PIE Numeralia

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PIE Numeralia

Post by L.E.G.von Trips »

k^j stands here for PIE palatalized velar.

1)
Sihler and Beekes give the PIE forms as follows respectively :

ten < *dek^jm(t) / *dek^jmt
twenty < *widk^j(o)mt- / *dwidk^jmt-
thirty < *tridk^j(o)mt- / *trih2dk^jmt-
hundred < *dk^jmt-om / *dk^jmt-om

Moreover, Sihler provides *tusdk^j(o)mt- for one thousand (for Baltic, Slavic and Germanic).

The late PIE numeral system appears to be decimal with the root for ten being *dek^j- / dk^j-.

2)
There's a PIE verbal root *deik^j- meaning "to show, to point out" (in Lat. dicere, digitus; Goth. gatihan "announce, tell", NHD zeihen, zeigen, r Verzicht; Eng. teach, token (from Pokorny)).

=>
Possibly the PIE numeral root *dek^j- "ten" and the verbal root *deik^j- "to point out" can be related. Semantically this seems pretty plausible when one thinks of ten fingers on a hand.
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Post by Colzie »

This sounds like the same argument for the PIE word for 9 being related to the word for new, as though they had just invented the concept of 9, and were calling it "the new number".

If '10' were really from deik_j, one would expect it to be dik_j plus a suffix, not dek_j.
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Post by L.E.G.von Trips »

The argument about new had to do with the presumption of original binary numeral system.

I don't mean a relation of the kind like déik^j-e/o- -> dik^j-tó-. But possibly a more distant one.
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Post by Bryan »

L.E.G.von Trips wrote:The argument about new had to do with the presumption of original binary numeral system.
Wow, I've never heard that before. Any links or book references?

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Post by alice »

Another such thing is the PIE word for "five" being related to the (unattested) Germanic source of "finger".
Zompist's Markov generator wrote:it was labelled" orange marmalade," but that is unutterably hideous.

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Re: PIE Numeralia

Post by hwhatting »

L.E.G.von Trips wrote: twenty < *widk^j(o)mt- / *dwidk^jmt-
thirty < *tridk^j(o)mt- / *trih2dk^jmt-
hundred < *dk^jmt-om / *dk^jmt-om
Actually, the /d/ in these forms is not directly reconstructable - the IE languages point to forms *wi( : )k^j(o)mt-, *tri(H)k^j(o)mt-, *k^jmt-om.
Many IEanists assume (and explain the variations of the vocalism in the forms for 20, 30, etc. in this manner) that these forms originally had a /d/ that was dropped / assimilated to the following /k^j/, but this is already an attempt to find an internal etymology for these forms.
The link with *deik^j- has the problem that it's really hard to get from there to *dek^jm.(t)-. You'd have to assume that the /i/ in *deik^j- is some kind of infix.

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Post by sangi39 »

I've read ideas that *dek^jm=t may have arisen from *dweh3+*k^jomt, literally "two hands", which eroded to *de+*k^jomt and finally to *dek^jm=t. This would make sense in that two hands have ten fingers, but the people supporting this idea, so far as I've read, haven't found a reason why *dweh3 would become *de-.

Another possible origin for *dek^jm=t might be *dek^k+*k^jomt, literally "right hand" under the idea that PIE speakers originally counted on the hands from left to right.

A third interpretation is that *dek^j may have meant "reach", indicating, under the saem assumption as above, that on counting on the hands one has reached the end of counting.

It might be possible then that *deik^j+*k^jomt may have some meaning like "show the hands" in the sense that when one has counted to ten on the fingers the palms of the hands are shown.
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Post by L.E.G.von Trips »

Actually, the /d/ in these forms is not directly reconstructable - the IE languages point to forms *wi( : )k^j(o)mt-, *tri(H)k^j(o)mt-, *k^jmt-om.
When it comes to the d-element, it might be attested from lithuanian tukstandi- "one thousand" where the -kst- were presumably how the cluster -sdk^j- of *tusdk^j(o)mt- would be resolved.
I've read ideas that *dek^jm=t may have arisen from *dweh3+*k^jomt, literally "two hands", which eroded to *de+*k^jomt and finally to *dek^jm=t. This would make sense in that two hands have ten fingers, but the people supporting this idea, so far as I've read, haven't found a reason why *dweh3 would become *de-.
Yes. However, I have come across another objection that if ten had denoted "two hands" the same root would have been expected to form the word for five as well.
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Post by sangi39 »

L.E.G.von Trips wrote:
I've read ideas that *dek^jm=t may have arisen from *dweh3+*k^jomt, literally "two hands", which eroded to *de+*k^jomt and finally to *dek^jm=t. This would make sense in that two hands have ten fingers, but the people supporting this idea, so far as I've read, haven't found a reason why *dweh3 would become *de-.
Yes. However, I have come across another objection that if ten had denoted "two hands" the same root would have been expected to form the word for five as well.
Could it be possible that for some reason, possibly taboo, that the original word for "ten" became replaced by a word of internal construction. That is to say that "penkwe" wouldn't be "hand" because the original word for ten wasn't "two+hand" but became so at some later time.

It could be that *dek^j happens to be the older PIE word for ten and the through some reason, the additional k^jomt was added, possibly in order to distinguish it from similar words, essentially reinforcing its meaning.

It could also be that dek^jm=t is the original PIE word for 10 and that shortening of it to somthing else and the apparent compound-nature of the word make modern scholars interpret it as having some longer history.
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Post by gsandi »

Anything could be, but we need evidence to support it. If *dekm < *deikm, we need similar developments (loss of the high front feature) in other situations to make it plausable.

On the whole, I don't think that number words in PIE (except for some of the ones for "one") are replacements for earlier, different words. I think that it is more likely that there there had been no specific words past, say, 6, and PIE (or its ancestor) created a more complex number system because it was needed for an emergent pastoral economy. They had to have words to count their sheep, cattle and so on.

Proto Uralic, a language probably used by a hunting-fishing culture, doesn't seem to have numeral words past 6. Words past that number are normally ones in Uralic languages that are either borrowings or obvious compounds. When this is not the case in a Uralic language, there are no obvious cognates in Uralic languages outside their immediate branch.

(Hungarian hét 7, tíz 10, száz 100 and ezer 1000 are all IE loanwords)

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Post by hwhatting »

L.E.G.von Trips wrote:When it comes to the d-element, it might be attested from lithuanian tukstandi- "one thousand" where the -kst- were presumably how the cluster -sdk^j- of *tusdk^j(o)mt- would be resolved.
Are there any other examples for such a cluster resolution? IIRC, Lithuainan has other cases of a seemingly unmotivated /k/ being inserted in similar enviroments, e.g. aukšas "gold" from PIE *auso- (cf. Lat. aurum), so this insertion may be etymologycally meaningless.

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Post by sangi39 »

gsandi wrote:Anything could be, but we need evidence to support it. If *dekm < *deikm, we need similar developments (loss of the high front feature) in other situations to make it plausable.
I think the main point was that *dekj may have somehow derived either from *deikj or from some older word. Personally I find the problem here to be that most often where to elements are related and one contains -ei-, the other contains -i-, the 0-grade of -ei-. So the expected counterpart of *deikj should really be *dikj rather than *dekj, at least as far as I'd guess.

EDIT: Never mind, thinking about it, if we could show a different kind of vowel alteration involving -ei->-e-, like some kind of reverse 0-grade, that wasn't productive in PIE-Proper. So, agreed, we'd need to find semantic similarities in words like *tekj and *teikj, *bheikj and *bhekj, etc. and maybe other CeC-CeiC pairs.
gsandi wrote: On the whole, I don't think that number words in PIE (except for some of the ones for "one") are replacements for earlier, different words. I think that it is more likely that there there had been no specific words past, say, 6, and PIE (or its ancestor) created a more complex number system because it was needed for an emergent pastoral economy. They had to have words to count their sheep, cattle and so on.

Proto Uralic, a language probably used by a hunting-fishing culture, doesn't seem to have numeral words past 6. Words past that number are normally ones in Uralic languages that are either borrowings or obvious compounds. When this is not the case in a Uralic language, there are no obvious cognates in Uralic languages outside their immediate branch.
I think that makes sense. IIRC, PIE was spoken either during or after the development of agriculture, depending the ideas regarding where and when it was spoken so it could be that PIE was spoken by a group of people who had only recently adopted agriculture. If we assume that underived numbers for "ten" do not occur in hunter-gatherer societies then it might be possible to suggest that the number *dek^jm=t might either be derived at some relatively recent point or that it was derived at ome point where the link to the base of derivation would have been lost.
Last edited by sangi39 on Tue Jan 19, 2010 2:27 pm, edited 1 time in total.
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Post by gsandi »

sangi39 wrote:
gsandi wrote:Anything could be, but we need evidence to support it. If *dekm < *deikm, we need similar developments (loss of the high front feature) in other situations to make it plausable.
I think the main point was that *dekj may have somehow derived either from *deikj or from some older word. Personally I find the problem here to be that most often where to elements are related and one contains -ei-, the other contains -i-, the 0-grade of -ei-. So the expected counterpart of *deikj should really be *dikj rather than *dekj, at least as far as I'd guess.
I know as much about ablaut grades as most people, I think.

If we suspect an alternation ei/e, it is not a good counterargument that it doesn't fit the traditionally recognized PIE ablaut alternation patterns. Who says that there could not have been a conditioned phonetic change (or a random, irregular, change) of this kind? Even if we don't find an example, it could have happened - but if we find a few other examples, this would reinforce the suggestion.

Say, when trying to explain the pronunciation of 'one' in English, we would say, no, this has nothing to do with OE án, because this would have developed into /oun/, as it has in the compound 'alone'.

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Re: PIE Numeralia

Post by David McCann »

L.E.G.von Trips wrote:There's a PIE verbal root *deik^j- meaning "to show, to point out" (in Lat. dicere, digitus; Goth. gatihan "announce, tell", NHD zeihen, zeigen, r Verzicht; Eng. teach, token (from Pokorny)).

=>
Possibly the PIE numeral root *dek^j- "ten" and the verbal root *deik^j- "to point out" can be related. Semantically this seems pretty plausible when one thinks of ten fingers on a hand.
Also Latin digitus and English toe may be involved here: finger, point, set of fingers = ten. Of course, that's going back a long way before PIE, and we might bring in Old Korean tēk 'ten', Ainu teke 'hand' and atiki 'five', Proto-Eskimo tik 'finger'.

Another case of a numeral that can be analysed is oktōu 'eight': clearly a dual, and there's a Dardic (?) language with a descendant of oktos for 'palm of the hand'.

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Post by L.E.G.von Trips »

The formation of *dek^j-m-t with respect to *dk^j-m-t-om resembles that of the so called amphikinetic accent-ablaut type (like *pent-oh2-s / *pnt-h2-es). The two must be root related not by k^jmt but by dek^j-. (Moreover, I wouldn't even expect a root of k^jmt to exist, but rather a k^jnt- instead.)

But then, what is the function of the -t- and -m- elements added to the numeral roots in: *dek^j-m-t, *h1neu-m, (eight doesn't have it because of the prominent dual ending, but perhaps there's the -t- at least), and even with switched order in *sep-t-m ?
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Post by Etherman »

gsandi wrote:Anything could be, but we need evidence to support it. If *dekm <deikm> CeCVC, but other times CVC > CiCVC.

In order to explain the pronoun forms I came up with the following developments for Pre-PIE *i:

1) In monosyllables *i > *i
2) In polysyllabic words:
a) *i > *e in closed syllables or open syllables followed by a resonant
b) *i > *ei (>*i when unstressed) in open syllables not followed by a resonant

These developments can also be applied to the reduplicated forms, at least with a degree of success. Unfortunately, sometimes the languages disagree on whether *i or *e should be reconstructed for the same word. And then there's the questions of how much, if any, analogical levelling took place and what effect the continued productivity of reduplication has had even after the breakup of PIE.

This theory might explain the *dek^jmt~*deik^j alternation, but I'm very skeptical. Perhaps the root was originally *dejk but there was a metathesis which resulted in *dekj. Both forms were retained and the *j caused palatalization of the *k.
On the whole, I don't think that number words in PIE (except for some of the ones for "one") are replacements for earlier, different words. I think that it is more likely that there there had been no specific words past, say, 6, and PIE (or its ancestor) created a more complex number system because it was needed for an emergent pastoral economy. They had to have words to count their sheep, cattle and so on.
I've often wondered if the word for 2 was a borrowing from a West Caucasian language. Starostin's database is currently down so I can't provide exact forms, but IIRC the Ubykh form was something like t'w@.

The words for 3, 6 and 7, look like the Semitic words for 3, 6, and 7.

The word for 8 is a dual and looks a lot like the Kartvelian word for 4.
Proto Uralic, a language probably used by a hunting-fishing culture, doesn't seem to have numeral words past 6. Words past that number are normally ones in Uralic languages that are either borrowings or obvious compounds. When this is not the case in a Uralic language, there are no obvious cognates in Uralic languages outside their immediate branch.
IIRC the Proto-Samoyedic numerals are not cognate with the Proto-Finno-Ugric numerals, so Proto-Uralic may not have had any numerals.

Edit: Fixed really weird typo.
Edit Part Deux: After fixing the weird typo (I thought) the message has become partly garbled for no apparent reason.
Last edited by Etherman on Tue Apr 06, 2010 9:54 pm, edited 3 times in total.

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Post by tezcatlip0ca »

I have always thought IE and Semitic to be related, though definitely not by 0(+4\/14|\|0's strange (to say the least) thinking.

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Post by tezcatlip0ca »

Tried to 1337 the name without it being incredibly obscure.

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Post by hwhatting »

Etherman wrote: We do, as it happens. The interrogative pronoun has *(e)i~*e alternations, as does the demonstrative *h1(e)i~*H1e. We also have an alternation of *i(<ei> CeCVC, but other times CVC > CiCVC.
We also have things like Balto-Slavic *tre-tyo- "3rd" vs. the usual forms with *tr(e)i- for the numeral "3". But I don't think that these instances necessarily are traces of a sound law; this may simply be an old affix **-i/y- that was reinterpreted as part of the root or put into service as reduplication vowel (I assume that's what you refer to with CeCVC vs. CiCVC?).

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Post by brandrinn »

Etherman wrote:IIRC the Proto-Samoyedic numerals are not cognate with the Proto-Finno-Ugric numerals, so Proto-Uralic may not have had any numerals.
Similarly, American English uses the word "trash" where British English would have "rubbish," so we can infer that 17th century English had no word for refuse.

I give it even odds he doesn't detect the sarcasm.
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Post by hwhatting »

brandrinn wrote:Similarly, American English uses the word "trash" where British English would have "rubbish," so we can infer that 17th century English had no word for refuse.

I give it even odds he doesn't detect the sarcasm.
Well, actually that sarcasm is misplaced:
1) In many language families, number systems are quite stable over time; so the absence of any shared number lexeme is much more likely to indicate absence of a fixed number system than the difference in a word for "trash" is to indicate the absence of such a concept in a parent language - "trash" is a concept that shows high variation in lexemes for even closely related languages and for which in many languages a lot of synonyms and slang words exist.
2) It seems quite likely that fixed sets of number words are something that comes into existence with the development of agriculture and pastoralism, so PU not having a fixed set of number words is not unrealistic.
3) Etherman says "may not have had", not "didn't have had".

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Post by zompist »

In researching number systems, I came across several cases (unfortunately I don't have them at hand) where variants were reported for the same language. Often this was at the stage when number names are transparent, so people can simply come up with multiple ways of referring to the same number. Sometimes we can see this indirectly in that related languages will have wildly different numbers— as random example, the Mascoyan family has pestin, thlama, molek, insxipoèé as words for 1.

As well, many languages have changed number systems, often for a simpler system used by a high-prestige group. As a single example, compare Yameo ískō 9, borrowed from Quechua, with its sister language Yagua's nairukuiniu-niatea.

For both reasons I don't think the stability of a number system allows inferences about what came before.

But even more importantly, it's a big, surprising thing to say that a language has no number system. Out of 5000 languages I've collected, precisely two are said to have no number system at all, and of course that 5000 includes hundreds of hunter-gatherer languages. Many have just a few number words, but they still have those. One shouldn't posit a lack of number system as if it's a quite natural state of affairs.

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Post by Etherman »

hwhatting wrote: We also have things like Balto-Slavic *tre-tyo- "3rd" vs. the usual forms with *tr(e)i- for the numeral "3". But I don't think that these instances necessarily are traces of a sound law; this may simply be an old affix **-i/y- that was reinterpreted as part of the root or put into service as reduplication vowel
Last night I realized there's another place where my proposed sound laws might evidence themselves: The verbal agreement suffixes. The primary endings in the singular have *-i, but in the plural have *es or *en. I hesitate to claim victory here since there's uncertainty, indeed inconsistency, in the plural formations which might have *-esi. Of course there may be another sound law preventing two successive high vowels from occurring.
(I assume that's what you refer to with CeCVC vs. CiCVC?).
I was thinking more in terms of verbs with reduplication, though your Balto-Slavic example might fit. OTOH, it could be a local innovation which would have occurred long after the proposed sound laws were in effect.

Consider, for example, the Greek word leipo: "I leave". The perfect form of the verb is leloipa. If we assume that the reduplicating vowel was *i and underwent the sound changes I proposed earlier then the -e- is the expected form of *i before a resonant. Compare that with the reduplicated verb dido:mi. Here, as predicted (aside from the annoying fact that the reduplicated vowel is stressed, which may be a secondary, but still PIE, development anyway), the vowel is -i-. Alas, Sanskrit has, for this very same word, dada:mi, with the unexpected vowel -a- (< *e).

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Post by Etherman »

brandrinn wrote:
Etherman wrote:IIRC the Proto-Samoyedic numerals are not cognate with the Proto-Finno-Ugric numerals, so Proto-Uralic may not have had any numerals.
Similarly, American English uses the word "trash" where British English would have "rubbish," so we can infer that 17th century English had no word for refuse.

I give it even odds he doesn't detect the sarcasm.
Sounds like a lot of garbage to me.

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Post by Etherman »

hwhatting wrote:3) Etherman says "may not have had", not "didn't have had".
Off topic:

You know, I intentionally put these kinds of qualifiers in my posts, and more often than not they are ignored. I wonder if there's some kind of weird psychological artifact that causes most people to gloss over them.

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