14 Feb 2008

The hidden binary behind the Japanese numeral system

I've been inspired to write this after recent comments on my ire-provoking entry How NOT to reconstruct a protolanguage showcasing Sergei Starostin's posthumous reconstructions as exemplary anti-scholarship.

One important fact that everyone needs to know about Japanese numbers before blindly reconstructing Proto-Altaic numerals for themselves is that the entire decimal-based system shows a series of pairs in Old Japanese that "rhyme" through the use of internal vowel alternations. Please direct your attention to the folowing table:

fitö- '1'futa- '2'
mi- '3'mu- '6'
yö- '4'ya- '8'

Everyone sees this phonetic/mathematic pattern crystal clear now, ja? The pattern is undeniable. We see two regular vowel alternations, one of i with u and the other of ö with a, by way of rounding and derounding vowels in one root to derive the other. This was written about in detail by Miller in 1967[1]. However, it seems upon my brief Google Book search that it was remarked upon as far back as 1873 by Ellis[2]!

So when poor ol' Mr. Starostin had reconstructed *ŋ[i̯u] "3" and *ńu- "6" (using both Old Japanese mi- '3' *and* mu- '6' as examples in the two cognate sets), I can only assume that he lacked adequate literature in his local library to have possibly overlooked this simple fact about binary vowel alternations in Old Japanese numerals. Oopsy daisy! Naturally, it shouldn't have to be explained that only one of each pair in the table above may logically ever be attributed to Proto-Altaic. We have to choose one. This is yet another reason why Starostin's online database of reconstructions must be taken with a big pinch of salt (or perhaps an entire truckload of salt).

(2010 Jan 28) I fixed the links to Starostin's reconstructions in his lingering database online. Someone wrote me lately that the reconstruction, *ŋ[i̯u] "3", shouldn't have brackets but they're clearly there in the database, only adding to the dubiousness of relationships claimed.

[1] Miller, The Japanese Language (1967), p.337.
[2] Ellis, On numerals as signs of primeval unity among mankind (1873), p.50 (see link).


  1. not to mention a shift of ń > m (where I'm guessing ń is a palatalised n) and ŋ > m is incredibly unlikely if not done due to assimilation of a following/preceding labial consonant (or maybe vowel).

    The other direction would've looked more likely (See Sanskrit doing this in Sandhi to some extent for example).

    It's hard to look at Starastin's reconstructions and believer he took himself seriously.

  2. hitotsu - futatsu
    mittsu - muttsu
    yottsu - yattsu

    I never noticed that before!

  3. Phoenix: "not to mention a shift of ń > m (where I'm guessing ń is a palatalised n) and ŋ > m is incredibly unlikely if not done due to assimilation of a following/preceding labial consonant (or maybe vowel)."

    Yes, exactly. If I were to look through Starostin's eyes for a moment, I would assume that he was thinking that the following *u, being labial by nature, would suffice in labializing a depalatalized *n-. That's the only way I can conceive of this happening. So his underlying assumptions seem to be A) that these onset nasals had a palatal element, B) that the nasals were depalatalized somehow and C) that the vocalism must be *u in both "3" and "6" in order to cause labialization to /m/ in both these numerals.

    It's all over the place but fortunately the Japanese pattern screws his whole ideas up nicely in one go anyways. So we don't have to ponder incessantly about a false claim.

    Personally, I think that if anything, the OJap roots fitö- '1', yö- '4' and mu- 'six' are the only ones that can be plausibly related to Proto-Altaic. The root yö- is presumed to go back to Proto-Altaic *dȫr- (Turkish dört, Mongolian döröv) and there is a regular pattern of Altaic *d- > Japanese y-.

    Goofy: "hitotsu - futatsu mittsu - muttsu yottsu - yattsu I never noticed that before!"

    People might often miss this pattern because the 'rhymes' aren't one after the other. They're seperated by multiples of two. As well, before /i/, modern Japanese has changed the earlier bilabial fricative to /h/, obscuring the pattern a little between ひとつ hitotsu and ふたつ futatsu.

  4. I find a shift between word-initial [ŋ] and [m] very easy to imagine. Such a shift is the difference between the 1st pers. sg. pronound of Emeŋir and Emesal, for example. A shift between [nʲ] (and yes, that's what a Moscovian ń means) and [m] would be very surprising if it happened in one step, but if we start with a collapse of the /n/-/nʲ/ distinction and then have a somewhat strange assimilation in labialisation from /nu/ to /mu/, I wouldn't really call it "incredibly unlikely". Tomorrow I'll check the preface of the EDAL to find out if that's what Starostin, Dybo & Mudrak postulate.

    Besides, I wouldn't be surprised at all if this amazing binary system were a post hoc interpretation, at the origin of which could be a few analogical developments like those seen several times in IE 4 and 5 (and, according to some, 6 and 7). Indeed, Starostin et al. postulate just that for an otherwise irregular /k/-/p/ correspondence between... I think it was 2 and 20, I'll check that, too.

    Question: Does word-initial /ŋ/ occur in Emesal?

  5. David Marjanović: "I find a shift between word-initial [ŋ] and [m] very easy to imagine. [...] Besides, I wouldn't be surprised at all if this amazing binary system were a post hoc interpretation."

    Whether you feel this is "likely" or not is somewhat moot because, as I just wrote, Starostin's claim is falsified by the data supplied. Rather than address this inconvenient fact, you're choosing to fit the facts to your preconceptions rather than deriving your views from the facts. I'm not the type that humours indulgent sub-optimal conjectures. If you indeed believe that the Japanese pattern is merely a "post hoc interpretation", the onus is on you, not I, to supply evidence in support of your claim. So far, I'm winning this debate and you can't let me do that, right? >:)

    "Question: Does word-initial /ŋ/ occur in Emesal?"

    Yes, it appears so. I would say that it's more common for initial /m/ to deround to /n/ or /ŋ/ than vice versa, because this only requires the weakening of bilabial closure. I would reckon that the addition of the feature of lip closure to an initial /n-/ requires some very strong motivation for this added articulatory effort. While analogical change within the numeral set is common and possible in general, it doesn't appear probable here when Starostin's typically "parenthetic" *ŋ[i̯u] "3" has not been demonstrated with regular sound correspondences using a competently reconstructed phonology that doesn't violate phonemic markedness at every turn.

  6. Is there any attested natural language that productively forms larger numbers by doubling smaller ones? Or that forms larger units by ablaut of smaller ones? If either of these phenomena are well-attested, it would be easier to believe that this pattern reflects a productive process in pre-Japanese rather than a coincidence - but I don't recall ever observing anything similar. To me, random coincidence seems a less marked explanation of these particular correspondences than postulating that Pre-Japanese formed numbers in a manner unlike any other known language. If it had an ablaut-causing dual or something, that would help - but I don't know of any independent evidence for that.

  7. Lameen Souag: "Is there any attested natural language that productively forms larger numbers by doubling smaller ones?"

    Excellent question. The pattern here is, you have to admit, unusual. The statistical chances of something like this being coincidental (i.e. the phonetically coherent ablaut pervading the numeral system in clockwork fashion and the common consonantism between all pairs while simultaneously showing a conscious mathematical pattern of doubling) are too comically insignificant to entertain.

    So I think the only valid question remaining is whether this is the product of conscious derivation or mere analogical assimilation within a numeral system. It's true that the latter phenomenon is well attested throughout the world (e.g. Latin quattuor & quinque < PIE *kʷetwóres & *pénkʷe).

    However there are a number of languages that derive new formations from ablaut such as the broken plurals of Arabic, Middle Egyptian and Coptic (e.g. Sahidic noute 'god' < *nuṯar vs. entēr 'gods' < *naṯūru). If ablaut and plurality can go hand-in-hand, why is it so objectionable for Japanese to employ the same feature particularly when vowel harmony is a distinctive feature of Altaic languages?

    Now, while I think that the mechanism for this alternation is not unusual, I personally still need to research the possible extent of such "broken plurals" (if any) in Old Japanese or Proto-Japanese to add further weight to the case.

    The pattern is clear and it's clear that Starostin's reconstructions are dismissive of these facts but what's unclear is how this particular pattern arose in Japanese. I have my suspicions though.