Interesting question.
Here's the deal:
1) What we are talking about with the concept of "in time" how core languages are changing has primarily to do with population and the evolution of mass media for sharing such languages. To the extent that you are willing to see a diminution of the complexity of "a language" as such, you are also necessarily going down the same path as people like Marshall McLuhan who have been thinking of mass media in terms of, well, to quote the cliche: *the medium is the message [massage]."
When we talk about "millennia," we have evidence of language in writing on any meaningful scale going back only six thousand years. Alphabet-based writing going back only just over five thousand. So, the simple observation that contradicts the notion that "all languages get grammatically simpler" is that languages must be developed in the first place. They are not creatio ex nihilo as the invocation of the Story of the Tower of Babel implies.
Therefore:
2) It should not be forgotten that language itself in the past has necessarily grown in complexity in all kinds of different ways (from "ug!" to "ug! ug!", that is counting, and beyond to the Egyptian alphabet), and that whatever mythical notion of a point in time such as the "Tower of Babel" might have existed, one must keep in mind that it is but a myth.
I would strongly caution against romanticizing a past by which the only way we know it is by upper-class speech (and the media by which it was recorded). There is in fact no evidence that I can discern that our present-day upper-classes have lost any amount of focus whatsoever on the degree to which the complexity (and rigidness) of grammar to this day serves as not merely a 'class differentiator' but a real-world competitive advantage in manipulating the mass cultural symbols (as I like to say) by which all of us adjudicate all things within language -- from the law to lightest nuances of public rhetoric that sway mass opinion (from politics to commerce and the advertising of them both).
Nevertheless, even privileged speech is moving more toward simplicity at the current time than away from it. I am not aware of any observation or research that would say our modern languages are not growing simpler, generally. There are number of reasons why this is so having largely to do with 1) the limits and demands of the technological media that we use to convey media to large audiences and 2) changes in cognitive assumptions upon which foundational distinctions are made, animate vs. inanimate, gender, etc. that as little as 1500 years ago seemed very important, but do not appear to be of much consequence today.
But these things are not inherent to "language" per se, so the troubling thing about your question is that it is more complex than it seems. To the extent that it is a law of nature that if you drive a car with wooden, octagonal wheels far enough, the corners of the wheels will become increasingly rounded, then I think it is fair to say that linguistic codes are the same as they are used and reused and shared among wider audiences. But what does that really mean? To say that it is a law of nature that all octagons eventually become circles is false. Therefore, I say similarly that to say that it is a law of nature that languages necessarily grow simpler over time is false.
[Biographical comment about the McWhorter removed, because it was not relevant.]
Comment from Mikhail
Sorry, but I am not satisfied with your answer. 1. I am not talking about complexity of "a language" but about complexity of the grammar. 2 "Story of the Tower of Babel" is just the name of the book, not its content. 3 Who is romanticizing what? 4. Does "mass media" or "upper-class speech" can be applied to hunters-gathers (my question is about change over millenia)? 5. If all evidences points that all grammars get simpler over time than scientifically speaking it is a law of nature, isn't it? – Mikhail Aug. 14, 2010
Reply:
Ah! Now this is a conversation! I believe that you have yet to fully digest the concept of the development of languages and grammar in the first place. If you reject the 'creatio ex nihilo' concept of language, which scientifically, I believe you must, then one is constrained to say also that "some grammars get more complex over time."
There is a flaw in the nature of your question itself that must be grappled with. At best, all you are going to be able to assert is that there is a relative threshold of complexity for the grammar human languages that after reached tends to subside. And then there will be a point at which an equilibrium is reached. I think the notion that it could be a natural law that they continue through millennia to get simpler until we don't say anything any more is easily rejected out of hand.
One must also consider that the discipline of the study of grammar as we know it today does not actually possess the fixed framework for comparison that we have historically imagined. Grammar is in fact only a discipline about our ability to describe language, and our ability to describe language as having "grammatical modes and properties" has changed and morphed dramatically in recent years. Grammatical inquiry, especially in English, has historically been Latin-centric, and rigidly so. But today, any decent contemporary linguist is quite at home talking about multiple grammars. Discussing "natural law" in this context is inherently a dicey proposition once we dare venture outside the narrow constraints of ancient Latin.
Regarding hunter-gatherers and privileged speech. Yes, absolutely, it applies. And my point about it applies to an inherent inability to accurately assess supposedly "decayed" or "fallen" adherence to grammatical convention based on the fact that the technology for preserving language has not been available to "the masses" until very recently. You simply cannot assess change over millennia if you do not have accurate data or are not comparing apples to apples.