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
Singular
Masc.   hic     huius   huic    hunc    hoc
Fem.    haec    huius   huic    hanc    hac
Neut.   hoe     huius   huic    hoc     hoc
Plural
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.