The worry djr33 raises may be implemented here by worrying about just how large n needs to be, and how to translate this into years. That's still a valid worry; as far as I know, there's no way to derive how large n needs to be (and there's a huge incentive to be able to do this for general ergodic chains). I just wanted to distinguish this case, where information is gone, from the case where information is hard to get.
Thanks

Informative post.
But as you say, we still don't really know exactly when this information disappears. It seems to be sometime before PIE and yet after when Ruhlen is trying to reconstruct. But we have no particular evidence for that. It seems obvious, but supporting that, I still maintain, seems challenging.
We don't need to know how quickly language changes. We don't need to know which words are preserved and which are lost. We don't need to know how old language is. That's just not how reconstruction works because (and this is the key point!) that's not how language works.
Huh?
If Pre-PIE changed at a rate of 1% of the speed of post-PIE, then surely we could reconstruct, with a little effort, languages ten or twenty thousand years earlier than that. Speed and such are crucial here.
Obviously there is some speed at which change occurs, and there is some corresponding cutoff point where too much information is lost. But again, we can't be certain, due to
having no evidence, that the cutoff point is after the time Ruhlen is working with.
I'm just repeating myself here, and I don't know how else to say it. jkpate provides an excellent summary of the problem in information theoretic terms. The way we do historical reconstruction is by postulating intermediate nodes in a Markov transformation chain and then comparing the resulting power of explanation against the possibility that the observed similarities came about by chance. Thanks to the techniques that jkpate talks about, we've been able to quantify this increasingly well over the last few decades (with the lovely consequence that we can now trace fainter lineages than ever before), but the core principles at stake here are as old as the hills. Heck, it was in exactly these terms that Saussure got this whole field started with his postulated (and later vindicated) laryngeal consonants.
Fine. And you have not given any indication whether a cutoff point is at 5,000, 20,000 or 50,000 years ago.
Therefore, whether or not Ruhlen is doing it correctly, we might be able to reconstruct languages that are 100,000 years old. It's highly implausible, but there's no concrete evidence against that.
A critique of Ruhlen in scientific terms is simply that his conclusions are not the product of a scientific methodology. He's not, in short, doing what the bolded sentence above requires. Instead, he's gazing at a bowl of tea leaves and telling the world what he sees. He simply does not have access to the information necessary to make the claims he's making.
This I agree with. And this has nothing to do with him doing it "too early" or any of the major complaints I've seen against him. It's just that he's doing it the wrong way. I think almost everyone can agree on that: his methodology is not rigorous and skips steps.
I think I've confused the matter by not making it clear that I'm talking about possible time depths for comparison, not whether Ruhlen is actually using the best methodology. (Still, Ruhlen's methodology is just fine for showing that, say, English and Swedish are related. So it still would be nice to have a metric to show just how far back that methodology can go.)
Nonsense. I pointed you towards Juliette Blevens and George van Driem, and told you very specifically that Anthony Fox's work on chain shifts in the history of reconstruction should fill in a critical piece that you seem to be missing. I'm happy to provide more, but first I'd have to know why those didn't work for you as starting places.
Hm, ok. My fault-- you did mention a couple names. I'll check out their CVs when I have some time.