautiful - its demonstrative and interrogative pronoun system. Words are inflected by class (specifically, how far away the thing being referred to is) and form (whether it's a noun form, adjective form, etc.) as shown:
        Near    Far     Further Int.
Noun kore sore are dore
Adj. kono sono ano dono
Example konna sonna anna donna
Manner koo soo aa doo
Place koko soko asoko doko

In case it's not obvious, the English translation of the first column would be: "this thing" (noun), "this" (adjective), "such as this" (example), "like this" (manner), and "here" (place).

Thus, knowing only the four distance class prefixes and five word form suffixes, we can form all 20 combinations while only having to remember a single irregularity - asoko ("way over there" or some such). This is taken even further with indefinite pronouns, in which further suffixes are added to the interrogative forms above (we'll use "doko" - "where" - as an example), for forms such as "somewhere", "nowhere", "anywhere", "everywhere".

Additive >> multiplicative. Especially in Caia, where I intend to encode a LOT of information into pronouns and conjugation islands.

1 comment:

Anonymous said...

Speaking as someone just learning Latin now, not an expert nor a linguist in any sense.

It's interesting that you chose hic, because it's the most irregular pronoun I know. This is what you need to memorize to accurately remember hic, given previous knowledge of the Latin patterns:

1. The stem: h-
2. The ending (for all singular forms except genitive): -c (this is only pronoun I know with an ending)
3. The fact that the singular genitive and dative forms are derived from the -ius pattern
4. The altered stem of hu- for the singular genitive and dative (only pronoun I know of where this is the case)
5. The neuter plural nominative (and, by extension, the accusative) is irregular: haec

I see your point, but where I noticed the multiplicative complexity is really in Tense * Voice * Conjugation or Case * Declension, not Gender * Number * Case—which is fixed at 30 and memorizable just one time, as opposed to growing as you continue to learn.