Why do quite a few North American languages have such convoluted verbs?

Vinny, I agree with you. Its easy to imagine languages startnig with nouns for geographical features, foodstuffs or tools. Then you can imagine verbs in the present tense. Just because its easy to imagine doesn't mean its what happened, of course.

Its much harder to imagine how a pluperfect subjunctive tense came about. AFAIK, to the extent we have written records of language, these all show reductions in grammatical complexity. Its frustrating that we have no recorded historic examples of increasing complexity that we could use to study how this change happens. Maybe there's something about language being recorded that brings complexity to a shuddering halt.

If number of tenses is a measure of complexity, then I think we have plenty of recorded examples. The progressive/continuous tenses in English are one example. Shakespeare would have said "He sleeps" where we would say "He is sleeping." The passive continuous tenses ("The house is being painted") only arose in the eighteenth century and were still being denounced by prescriptivists in the nineteenth. Can we say "The house will have been being painted" even today? I don't think so, but maybe next century it will seem normal.

I'm not satisfied that we have a satisfactory definition of complexity, by the way.

I guess we'd also have to ask why certain individual languages (like Navajo) have verb rules that are even more complex than nearby "peer" languages such as Hopi, which was spoken in some of the same geographic areas as Navajo. Hopi verbs are complicated, but that language is regarded by linguists as easier to for outsiders to learn than Navajo.

As for the Navajo grammar book, you can preview parts of it on Google Books:

The Navajo Verb, by Dr. Leonard M. Faltz

I rather suspect the writer of your Navajo text may have fallen into the same trap. Maybe he learnt grammar from Kennedy's Latin Primer and now he wants to describe Navajo in a similar tome.

Well, he studied Navajo for decades; I think he's using the verb as a window to describe the whole language, since so much of Navajo is encoded by verbs. Nouns get rolled into verbs. I've seen Navajo verbs described kind of like this (though this particular example is general and may not be grammatically accurate):

In English, you would use a sentence like "She picked up the things," and "things" might be any noun. Eg, "She picked up the sticks" or "She picked up the flower" or so on. The noun at the end of that sentence leaves the other parts of the sentence intact.

In Navajo, most or all of that information gets encoded by a single word which acts as a verb. The literal translation of such a verb might be something like "The act of a female human bending down and retrieving two stickish objects with her hand, with the speaker as the observer."

If you change any part of that (with a third party as the observer, with a male human, with three sticks rather than two, etc.) the whole verb changes.

Well then, that's why Navajo verbs are so complicated. Because they convey a lot more information than, say, English verbs do.

I will check my reference material when I get home, but I don't remember complexity in the verbs in Eskimo languages (note that Eskimo is the polite term in Alaska and Inuit is not.) I do remember a lot of complications with demonstratives, though. I'll post more when I get home from work.

Following up on what I posted in #13, it looks like the verbs are similar to what is written in #12, although I don't see a marker for gender.

Regarding the demonstratives, here are a few interesting ones:

-that, for a thing that is visible to us and across a river or on the coast
-that, for a thing that is not visible to us now because it is behind a barrier, like a wall
-that, for a thing that is inside a house and in a large container
-that, for a thing that is not visible to us because we are in a house and it is on the enclosed front porch

And, VinnyD, #14, another reason that Navajo has such complex verbs, IN ADDITION, to the reasons posted by folks more knowledgeable than me, is that Navajo verbs have no "time tenses" as we are accustomed to. If a verb needs to indicate the future or the past, there's a whole NEW word used, rather than the various conjugation schemes used in European languages. At least that's what I have been told (by both native-speakers of Navajo and by students of the language). I'm far to linguistically challenged to have learned much more than some common politenesses in Navajo, even though I lived "next door" and did business on the Navajo Nation. Even in Spanish, now my second language after nearly 15 frustrating years, I can only claim to be at the "me defiendo" – I get by. – level, even though it's the only language spoken in my house. I'm a terror in simple, well-pronounced Spanish, though, with the emphasis on SIMPLE.

#15--

Those demonstratives look like something Borges might have invented, Diana. Very cool, assuming one isn't going to have to memorize it all.

#16--

It seems to me that that would make the verbs more numerous, but less complex (as we have been using the term). More vocabulary, less grammar.

For what it's worth, there are lumpers who think they can identify three superfamilies of American languages. Eskimo-Aleut, Na-Dene (which includes Navajo, the Apache languages, and a dozen other, mostly Canadian, languages), and all the others, including Hopi. Nobody puts Hopi and Navajo and Yupik (or any other Inuit/Eskimo language), or any two of them, into the same family. Most linguists, as far as I know, think the idea of the "all the others" superfamily remains to be proven.

If a verb needs to indicate the future or the past, there's a whole NEW word used, rather than the various conjugation schemes used in European languages.

All languages need to deal with the situation that someone constructs a new word, what endings to give it, how to express it in the past. So I suspect that there is something you do when there is a new verb, to create these "new words" from it for the other time senses. For example, in German, 80% of plurals are "irregular", but there is a regular ending for new nouns.

This verb situation isn't completely dissimilar to the situation in Russian. Russian verbs come in pairs, perfective and imperfective, to get all the tenses, and, like the German nouns, mostly you need to learn them as a pair, as there is not a regular formation in the broad generality of cases. Though if someone invents a new verb, people will know what to do.

Perhaps there is another factor I haven't thought of before. Perhaps when a people lives in a small and fairly well-contained language unit for a very long time, like for example appears to have happened in New Guinea to create the enormous language diversity there, where many languages are only used by a handful of villaegs, perhaps these small languages can become really, really complicated and really really irregular, because these idiosyncrasies can be shared within a small community in a way that just wouldn't transmit to a larger language community.

It occurs to me that English has a couple of verbs along the lines that mazgringo says are typical for Navajo. If you want to use "go" in the past, you have use an entirely unrelated word, "went". If you want to make a past of "I am" you have to reach for the unrelated "I was"; for the present perfect, "I have been, unrelated to either. The past of Latin fero, I bear, was the unrelated sustuli. The past participle was sublatus, unrelated to either (except for the prefix shared with sustuli).

They're called suppletive paradigms, and it may be that Navajo has a lot more of them.