I have been baffled by the languages of the Americas.

The Americas were populated just about 15000 years ago, ostensibly by a few tribes of people originating in NE Asia, migrating across the then-exposed land of Beringia. Presumably the original tribes were closely related (see e.g. genetic studies). What I would like to understand is this:

Why are there so many language families in the Americas? And why is none of them related to any other languages of the world, especially to the languages of NE Asia? Did dozens of totally unrelated language families get generated de novo in a few thousand years? How would that be possible?

Thanks

Thanks for your exhaustive response. I still feel that a continent, which has been populated by humans 15000 yeas ago, would have less languages, and language families than the continents where people have been living for hundreds of thousands of years. Unless we postulate that, e.g., a continuously  existing population can transform its language from one form to something structurally completely unrelated after a certain number of generation of speakers. So for instance we have a tribe speaking something like Chinese, one half goes left, the other half goes right,  and 2000 years later one descendants speak something like Sanskrit and the other something like Bantu. Or that languages are completely forgotten at times and then reinvented from scratch. Or, that languages started to be spoken only about 15000, maybe 20000, years ago.

I just feel that a continent that has been populated much later and has had a much small number of inhabitants than the rest of the world "should" be linguistically more homogeneous than the rest of the world. But it isn't so there has to be some explanation.

Asu:

I still feel that a continent, which has been populated by humans 15000 yeas ago, would have less languages, and language families than the continents where people have been living for hundreds of thousands of years.

Fact check:
1. Modern humans have not been living anywhere outside Africa for "hundreds of thousands of years". The Americas are relatively recently settled, but not by as much as you suggest.
2. The Americas were settled in waves (maybe three, see above). You can see some information here: https://en.wikipedia.org/wiki/Settlement_of_the_Americas -- according to that page the settlement of the Americas was "not before 20,000 years ago". Different languages/cultures might have arrived there thousands of years apart, but none were there more than about 20,000 years ago.
So your impression is irrelevant to the facts: there ARE many languages in the Americas, and they did get there around 15,000 years ago, give or take a few thousand years. The diversity is quite high (partly explained as I noted above by there being many small groups), and somehow that happened over the last 20,000 (or fewer) years.
There are various questions you could ask:
1. Is that 20,000 year limit really true? I'm not the person to ask, but I'll assume that's a reasonable approximation unless you have some very strong evidence otherwise.
2. What was the diversity like when the languages arrived in the Americas? Maybe only three languages came over (the ancestors to the three groups Greenberg proposed). Maybe dozens (or more) did, independently (but perhaps in larger waves). Or maybe only several migrations of large groups occurred, but within those groups multiple languages were spoken (just like the Europeans simultaneously brought Spanish, English, Portuguese, French, Dutch, etc., to the Americas).
3. How did the relatively little diversity become the greater diversity we see today? See my answer above for a broad perspective on that. It's a good question.

Unless we postulate that, e.g., a continuously  existing population can transform its language from one form to something structurally completely unrelated after a certain number of generation of speakers. So for instance we have a tribe speaking something like Chinese, one half goes left, the other half goes right,  and 2000 years later one descendants speak something like Sanskrit and the other something like Bantu.

Well, yes... exactly. Almost. Languages do change over time, and over enough time those changes accumulate. What you hint at (maybe unintentionally) is that Chinese is an isolating language (with little or no morphology), Sanskrit is a fusional/inflectional language (with 'paradigmatic' morphology that encodes multiple features at once, like one ending for tense/person/number/mood/etc.), and Bantu languages like Swhaili are agglutinative (stacking multiple morphemes one after the other, not overlapping like fusional languages, but also having complex words unlike isolating languages). There is a cycle from which isolating languages become agglutinating (independent words start to stack as affixes), then agglutinating languages become fusional (the once-independent stacked morphemes start to overlap/fuse), and then fusional languages become isolating (losing their morphology), and repeat. Any given language is somewhere in that continuum (not exactly at any particular extreme). For example, aspectual particles in Chinese look a lot like suffixes and there is a lot of compounding in the language (hinting that it might be becoming agglutinative), Old English was fusional but is now close to isolating, and so forth. So, yes, that is almost exactly what linguists would say about how the diversity in the Americas came about.

Remember, the Indo-European family has had about 6,000 years to diversify. But over 12,000 years that would not be double the diversity, but actually 4 times (approximately-- exponential anyway), because changes accumulate and go in different directions. And even more at 18,000 years, the approximate age of the oldest American languages.

Note also that the similarity between the youngest group (Eskimo-Aleut) is so different than the diversity of the oldest group ("Amerind", if that is indeed one group, but either way, there's a lot more diversity among those languages than Eskimo-Aleut).

Or that languages are completely forgotten at times and then reinvented from scratch

Through mixing and contact (as in creole languages due to colonization today) that might have happened. Or at least reshaped some of the languages in some ways. That's why Greenberg's observations are probably of contact rather than really reflecting the origins of the languages.
On the other hand, if by "reinvented" you would allow for a language to be "completely replaced", then that might have happened in a sense. Linguists estimate that by around 10,000 years there has been so much borrowing it is no longer possible to clearly distinguish the 'signal from the noise' in the sense of which words are original and which are borrowed, so reconstruction and determining relationships is nearly impossible. So by cycling through 10,000 years of changes and contact, indeed languages would look almost nothing like they did originally. With small groups and nothing to connect the once unified language families, diversity is predicted.

Or, that languages started to be spoken only about 15000, maybe 20000, years ago.

No, not at all. There are various reasons for that, but this is not evidence in support of that argument anyway.

I just feel that a continent that has been populated much later and has had a much small number of inhabitants than the rest of the world "should" be linguistically more homogeneous than the rest of the world.

Rome was the first city in the world to have 1 million people. But aside from a few population centers like that (and there were some in the Americas too!), people have lived in small groups of a few thousand people all around the world. I don't know why you would assume the Americas were less populated throughout their history (after the initial settlement of course) than elsewhere. Of course Europeans killed a huge number later, but before they arrived the continents were empty or even sparsely populated. They were populated like anywhere else. I mean... that's how the Europeans found them... right? It wasn't just by chance that they happened to come ashore where one of the few tribes was living, but that anywhere they would have ended up would have already been populated.

Also, just compare the Americas to Europe: about 15,000 years to diversify vs. only about 5,000 years (plus a few non-Indo-European languages), with a lot of contact and borrowing especially recently. We should expect the Americas to be less diverse than Africa or Asia (for example) but more diverse than Europe. And that's about what we see. There's a huge amount of diversity in the Amazon in particular, so that's where research along these lines must focus (and there is a lot ongoing). But since the groups there were especially small, more rapid change can make sense.

I wonder about the differences between the Americas and Australia. According to Wikipedia Australia's first inhabitants arrived there around 50,000 years ago: https://en.wikipedia.org/wiki/Indigenous_Australians -- So we should expect much more diversity than in the Americas
But actually Australian languages are mostly very similar today. Our perspective is biased, though, because so many of the languages were wiped out that we only have a fraction left, mostly in the same geographic areas. For example, we don't know much about the language(s) spoken in Tasmania, although a few words were recorded by the earliest Europeans there. The majority of Australian languages today are from the Pama-Nyungan: family https://en.wikipedia.org/wiki/Pama%E2%80%93Nyungan_languages -- containing hundreds of languages, many of which are extinct or severely endangered now. But these languages are fairly transparently related, representing a time depth of only a few thousand years (roughly parallel to Indo-European), nothing like the ~15,000 years of diversity in the Americas:

Proto-Pama–Nyungan may have been spoken as recently as about 5,000 years ago, much more recently than the 40,000 to 60,000 years Indigenous Australians are believed to have been inhabiting Australia. How the Pama–Nyungan languages spread over most of the continent and displaced any pre-Pama–Nyungan languages is uncertain...

So what we see in Australia today does not represent the original diversity at all, really. There are some non-Pama-Nyungan languages in the periphery still spoken, and they are indeed very different, although in some ways they still have some similar features, probably due to contact.

A point to take away from all of that is that languages spread in waves, and also can fade away. (Specific) diversity is a temporary condition, rather than entirely an accumulated result. The history of the languages in the Americans almost certainly represents more diversity than we can observe today (as we know is true for Australia), so the idea of how diversity came about historically is even more interesting: it's not just that it was able to get to the current state, but that it was probably even more layered and diverse over the past thousands of years. Languages don't just spread 'outward', but also across, and under, and on top, and through. And when that happens it can cover up what came before.

In short, 15,000 years is more than enough to get a lot of diversity!

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FlatAssembler,

The most widely accepted language family that connects the Old World and New World is probably Dene-Yeniseian languages.

Aside from Eskimo-Aleut, you're right. The Dene-Yeniseian proposal is better than the Dene-Caucasian ones, although those have been around longer.
https://en.wikipedia.org/wiki/Na-Dene_languages#Den.C3.A9.E2.80.93Yeniseian
But also note that Dene-Yeniseian is a sub-set of the languages of the larger Dene-Caucasian proposal (assuming the proposed languages in each as-is, at least).

I don't really know what's the basis for the assumption that Proto-Afro-Asiatic was spoken that early.

We know which languages are related. And we have early attestations of some of them. We also have a general sense of how long the changes might have taken. It's not precise at all, but we can guess that it was at least a few thousand years for some things to happen. Since Ancient Egyptian is attested from almost 5,000 years ago (and Akkadian soon after, which was not the parent of the other Semitic languages but rather a different daughter of Proto-Semitic that had already had some time to change on its own), the idea of Afro-Asiatic unity being younger than 10,000 years is implausible. So 15,000 is a rough approximation, and we can say 15,000±5,000. Something like 10,000-20,000 is reasonable. That's not my number anyway. I looked it up on Wikipedia to get some idea of what people thought, but I don't take the actual number very seriously. Proto-Indo-European is around 6,000-8,000 years old, and Proto-Semitic is parallel to that. Overall we don't know much for certain, but 15,000 is a reasonable guess.

It's a well-known thing that glottochronology can greatly overestimate the age of a language family that's spread over a large area.

"Glottochronology" usually refers to a specific method based on looking at the number of cognate words in a word list and then estimating a rate of change (borrowing or coinage) and figuring out distance based on that word list data. That method is highly problematic, but that's just one approach. The basis for the 15,000±5,000 years for Afro-Asiatic is also based on other factors like anthropological evidence, the observed rate of change for the 5,000 years of attested history, and so forth. It's not just word lists. In fact, word lists for Afro-Asiatic as a whole are harder to establish than for other language families, because the time depth is so great. Still there are recurring patterns that support the hypothesis that these languages are related, but reconstruction (and other details) remain difficult.

Fascinating. I am not sure where the 20000 years inhabitation time comes from: to the degree that Wikipedia is correct, there have been no settlements older than 15000 years discovered in the Americas. (And the Southern settlements, in average, are not younger than the Northern ones, another baffling fact).

Not my area, so I can't say much about it. However, despite the uncertainty of the linguistic evidence for the 'three wave' settlement model, recent DNA evidence has supported that approach, I believe. So that might be one area of research for you to look into if you want to know more about the settlement timeline. Regardless, from a linguistic perspective, 15,000 years is reasonable amount of time to have the current diversity, so that in itself is not a counterargument to the current theories about settlement.

You say that in 2000 years a language can completely change structure, to the degree that it will be an "unrelated" language

No, not unrelated, but mutually unintelligible. Just look at a text from Old English from 1000 years ago: you won't be able to read it (unless you happen to know German and make a lot of good guesses). On the other hand, Old Norse and Modern Icelandic are so close that Icelanders today can more or less read Old Norse, also from about 1000 years ago. So 2000 years is a reasonable (but arbitrary) "cutoff" between "the same language" and "its [distinct] ancestor", if we want to make that kind of distinction (it is an odd one to make, but relevant in this context). So basically every 2000 years (or so) you can think of there being "new languages" simply due to accumulated changes that have made the languages different enough. Spanish, Italian and French are also about 2000 years from Latin, and they are very different indeed, but still recognizable as related. We can compare languages today similarly based on time depth: Spanish and French less than 2000 years different; English and Hindi are about 6,000 years different, and so forth. The relationship is only clearly established by looking at Old English and Sanskrit, not the modern languages.

I do not believe that in the past several millennia, well documented languages like Chinese or the various Indo-european ones, have changed so drastically.

We have few languages clearly documented for thousands of years. There are usually gaps or limited records. But we do have some cases we can consider:
1. The most obvious is Latin becoming the Romance languages, around 2000 years.
2. Greek has around 3000+ years of recorded history (much less is known past about 2500 years, with some very limited data from before 3000 years, e.g., https://en.wikipedia.org/wiki/Mycenaean_Greek )
4. Ancient Egyptian became Coptic, which is actually still spoken by at least one person in Egypt today (a native speaker was found recently according to this article: http://web.archive.org/web/20110929192705/http://www.dailystaregypt.com/article.aspx?ArticleID=106, as well as use as a liturgical language for Egyptian Christians). That's about 5000 years of recorded history. It has changed substantially. It's the only example of a language that I know of that seems to have gone through (in some sense) all three of the stages of the mrophological cycle. The research on it can be a bit difficult for a non-expert (not just a linguist, but a specialist in Coptic/Egyptian), but it's fascinating.
4. Guy Deutscher has a nice book looking at the history of Akkadian over around 4000+ years.
5. Chinese is a problematic example because the writing system has changed very little (visually yes, structurally no) over the past 3000 years or so. Some linguists think that, for example, Ancient Chinese actually had a lot of morphology, just that the writing system didn't represent the suffixes so we have no evidence of it. Although Ancient Chinese texts (such as what was written in the Oracle Bone carvings) can be deciphered well, we don't know exactly how it was pronounced, as is shown by how some characters cannot be translated (as pronunciations) because we know they refer to certain family/tribe names, but not what the associated sounds were at the time.

As you can see our evidence is limited (there are 6,000 languages in the world, and the vast majority have only been written within the past few hundred years; some are still unwritten), and also biased toward certain areas and certain types of languages. But there is some evidence out there, and there is a lot more in the form of comparative reconstruction where linguists have figured out how the diverse modern states came about from the earlier (unattested) proto-languages. There is quite a bit of research about that for indigenous American languages if you want to read it. Many small families are well established (while the question of a large "Amerind" family is up for debate and maybe not wrong but not supported yet by any substantial data).

And remember: the sociolinguistic situation in the Americas is different from what we have for languages that were written. Standard languages tend to change slower, and it is standard languages that are written, not vernaculars and dialectal variation, etc. Just look at English spelling that doesn't match at all how we pronounce words today.

A related question: what is the effect of writing on the changing of languages.

A different and complicated question in itself, but as a brief answer: very little. Writing is used as a way to write spoken languages, rather than speaking being a way to pronounce written languages. People often think of writing as the "real" or "standard" or "correct" form of language, but that's not how languages really work. And they change based on how they are spoken, not how they are written, for the most part.

I know of at least two ways in which writing can result in changed languages, though:

1. Writing relates to standardization. Thus variant dialects are marginalized, and the standard language may change a little slower because it is attached to a written (perhaps frozen) form. Consider English "who vs. whom" that some English teachers will still correct you about (that's about 200 years old), compared to "you vs. thou" which is no longer considered a 'proper' distinction (that's about 400 years old). So standardization can slow language, reduce diversity, and sort of 'echo' earlier language. Since there was little writing in the Americas, there may have been more diversity due to that.
2. Complex sentences with more than one clause do not need specific conjunctions to link them in spoken language, and often just intonation does fine. We can SAY in English "I got home, I ate a sandwich", but we might be told (again by that same English teacher) that we need to have a conjunction ('and') in the sentence. Writing doesn't have intonation to express that sort of thing, so writing tends to encourage the development of conjunctions. Similarly, contact can do the same. So many languages in the Americas do not have a word for "and" (instead they just say "mother, father" or "sing, dance"), while others have now borrowed European words (English 'and', Spanish 'y', etc.).

So there are some ways in which writing can affect spoken language (mostly it's the other way around!), but if anything that would support there being diversity in the Americas.

Europe is a relevant example: the spread of Indo-Europeans wiped out almost all of the languages there before them. That happened within the last 6,000 years or so. Basque is still very different, obviously. And then there are the few Uralic (Finno-Ugric) languages to the east. So there is some diversity in Europe. Just imagine what it would be like without those large conquests (and even conquests/wars within the Indo-European groups later), and if the groups were all much smaller as they are in the Amazon or in coastal areas that can support large populations (still in small groups) like in California.

Or compare it to Australia, as I described above, where most of what we see now is the relatively recent (parallel to Indo-European) expansion of one group despite humans having been there for many tens of thousands of years.

So what is interesting about the Americas is that we have maintained diversity without those huge conquests (until the Europeans arrived) wiping out that diversity.

In other words, for many places in the world, we really are not looking back farther than 15,000 years in terms of diversity.

And I shouldn't suggest that the Americas have had no large expansions. The Iroquoian languages spread out quite a bit in North America. The Eskimo (Inuit) group spread all the way out from Alaska to Greenland (relatively recently, as that last wave). The Uto-Aztecan and Mayan languages also spread out in large areas. And in South America there were some similar expansions too, such as "Quechua" (really a very large dialect continuum consisting of many distinct languages), which is also probably related to Aymara, another major language group today still with a large population. The Tupi-Guarani family also expanded relatively recently in Brazil and nearby areas, sort of parallel to the Bantu expansion in Africa, which occurred before Europeans arrived and shaped our impression of how the continent was, despite really covering up a lot of earlier diversity. We don't know too much about the Tupi-Guarani expansion because it was prehistoric (before recorded history) but we can gather some information from at least the distribution of languages, and some other sources (including oral histories/myths, genetics, etc.).

out of 3 separate migrating groups and no further influence

Just two clarifications:
1. There do appear to be 3 groups genetically (check on those studies: it's not my area, but that's what I last heard about that area of research), but the idea of 3 language families is highly controversial. If Greenberg was right (it seems somewhat plausible to me), then it was actually for the wrong reasons (and sort of process of elimination with that huge 'Amerind' group of leftovers that didn't really fit into a more precise analysis-- maybe because they really are the oldest group and have had more time to diversify and therefore hide their original unity-- if that is correct).
2. What other influence could there be? The vikings did reach eastern North America but don't seem to have had any major linguistic (or cultural) impact. And even the Basques might have reached there (they seem to have done a lot of cod fishing in the area of the Atlantic closer to North America than Europe, at least), but the same applies. And in the west (from the east), the Polynesians might have reached South America (I think that's a fringe theory, but not entirely implausible) but also didn't have much of a lasting impact if so.