OneLaryngealVocalicTheory.htm
ONE LARYNGEAL
(VOCALIC) THEORY
of Proto-Indo-European
PALATALIZATION and VELARIZATION
۩ dedicated to the memory of Winfred P. Lehmann ۩
(Nostratic Hypothesis)
by Patrick C. Ryan
2-12-2001
(rev. 6 / 8 / 2008)
The purpose of this short essay is to propose as a hypothesis that the so-called
'Laryngeal' Theory, which most PIEists currently endorse,
should be replaced by
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The Vocalic Theory
According to the Vocalic Theory, the qualities of the PIE long vowels ( *e: / *a: / *o: ) and the quality of the short vowel *a can be better explained by assuming, that, in the Pontic stage of Nostratic, i.e. pre-PIE:
1) there was a single 'laryngeal' that had the phonological value of [h]; and
2) the retention in PIE of short vowel qualities ( [ *e / *a / *o ] ), originating in pre-PIE, was due to their being lengthened by [h]: ( *e: / *a: / *o: );
3) which lengthened the short vowels by being placed either immediately before or after them;
4) in addition, that that were three naturally long vowels ( *e: / *a: / *o: ) which arose through compensation when the aspiration of aspirated voiceless stops ( *p(h), *t(h), *k(h)(1) ), aspirated spirants ( *fh, *sh, *xh ), aspirated nasals ( mh, *nh, *nkh ) and the aspirated rhotic ( *rh ) —— was relinquished; and these consonants merged with their unaspirated counterpart voiceless stops, spirants, nasals, and rhotic;
5) PIE short *a has only one source: the 1)) shortening of PIE *a: according to the Law of Phonological Entropy, v. infra;
6) since all pre-PIE short *a had become *A, v. infra;
7) or 2)) shortening due to the closing of a formerly open syllable ending in a:.
Historical Development
PIE is ultimately descended from an ancestor, which, I term the Proto-Language.
The Proto-Language had three vowels: E, A, and O, which notate a front, central, and back vowel at any height: low, mid, or high.
After passing through a number of other nexus, which seem not to have affected vowel quality, PIE and PAA came under the nexus Nostratic, in which the three inherited vowels were realized as: *i, *a, *u.
During the final Pontic stage of Nostratic, in pre-PIE only, the distinction among Nostratic *?, *h, and *ħ was lost; and all merged into pre-PIE *h, with the exception of some Anatolian languages which retained *? written as <Ø>.
Nostratic *i, *a, *u, which had become pre-PIE *e, *a, and *o during its Pontic stage, which were lengthened by a preceding or following avocalic *h ( which is termed 'laryngeal': *H ), became pre-PIE *e:, *a:, *o:. These lengthened vowels were not reduced to *A(blautvokal) as were all short vowels. Lexical integrity and continuity was maintained by the introduction of a palatal glide ( *y ), no glide, or a velar glide ( *w ) to indicate former *e, *a, *o but also redundantly for *e:, *a:, *o:. When the palatal and velar glides subsequently disappeared (v. infra), the quality of the lengthened vowels remained intact in PIE.
In a further development, during the Pontic stage of Nostratic, shared by both pre-PIE and pre-PS ( Proto-Semitic and Hieroglyphic Egyptian branches of pre-PAA), all short vowels became *V(owel) [or *A{blautvokal}], which may have been realized as [a] ( central low — possibly with a stress-unaccented schwa {ə} allophone ).
1. In PIE, *A became *é, *ò, *° ( currently written *e, *o ) or *Ø, according to the Ablautsstufe or stress-accent-grade required by the workings of the stress-accent,
which stress-accented the root vowel in a *CÁC(V) form
for a singular nominal or punctual (momentary) verbal root (citation form);
or the final vowel (*CACÁ)
for a plural nominal or durative (non-momentary) verbal root;
and moved the stress-accent to the right one syllable for every additional formant added:
CÁCA + NA 
*CACÁ(-)NA.
Similarly, lengthened vowels had a reduced grade showing the same vowels as short, and a zero-grade of [*ə] ( 
[ *ɦ ] ).
a. The glides subsequently disappeared in PIE, leaving only dorsals (*g^, *g^h, *k^, *k^(h)) and dorsal nasals ([n]g^, [n]k^) palatalized by *y, and notated here by ^; and a few apicals (*dw, *tw, *dhw, *t(h)w, *sw) and dorsal nasals (*[n]gw, *[n]kw) velarized by *w.
2. In PS, a branch of PAA, the glides and no glide + *A became *i, *a, and *u; and the glides were eliminated.
a. In PS, Proto-Semitic, all vowels (no phonemic long vowels in PAA) were merged into *a but *i and *u (as well as *Ø) lived on as allophones of *a employed to mark various grammatical forms (vowel patterning) but no longer lexical (semantic) distinctions; it is possible that some root nouns retained original *i(:), *a(:), and *u(:) but not conclusively proven.
3. In other Nostratic-derived languages like Sumerian, the Nostratic vowel qualities of *i, *a, *u were retained as i, a, u.
These developments produced a vowel inventory for Pontic and pre-PIE of *e:, *a:, *o:, and *A (not including the impure vowels *i and *u derived from avocalic *y and *w).
The 'Laryngeal' Theory
(Wikipedia has a rather good description of the 'Laryngeal' Theory.)
First, it must be commented that 'laryngeal' is hardly the proper term for the theory as it is presently conceptualized since the only two laryngals, [?] and [h], that have been consistently proposed in the past as one of the three or four 'laryngeals', are today replaced by [x] and [xw], dorsal fricatives.
Second, it betrays the inherent weakness of the 'laryngeal' theory that after so many years, even its proponents can scracely agree on the phonological nature of the usual three 'laryngeals': H1, H2, and H3 (N.B. I will notate the laryngal fricative I propose to replace these three as H, with no subscript).
The 'Laryngeal' Theory was ostensibly originated to address several anomalies(2) in PIE. This it did in a splendid way but what has not been generally noticed is that the majority of the solutions could have been made possible by supposing the 'laryngeal' to have simply been a [h]-like consonant that subsequently disappeared —— without relying on the so-called 'coloring' imparted reputedly by H2 ('a-coloring'), H3 ('o-coloring'), and sometimes H1 ('e-coloring' but more often 'neutral').
Thus, the great majority of the solutions can also be effected more simply with a single laryngal as Szemerényi noticed before me (v. infra), [h], which the Vocalic Theory proposes, and notates as *H.
The Characteristics of 'Coloring'
According to the 'Laryngeal' Theory, *H2 imparts an *a-coloring to preceding é (but not to *e: or *o / *o:) and does not lengthen it; lengthening is accomplished by a following 'laryngeal'. The most coherent theory is that *H2 has that affect because it was phonologically [ħ], a pharyngal fricative, which has the property of coloring a front vowel in the same syllable by lowering and causing it to be retracted, producing an a-like quality; this happens today in most Semitic languages but results in an allophone not a new phoneme where front [æ] acquires the central allophone [a].
This ostensibly sensible proposal fails miserably because *H2 does not 'color' [*é:], which is, after all, simply [*e] + [*e]. If *H2 actually 'colored' anything, it should 'color' [*e:] —— or, at the very least, its first component: [*e] so that a 'broken' vowel was formed ([**ae]); that it fails to do so, proves conclusively that it can only lengthen vowels; and, with any already lengthened vowel, its actual effect is non-existent if we do not entertain triple-length vowels for PIE.
But it has also been supposed by some that *H2 does 'color' *o to *a. This makes no rational sense at all because while [*ħ] might have caused *o to be lowered, it can hardly be expected to 'extract' the tongue farther forward from the back position of the [*o] when, at the same, it is claimed to have 'retracted' [*e] to [*a]; no phone can reasonably do both.
Yet another opinion is that *H2 does not 'color' *o to *a because *o stems from *a:, presumably in earliest IE as the result of vŗddhi. I have stated my reasons for not accepting vŗddhi for (P)IE below.
The phonological characteristics of *H3, the *o coloring 'laryngeal', are similarly ill-conceived. Under the rubric of a phonological [*xw], it is supposed that *e, a front vowel, can be retracted not one but two vocalic articulatory positions:
FRONT CENTRAL BACK
.
This is a feat no phone, of which I have knowledge, is capable of completing. In fact, I would hazard the guess that it is impossible. The rounding effect of the glide producing rounding in the supposedly resultant *o is just a grace-note on the retraction movement. PIE *o could well have been an unrounded back vowel.
If *H2 cannot color vowels (and the same will be true of *H3), there is no need to differentiate among the various forms of *H; and there should be no objection to identifying it as [*h], and notating it as *H, making it, de facto, the phoneme proposed by the Vocalic Theory.
In addition, in those cases where a stress-un-accented lengthened vowel (*e: / *a: / *o:) shows up as a vowel in a PIE-derived language as a or i, and is notated as PIE *ə(1), schwa (primum indogermanicum), it is easy to suppose that the voiced laryngal fricative, [*ɦ], the counterpart of the voiceless laryngal fricative, [*h], proposed by the Vocalic Theory, could develop from PIE [*h]; and then into a vowel far more naturally than [x] or [xw].
I think there is a good possibility that the earliest phonological realization of what we notate as *e: / *a: / *o: was actually [*ɦe / *eɦ *ɦa / *aɦ, *ɦo /*oɦ] when contiguous *h was simply voiced to *ɦ initially or in a closed syllable formed when the syllable, for which it was the initial, lost its vowel due to stress-accent placement on any other syllable.
PIE Root Definition
The PIE root syllable comprises one or two morae(6): *me, e.g. has one mora; an additional consonant including the 'laryngeal' provides the second mora: e.g. *men- or *me:(-).
Thus, a PIE root like *pel-, which appears in these different forms: *ple:-, *pla:-, *plo:- — these forms are presumed by the 'laryngealists' to be caused by the addition of a following H1, H2, or H3 to *plé.
This seems a real oddity: the addition of the 'laryngeals' under apparently identical phonotaxis produces three lexically different roots: *1. ple:-, 'pour'; *2. a. pla:-, 'put in motion by pushing or beating'; and *9. plo:-, 'burn'.
How much more straightforward it seems to assume that we are dealing with three different roots, which in pre-PIE had the forms: *pÁle:-/*pAlé:-, *pÁla:-/*pAlá:-, and *pÁlo:-/*pAló:-; and that the final vowel differentiated them lexically. The [l] in these roots was formerly [lh]; and when it gave up its aspiration, the original vowels following it were compensatorily lengthened, and their vowel qualities maintained.
So it seems that pre-PIE, in opposition to PIE, allowed roots with one mora, two, and three, or four, five, and six morae: *CV/V: or *CV(:)(-)C/V(:).
The third source of long vowels in PIE is the pre-PIE combination of a word with a short vowel and a morpheme which had the form of *H(a), which I designate as a stative suffix, e.g. *ma, 'breast' + *Ha, stative *maHa, 'be full, ripe'; and then *má:- in PIE.
A fourth source of long vowels has been proposed for pre-PIE in the form of an inflectional but possibly also lexically differential lengthening of the root vowel. This is a known phenomenon from the PIE-derived Indo-Iranian branch, where it is called vŗddhi but is scantily attested (if at all) in the other branches. Until more evidence is forthcoming from other branches, I reject this as a pre-PIE source of lengthened vowels, and will regard it as a strictly Indo-Iranian viz. (P)IE innovation but not pre-PIE.
Law of Phonological Entropy
One of the reasons the 'Laryngeal' Theory was constrained to distinguish the effect of a preceding 'laryngeal' (*HV) from one following (*VH) was that it needed to provide for instances of (initial) *a in, e.g. PIE *ak^-, 'sharp', in which the *a is short and not attested otherwise as **a: in this word.
The 'Laryngeal' Theory therefore presumes that all short *a arises from contact with a preceding a-coloring 'laryngeal', namely *H2; and, just as importantly, that *VC is not a permitted root form.
According to the 'Laryngeal' Theory, *H2Ák^- (also written: *H2ék^) would produce PIE *ák^-, i.e. *H2 would a-color the *Á but not lengthen it. The circumstance that *i and *u do not participate in Ablaut suggests strongly that they must be in a separate though related category from *e and *o.
This has the further implication that short *a was not a constituent of the pre-PIE inventory of 'pure' vowels beside *e and *o (*i and *u being 'impure' vowels deriving from *y and *w).
Another opinion among some subscribers to the 'Laryngeal' Theory is that some long vowels are 'natural', i.e. are retentions of original vowels and original vowel qualities from pre-PIE. The is, of course, in conflict with the asssumption of the 'Laryngeal' Theory above unless we assume *pla: is the result of pre-PIE **plH2éH(1, 2, 3)- which seems quite unlikely (**CCCVC), and would certainly not conform to the normal definition of a root.
The Vocalic Theory expects **Hak^ only if the pre-PIE **Ha:k^- was shortened to *Hak^- through the operation of the Law of Phonological Entropy (v. supra) since it holds that any pre-PIE unlengthened *a would have been subsumed under *A.
To explain the short vowel we actually find, the Vocalic Theory proposes the Law of Phonological Entropy, which states:
any phonological feature which does not
lexically distinguish one root from another
is subject to loss as non-functional.
Thus, in the case of predicted *a:k^-, since no root of the form *ak^- exists, *a:k^- can be reduced to *ak^- with no loss to lexical integrity; and usually is so reduced.
The innumerable entries of the form *CV:/VC like Pokorny's *1. bha:/au-, 'beat, push', show this law in operation. 'Laryngealists' will want to explain the short vowel as a reduction due to the shiftng of the stress-accent.
An objection that has been raised against the Law of Phonological Entropy is that it "is little more than a license to to make arbitrary adjustments to adjust the theoretically predicted forms to fit the actual data".
It is instead a phonological change that is familiarly conditioned — though not by the immediate phonological environment as is usual but rather by the peripheral phonological environment in the form of similarly constituted syllables differing semantically.
It, therefore, is not a "license" for convenient change but rather a guideline for when change is likely to be observable.
It has also been stated that the "supposed law of phonological entropy operates at the level of individual roots and isn't, properly speaking, phonological at all".
I contend that all phonological change operates "at the level of individual roots" else how could we actually observe it? and a change from *a: to *a is 'phonological' in any full sense of the word.
Four Vowel Grades
The Vocalic Theory proposes four vowel grades as against the three vowel grades now generally assumed:
COMPARISON OF PROPOSED PIE VOWEL-GRADES
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.
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Lengthened Grade
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Full Grade
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Reduced Grade
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Zero-Grade
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SHORT VOWELS
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*é: / *ò:
( arising from (pre-)PIE compensatory lengthening, including vŗddhi )
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*é / *ò
( *A )
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_*°_
currently written
_*e_ / _*o_
( *A )
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*Ø
( *A )
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LONG VOWELS
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*e: / *a: / *o:
( arising from adjacent *H
or
preceding voiceless aspirated stop; aspirated fricative, nasal, or rhotic
in pre-PIE )
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*e / *a / *o
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*ə1
( [ *ɦ ] )
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*ə
( where it is now claimed to be *Ø, the reconstruction is incorrect )
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SEMIVOWELS
( *y / *w )
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*é:i / *ò:i /
*é:u / *ò:u
( arising from adjacent *H
or
preceding voiceless aspirated stop; aspirated fricative, nasal, or rhotic
in pre-PIE )
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*éi / *òi /
*éu / *òu
( *Ai / *Au )
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*i / *u
( *Ai / *Au )
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*i / *u
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The Phantom of *H1
*H1 is often termed 'e-coloring' to make a triad with the '*a-coloring' and '*o-coloring' 'laryngeals'. However symmetrical that may be, the better terminology is 'neutral' because it appears where we ordinarily would expect *é(:), contributing to a lengthening effect to the following vowel.
It was invented to explain cases where Hittite had he-(e-), i.e. wrote h while indicating either a short or long e and not showing 'coloring'. So far as I know, no 'laryngealist' has asserted that *H1 will 'color' any other vowel to *e(:) but it is used to explain initial long Ce-e.
It is, of course, obvious that the demonstrated effects of *H1 could be produced by the simple *H proposed by the Vocalic Theory.
No Necessity for *H4
The prevalent view is that the first branching of PIE was formed when IE and Hittite (and, probably all PIE-derived Anatolian languages) parted company.
In order to economically account for those cases where Hittite shows no h and IE shows the effect of a 'laryngeal' (*H) with *e(:), we need only assume that Hittite maintained the distinction between Nostratic *? and *h/*ħ, which it wrote as Ø and h while (non-Anatolian) IE did not so IE *H represents both.
Though Occam's Razor has been too frequently inappropriately invoked, I believe
it is legitimate to apply it here.
In order to produce an initial sequence of *a:C-, proponents of the 'Laryngeal' Theory
need to specify two 'laryngeals':
*H2ÁH1,2,3
The Vocalic Theory requires but one:
*HáC
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SUMMARY
Although the data shows the necessity for a consonantal phoneme for PIE, which subsequently disappeared after lengthening some vowels, or after being shortened to *ə, phonologically, it is crystal-clear that the likeliest phone for it is [h]; and an adequate notation for non-Anatolian IE requires only *H, without any subscripts since it is regular in its effects, principally lengthening, without any effect on the quality of the vowel preceding or following ('coloration').
The late philologist Oswald Szemerényi proposed a phonological value of [h] for the 'laryngeal(s)' many years ago. I was unfamiliar with his proposal when I originated this theory. I have since obtained a copy of Introduction to Indo-European Linguistics, in which he describes his ideas about 'laryngeals' on pp. 121-154. Aside from his identification of *H1, *H2, *H3 as *H, with a phonological value of [h], and his conviction that some roots entered PIE with naturally long *e:, *a:, *o:, his ideas and mine have nothing in common that I can discern.
While I was refining this essay, a friend told me he had an example that could not be explained by the Vocalic Theory. Sadly, he was in error.
Another critic wrote that the multiple occurences of the roots *ag^- and *al- could be "explained" by the 'Laryngeal Theory'. This claim seems to me to also be baseless.
An excellent online resource is at the
TOWER OF BABEL, founded by Sergei Anatolyevich Starostin, and now part of the Evolution of Human Languages project at the Santa Fe Institute.
An important new resource for Nostratic studies is the website Nostratica, instituted by Kirill Babaev, the founder of the Cybalist language discussion group at Yahoo! Groups.
Although there has been an understandable negative reaction to linking 'race' and language notably because of the racial doctrines of the former National Socialists, responsible scholars have now begun to re-investigate the connections among genetic profiles of populations and culture and
language, with the result that the basic Monogenetic Hypothesis (and with it, monogenesis) is gaining substantial credibility through the results of research by
physical scientists.
The kind of solid data being generated and careful analysis cannot be "quibbled away" by the liberal ideologues who still chase the butterflies of independent language invention
and "borrowing frenzy".
The author has originated a Table of Correspondence for the Proto-Language, IE and
Afrasian, Altaic, Basque, Beng (Southern Mandé), Blackfoot (Algonquian), Dravidian (incomplete), Etruscan, Hurrian-Urartian, Japanese, Mon/Hmong, Nama, Pama-Nyungan (incomplete), (Sino-)Tibetan, Sumerian, and Uralic.
PROTO-LANGUAGE MONOSYLLABLES
In order for readers to judge the semantic plausibility of
the analysis of Proto-Language (PL)
elements suggested here, I am including access to a listing of Proto-Language
monosyllables and the meanings I have provisionally
assigned.
Most assignments can be exhaustively supported by data from
actually attested forms but a few animates are very doubtful; and
this list does not represent the "final" solution of
these questions, which will only be approached when other
scholars assist in refining it.
Patrick C. Ryan
Summer 1998
|
the latest revision of this document can be found at
HTTP://WWW.GEOCITIES.COM/proto-language/OneLaryngealVocalicTheory.htm
Patrick C. Ryan * 9115 West 34th Street - Little Rock,
AR 72204-4441 * (501)227-9947
PROTO-LANGUAGE@msn.com
NOTES
1. pre-Pontic Nostratic [*pfh, *tsh, *kxh]
2. Apart from PIE Ablaut patterns, which become more regular with laryngeals, the following are significant:
(Anomalies that can be explained by a 'laryngeal' that has no coloring properties, i.e. simply [ ɦ ] are marked by √.)
√
a. Set roots in Sanskrit: set roots show a variation in a number of forms (about 6 unrelated forms), while anit roots do not. With laryngeals both types show the same pattern.
√
b. The "prothetic" vowel of Greek and Armenian — which just happens to explain certain sandhi phenomena in Sanskrit as well — can be understood if the prothetic vowel were originally a laryngeal consonant.
√
c. Brugmann's law becomes regular; and the cakara / caka:ra variation in Sanskrit is explained, as well as the failure to lengthen the vowel in causatives from set roots.
√
d. The complementary distribution in Indo-Iranian of (using T as a simple voiceless stop) TH, TV:, TI.
√
e. Situations where palatalization does not occur in Indic: the laryngeal intervenes.
√
f. Probably the Greek lengthened augments and reduplications.
√
g. Rigveda scansions of a: as two separate vowels, where Greek and Baltic have circumflex.
√
h. Probably many of the voiceless aspirates of Indic (e.g. a-khya compared with the cognate cayati).
√
i. Probably certain cases of hiatus in Sanskrit.
√
j. The skewed distribution of the vowels /a/ and /o/.
√
k. The na: present in Sanskrit becomes regular.
√
l. The variation of a: / i in the neuter plural in Sanskrit, compared with Greek and Latin /a/.
√
m. The "Schwebeablaut" pattern *ReC / *aRC.
n. Other suggestions are still disputed, but some are plausible, e.g.:
● Germanic "Verschärfung";
● Latin -v- prefects;
● Greek -k- perfects;
● Sanskrit duals in -u;
● Sanskrit perfect forms in -au (dadau, paprau, etc.).
3. The differentiating procedure called vŗddhi is commonly regarded as a lengthening of the root vowel but the apparent employment of infixed *e in roots with resonants in zero-grade (e.g. diu-, 'sky', zero-grade of *deyew- deiwó-s, 'divine') shows us its actual mechanism. In a root sylable with *é, the two combine to produce *e:, hence are 'lengthened'.
I prefer to think of this as adding a mora to the root syllable rather than 'infixing' anything.
4. Oswald J. L. Szemerényi. Introduction to Indo-European Linguistics. Oxford University Press, Oxford. 1990.
5. The first example he gave was the instrumental singular inflection of the -ia: class of (P)IE *a:-stem nouns.
He analyzed the components of the inflection to be:
a. the thematic vowel (-*o-) +
b. the feminine marker, -*yeH2 -iH2, i.e. -*ia: +
c. the instrumental ending, -*eH1, producing
d. -*yH2eH1, or simply -*ia:.
First it must be said that my sources interpret instrumental singular -*ia: as a -*Ø inflection since it is identical to the nominative less -*s; and I can find no trace of a thematic vowel being employed in the example he actually furnished. He claimed that -*ia: illustrated the workings of the 'Laryngeal' Theory and that the Vocalic Theory could not explain them; -*Ø requires no explanation from either theory as far as I can see.
A second example was vŗddhi, which he claimed accounted for some instances of naturally long vowels in (P)IE (by 'naturally long' is meant a vowel that has been lengthened without the agency of a 'laryngeal'), for which, see Note 3. above.
The example he used was *swék^ur-, 'father in law' *swe:k^urós, 'brother in law'.
This procedure, while interesting, has, as far as I can see, no actual bearing on the 'Laryngeal' Theory or the Vocalic Theory either.
6. A root of the form *CV:C would contain three morae, and appears to have been generally discouraged if not being outright impermissible, reverting to *CVC.
When we see a root of the form *CaC, we should understand that it earlier was **Ca:C. Why, then, was the long *a: preserved? Apparently, the root even earlier had the form *Cá:CA, which opened the root syllable for a permissible long vowel. Subsequently, the stress-accent on the long vowel made the *A become *Ø, thereby closing the syllable; and eventually occasioning the shortening of *a: to *a.
The same will be true of a root of the form *CoC.
With a root of the form *CeC, it will be impossible to determine if it passed through an earlier form of **Ce:C or not.
7. We can begin by looking at *ag^-, 'drive, goad'; and *a:/ag^, 'goat'.
I am at a loss to understand what bearing this pair has on the 'Laryngeal' Theory. The difference between
*ag^-, 'drive, goad'; and
*a/a:g^-, 'goat',
is simply that they are differently derived.
*á/:)g^- Pontic *Há:gyA Nostratic *?ági Proto-Language ?A-K?E, 'plant-top + poke'.
*á(/:)g^- Pontic *Há:g(A)yA Nostratic *?agayi Proto-Language ?A-K?A-¿E, 'plant-top + jaw-like = 'chew'.
I am afraid I cannot see any more revealing application of the 'Laryngeal' Theory to the six roots grouped under *al- in Pokorny, which are:
1. *al-, *ol-, 'on the other side'; 2. *al-, 'grow'; 3. *al-, 'wander aimlessly'; 4. *al-, 'burn'; 5. *al-, 'grind'; and 6. *al-, 'white, gleaming'.
To begin with, from a strictly semantic point of view, I would group these roots as follows:
A. 'other': 1. *al-, *ol-;
B. 'grow': 2. *al-;
C. 'grind': 5. *al-; and
D. 'move erratically': 3. *al- (stagger); 4. *al- (flicker); and 6. *al- (shimmer).
These totally semantically separate categories are a direct result of the
circumstance that PIE initial *a- is shortened from *a:- deriving from pre-PIE *Ha(:)-, itself the result of Nostratic *?a, *ha, and *ħa (Nostratic *ħ = voiceless pharyngal fricative, Arabic dotted h; contrasting with pre-PIE *H, which is simply [h]).
In D., Nostratic (and PIE) *la:- means 'move back and forth'; and *ħa, which becomes pre-PIE *Ha(:) means 'water'; combined, this root, Nostratic *ħála:- means to 'wander back and forth as light does on water in gentle motion'; and is the source of *al- listed under D.
C. also is built on this same second element: *la:-, 'move back and forth'; but the first element, pre-PIE *Ha(:) derives from Nostratic *?a, 'top'; so, to 'move back and forth on top of' = 'grind'.
B. has the same elements as C. but interpreted differently: *Há(:)la:-, 'move back and forth at the top' = 'gently sway at the top as tall grass does in a gentle breeze'.
A. is built on *la:- again but with the first element Nostratic *ha, 'be across from': pre-PIE *Há(:)la:-, 'move back and forth at a point across from' = 'be (in motion) on the other/opposite side'.
It is annoying that none of these roots can be attested in the canonical citation form: *Há(:)l- / *Há(:)lə- / *Ha(:)lá:- but that is the luck of the draw.
