07 October 2014

Two Is Company, Four Is a Party

Neuter nouns with the suffix *-wr̥/*-w(e)n- are relatively rare in most branches of Indo-European. The only group where they can be found in great numbers is Anatolian. In Hittite, the suffix productively  formed verbal nouns (names of actions), but there are also examples of nouns that had  become independent lexical units, no longer bound to a particular verb paradigm. They had usually acquired a concrete meaning (referring to a thing or substance rather than an abstraction). One of such nouns is Hitt. pahhur/pahhuen‘fire’, evidently an ancient word, preserved in many branches of the family and showing evidence of archaic vowel alternations and mobile stress: nom/acc.sg. *páh₂wr̥, gen.sg. *ph₂wéns, etc. It may be etymologically connected with the verb *pah₂- ‘guard, protect’, but it’s doubtful if even the speakers of Hittite were still aware of any such connection: the semantic distance between the verb and its derivative was already too great.

Outside Anatolian, the suffix does not play any major role. The nouns that contain it are scattered remnants of a Proto-Indo-European pattern of word-formation. Their attestation is very uneven. They are quite well represented in Sanskrit and Greek, but only isolated examples are found elsewhere (the ‘fire’ word, which became part of Indo-European basic vocabulary sufficiently early, is exceptionally well attested). Here are a few typical *-wr̥/*-w(e)n- nouns evidently connected with known verb roots:

  1. *h₂árh₃-wr̥, gen. *h₂r̥h₃-wén-s  ‘arable land’ (root *h₂arh₃- ‘till, plough’);
  2. *snéh₁-wr̥, gen. *sn̥h₁-wén-s ‘string, sinew’ (root *(s)neh₁- ‘spin, twist’);
  3. *séǵʰ-wr̥, gen. *sǵʰ-wén-s ‘steadfastness’ (root *seǵʰ- ‘conquer, take possession of; hold, own’);
  4. *h₁éd-wr̥, gen. *h₁d-wén-s ‘food’ (root *h₁ed- ‘eat’).

Their reflexes in the historically documented languages rarely display the whole range of vowel, consonant and stress variations, most of which were levelled out analogically in prehistoric times. Still, these alternations are reconstructible thanks to the fact that different fragments of the pattern have been preserved in different languages. They can be reassembled into a complete picture like the pieces of a jigsaw puzzle or the disarticulated skeleton of a fossil animal.

Got wheels?
A four-wheeled toy from the Cucuteni-Trypillian culture;
the early fourth millennium BC.
Neuters of this kind formed collectives by inserting a lengthened *ō into the suffix. The collective of a count noun denotes simply a set of objects (a collective plural), while the collective of a mass noun like ‘fire’ denotes a particular quantity or sample of the thing in question (‘a fire, a burning mass’). This became one of the derivational mechanisms by which Indo-European mass nouns could be transformed into count nouns. The accent was commonly shifted to the suffix in the process, causing the reduction of the root vowel: *páh₂wōr (collective) > *ph₂wṓr > *pwṓr (a countable neuter with its own case forms such as gen.sg. *p(h₂)un-és). Still later, the distiction between the original mass noun and its collective could be blurred and abandoned, the younger form ousting the older and serving in both functions (‘fire’ or ‘a fire’). The archaic Proto-Indo-European form *páh₂wr̥ is unambiguously preserved only in Anatolian, while the remaining Indo-European languages show reflexes of *pwṓr or its further modified descendants.

Now we can view the reconstruction *kʷét-wr̥ in this light. Supposing it was derived from our hypothetical verb root *kʷet- ‘group into pairs’, the original meaning of *kʷétwr̥ (as a nomen actionis) would be something like ‘pairing’, and its collective *kʷétwōr would mean ‘a particular result of pairing, a complete set organised into pairs’. In the Proto-Indo-European world, there were many “natural” sets of things conceptualised as consisting of two pairs: human hands and feet; fore and rear legs of animals; the wheels of a wagon; the four directions, whether cardinal (east and west, north and south) or relative (forward and backwards, left and right); paired organs of perception (two eyes and two ears). This could have provided sufficient motivation for treating ‘4’ as the prototypical case of an “even collective”. An interesting parallel can be seen in the “fraternal” numeral systems widespread in Amazonia. In the languages that employ them, the numeral ‘4’ is derived from an expression meaning ‘each has a brother/companion/spouse’. At a more primitive stage, preserved in the Dâw language, there are only three “exact” lexical numerals, ‘1’, ‘2’, and ‘3’. The values from 4 to 10 are described as ‘even’ (‘has a brother’) or ‘odd’ (‘has no brother’). The precise value can’t be expressed linguistically, but the words ‘even’ and ‘odd’ can be supplemented by clarifying hand gestures:
Dâw speakers indicate ‘four’ by holding the fingers of one hand separated into two blocks; for ‘five’, they add the thumb; for ‘six’, they place the second thumb against the first to make a third pair; and so on until for ‘ten’ all fingers are grouped into five pairs, the thumbs together.
[Epps 2006: 265]
Once established as a concrete numeral (rather than part of an even-odd tally system), *kʷétwōr (or *kʷətwṓr) was interpreted as an ordinary neuter plural, and – like the numerals ‘1’, ‘2’, and ‘3’ – formally an adjective, inflected not only for case but also for gender. This resulted in the analogical creation of the animate plural in *-wor-es (and the periphrastic feminine ‘four females’, soon univerbated and phonetically mutilated in the process). Note that if the adjective had been formed directly from the verbal noun *kʷétwr̥/*kʷ(ə)twén-, its animate plural would probably have ended up as *kʷet-won-es. In addition to the Greek and Vedic words for ‘fat’, already discussed, compare Greek peîrar (gen. -atos) ‘boundary’ < *pér-wr̥/*pr̥-w(e)n- versus the Homeric adjective a-peírōn (animate) ‘boundless, endless’ < *n̥-per-wōn.

All this suggests that the word *kʷétwr̥ (coll. *kʷétwōr) was transparently derived from a verb root and adopted as a cardinal numeral at a rather late date, perhaps in “Core Indo-European” (the non-Anatolian part of the family) rather than in Proto-Indo-European proper. It is a well-known fact that Anatolian has a different word for ‘4’, *meju- (Hittite meu-/meyau-, Luwian māwa-). Since the jury is still out on whether Hittite kutruwa(n)- ‘witness’ has anything to do with the numeral ‘4’*), we should seriously consider the possibility that the familiar reconstruction *kʷetwores is not Proto-Indo-European at all but represents a “dialectal” innovation which replaced its older synonym in the common ancestor of Tocharian and the extant branches of the family.

If this were a journal article rather than a blog post, I would now be obliged to account for every puzzling irregularity in the branch-specific reflexes of *kʷetwores and its variants. I will spare my visitors such excruciating details, but if anyone is really interested in discussing them, welcome to the Comments section.

And now back to other matters – next time.

*) A witness in court could be denoted as ‘the fourth man’ (beside the two contracting parties and the judge).


Epps, Patience. 2006. “Growing a numeral system: The historical development of numerals in an Amazonian language family”. Diachronica 23(2): 259-288. [a preprint version is available here]

02 October 2014

Only Connect: The Strange Triangle

The Latin adjective triquetrus ‘triangular’ (neuter -um, feminine -a) is baffling. It’s obviously a compound, and it obviously contains the compositional form of the numeral ‘three’, *tri-. What else it contains is anything but obvious. Unfortunately, it’s the only specimen of its kind. The mysterious element -quetrus does not occur in any other Latin compound. It looks as if it could have something to do with quattuor ‘four’. When ‘four’ occurs as the first part of a compound, it has the shape quadru/i-. This form must somehow go back to *kʷətwr̥-, its metathetic variant *kʷətru-, or a hybrid combination of both, but the voicing of the *t is odd, not to say perverse, because its exact opposite, *dr > tr, was a regular change in the prehistory of Latin. The word ‘four’ is evidently such a fickle fellow that it just can’t resist breaking some established rules. For greater inconsistency, the adverbial numeral quater ‘four times’, which in other IE languages (and presumably in Latin as well) derives from *kʷ(e)twr̥-s ~ *kʷ(e)tru-s, shows no voicing. We see a voiced stop again, though, in the denominal verb quadrō ‘to square; put in order, arrange’ and a few related words such as quadra ‘square piece or slice, plinth, dining table, etc.’ and quadrātus ‘square (n. and adj.)’.

Some connections are impossible.
The second part of triquetrus doesn’t simply reflect *kʷetru- (or *kʷatru- < *kʷətru-), because the word is a second-declension o-stem, which means that its pre-form ended in *-tro- rather than *-tru-. The form *kʷetro- (or possibly *kʷatro-, since pre-Latin *a would have merged with *e in this position) does not otherwise occur as a variant of ‘4’ in Latin, but since we are dealing with a capricious word-family, it’s hard to rule out a connection. If it does mean ‘four’, however, why’s that? A triangle has three sides, it has three angles, but has it got three “fours”? It would not be strange if a word for the right angle had something to do with squares or rectangles, and therefore indirectly with the numeral ‘4’, but a triangle can have at most one right angle, certainly not as many as three (the Penrose tribar, shown on the right, would be an exception if it could exist in ordinary Euclidean space).

Can external cognates help? It’s tempting to compare triquetrus with Old English þrifeoþor (sometimes glossed as ‘triangular’ in reference books such as Bosworth and Toller’s Anglo-Saxon Dictionary). It has been suggested earlier by one of the commenters on this blog [Douglas G. Kilday] that the Old English word is a loan from (unattested) Gaulish *petros ‘corner’ (< *kʷetros), which became Germanic *feþra- after the operation of Grimm’s Law. This tantalising suggestion, however, can’t be correct. The word þrifeoþor appears in Old English glossaries (Corpus, Erfurt, and Épinal) three times (spelt ðrifeoðor, trifoedur, ðrifedor), and is translated into Latin as triquadrum. One might think that triquadrum is a distortion of triquetrum caused by “folk etymology” (the mistaken identification of the second part as the compositional form of ‘4’), but in fact it’s no such thing. Old English authors took the adjective triquadrus from Orosius, a Christian priest and scholar from the Roman province of Gallaecia (today’s Galicia, Spain). Orosius, active in the first decades of the 5th century, was the author of several enormously influential works, including  Historiae Adversus Paganos, with a chapter on the geography of the world. Here is the relevant passage (Book 1, Chapter 2; emphasis added):
Maiores nostri orbem totius terrae, oceani limbo circumsaeptum, triquadrum statuere eiusque tres partes Asiam Europam et Africam uocauerunt, quamuis aliqui duas hoc est Asiam ac deinde Africam in Europam accipiendam putarint.
[Our elders made a threefold division of the world, which is surrounded on its periphery by the Ocean. Its three parts they named Asia, Europe, and Africa. Some authorities, however, have considered them to be two, that is, Asia, and Africa and Europe, grouping the last two as one continent.]
The epithet triquadrus refers to “the circle of all the earth” (orbis totius terrae = the world). Orosius certainly doesn’t mean that the Earth is a triangular circle, or that it has three corners. He means that the landmass of the world (as he knew it) is tripartite, divided by most ancient geographers into three continents (in this context, quadra means ‘part, division, area’, not literally a square). Anglo-Saxon translators coined a calque, mechanically replacing Latin quadr- with feoþor- < *kʷetwr̥-, the compositional form of Old English fēower ‘four’. Þrifeoþor was never intended to mean ‘triangular’. Its second member is the same feoþor- (= Late West Saxon fiþer-, fyþer-) that we find as the first element in numerous Old English compounds, e.g. fiþerfēte ‘four-footed’ (= Latin quadrupēs).

External support for *kʷetro- thus evaporates, but triquetrus still has to be explained somehow. I would suggest that its second element is a derivative of *kʷet- ‘join pairwise’ with the instrumental suffix *-tro-. When the suffix was added to a root ending in a dental stop, the last segment of the root was dropped already in Proto-Indo-European (this process is known as “the metron rule”). Thus we get *métrom (Greek métron ‘measure’) from *méd-trom (*med- ‘allot, mete out’), and *h₁étrom (Vedic átra- ‘nourishment’) from *h₁éd-trom (*h₁éd- ‘eat’). The noun *kʷétrom < *kʷet-trom would be ‘something that holds a pair of things together’, hence ‘joint, connection’ or the like. There were several Proto-Indo-European roots with similar meanings, and accordingly several nearly synonymous nouns for things like woodworking joints; joint itself comes (via French) from Latin iunctus ‘connected’ (the root here is *jeug-, as in yoke). Tri-quetrus (< *tri-kʷetro-) is built exactly like tri-angulus (a noun is used as the second member of a compound adjective without altering its stem class), and its etymological meaning is ‘having three connections (between pairs of sides)’.

The next post, in which I shall return to the numeral ‘four’ itself, will be the last in this series.

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