Nostratic, Eurasiatic, Mitian, ...

[KathTheDragon]

I'd love to go through your post in detail and pick it apart, Howl, but there's rather too much for me to hold in my head long enough to write a coherent reply, so I'll pick a few bits that caught my eye.

Firstly, on the Celtic and Italic reflexes of *pénkʷe, these are regular through the assimilation *p...kʷ > *kʷ...kʷ, also observed in Latin coquō < *pekʷ-.

Secondly, the Uralic stem *mi need not have anything to do with the PIE stem *kʷi-, since there's another PIE pronominal stem starting with an *m, though the reflexes are sparse and the semantics are unclear, but it's very possible that it had interrogative semantics.

[Hydroeccentricity]

It has often been speculated that the IE words for 4 (*kʷetwores) and 8 (*Hoḱtṓw)
are related. If that is true, they should come from an earlier form like **kʷoktw.
In the word for 4 the 't' was elided, and a suffix was added. 
In the word for 8 the inital kʷ was lenited to a laryngeal.

This is the Greenberg method: reconstruct a proto-language by combining all relevant segments, then weed out the ones you don't want with sound changes.
Proto-Anglohispanic *waguater
English medial gw drops, adjacent identical vowels coalesce > water
Spanish final -ter elides, initial approximants eliminated > agua
And these sound changes will work when applied to lots of other words, because when you're adding extra -ter to all the Spanish words or extra -gw- to all the English words, the sound changes that eliminate them will be broadly applicable. Hence your sound change that turns all the imaginary kw in PIU into m, w, or k in PU. But it's not convincing for the same reasons that Greenberg isn't convincing (he once postulated *malq'wa as a Nostratic root for "milk" or "suck" because you could reconstruct any word you wanted from it).

[Tropylium]

if we look at the reconstructed
Uralic numbers, we find more forms that look eerily alike:

PU: *(w)ük(t)i one (w reflected in Mordvinic)
PU: *käktä two
PU: *witte five
PU: *kutte six

Some of this "eerie similarity" between these might be not because they come from the diversification of a single root, but rather from containing a common numeral suffix. There's a clear doublet with the forms for "one": forms like Finnish yksi : yhte- suggest *üktə, while a few others have no trace of a *t: Mordvinic *vejkə (from something like *ükə-kkV; NB *ü- > *wi- > *ve- word-initially is regular), Mansi *äkʷə < *ükkV.

Now, Mari has two different forms of each numeral: an attributive short form ("one noun"), and a predicative longer form ("there is one"). The predicative ending is /-ət/. There's a similar attributive/predicative contrast for '2' in the Ugric languages, marked again by a /t/ element + also the usual dual ending *-kA: e.g. in Hungarian, attributive két < *kätV < *kättV, predicative kettő < *kättəɣ < *kättV-tV-kä. So at least some part of this system probably comes from proto-Uralic, and the predicative marker was likely *-t- or *-tV. This in mind, a good explanation for the situation with "1" will be to assume original attributive *ükə, predicative *ükə-tə > *üktə.

The words for "5" and "6" might, then, also contain this suffix, since they also end in *-tə (Finnish viisi : viite-, kuusi : kuute-). That only leaves *wiC-, *kuC-. Since PU allowed *-kt- just fine, this final -C- was probably not **-k- (though there would be a few other options).

As for "2", the usual reconstruction **käktä is actually a compromise mashing together a few distinct sets of forms: western languages point to *kaktV, eastern ones best to *kättä or *kettä, and Permic (with /kɨk/) to something else yet, perhaps *kukkV.

The 's' in the word (s)weks was later added by analogy with the Semitic word for six.

More probably: by analogy with the PIE word for "7".

[Howl]

It has often been speculated that the IE words for 4 (*kʷetwores) and 8 (*Hoḱtṓw)
are related. If that is true, they should come from an earlier form like **kʷoktw.
In the word for 4 the 't' was elided, and a suffix was added. 
In the word for 8 the inital kʷ was lenited to a laryngeal.

This is the Greenberg method: reconstruct a proto-language by combining all relevant segments, then weed out the ones you don't want with sound changes.
Proto-Anglohispanic *waguater
English medial gw drops, adjacent identical vowels coalesce > water
Spanish final -ter elides, initial approximants eliminated > agua
And these sound changes will work when applied to lots of other words, because when you're adding extra -ter to all the Spanish words or extra -gw- to all the English words, the sound changes that eliminate them will be broadly applicable. Hence your sound change that turns all the imaginary kw in PIU into m, w, or k in PU. But it's not convincing for the same reasons that Greenberg isn't convincing (he once postulated *malq'wa as a Nostratic root for "milk" or "suck" because you could reconstruct any word you wanted from it).

Your example is a straw man. We know the documented history of these English and Spanish. We have credible reconstructions of both agua and water up to the PIE level.

But when you are looking at two languages that may be related, you start at zero. You do not know if two words are related. So you try to figure out the sound correspondences. This is speculative work by nature. The following article explains this much better.

https://protouralic.wordpress.com/2017/ ... nguistics/

A more detailed workflow for historical linguistics, if starting from zero, would therefore look something like the following:

1. Acquire data; sort out some initial vocabulary comparisons that look promising.
2. Analyze sound correspondences; use these to look for more comparisons.
3. Look at the big picture to see if some particular subset of languages should be indeed considered related.
4. Attempt reconstructing the proto-language.
5. Use the proto-language POV to clarify the status of issues like problematic etymologies, possible external relatives, or possible subgroups.
6. Use modified analyses of data to improve the proto-language reconstruction.
7. Iterate 5 and 6 until you’ve run out of insights to gain from the data.

This could also work as a kind of a typology of how far along research on a particular language family is. To date, I don’t think any language family has yet exhausted stage 7. Most are stuck in limbo somewhere around stage 3; only a few have reached stage 5, and Indo-European might be the only one to have indisputably gone through one cycle of stage 7. Big disputed hypotheses grouping well-accepted families together can probably be divided according to if they’re closer to stage 1 (e.g. Amerind, Nilo-Saharan) or stage 2 (e.g. variations of Nostratic). Smaller disputed hypotheses often seem to be either at stage 2 or stage 4, depending on who you ask (e.g. Altaic). (To which I might reply: if these really are supposed to be already at stage 4, bring on stage 5, please.)

But since you mentioned water:
The PIE form is *wódr̥/*wédn̥ which is composed of a root *wed and a r/n stem suffix.
PU has a very similar word for water: *wete-.
Is it so crazy to think that there may be a relationship? Is it more crazy than the (well attested) relationship between English 'water', Danish 'vand' or Modern Greek 'idor' ?

Or your milk word:
PIE: *h₂melǵ- 'milk'
PU: mälke (mälγe) 'breast'
Again, is it so crazy to think there may be a relationship? Is it more crazy than the (attested) relationship between Modern Greek amergo 'to milk', Persian mâlidan 'to rub/to massage/to smear' or Irish bleacht 'milk, milk yield'?

[Howl]

Some of this "eerie similarity" between these might be not because they come from the diversification of a single root, but rather from containing a common numeral suffix. There's a clear doublet with the forms for "one": forms like Finnish yksi : yhte- suggest *üktə, while a few others have no trace of a *t: Mordvinic *vejkə (from something like *ükə-kkV; NB *ü- > *wi- > *ve- word-initially is regular), Mansi *äkʷə < *ükkV.

Now, Mari has two different forms of each numeral: an attributive short form ("one noun"), and a predicative longer form ("there is one"). The predicative ending is /-ət/. There's a similar attributive/predicative contrast for '2' in the Ugric languages, marked again by a /t/ element + also the usual dual ending *-kA: e.g. in Hungarian, attributive két < *kätV < *kättV, predicative kettő < *kättəɣ < *kättV-tV-kä. So at least some part of this system probably comes from proto-Uralic, and the predicative marker was likely *-t- or *-tV. This in mind, a good explanation for the situation with "1" will be to assume original attributive *ükə, predicative *ükə-tə > *üktə.

The words for "5" and "6" might, then, also contain this suffix, since they also end in *-tə (Finnish viisi : viite-, kuusi : kuute-). That only leaves *wiC-, *kuC-. Since PU allowed *-kt- just fine, this final -C- was probably not **-k- (though there would be a few other options).

Thanks for your explanation! I really appreciate it. Even though it means for me that I now have to shelve this idea.

[jal]

Your example is a straw man. We know the documented history of these English and Spanish. We have credible reconstructions of both agua and water up to the PIE level.

No, a straw man is something attacking something you didn't propose. This is just a comparison to something hypothetical, that could follow the same path as what you propose.

But when you are looking at two languages that may be related, you start at zero.

No you definitely don't. You look at the way languages that we do know are related. Proposing sound correspondences that are based on a whole heap of ellision is not a good method, for exactly the reason that Hydroeccentricity explained with a nice example.

This is speculative work by nature.

Some speculation is more equal than others.

The following article explains this much better.

I don't think we need lecturing on how historical linguistics work.

Is it so crazy to think that there may be a relationship?

Yes. Because you have nothing but the observation they sound alike. You need to read up on [url=http://www.zompist.com/chance.htm]Zompist's article[/quote] on apparent sound correspondences.


JAL

[Salmoneus]

Could someone just point out that numerals are perhaps the worst possible set of roots to reconstruct the fine details of? Their extremely common use (and in inflecting languages their common use in inflected forms) can produce a lot of irregularity, and the practice of counting tends to produce secondary similarities between nearby numbers.

As an extreme example (from a set of numerals only used for counting, so more exposed to this): is -era in Borrowdale counting a numeral "suffix"? [and analogous forms across the British isles] No, it's just spread from the -er in the number 4, probably because that's the only bisyllabic numeral, and the second syllable has just been exported to the numbers 3, 6, 7, 8 and 9 by analogy. [yan, tyan, tethera, methera, pimp, sethera, lethera, hovera, dovera, dick; "dovera" seems to have been created entirely from bits of other numbers...]

The same thing also commonly happens in a less extreme form in numeral systems that aren't just used for counting. So, for instance, PIE kw- in "4" became Germanic f-, presumably due to influence from adjacent "5"; is that also why the second stop in "5" likewise went from labiovelar to labial? And then the medial *d in "4" dropped, and then in Old Norse a suffix was stuck on the end. [god only knows where the pronunciation of modern English "one" comes from...]

Comparing numerals is useful when looking for general similarity between languages, because they tend not to be replaced. But it's not very useful when looking at fine details, and particularly not when comparing numbers in the same numeral set, as they may have influenced one another irregularly.

[Nortaneous]

We have a pretty good idea of where the pronunciation of "one" comes from -- it's a relic of a sound change that otherwise didn't stick:

As it happens there is a late ME tendency for [j] to be inserted before long mid front vowels and, a little less commonly, for [w] to be inserted before word-initial long mid back vowels. This glide insertion only happened in initial syllables, and usually only when the vowel was word-initial or the word began with [h]; but there are occasional examples before other consonants such as John Hart’s [mjɛ́ːn] for mean. The Hymn of the Virgin (uncertain date, 14th century), which is written in Welsh orthography and therefore more phonetically transparent than usual, evidences [j] in earth. John Hart records [j] in heal and here, besides mean, and [w] in whole (< OE hāl). 17th-century phoneticians record many instances of [j]- and [w]-insertion, giving spellings such as yer for ‘ere’, yerb for ‘herb’, wuts for ‘oats’ (this one also has shortening)—but they frequently condemn these pronunciations as “barbarous”. Christopher Cooper (1687) even mentions a pronunciation wun for ‘one’, although not without condemning it for its barbarousness. The general picture seems to be that glide insertion was widespread in dialects, and filtered into Standard English to some degree during the 16th century, but there was a strong reaction against it during the 17th century and it mostly disappeared—except, of course, in the word one, which according to Dobson the [wʌ́n] pronunciation becomes normal for around 1700. The [nʌ́n] pronunciation for ‘none’ is first recorded by William Turner in The Art of Spelling and Reading English (1710).

[Hydroeccentricity]

Howl, that's not how strawmen work. I illustrated how this method could be applied. The fact that we already know the relationship between English and Spanish is what makes the example obviously incorrect. Pointing out that the relationship between English and Spanish cannot be demonstrated in this way is the whole point of the example.

As for your milk and water examples, you have explained the flaw in your reasoning better than I ever could. We know that water and idor are related, not because of, or even in spite of, their similarity or difference in phonological form, but because they adhere to regular sound changes, sound changes which do not need to combine and eliminate extra segments in an artificial manner do derive a proto-language. There is infinitely more evidence for "wheel" being related to "chakra" than any of your examples. Pointing to similar sounding words and saying “is it so crazy?” is exactly what historical linguists don't do.

It is entirely possible that PIU existed. Of course there would be speculative work involved at some stage in reconstructing it. But what you're doing right now is not rigorous science. It is the equivalent of an aspiring doctor treating patients with voodoo charms.

[Tropylium]

The PIE form is *wódr̥/*wédn̥ which is composed of a root *wed and a r/n stem suffix.
PU has a very similar word for water: *wete-.
Is it so crazy to think that there may be a relationship?

Well, it's not crazy; they're definitely fodder for a hypothesis that PIE and PU are related. It's one of the starting points everyone has latched on for, I don't know, maybe 150 years by now, after all.

OK, 'water' looks related. How would, say, 'fire' fare? Generously enough, we find two reasonably well-established roots for 'fire' in both IE and Uralic:
– PIE *h₁n̥gʷnis 'fire (animate)'
– PIE *peh₂wr̥ 'fire (as substance)'
– PU *tulə (widespread)
– Ugric *tüɣVtV
Whoops: we would have had four different possibilities for a match, and yet none of these works.

How about 'wood'? PIE *doru ~ PU approx. *puwə; no match. 'Earth'? PIE *dʰegʰōm ~ PU *muďa, clearly no match. 'Stone'? PIE *h₂eḱmon- ~ PU either *kiwə or *pije — maybe if you squint just right (PIU *xikmV, *km > *w in Uralic??) and ignore that the PIE form is though to derive from 'sharp'.

That's the annoying thing about Indo-Uralic: there are a handful of what seem like very easy pickings, but it seems nearly impossible to go deeper than that.

[Soap]

Just a comment, PIE just seems to have a lot of long roots. 4 consonants just to say "fire"? (assuming laryngeals are consonants, which almost everyone now agrees). The root for milk has 4 consoinants too, and the root for "four" has either three or four depending on how you count. If most of its words for basic concepts are compounds, it's no surprise to me that there are hardly any cognates.

I do believe that U and PIE are related, based on strong morphological resemblances as detailed further upthread and in the separate PIE thread, but Ive always been struck by how surprisingly low the number of likely cognates is. Perhaps the PIE lexicon was spoiled somehow? Winfred Lehmann reconstructed an early stage of PIE with a phonology consisting entirely of consonants, with neither vowels nor a stress accent on. If so, the vowels of Uralic are useless in reconstruction of a relation, unless they can be shown to somehow affect the consonants.

Even more moderate ideas of PIE phonology acknowledge that there was an ablaut system and that /e/ was by far the most ocmmon root vowel, so the vowels of Uralic are still mostly irrelevant since it seems that there was a major collapse at some point on the IE side only. It could be that this caused the IE lexicon to be rebuilt with heavy reliance on compounds and derivation even for simple concepts.

[jal]

Just a comment, PIE just seems to have a lot of long roots. (...) If most of its words for basic concepts are compounds, it's no surprise to me that there are hardly any cognates.

1) What's "long"? Is there a linguistically agreed on concept of "long" vs. "short" roots? And how common or uncommon would either be, cross-linguistically? For all we now, four consonants is bog-standard across the world's languages.
2) Words needn't be compounds even assuming four consonants is long for roots. There could be affixes, reduplication with sound changes, borrowings, and so on.
3) I still would find it surprising there are hardly any cognates, even with compounding and the like. Especially amongst the "short" roots, and stuff like pronouns, counting words etc.

I do believe that U and PIE are related, based on strong morphological resemblances

That could be an areal feature, or just chance.

Perhaps the PIE lexicon was spoiled somehow?

Why not PU?


JAL

[Nortaneous]

Lexical corruption or mass replacement seems more likely in PIE than PU, just because PIE has the monosyllabic root deal and PU doesn't.

How much do we know about the emergence of that sort of system? Semitic triconsonantal roots in the AA context, that sort of thing.

[Howl]

OK, 'water' looks related. How would, say, 'fire' fare? Generously enough, we find two reasonably well-established roots for 'fire' in both IE and Uralic:
– PIE *h₁n̥gʷnis 'fire (animate)'
– PIE *peh₂wr̥ 'fire (as substance)'
– PU *tulə (widespread)
– Ugric *tüɣVtV
Whoops: we would have had four different possibilities for a match, and yet none of these works.

How about 'wood'? PIE *doru ~ PU approx. *puwə; no match. 'Earth'? PIE *dʰegʰōm ~ PU *muďa, clearly no match. 'Stone'? PIE *h₂eḱmon- ~ PU either *kiwə or *pije — maybe if you squint just right (PIU *xikmV, *km > *w in Uralic??) and ignore that the PIE form is though to derive from 'sharp'.

That's the annoying thing about Indo-Uralic: there are a handful of what seem like very easy pickings, but it seems nearly impossible to go deeper than that.

It's not as easy as reconstructing a common parent to Latin, Greek and Sanskrit, sure.

There is semantic shift. So you simply can't pick the word 'fire', open an Uralic and a IE dictionary and expect to find the first words to be possible cognates. You must also look at words like 'burn' (FU: äŋɜ, FP: porɜ), 'warmth', 'heat. (U päwe). And then *h₁n̥gʷnis and *peh₂wr̥ suddenly don't look so daunting.

Another problem is that both proto-Uralic and proto-IE are reconstructions. They are only educated guesses about how that language must have sounded thousands of years ago. And that creates its own issues.

[Salmoneus]

There is semantic shift. So you simply can't pick the word 'fire', open an Uralic and a IE dictionary and expect to find the first words to be possible cognates. You must also look at words like 'burn' (FU: äŋɜ, FP: porɜ), 'warmth', 'heat. (U päwe). And then *h₁n̥gʷnis and *peh₂wr̥ suddenly don't look so daunting.

Very insightful. And have you considered extending this to the Malayo-Polynesian languages? PMP "bangi" (to cook over a fire) looks related, no? And "dangdang" (to warm by a fire) - PMP has plenty of little prefixes like those b- and d-s, and reduplication is common too. What about Old Javanese's "apwi", "fire"?
come to think of it, austonesian generally shows competition between two words for "water": cognates of "danum" (clearly related to the old PIE river-name "danu-" (as in Danube, Don, the ossetian word for "water", etc), and cognates of "wahir", as in Wedau "waira" and fijian "vaitupu".
I think we're onto something here!

[jal]

suddenly don't look so daunting.

Look, you clearly don't know the way historical linguistics are meant to be done, or just don't care, and that's fine. Just don't expect anyone here to agree with you, and preferably stop wasting our time.


JAL

[Tropylium]

There is semantic shift (…)

Sure, but that doesn't actually help. Semantic shifts are one-by-one with no overarching systematic patterns. (There's some typology to it, but not enough to actually predict what has changed meaning to what when and where.) They only add assumptions to the system of comparisons. Add enough of these and you can compare anything with anything (is PU *padV 'wall, dam' perhaps akin to PIE *ped- 'foot', through an intermediate meaning 'basis, foundation'? it might be).

Consider nontrivial semantic changes in languages with a well-recorded history; e.g. Modern German Kopf 'head' from Latin cuppa 'cup'. Why do we believe that this was a real change, and not just two unrelated words that happen to look similar? A big part of this is because the sound changes happen to work regularly. Without this, all you'd have to go on would be vague similarity, which is just plain not good enough.

The principal way to make progress in comparison from the mere look-alike stage is to identify some non-trivial sound changes. If we have, say, word-initial examples of PIE *h₂- ~ Uralic *k- in isolation, they could always be simply analyzed as loans, since PU did not have word-initial *x- or *ħ- or anything. You could also assume a PIU *x that then merges with *k in Uralic. But suppose that we find something along the lines that PU *ka- corresponds to PIE *h₂a-, while PU *kä- corresponds to PIE *ka-? We would now be able to propose a different approach: PIU did not have a separate *x, but instead *k becomes PIE *h₂ before PIU *a. This gets along with fewer PIU phonemes and makes specific predictions about what's related and what is not; e.g. anything with IE *ka- ~ Uralic *ka- will then be better considered a loan or a mere chance resemblance.

[Howl]

The principal way to make progress in comparison from the mere look-alike stage is to identify some non-trivial sound changes. If we have, say, word-initial examples of PIE *h₂- ~ Uralic *k- in isolation, they could always be simply analyzed as loans, since PU did not have word-initial *x- or *ħ- or anything. You could also assume a PIU *x that then merges with *k in Uralic. But suppose that we find something along the lines that PU *ka- corresponds to PIE *h₂a-, while PU *kä- corresponds to PIE *ka-? We would now be able to propose a different approach: PIU did not have a separate *x, but instead *k becomes PIE *h₂ before PIU *a. This gets along with fewer PIU phonemes and makes specific predictions about what's related and what is not; e.g. anything with IE *ka- ~ Uralic *ka- will then be better considered a loan or a mere chance resemblance.

That is also the kind of analysis I'm trying to do. First for the vowels and the laryngeal(s), which are simpler but definitely not trivial. Etherman's old thread (viewtopic.php?f=10&t=33695) also contained a lot of useful information for me.

Basically:
The 'vowel color' of the PIE laryngeal mostly corresponds to the PU vowel (others have made the same observation).
PU i-ü corresponds to the ei-oi-i series unless lowered (which regularly happened before resonants).
PU u corresponds to the eu-ou-i series unless lowered (also regularly before resonants)
PU e becomes e-o-ø
PU a becomes e-o-ø but is very often accompanied by h2.
PU ë becomes e-o-ø but is very often accompanied by h1.
PU o becomes e-o-ø but is sometimes accompanied by h3.
- but o sometimes behaves a 'a' or 'u'
PU ä behaves as either e, a or i

There seems to be no difference in the correspondences of the different laryngeals h1, h2, h3 to PU consonants except the vowel they are adjacent to. The PIE laryngeal(s) correspond to PU k, č, the PU 'laryngeal' x (if such a thing existed) or nothing at all (mostly h1 and h2).

[Tropylium]

That is also the kind of analysis I'm trying to do. First for the vowels and the laryngeal(s), which are simpler but definitely not trivial. Etherman's old thread (viewtopic.php?f=10&t=33695) also contained a lot of useful information for me.

Basically:
The 'vowel color' of the PIE laryngeal mostly corresponds to the PU vowel (others have made the same observation).
PU i-ü corresponds to the ei-oi-i series unless lowered (which regularly happened before resonants).
PU u corresponds to the eu-ou-i series unless lowered (also regularly before resonants)
PU e becomes e-o-ø
PU a becomes e-o-ø but is very often accompanied by h2.
PU ë becomes e-o-ø but is very often accompanied by h1.
PU o becomes e-o-ø but is sometimes accompanied by h3.
- but o sometimes behaves a 'a' or 'u'
PU ä behaves as either e, a or i

This is not trivial as stated, but it is trivial in that everyone already assumes that PIE ablauting single vowels come from a single unalternating proto-vowel, let's say *a, while ablauting diphthongs come from *i and *u; and, since PIE has no *CVyR or *CVwR, we will also assume that pre-PIE *iR and *uR give something else. Then we simply hypothesize trivial equivalences like PU *i, *ü = pre-PIE *i; PU *u = pre-PIE *u. You could put those together from just looking at the phoneme inventories and root structures of PU and pre-PIE, without looking at any data whatsoever.

Vowel systems like that of PU are however extremely volatile. It's pretty much implausible that the PU vowels would have a unique single corresponding PIE equivalent.

For comparison, here's the development of *i and *ü in various Uralic languages:
– by default remain as /i/ and /y/ in Finnic, but also *ijə *ü{j w}ə *ijä *ü{j w}ä > /iː/ /yː/ /eː/ /øː/, *iwä > /yvä/, and *ix > /ei/; *iCü > /yCy/ and *iw > /iy/ > /yː/ late on in Finnish;
– both merge as *ë in Proto-Samic, which then however proceeds to split the fuck up into /ɑ/, /ɑː/, /ʌ/, /ɤ/, /i/, /y/ etc. depending on the context and the language;
– both generally merge as /e/ in Mordvinic, though a few cases have /i/, /o/ or /u/, and word-initial *ü > /ve/;
– Mari has /ɪ/, /ʏ/, except /i/, /y/ in monosyllables; labiality is extremely unstable, depending on adjacent consonants;
– Permic has mainly *i > /i/ and *ü > /ɨ/, but also a few cases of the inverse with conditions still not clear on (*i > /ɨ/ or *ü > /i/), as well as cases with > *e > /e/, /ɤ/, /o/; also, later on /ɨ/ > /i/ often when adjacent to palatals;
– Hungarian has by default *i > /e/, *ü > /ø/, but also *wi > *ü > /ø/; *ij *iɣ *üɣ > /iː/ ~ /i/, /yː/ ~ /y/, /yː/ ~ /y/; *ijə *iɣə *üɣə > /eː/ /øː/ øː/.
So already from just *i you get about four to ten different sets of vowel correspondences between any two modern languages. Also, already with just 4-5 languages, there will be no recurring cases whatsoever that have the exact same vowel outcomes in all of them.

So by "non-trivial sound changes" I don't just mean anything more complex than exact identity. I mean cases where, say, PIU *i gives PU *ü under some specific identifiable conditions, or PIE *ye (~ *yo ~ *i) under some other specific identifiable conditions…

[Howl]

That is indeed a good point. In any language group with that much vowel qualities, the vowels tend to be unstable. See for example the development of the Romance languages (Latin had different vowel qualities for short and long vowels). And the Germanic languages also offer plenty of examples like the Great Vowel Shift of the English language.

But I'm running into the same problem as everyone. Too little data.. I started looking into this because I wanted more data for my vowel model, especially the development of the laryngeals. But I find Indo-Uralic interesting in its own right. And getting more data requires a lot of time. And better dictionaries. For example, Uralonet (UEW) is great for searching, but their reconstructions are problematic. I'm still wondering what they mean with O-breve and O-breve-umlaut. For now, I just replace that with a schwa in my data.

Also, even if someone makes a Proto-Indo-Uralic reconstruction, it won't mean that everyone will suddenly see PIU as a real thing. It will probably end up in a situation similar to Proto-Altaic. Yes, it is possible to make some reconstruction, but how much **akwater will it have?

One example of why I'm not at all optimistic is PU ś.
I think it corresponds to PIE consonant clusters involving s, like sk, sp, st:

PU: śota, śoδa, śoδ̕a 'fight (n), struggle, war; fight, struggle (vi)' UEW#1597 FW
PIE: sperdʰ 'to compete, contest, struggle'

PU: śakkɜ (śukkɜ) 'piece, bit, part ' UEW#924 Ug ??FU
PIE: (s)tewg- 'to break, piece' (cognate germ. Stück)

PU: śu-re FW 'mush, groats, pulp' UEW#1601
PIE: (s)poH(y) 'foam'

But with the IE s-mobile phenomenon, this means ś can correspond to anything.
And then you can make correspondences like:

PU: śiδä (śiδä-mɜ), śüδä, śüδä-mɜ U 'heart ' UEW#960 U
PIE: ḱerd 'heart' from earlier **sḱert ??
(or PIE: psten 'breast, teat')

PU: śänčɜ 'knee ' UEW#949 U
PIE: kenk ‘knee-cup, heel’ from earlier **skenk??

PU: śulɜ U 'vessel ' UEW#982 U
PIE: pel 'container, vessel, dish' cognate Latin pelvis, from earlier **spel??)

A couple more sound changes like this, and critical linguists will be tearing PIU to pieces.

[Tropylium]

Uralonet (UEW) is great for searching, but their reconstructions are problematic. I'm still wondering what they mean with O-breve and O-breve-umlaut.

It's not O breve, it's an OU digraph, and they stand for "some back vowel of unknown quality" and "some front vowel of unknown quality". Compare below in large size:
ȣ ȣ̈

This is often also a good sign of an unreliable "junk" etymology. The UEW actually notates these fairly well: the reconstruction level is given as bolded (U) for good realiable reconstructions, unbolded (U) for possible ones, and attached with a question mark (? U) for uncertain ones.

The biggest immediate problems in your comparisons below is not actually the phonetics (*sP > *šP > *ś is entirely possible, as per German), as much as semantics and morphology:

PU: śota, śoδa, śoδ̕a 'fight (n), struggle, war; fight, struggle (vi)' UEW#1597 FW
PIE: sperdʰ 'to compete, contest, struggle'

'Struggle' for Uralic is a mis-translation of German 'Kampf'. The original meaning was clearly just 'war, fight'. On the IE side, it's 'race, compete'. This doesn't leave enough common ground that I'd want to rely on this.

PU: śakkɜ (śukkɜ) 'piece, bit, part ' UEW#924 Ug ??FU
PIE: (s)tewg- 'to break, piece' (cognate germ. Stück)

Nothing obviously wrong here, but both PU and PIE have like a dozen different terms for 'break, piece, bit', so accidental similarity is very likely (also within each indvidual family).

PU: śu-re FW 'mush, groats, pulp' UEW#1601
PIE: (s)poH(y) 'foam'

'Mush' as in 'porridge' in Uralic, not 'any kind of a mushy substance'. 'Pulp' is a mis-translation of the original German gloss 'Brei'. Also, you cannot just ignore the 2nd syllable in Uralic.

But with the IE s-mobile phenomenon, this means ś can correspond to anything.

S mobile is a prefix; you cannot particularly plausibly derive plain stops from earlier *sP-. Mis-segmentation is sometimes possible(gruntled from disgruntled etc.) but you need to first have evidence for the non-mis-segmented starting point.

PU: śänčɜ 'knee ' UEW#949 U
PIE: kenk ‘knee-cup, heel’ from earlier **skenk??

The widespread and well-established PU word for 'knee' is *polwə, the widespread and well-established PIE word is *ǵonu, so you'd need to assume a couple of parallel semantic shifts to get anywhere with these. Also, off the cuff I can't find any references for a PIE root for 'knee cup, heel' of this shape.

Interestingly you can find a fairly similar word with clear *sk- in Germanic (English shank etc.). This is from the root that LIV gives as *(s)keng- 'to limp' however, which is semantically only getting further off course. Being vaguely related to legs is not good enough.

PU: śulɜ U 'vessel ' UEW#982 U
PIE: pel 'container, vessel, dish' cognate Latin pelvis, from earlier **spel??)

This is clearly a junk etymology on the Uralic side. The Estonian looks like it's just the genitive of sulg 'pen, corral' (though I can't find the meaning 'trough' in modern Estonian dictionaries); the Udmurt looks like it might be derivative from /śul/ 'sled runner' (earlier 'pole', per other cognates such as Fi. salko) (so 'pole-ie' > 'long spoon' > 'long trough'); the Selkup is, as already given in the notes, probably from Turkic; this just leaves Enets and Nganasan, and they don't even correspond to each other.

All this only leaves the "heart" case, and it would seem that we could just as well assume *ś ~ *ḱ in that.

[WeepingElf]

What Howl does seems to be quite similar to what I called "system comparison" until I realized that it was fallacious. "System comparison" was the comparison of phonological systems without the drudgery of finding lexical cognates. This can easily go wrong badly. Consider Greek and Armenian. These two languages have similar-looking stop systems, each with aspirated, voiceless and voiced stops. By "system comparison", one could easily arrive at such "sound correspondences" as Arm. th = Gk. th, Arm. t = Gk. t, Arm. d = Gk. d. As is well-known, though, these are actually wrong, it is Arm. th = Gk. t, Arm. t = Gk. d, Arm. d = Gk. th. How to tell? Lexical cognate sets.

[Howl]

I have though long and hard about the criticism. What I posted was ongoing exploratory fast-and-loose dictionary comparison. This is of course can't withstand the critical debate that is normal within historical linguistics. And this approach is not very resistant to any prior assumptions that may come from 'System Comparison'.

I have thought of a new approach that is more systematic and meticulous, and can deal with small changes in semantics in a defensible way. It works like this:

1. Define a 'semantic cluster' of related meanings in which to search for possible cognates.
2. Create a list of all roots/words on both sides for that 'semantic cluster'.
3. Search for possible cognates.

By having the list of all roots within a 'semantic cluster', you know (1) what the alternatives are and (2) how big the pond is in which you are fishing for a match.

[mèþru]

By "system comparison" pretty much every Sprachbund is related. Also, French is obviously closer related to German than it is to Spanish!

[kanejam]

Also, even if someone makes a Proto-Indo-Uralic reconstruction, it won't mean that everyone will suddenly see PIU as a real thing. It will probably end up in a situation similar to Proto-Altaic. Yes, it is possible to make some reconstruction, but how much **akwater will it have?

Definitely. Just for a little bit of perspective, here is a very substantial proposal for Proto-Korean-Japonic with plenty of proposed cognates, yet Proto-KJ is still very tentative and controversial. If you want to see some real linguistic somersaults, check out the reconstructed numerals near the end.