PIE Numeralia

[Etherman]

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.

Perhaps true, but it leads to the obvious question: When was counting invented?

[sangi39]

Apparently, according to Wikipedia, An Introduction to the History of Mathematics by Howard Eves states that archaeological evidence for counting exists as far back as 50,000 years. Unfortunately wikipedia doesn't give the circumstances in which the counting occurred (what was being counted, how they were being counted, what for and who by) or the the numbers which were being counted to. Dirk Jan Struik, however, states that the earliest counting was typically in the form of tallies with more complex written number systems occurring in more complex societies where higher numbers became more commonplace. This may reflect the method of counting in the spoken language to some degree suggesting that early spoek counting reflected a more tally-like system consisting of combinations of smaller numbers, 5 typically derived from "hand", "palm", etc. 10 from "count", "hands" and so on and 20 from "feet" or "body". Other numbers either derived from the combination of numbers 1-4 with 5, 10 (20) or they could have derived from things that naturally occur in groups of a particular number.

That is to say, counting may be an inherently human process but our means of counting may be influenced by our circumstances and the relative occurrence of higher numbers.

[Etherman]

Apparently, according to Wikipedia, An Introduction to the History of Mathematics by Howard Eves states that archaeological evidence for counting exists as far back as 50,000 years.

Unfortunately Wiki doesn't state how he came to this conclusion. However the article on arithmetic states that the Lebombo Bone is the oldest mathematical artifact at 35000 BC. It's a bone that contains 29 notches. Wiki indicates that a number of bones show 28 to 30 scratches followed by a distinctive marker, which suggests that women were counting the number of days in a menstrual cycle.

[4pq1injbok]

Not making any particular point here, just a data point about numeral replacement: I was reading about the Anatolian numerals recently. We don't even know most of the Hittite numbers, since they were written logographically, but we do know the roots for 2, 3, 4, and 7. Three of these are the familiar non-Anatolian IE bases, but 4 meyu- isn't. And there's a cute piece of evidence that this was a replacement, in the word kutruwan- 'witness', alongside teriwan- 'judge': in a case that's a dispute between two parties, these would be the third and fourth parties (anti-respectively) called in, and their names reflect that using the non-Anatolian IE roots.

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

IIRC the case for 7 is actually kinda appealing -- there was some Semitic language around with [sab?\atum] as a form of 7, wasn't there?

and there's a Dardic (?) language with a descendant of oktos for 'palm of the hand'.

Ooh, that'd be neat to see properly tracked down.

[hwhatting]

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.

OK, let me clarify what I wanted to say. I was not intending to say that before the advent of agriculture and pastoralism people did not have number words. What I think is that the situation you describe in the first paragraph was typical - that languages didn't have a fixed set of number words, but that number words could be made up and would vary from (say) band to band or village to village. Fixed sets with only occasional changes or replacements, consisting of etymologically opaque lexemes, became the norm only when societies grew and trade relationships became more complex. I admit that's hard to prove, but to me the fact that in reconstructing protolanguages, you come to a point where you can reconstruct many lexemes, but not a number system, while in later stages the number system is one of the more conservative subsystems, shows that at one point (which may vary in different parts of the world) number systems switched from being open to change, replacement, and being etymologically transparent (e.g. based on body part count systems), to being stable and etymologically opaque.

[hwhatting]

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.

That assumes that there is any relationship between the *-e in the plural and the *-i in the singular, which I doubt, as the *-e is there in the plural also in the secondary endings (*-me, *-te).

(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.

That's what I meant when I referred to "affix **-i/y- that was reinterpreted as part of the root or put into service as reduplication vowel ".

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.

I actually assume that the Vedic and Latin reduplication type CuCouC- / CiCoiC-is original for the perfect for diphthong roots and that the e.g. Greek state with a reduplication syllable Ce- everywhere in the perfect is due to analogical spreading.

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

FWIW, LIV sees the Vedic formation as the older one for this specifc verb. The water is muddied even more by the Balto-Slavic forms, which point to something like *do-dH3-. My explanation of the -i- in this formation would be that the "actuality" particle *-i (the same as in the primary ending) was infixed between the reduplication syllable and the root.

[Etherman]

That assumes that there is any relationship between the *-e in the plural and the *-i in the singular, which I doubt, as the *-e is there in the plural also in the secondary endings (*-me, *-te).

Indeed, that is a problem. Maybe it can be resolved through analogical spreading? In Gothic there's the ending -ts. IIRC it's generally explained as coming from *-thes with fortition of th after the loss of the vowel (by why is the vowel lost?). Could it be that it's a relic of original *-ts, that is the original plural formation before the analogical spread of the primary endings? I haven't really investigated this line of thought so I could be all wrong.

FWIW, LIV sees the Vedic formation as the older one for this specifc verb. The water is muddied even more by the Balto-Slavic forms, which point to something like *do-dH3-. My explanation of the -i- in this formation would be that the "actuality" particle *-i (the same as in the primary ending) was infixed between the reduplication syllable and the root.

If this is an infix between the reduplicated syllable and the root then shouldn't the reduplication of CVC be CViCVC?

[Etherman]

Not making any particular point here, just a data point about numeral replacement: I was reading about the Anatolian numerals recently. We don't even know most of the Hittite numbers, since they were written logographically, but we do know the roots for 2, 3, 4, and 7. Three of these are the familiar non-Anatolian IE bases, but 4 meyu- isn't. And there's a cute piece of evidence that this was a replacement, in the word kutruwan- 'witness', alongside teriwan- 'judge': in a case that's a dispute between two parties, these would be the third and fourth parties (anti-respectively) called in, and their names reflect that using the non-Anatolian IE roots.

Interesting. I had always wondered if the Hittite word was original or an innovation. This looks to be pretty good evidence that the Hittite numeral is an innovation.

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

IIRC the case for 7 is actually kinda appealing -- there was some Semitic language around with [sab?\atum] as a form of 7, wasn't there?

Akkadian has sebe. There appears to be some numeral suffix in IE of the form *tm or *mt. So *sebe-tm > *sebtm (why the syncope?) > *septm.

The Semitic connection to 3 and 6 are less clear (and thus less likely). A number of Semitic numerals for 3 have a t-l-t structure. Some of these have an initial cluster of tl. It's not hard to imagine a dissimilation of tl > tr in IE. More often than not the vowel is -a- instead of -i-, but sometimes -i- is found which could lead to *ei in my system. The second t would have to be lost somehow, by why? For the number 6 most Semitic languages have something like sitta or shesh. Akkadian in particular has shishshu. PIE has *swek^s. A borrowing of Akkadian sh > PIE *sw is not implausible, but where would the *k^ come from? Dissimilation perhaps?

[hwhatting]

Indeed, that is a problem. Maybe it can be resolved through analogical spreading? In Gothic there's the ending -ts. IIRC it's generally explained as coming from *-thes with fortition of th after the loss of the vowel (by why is the vowel lost?). Could it be that it's a relic of original *-ts, that is the original plural formation before the analogical spread of the primary endings? I haven't really investigated this line of thought so I could be all wrong.

I see that as hardly likely. It seems likely that PIE simplified dental plus final /s/ to *-s#, so in this case Gothic -ts could not continue PIE *-ts. On why the vowel would be lost, IIRC, PIE*-es# -> PGmc *-iz/s ; the loss of /i/ in this position is regular in Gothic.
I don't think the *-e in *-me, *-te has anything to do with the *-i of the sg. and 3pl. primary endings; this ending set, like most others in PIE, is heterogenous

If this is an infix between the reduplicated syllable and the root then shouldn't the reduplication of CVC be CViCVC?

Not necessarily. The original reduplication vowel may have become elided before the infix. Or the formation is old enough to have undergone ablaut (Cei > Ci), with the reduced grade having spread through the paradigm later.

Akkadian has sebe. There appears to be some numeral suffix in IE of the form *tm or *mt. So *sebe-tm > *sebtm (why the syncope?) > *septm.

The Semitic connection to 3 and 6 are less clear (and thus less likely). A number of Semitic numerals for 3 have a t-l-t structure. Some of these have an initial cluster of tl. It's not hard to imagine a dissimilation of tl > tr in IE. More often than not the vowel is -a- instead of -i-, but sometimes -i- is found which could lead to *ei in my system. The second t would have to be lost somehow, by why? For the number 6 most Semitic languages have something like sitta or shesh. Akkadian in particular has shishshu. PIE has *swek^s. A borrowing of Akkadian sh > PIE *sw is not implausible, but where would the *k^ come from? Dissimilation perhaps?

Didn't we have a discussion about this some time last year on this board? I remember it being argued that these may not be direct loans from Semitic but regional wanderwörter, as similar number words also crop up in Caucasian languages.

[Khvaragh]

Interesting. I had always wondered if the Hittite word was original or an innovation. This looks to be pretty good evidence that the Hittite numeral is an innovation.

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

IIRC the case for 7 is actually kinda appealing -- there was some Semitic language around with [sab?\atum] as a form of 7, wasn't there?

Akkadian has sebe. There appears to be some numeral suffix in IE of the form *tm or *mt. So *sebe-tm > *sebtm (why the syncope?) > *septm.

The Semitic connection to 3 and 6 are less clear (and thus less likely). A number of Semitic numerals for 3 have a t-l-t structure. Some of these have an initial cluster of tl. It's not hard to imagine a dissimilation of tl > tr in IE. More often than not the vowel is -a- instead of -i-, but sometimes -i- is found which could lead to *ei in my system. The second t would have to be lost somehow, by why? For the number 6 most Semitic languages have something like sitta or shesh. Akkadian in particular has shishshu. PIE has *swek^s. A borrowing of Akkadian sh > PIE *sw is not implausible, but where would the *k^ come from? Dissimilation perhaps?

*sab?\atum is a PS reconstruction. Arabic has Classical /sab?\atun/.
In terms of 3, Syriac has masc. /tla:ta:/ fem. /tla:t/...but also for two it has masc. /tre:n/ fem. /tarte:n/, Old Aramaic <tryn> and <trtyn>. Maybe some early confusion?