Bengtson & Ruhlen, Global Etymology

[freknu]

I forgot to post the link to the criticism:

What can we learn about the earliest human language by comparing languages known today?, Lyle Campbell

So, what can we find out or reasonably hypothesize about the earliest human language(s) from looking back from evidence in modern and attested older languages? We can speculate, perhaps even reasonably in some cases, but we can 'know' extremely little. What can we find out from lexical comparisons? Answer: essentially nothing, though we can learn object lessons from the many problems found in the methods which have been utilized to attempt to get at 'global etymologies.' Perhaps because of the assumption that all the world's languages are genetically related, descendants of 'Proto-World,' global etymologists are disposed to believe in etymological connections among words in contemporary languages, and this will to believe permits them to accept as related forms which do not exceed sheer accidental similarity as a more plausible explanation. I conclude with Bender (1993:203), ''global etymologies' are an illusion. They are an artifact of too much freedom of choice and the loss of control.' The global etymologists have not met their burden of proof. In the long time since the origin of human language(s), so much vocabulary replacement has taken place that in effect no forms once found in 'Proto-World' could have survived. Moreover, if some form had survived (and I assert it did not), after so much change it could not be recognized, and, if it should preserve a recognizable shape (and again I assert it could not), there would be so few such surviving forms that it would be impossible to distinguish successful survivors from forms similar by sheer accident. In short, the search for global etymologies is at best a waste of time, at worst an embarrassment to linguistics as a discipline, confusing and misleading those who might look to linguistics for understanding in this area.

What can we find out Proto-World from structural comparisons? Answer: nothing especially useful, though functional typological and structural considerations may provide broad guidelines to what even the earliest human language would have to have in order to qualify as a human language. Again, though, we learn object lessons from the problems encountered in such structural comparisons. In particular, we learn that there is no correlation to be found between size of speech community or social organization and structural aspects of languages. We can speculate that the design features of human language give us a small handle on the necessary nature of the earliest human language(s), but these are so broad that essentially any linguistic structure known in any language today would qualify as possible.

Quite a biting conclusion. I'm not so sure I agree with everything he says, but I can't say I see any major issue with his conclusion, either.

[Daniel]

In particular, we learn that there is no correlation to be found between size of speech community or social organization and structural aspects of languages.

A lot of linguists would disagree. I'm not sure that I do. But the idea that culture and language are closely connected is certainly popular.
At least one property of small speech communities is the use of local geography in the grammatical system. That disappears with globalization (if not much sooner). And there are probably more things. I'm not sure why Campbell wrote that particular part.

We can speculate that the design features of human language give us a small handle on the necessary nature of the earliest human language(s), but these are so broad that essentially any linguistic structure known in any language today would qualify as possible.

This I agree with. (But of course, many would not-- those who believe that UG is fairly constrained, for example.)



As for the issue of reconstruction, I still want to go back to my earlier point that the best way (to whatever degree there is any chance of a good way) would be through intermediate reconstructions. Surface comparisons of modern languages is silly, for the reasons outlined well above-- we'd expected differences, not strong similarities at this point. But none of this means we absolutely can't get back that far.


Additionally, there is one interesting perspective that Campbell, I assume unintentionally, hints at: if the issue is borrowing and the messiness of data, one odd but interesting argument for a Ruhlen type approach to Proto-World is that borrowing is indeed accounted for at that level. Comparing these words across all languages, and including all changes and all borrowing, there may be some way to just average that all out and see what Proto-World was like. Overall it's still not going to happen. But at the level of Proto-World, borrowed words aren't "noise" per se, but rather just more data, with a different path.

[MalFet]

Once you get past a certain point, the system contains enough mutation to push the similiarities into a band of probability that makes it fundamentally impossible to separate from chance.

WHAT POINT?
That's my entire objection. You're hand-waving if you can't give a date (or general window) for that point.
And, yes, that "point" is the barrier/wall/limit I've been talking about.

I know this is your entire objection, but it's the wrong objection. That's what I keep trying (but failing) to explain. There is no simple "point" in historical time beyond which reconstruction is impossible. That's just not how it works. For any particular dataset, however, there are some hard methodological limits on how much mutation can be reliably extrapolated in the absence of actual, attested datapoints. Any good textbook on historical linguistics should cover this.

When you start postulating beyond the reach of your dataset (as Ruhlen insists on doing), it becomes statistically impossible to distinguish between similarity as a consequence of relatedness and similarity as a consequence of chance. Put simply, Ruhlen is making **** up and telling people to prove him wrong. That's not science. It's not even mediocre science. It's sitting around the campfire telling just-so stories.

What's the coherent and specific argument against Ruhlen et al then?

Precisely what I've said in every post in this thread. Most historical linguists feel that it is necessarily to test claims of relatedness against the null hypothesis...namely, that observed similarities between languages are the product of coincidence. Ruhlen does not do this, and when others have done it for him his hypotheses tend to collapse under the weight of analysis.

[Daniel]

I agree with you completely, except that I see this as a gradient distinction, not a categorical one.

For any particular dataset, however, there are some hard methodological limits on how much mutation can be reliably extrapolated in the absence of actual, attested datapoints. Any good textbook on historical linguistics should cover this.

Can you be more specific?

Certainly there are limits, but I'm not sure how we know what those limits are. I can tell which argument is a better argument, but not exactly where a hard limit is.

[MalFet]

I agree with you completely, except that I see this as a gradient distinction, not a categorical one.

For any particular dataset, however, there are some hard methodological limits on how much mutation can be reliably extrapolated in the absence of actual, attested datapoints. Any good textbook on historical linguistics should cover this.

Can you be more specific?

Certainly there are limits, but I'm not sure how we know what those limits are. I can tell which argument is a better argument, but not exactly where a hard limit is.

If I try to throw a quarter into a cup, the probability that I will be successful decreases as the cup gets farther away from me. This decrease is a gradient change. If the cup is sitting on the moon, however, it's pretty darn categorical that I'm not going to land a quarter in it.

If you're interested in historical reconstruction, you might look at something like Anthony Fox's book. He doesn't provide much by the way of cutting edge statistical methodology, but his historical overview is the next best thing to actually doing some of this work yourself. The material on transformation chains, in particular, should make it very clear why Ruhlen's claims sit a few million miles north of this notional "hard limit" that you keep wanting to locate.

[Daniel]

If I try to throw a quarter into a cup, the probability that I will be successful decreases as the cup gets farther away from me. This decrease is a gradient change. If the cup is sitting on the moon, however, it's pretty darn categorical that I'm not going to land a quarter in it.

That's exactly the sort of hand waving that I'd like to avoid. It's an unscientific argument against what you're claiming is an unscientific approach.

Again, I agree with you. This is all intuitive and Ruhlen is looking way too early. But I don't know that for scientific reasons.

Scientifically, all I know is that you almost certainly won't hit the cup. But you might.

The material on transformation chains, in particular, should make it very clear why Ruhlen's claims sit a few million miles north of this notional "hard limit" that you keep wanting to locate.

So let's, for argument's sake, assume that the hard limit is somewhere between 1,000 and 50,000 years ago, still far from the reconstructions Ruhlen proposes. How do we establish with relative certainty that the limit is indeed within that window?

[freknu]

Scientifically, all I know is that you almost certainly won't hit the cup. But you might.

Scientifically, there is no evidence to support the notion that he could complete said task. If you have evidence to the contrary, you are free to prove how he could do it — the burden of proof is on you.

So let's, for argument's sake, assume that the hard limit is somewhere between 1,000 and 50,000 years ago, still far from the reconstructions Ruhlen proposes. How do we establish with relative certainty that the limit is indeed within that window?

Statistics is not one of my stronger points, but here goes ...

1. attested data point
2. extrapolated data point
3. extrapolated data point, k=√(k₁²+k₂²)
4. extrapolated data point, k=√(k₁²+k₂²+k₃²)
5. extrapolated data set, k=√Σk_i²

How long before your uncertainty is so far off the scale that you need a magnifying glass just to see it?

There is not just a single step from modern language to PIE, it already involves decades of work and layers upon layers of reconstructions and uncertainties. Going from PIE to any hypothetical earlier superfamily is likewise going to require many layers of reconstructions, it's not going to be one single swift step.

As Campbell mentioned in his critique, the time depth of PIE is around 6,000 years, and to find any relation to Proto-Uralic (probably the nearest and most likely candidate) to form Proto-Indo-Uralic one might very well add another 6,000 years worth of change. At least PIE and PU are reconstructed from attested data points which "document" the changes over time; PIU on the other hand would be entirely reconstructed from extrapolated data points. Even further back and you have extrapolated data points from extrapolated data points from extrapolated data points ... and so on.

[Daniel]

To summarize my position: I'm not at all advocating Ruhlen's method. But I want to question the specific arguments against it. I think pushing these limits back is a very interesting topic, and I'm far from convinced we'll find some kind of hard limit at, for example, 10,000 years. Instead, I think it will become increasingly difficult to push it back further and further. But I see no reason why we cannot continue to push that limit back, very slowly, with continued research.




Details:

Scientifically, there is no evidence to support the notion that he could complete said task. If you have evidence to the contrary, you are free to prove how he could do it — the burden of proof is on you.

Scientifically, we only disprove (falsify) things. So the burden of proof is on proving that Ruhlen cannot do this-- otherwise it's just hand-waving, which is what I've been saying.
I don't need to "prove" that he can do what he's doing. I'm actually seeking a way to prove that he cannot, if there is indeed such a way.

How long before your uncertainty is so far off the scale that you need a magnifying glass just to see it?

Of course. But why believe anything about PIE then?
The whole point is that if you do it well enough, maybe that result you can only see with a magnifying glass is correct. So the burden of proof is on you to show why you cannot possibly, even with a magnifying glass, come to a reasonable conclusion at 100,000 years ago.
And I've said we can't: for the same reasons you showed, that it becomes statistically uninformative over time, so earlier is less information -- we'd need a magnifying glass then. But that still doesn't provide us with a cutoff between "can" and "can't" time periods.

There is not just a single step from modern language to PIE, it already involves decades of work and layers upon layers of reconstructions and uncertainties. Going from PIE to any hypothetical earlier superfamily is likewise going to require many layers of reconstructions, it's not going to be one single swift step.

I agree. And this is the weakest part of Ruhlen's approach, just skimming the surface of modern languages. It doesn't mean we "can't" go back farther, just that it would be hard to do so. It might be impossible, but this just means it is hard.

As Campbell mentioned in his critique, the time depth of PIE is around 6,000 years, and to find any relation to Proto-Uralic (probably the nearest and most likely candidate) to form Proto-Indo-Uralic one might very well add another 6,000 years worth of change. At least PIE and PU are reconstructed from attested data points which "document" the changes over time; PIU on the other hand would be entirely reconstructed from extrapolated data points. Even further back and you have extrapolated data points from extrapolated data points from extrapolated data points ... and so on.

Indeed. And what's, technically speaking, wrong with that?
It's obviously a lot less reliable than something easier, but that's why these hard questions are interesting. We might be able to come up with a good theory about these things. We might not.


To me, a very interesting question is just how far back we can push these limits. I think it's crazy to start at 100,000 years ago. But I would be very interested in exactly the question you pose: what's just before PIE? However, to answer that question we need to work with many complex details of PIE itself (and other proto-languages), some of which are still being worked out. I think it's incredibly hard but not necessarily impossible.

Another major issue here is the rate of change. While 6,000 years of PIE might show a lot of change, maybe 6,000 more years before that would not. There does seem to be evidence that intense language contact increases the rate of change, and this is exactly what happened to make IE spread out so much. Before that it may have been relatively unchanging for 6,000 years. If that is the case, then going back farther would be relatively easier, helping us to make up for some of the limited data.

[freknu]

To summarize my position: I'm not at all advocating Ruhlen's method. But I want to question the specific arguments against it. I think pushing these limits back is a very interesting topic, and I'm far from convinced we'll find some kind of hard limit at, for example, 10,000 years. Instead, I think it will become increasingly difficult to push it back further and further. But I see no reason why we cannot continue to push that limit back, very slowly, with continued research.

No one, absolutely no one has been arguing that it is a static and immovable limit, that was the whole point of my attempt at an analogy — it is dynamic and movable. Hence according to the properties of your current set of data and understanding you approach a statistical limit where any result is pretty much indistinguishable from noise — pure chance. It is entirely dependent upon your current set of data and understanding, increase the set and the circumstances are no longer equal and the previous limits no longer apply. Hence it is always possible to push it farther and farther back, provided that your set of data and understanding allow this.

Scientifically, there is no evidence to support the notion that he could complete said task. If you have evidence to the contrary, you are free to prove how he could do it — the burden of proof is on you.

Scientifically, we only disprove (falsify) things. So the burden of proof is on proving that Ruhlen cannot do this-- otherwise it's just hand-waving, which is what I've been saying.

Que!? The burden of proof is on proving that Ruhlen's material is valid ... the bloody hell :/ It's his job to prove his claim, it's not my bloody job to prove it wrong. Not being able to disprove something does not make it correct, it only makes it unfalsifiable.

Another major issue here is the rate of change. While 6,000 years of PIE might show a lot of change, maybe 6,000 more years before that would not. There does seem to be evidence that intense language contact increases the rate of change, and this is exactly what happened to make IE spread out so much. Before that it may have been relatively unchanging for 6,000 years. If that is the case, then going back farther would be relatively easier, helping us to make up for some of the limited data.

Rate of change is certainly and intriguing question, but PIE would still have had to change considerably (as would the other families) to allow for a merging into a superfamily. It may very well be much slower than currently, but that doesn't exactly help, as it only means there was a particularly stable pre-PIE stage — it doesn't give you a get-out-of-jail-free card.

It also ignores the fact that apart from a very few select words of core vocabulary, there may simply not be any cognates available. Going from modern language to PIE you are left with a thousand or so roots (even less if you only count strict roots, and even less if you only count known reduced roots). How many of these do you think are shared by all later branches of IE? How many do you think will be left, if hypothetically, it was possible to merge a handful of families with cognates is all families?

[Daniel]

No one, absolutely no one has been arguing that it is a static and immovable limit, that was the whole point of my attempt at an analogy — it is dynamic and movable. Hence according to the properties of your current set of data and understanding you approach a statistical limit where any result is pretty much indistinguishable from noise — pure chance. It is entirely dependent upon your current set of data and understanding, increase the set and the circumstances are no longer equal and the previous limits no longer apply. Hence it is always possible to push it farther and farther back, provided that your set of data and understanding allow this.

This still doesn't address then why working on PIE or Proto-PIE is acceptable, while Proto-World is not. That categorical distinction is not yet supported.

Que!? The burden of proof is on proving that Ruhlen's material is valid ... the bloody hell :/ It's his job to prove his claim, it's not my bloody job to prove it wrong. Not being able to disprove something does not make it correct, it only makes it unfalsifiable.

Of course-- you can show that it's unfalsifiable (and thus unscientific) as well. I didn't mean to suggest otherwise.
But to be fair to Ruhlen, it really isn't possible to prove it correct or prove that he can really reconstruct Proto-World. It's only possible to falsify, or to show that it is unfalsifiable.
Just because an approach seems strange doesn't mean we can dismiss it (except from a practical "I don't want to do that personally" perspective), unless we can falsify it or demonstrate unfalsifiability.

Rate of change is certainly and intriguing question, but PIE would still have had to change considerably (as would the other families) to allow for a merging into a superfamily. It may very well be much slower than currently, but that doesn't exactly help, as it only means there was a particularly stable pre-PIE stage — it doesn't give you a get-out-of-jail-free card.

That's a good point, and one of the few pieces of concrete evidence we have: we'd need to go back in time far enough and through enough changes to eliminate the diversity found in any two families to be related through these methods. Of course it's possible some variation would be eliminated via the first round of reconstruction (proto-languages for each) but there would still be a good bit to account for.

It also ignores the fact that appart from a very few select words of core vocabulary, there may simply not be any cognates available. Going from modern language to PIE you are left with a thousand or so roots (even less if you only count strict roots, and even less if you only count known reduced roots). How many of these do you think are shared by all later branches of IE? How many do you think will be left, if hypothetically, it was possible to merge a handful of families with cognates is all families?

This gets us into more interesting questions. Ruhlen et al claim that some particular roots are more likely to survive due to frequent use.
You say 1000 in PIE. That might be because 90%+ of the vocabulary disappears over 6,000 years, or it may be because those 1000 words are the sort that stick around. I'd guess a combination. There are some issues with reconstruction, such as names for particular local tree species. Therefore, those will be eliminated. But the core 1000 may be the sort of words that would potentially stay in use for 6,000 or 12,000 years because they aren't, semantically/culturally, likely to be discarded. There's still the potential for borrowing and so forth.

In the end, this may give us a better approximation of the statistics:
0 years = 10,000+ words
6,000 years = 1,000 words
12,000  years = 100 words??
18,000 years = 10 words?
25,000 years = ~1 word?

There's a lot of guesswork in that. And we'd need to come up with supporting evidence. If that's true, then the 100,000 year time depth isn't going to work at all. But if the rate of losing words changes, perhaps at 100,000 years there could still be 10 core words left. These are unclear issues, and I have no idea how we'd hope to get data to tell one way or the other.



----
Also, importantly, I think we need to determine one more thing:
Aside from time-depth, what do we hope to do at that time-depth? I can think of a few goals:
1) Show relatedness of languages.
2) Reconstruct the proto-language.
3) Show development from proto-language to all daughter languages.

Those three tasks are increasingly difficult. At the very least I imagine we can potentially make great progress toward (1) even significantly earlier than PIE. Beyond that, it's much less likely. And for (3) we still have a lot of work to do for PIE, though chunks of (2) are already (reasonably convincingly) accomplished.

[MalFet]

If I try to throw a quarter into a cup, the probability that I will be successful decreases as the cup gets farther away from me. This decrease is a gradient change. If the cup is sitting on the moon, however, it's pretty darn categorical that I'm not going to land a quarter in it.

That's exactly the sort of hand waving that I'd like to avoid. It's an unscientific argument against what you're claiming is an unscientific approach.

Again, I agree with you. This is all intuitive and Ruhlen is looking way too early. But I don't know that for scientific reasons.

Scientifically, all I know is that you almost certainly won't hit the cup. But you might.

The material on transformation chains, in particular, should make it very clear why Ruhlen's claims sit a few million miles north of this notional "hard limit" that you keep wanting to locate.

So let's, for argument's sake, assume that the hard limit is somewhere between 1,000 and 50,000 years ago, still far from the reconstructions Ruhlen proposes. How do we establish with relative certainty that the limit is indeed within that window?

With the statistical entropy metrics I've been referencing throughout this thread. Some of the math depends on how much contextual phonology you're willing to bake into your model, but nothing from structuralism is going to get you much past 2-3 postulated intermediate states. Ruhlen is working with an arbitrarily large number. Alternately, you can use a purely stochastic model like the one jkpate linked to earlier for long reach but less specificity, but Ruhlen is most certainly not doing the legwork necessary for that either.

As I've said, any good textbook on historical linguistics, information theory, or plain ol' statistics will cover all this for you. I'm not sure why you're so willing to dismiss all that out of hand as "unscientific" when you seem not to know the first thing about it, but that's your choice. Perhaps you just like throwing quarters at the moon.

The rest of us, on the other hand, realize something very important: a quarter weighs 5.67 grams, a typical human's ulnar collateral ligament will break somewhere around 80 N*m, and the escape velocity of earth is 11.2 km/s.

[MalFet]

You say 1000 in PIE. That might be because 90%+ of the vocabulary disappears over 6,000 years, or it may be because those 1000 words are the sort that stick around. I'd guess a combination. There are some issues with reconstruction, such as names for particular local tree species. Therefore, those will be eliminated. But the core 1000 may be the sort of words that would potentially stay in use for 6,000 or 12,000 years because they aren't, semantically/culturally, likely to be discarded. There's still the potential for borrowing and so forth.

In the end, this may give us a better approximation of the statistics:
0 years = 10,000+ words
6,000 years = 1,000 words
12,000  years = 100 words??
18,000 years = 10 words?
25,000 years = ~1 word?

Yikes, no.

That's not how phonological change happens, not in the slightest. Exponential decay is precisely the wrong metaphor. It's all chain shifts, all the way down. You keep wanting to look at this in terms of x% change per y years, but that's a fundamental misunderstanding of the data and the methodology.

[Daniel]

Perhaps you just like throwing quarters at the moon.

Not at all. But my reasons for not doing what Ruhlen is doing are not scientific reasons: they're common sense reasons. I'd like a scientific reason to back this up.

The rest of us, on the other hand, realize something very important: a quarter weighs 5.67 grams, a typical human's ulnar collateral ligament will break somewhere around 80 N*m, and the escape velocity of earth is 11.2 km/s.

Strawman. And that's exactly the problem: in historical linguistics, we don't have any of those accurate measurements. We don't know how quickly languages change, we don't know what words are preserved and which are lost, we don't know how old language is, we have any way to test our predictions, and so forth.

With the statistical entropy metrics I've been referencing throughout this thread.

To be fair, hinting at. I asked for a reference. The closest you gave was "any historical linguistics textbook". I teach with one. I've read a handful. They certainly cover this in general terms, but they don't address the technical details at a scientific level, just descriptive. Maybe I missed it, not looking for this when I read the books, so feel free to point me in the right direction if so.

Ruhlen is working with an arbitrarily large number. Alternately, you can use a purely stochastic model like the one jkpate linked to earlier for long reach but less specificity, but Ruhlen is most certainly not doing the legwork necessary for that either.

Here I'll certainly agree-- Ruhlen is taking every liberty possible and then making some arbitrary guesses. That's a problem. But aside from throwing it out just for that, I am genuinely wondering what can be shown scientifically (unlike his methodology) to demonstrate that he's wrong to even attempt such a task. So far I haven't seen that argument.

As for jkpate's suggestion, it's interesting, but I specifically ignored that because it can't be the optimal methodology, in theory. So any weaknesses are irrelevant if there may be a better approach.

That's not how phonological change happens, not in the slightest. Exponential decay is precisely the wrong metaphor. It's all chain shifts, all the way down. You keep wanting to look at this in terms of x% change per y years, but that's a fundamental misunderstanding of the data and the methodology.

My comment was directed at freknu in terms of lexical statistics, how many words are reconstructed for PIE. I wasn't referring to phonological changes, at least not directly. And this also appears to be the explanation given by Ringe in the video I linked to earlier. Borrowing (and other kinds of lexical change) are responsible for the time-depth barrier, not (just) grammatical/phonological change.

Some of the math depends on how much contextual phonology you're willing to bake into your model, but nothing from structuralism is going to get you much past 2-3 postulated intermediate states.

Ok, and with these two comments I think we're getting somewhere: you're talking specifically about phonology, and the argument is within that context, rather than the big picture.
Extending that and rephrasing it to make sure I know what you mean...

As we go back in time and layer sound changes, they become undecidable and opaque from our perspective. Sounds change from A to B then back to A, so that from a flat (synchronic) perspective, the diachrony is flat as well, hiding all of the important changes from us. By having a small (say <50) inventory of phonemes in an average language, and by having many changes over time, we necessarily run into such problems. The result is that, much like "flattening" an image in Photoshop, we can't reconstruct the layers without all of that missing information. We're left with a narrow view.

That's an interesting perspective, and likely one that is easier to defend (statistically) than some others. The trouble is that we still don't have all of the necessary data to know how quickly sound changes occur and so forth. So we don't have a baseline or a control, and we can't really know for sure how far back we can look.


Further, there's the interesting point made (in the video, for example) that some words seem to actually look like what they used to be in PIE, at least in some cases. Selecting arbitrary examples (as in the video) isn't too convincing, but the possibility is intriguing. I believe it was freknu who posted some evidence about similarities in agreement inflections in IE and Uralic, and maybe that's the sort of place we'd find evidence.



In the end, we all agree Ruhlen is looking too far back. I just want to know the best way to show that

[jkpate]

To me, a very interesting question is just how far back we can push these limits. I think it's crazy to start at 100,000 years ago. But I would be very interested in exactly the question you pose: what's just before PIE? However, to answer that question we need to work with many complex details of PIE itself (and other proto-languages), some of which are still being worked out. I think it's incredibly hard but not necessarily impossible.

The issue is not that the information about very ancient languages is hard to get, it's that the information just isn't there. To a first approximation we can view language change as a markov chain; a language at time t randomly changes into a language at time t+1, according to some transition kernel. The markov chain of language change may be ergodic, which essentially means that any language can eventually turn into any other language with non-zero probability. If it is ergodic, then, for large enough n, the language at time t is asymptotically statistically independent of the language at time t+n. In information-theoretic terms, the reconstruction task is sensitive to the conditional entropy of the language at time t, given the language at time t+n, which in turn is the entropy of both languages minus the entropy of the later, known language:

[latex]H(L_{t} | L_{t+n} ) = H( L_{t} , L_{t+n} ) - H( L_{t+n} )[/latex]

However, if n is large enough that the languages are statistically independent, then we have

[latex] H( L_{t} , L_{t+n} ) = H( L_{t} ) + H( L_{t+n} )[/latex]

So by substitution:

[latex]H(L_{t} | L_{t+n} ) = H( L_{t} ) + H( L_{t+n} ) - H( L_{t+n} ) = H( L_{t} ) [/latex]

That is, our uncertainty about the language to be reconstructed is the same, whether or not we know the later language. Our reconstruction does not depend on the evidence. Hard work can give us a better idea of what the transition kernel is (this is essentially the panchronic phonology that MalFet mentioned), but that does not address the core issue, which is the disappearance of information about earlier states. Information about the transition kernel is hard to get. Information about the state at time t is gone.

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.

[MalFet]

The rest of us, on the other hand, realize something very important: a quarter weighs 5.67 grams, a typical human's ulnar collateral ligament will break somewhere around 80 N*m, and the escape velocity of earth is 11.2 km/s.

Strawman. And that's exactly the problem: in historical linguistics, we don't have any of those accurate measurements. We don't know how quickly languages change, we don't know what words are preserved and which are lost, we don't know how old language is, we have any way to test our predictions, and so forth.

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.

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.

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.

With the statistical entropy metrics I've been referencing throughout this thread.

To be fair, hinting at. I asked for a reference. The closest you gave was "any historical linguistics textbook".

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. Until then, if you haven't done the work yourself, haven't read the literature, and won't take my word for it, I'm not really sure what else there is to say. I can't divine this all from first principles for you.