How to make a mockery of Proto-Japanese

"Nikolayev and Starostin 1994 offer many putative cognate sets and reconstructions for Nakh-Daghestanian and its branches, as part of a reconstruction of a putative North Caucasian comprising Northwest Caucasian and Nakh-Daghestanian. These two families have not in fact been shown to be related. Nikolayev and Starostin proceed by assuming relatedness and then assembling cognate sets so as to maximize recurrent correspondences." (Berkeley Linguistics Society. Proceedings of the Annual Meeting of the Berkeley Linguistics Society (1975), p.12)

Every once in a while I still get a few zealots from the long-ranger camp coming to the defense of Sergei Starostin's work with misguided and condescending comments to the effect of "How dare you criticize Starostin!" and "But look at all these correspondences". As to the first line of reasoning: a theory above rational criticism is called a cult. I don't do cults nor do I respect their followers. I also find it frustrating to talk to someone that persists on confusing academic criticism with personal attack and by so doing, creating arguments out of nothing. As to the second line of reasoning, it's the very implausibility of Starostin's correspondences that I object to, so showing me more of his paltry 'sound correspondences' is only being irritating and grievously wastes all of our time.

Recently, this letter was about the origin of Japanese numerals and it was evident that the commenter failed to absorb any of the simple facts I explained in The hidden binary behind the Japanese numeral system. So with guiltless glee I dropped his comment in the wastebasket with all the other troll trash. However, it's a chance to gloss over more pedantic silliness written by doctors of linguistics who should know better. Be brave; be self-sufficient; be curious; open your eyes wide and keep your brain closed to fantasy.

On page 341 of Choi, Japanese/Korean Linguistics, Vol. 3 (1993) (see link), in the article Notes on Some Japanese-Korean Phonetic Correspondences by Alexander Vovin, we see a list of reconstructed numerals comparing Proto-Japanese, Proto-Manchu-Tungus and Proto-Altaic. Notice, reader, how Proto-Japanese *mi 'three' is claimed to come from *ñi and that the attachment of *[ñ] to the Proto-Manchu-Tungus etymon is unexplained and ad hoc, together with the fact that a change of [ɲ] to [m] neighbouring a front high vowel is absurd and completely unmotivated from the perspective of rational notions of phonology. Compare also Starostin's *ŋ[i̯u] with Vovin's *ñïl₁ï and how fellow Altaicists aren't agreeing even on numerals or which cognates to use. We're led to believe that *mu 'six' is to be from *ñu as well and one might remark how curious it is that so many marked phonemes are being reconstructed for simple number terms. God knows why both his *-l₁ï in Altaic 'three' and *-ŋu in 'six' so conveniently disappear in Japanese, why *ñ- in '3' and *i- in '5' need to be added in Proto-Manchu-Tungus to smooth things over, et cetera ad absurdum. Indeed, maybe only God could explain such absurdity; one absurdity for another. Meanwhile, the *d- in 'four' and the same *d- in 'eight' are derived from different sources which, by doing so, ignores the unignorable vowel harmony inherent in the attested Old Japanese set (ie. mi- '3'/mu- '6'; yö- '4'/ya- '8')! No reasonable person can claim credibly that the consistent 'binary' pattern in Japanese numbers simply happened by chance from originally dissimilar roots as Vovin, Starostin et alia are effectively claiming by the shape of these reconstructions.

In other words, theory trumps facts just like we find in all religions. It's amazing what gets passed peer review (assuming such a thing was ever effective in weeding out nonsense).

Prehistoric isoglosses in Proto-Steppe

As you can see, I've been pondering on Proto-Steppe today. Many people refer to this early hypothetical language set most sensibly around 9,000 BCE as Indo-Uralic and it's called this because it's the common ancestor of both Proto-Uralic (PU) and Proto-Indo-European (PIE) afterall. However I still prefer my own term Proto-Steppe a) because it's more descriptive of the likely region where it was spoken and b) because PIE and PU aren't the only language groups implicated in the grouping. I made this simple isogloss map to show at a glance how I would explain Proto-Steppe's development into the later proto-languages known and studied and it relates, as always, to the unpixelated view of the Wave Model of language change. Thus far, I've been satisfied with a 4-vowel system of *a, *i, *u and *ə, forming a pleasant V-shape when you graph it out on paper using the dimensions of height and backness. V-shaped vowel systems are quite common around the world as far as vowel systems go.

Now to explain the three isoglosses I have on display above. I've been getting the impression for a while that Indo-Aegean (IAeg) and Altaic-Gilyak (AG) must have remained particularly close after diffusion of the Proto-Steppe community because I can think of at least two sure features that they share with each other that couldn't have been inherited from the parent language. One is the wholesale softening of word-final *-t to *-s as seen in the changes on animate plural marker *-it (n.b. further erosion of word-final *-s causes in turn Proto-Altaic *-r₂) and the other is an occasional correspondence of *a in IAeg and AG with Boreal *u in certain key words. I attribute this curious development to an original mid-central schwa *ə which could sit equally in accented positions as well as unaccented ones.

Upon revisiting these ideas, I've just realized an interesting minimal triplet in Proto-Steppe that serves as a simple but effective argument to justify the necessity of at least four reconstructed vowels at this stage:

• *ta 'from'
• *tu 'you (sg.)'
• *tə 'that (near you)'

The first becomes the source of the Indo-European ablative *-ód and Uralic partitive *-ta. The PIE form originated by agglutinating the postposition to the nominal stem in IAeg (thus *-ata), followed by Penultimate Accent Shift in Old IE which took the fixed accent off the initial (*-áta), then Syncope (*-ád̰) and finally Vowel Shift, yielding PIE *-ód with regular rules. The second and last examples show a vital difference between them since *tu becomes *tʷa (> PIE *twe, n.b. vocalism secondarily affected by *me < Proto-Steppe *mi 'I') while *tə becomes IAeg *ta without labialization of the preceding stop (>PIE *to-). This is explained if there was an unrounded vowel distinct from both low central unrounded *a and high back rounded *u, namely the mid central unrounded schwa which fits so nicely into an otherwise common 3-vowel system. Forms that suggest to some long-range linguists the apparent existence of a proximal demonstrative **ti on the Proto-Steppe level^[1] are, I figure, caused by later analogical derivation out of inherited *tə since this proximal demonstrative is only evidenced in Boreal and AG while IAeg seems to preserve only *ta 'that' (> PIE *to- and Aegean *ta) with a distinct proximal counterpart *ka (> PIE *ḱo- and Aegean *ka). I take the IAeg evidence to show an original word *ka 'this' in Proto-Steppe since, if this is not so, the source of the IAeg form would remain much more obscure than that of Boreal and AG's *ti vis-a-vis the securely inherited deictic *tə. The Altaic forms with word-initial sibilant in place of expected *t- are surely caused by pre-Altaic palatalization before high front vowels as has also apparently occurred in its second person pronominal forms.

All these speculative ideas while interesting and worthy of discussion are however, of course, subject to some range of interpretation. Debate remains open.


NOTES
^[1] See, for example, page 2 of Frederik Kortlandt's article Indo-Uralic and Altaic [pdf].

Back to business: emphatic particles and verbal extensions

Now, returning to the safer topic of comparative linguistics, I still am trying to account for how my new solution concerning the prehistoric genesis of Proto-Indo-European's uvular sounds helps (or maybe hinders?) my attempts at trying to figure out the origins of the emphatic particle *[ǵ/g](ʰ)[e/o] which is thus far so hideously reconstructed by current Indo-Europeanists.

However, if we take the velar contained in the nominative first person singular pronoun, which appears to contain the fossilized remnants of the earliest form of the emphatic particle when the pronoun was first coined in the Late Period (ie. *h₁eǵoh₂, literally "(as for) my being here" from *h₁e "here" + *ǵe [emphatic] + *-oh₂ [old 1ps subjunctive]; parallel in development to the 1ps pronouns of Inuktitut uva-ŋa, Aleut ti-ŋ, and Proto-Semitic *an-āku), we are pointed to *ǵe as the most appropriate reconstruction. Any other forms of this particle would then have developed later after presumably being influenced by or merging with other existing words or particles with similar phonetics and meaning. In the earlier Mid IE (MIE) stage, we could then posit an emphatic particle *g̰a derived from Indo-Aegean *k’ə. From there, if comparable to Uralic emphatic *-ka attached to some pronominal stems^[1], we might finally reconstruct a Proto-Steppe emphatic particle *k’ə to account for both the Indo-European and Uralic forms. Can you all swallow that? Granted, this all remains tentative for now, but it's worth a shot.

Considering the differing velar stop in the emphatic particle, the verbal extension with uvular stop, seen in PIE verbs like *yeu-g- "to join" whose *g-less counterpart has identical semantics, must not be related afterall as I had previously assumed. Instead I'd like to suggest that it derives from a Mid IE aspectual marker *-ɢ̰a-, which originally might have conveyed a perfective sense. This implies earlier Indo-Aegean *-k’a- (thus Etruscan -ac- [perfective] as in tur-ac-e "was given") and relatable then to the Uralic perfective in *-ka. In this case, a Proto-Steppe perfective suffix *-k’a would be in order to explain the later forms.

That so far is my solution concerning that. Let's see if this idea sticks.


NOTES
^[1] Fortescue, Language Relations Across Bering Strait (1998), p.113 (see link) confirms Uralic emphatic *-ka.

My suspicion regarding the source of *r2 in Pre-Altaic seems to be confirmed

I just came across this parenthesized snippet from page 75 of Street/Miller, Altaic Elements in Old Japanese (1975) (see link) which discusses the evidence for causative markers in Proto-Altaic:

"(This looks like pA *-r₁-/*-r₂i-, conceivably from pre-Altaic *-r-/*-ri- [i.e. *-r(i)-] before the phonemic split of the pre-Altaic liquid.)"

I find this fascinating because it seems to confirm something that I had reasoned long ago concerning the source of the phoneme *r₂ in the Altaic plural marker. I figured that if the original plural common to Proto-Indo-European (PIE), Proto-Aegean, Proto-Uralic and Proto-Altaic (PA) was *-it, then presumably PIE and PA share the isogloss of Sibilantization of word-final *-t. After becoming *-is, the ending would have rhotacized in Pre-Altaic to *-ir before being palatalized to *-(i)r₂. So it appears very strongly that the source of all instances of Proto-Altaic *r₂ lies in the early palatalization originating from a neighbouring *i in a Pre-Altaic stage.

Updating my Pre-IE pdf (already!)

Considering that I made my aforementioned pdf of Pre-IE changes on the fly, it's expected that I have much work to do before I can be reasonably satisfied that all the errors are ironed out and that it properly reflects my current views. Odd as it may seem, all these ideas and theories were off the top of my head and boy oh boy, did I ever feel a great weight lifted off my half-shattered brain as I poured them into that file!

Here is the second version of my file. I know it's rather soon but it's necessary to fix some errors Besides, I get off on being obsessive-compulsive, LOL!

DiachronyOfPreIE_2008Jul02.pdf

Hosted by eSnips

Now to explain the changes of my second draft of my Pre-IE theory. I recently remembered that the last time I had left the topic of Indo-Aegean Sibilantization, I had already renamed it Word-Final Lenition because word-final *-k may also have been reduced to a glottal stop at around the same time. Miguel Vidal had theorized something similar and I've come to grow fond of this spin on his ideas^[1].

I then rearranged the order of some changes in the Indo-Aegean section and added a very important sound change: Centralization. Centralization is the idea that an originally 3-dimensional vowel system was "centralized" and reduced to a 2-dimensional system. This new system that had developed would have had only a contrast in height between *a and *ə. This is also the point at which labialized stops first surface in the language. I suspect that this was an innovation spurred on by contact with an ancestral form of Proto-Abkhaz-Adyghe (aka Northwest Caucasian). This hypothesis is largely based on Allan Bomhard's theories on Nostratic and Pre-IE^[2] with a few notable twists and extra details which I've mentioned in the newest version of the pdf.

For Phoenix, I've added a few PIE examples (*wástu and *márḱos) to add support to the Labial Dissimilation Exception of Vowel Shift at the end of Late IE. Time will tell whether there are good objections against my hypothesis though.

I also corrected my error concerning "Root Aorists" in the Post-IE section since, based on the example I provided, obviously I meant to say "Thematic Aorist". Mea culpa. Thank you, Rob, for spotting that and asking questions. Verb forms like *likʷét "she left" and *widét "she knew" are now considered by Indo-Europeanists as a later innovation that can't be reconstructed for the Proto-IE stage.

NOTES
^[1] Miguel Carrasquer Vidal, "Re: [tied] Dissimilation of gW/kWVw to gVw/kVw", Cybalist (Yahoogroups) (Apr 19 2005) (see link). Here, he proposed that *-ku > *-kʷ > PIE *-h₃ while final *-ki > *-h₁. I feel that this is unnecessarily complex but that the idea of the dual ending evolving as *-ak > *-aʔ > PIE *-(i)h₁/*-e (via Laryngeal Vocalization) entoxicates me since it could potentially explain the relationship between PIE's dual on the one hand and Uralic *-k(V) & EA *-k on the other. Lenition already explains the connection between PIE *-es and Uralic plural marker in *-t.
^[2] Bomhard, Indo-European and the Nostratic Hypothesis (1996).

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).

UPDATES
(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.

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

How NOT to reconstruct a protolanguage

I wrote an article last month, The Tower of Babel, which was an unexhaustive critical assessment of the late Sergei Starostin's grandiose online language project that limps on today through the efforts of surviving project members. A recent troll on that page under an unconvincing disguise of "G.Starostin" sent me two messages, one visible because it was civil if not misguided, while the second was abusive and thrown in the trash after I took note of his IP address. In case anyone was confused, my blog isn't a mouthpiece for proto-world rhetoric and I'm an ardent defender of mainstream linguistics despite my moderate interest in long-range linguistics. It suffices to reject the Tower of Babel project based simply on the consistent use of outdated and even disprovable information. Things such as its Indo-European database, infected with Julius Pokorny's 1950s reconstructions which notoriously neglected to reconstruct laryngeals to properly account for reflexes in Anatolian languages like Hittite, Luwian and Lycian. When a word halχ is assumed to mean “10” a priori in Etruscan purely by eyeballing texts and ripping words out of context in order to reject what is already established to be śar (c.f. Bonfante, Reading the Past - Etruscan (1990), p.61), Starostin's supplied pdf entitled Etruscan numerals: Problems and Results of Research by S. A. Iatsemirsky^[1] is not credible enough to identify neither the problems nor the results of serious Etruscan research. Its Dravidian database is full of largely unaccepted reconstructions using voiced stops that are not proven to be necessary in that proto-language^[2]. Then the addition of a Nostratic database and "Long Range Etymologies" is sure to add to the air of mediocrity of the website, putting the cart before the horse in light of the numerous mistakes regarding the more accepted languages and language families I just mentioned. This is all on top of the decidedly negative assessments of North Caucasian pushed by Sergei Starostin during his lifetime (Johanna Nichols, Current Trends in Caucasian, East European, and Inner Asian Linguistics (2003), p.208). I personally believe in an efficient use of time. So if it's proven that this website is consistently at odds with the mainstream, one would be wise to obtain a higher quality of information elsewhere.

On that note, it's important to discuss how NOT to reconstruct a protolanguage so that we're all on the same page and can more easily distinguish between real linguists and narrow-minded loons, whether online or in print. Considering that even Merritt Ruhlen of "Proto-World" infamy^[3] has obtained his PhD from Stanford University, it's important to not be deceived by academic status. Theories can be ill-conceived no matter who one is or claims to be. So let's go through my cheeky list of important strategies that we can follow (using examples from the Tower of Babel project) if we want to isolate ourselves and be rejected by all universities around the world.

1. Use "phonemic wildcards" obsessively! Cast the net wider and you might catch something!

The abuse of mathematical symbols like C, V, [a-z], (a/é/ö), etc. are an excellent way to make your idle conjecture look like a valid theory. It might be called "reconstruction by parentheses" since parentheses are either explicitly shown or hidden by a single variable. An example of this is *k`egVnV (claimed to be the Proto-Altaic word for "nine" in the Tower of Babel database). Obviously, if V represents all possible vowels in this proto-language and there are, say, ten of them possible in either position, then the fact that there are two wildcards in the same word means that the word represents a humungous, two-dimensional matrix of ONE HUNDRED possible permutations (10*10=100):

*k`egana, *k`egena, *k`egina, *k`egüna, *k`egïna, etc.
*k`egane, *k`egene, *k`egine, *k`egüne, *k`egïne, etc.
*k`egani, *k`egeni, *k`egini, *k`egüni, *k`egïni, etc.
*k`eganü, *k`egenü, *k`eginü, *k`egünü, *k`egïnü, etc.
etc.

Since no single form is actually being posited when wildcards are present, any claim of regular correspondence by such a theorist can be easily identified as fraud. If such linguists can't take themselves seriously enough to hypothesize a structured and testable theory, why then should we take them seriously in turn?

Other hilarious examples of wildcard fairy tales on the Tower of Babel site include Nostratic *cUKV ( ˜ č`-) "bundle" (in other words, all four are wildcards... jackpot!), Dravidian *kaṬ- "to cut into pieces" (universal onomatopoeia, anyone?), Semitic *ʔVrib- "tie (a knot)" (based on a single language, Arabic) and North Caucasian *ƛ̣_VẋwV ( ˜ Ł_-)̆ "rake" (wow, the number of possible permutations in this wildcard buffet is positively mindboggling! 200 perhaps?).

2. Ignore Occam's Razor and never seek logical justification for your ideas! If an exotic phoneme gives you an orgasm, reconstruct it!

Most longrangers ignore Occam's Razor or fail to apply it in all aspects of their budding theory. It's easy to understand why it's not valid to reconstruct a sound in a proto-language which shows no regular correspondence in its daughter languages. However, even when one has justified a phoneme with evidence, one still has to justify the plausibility of the larger sound system that it's a part of. So if you have greater evidence for a palatal *ź than you do for its plain counterpart *z, you still have a problem to solve (c.f. phonemic markedness). If pronouns and common affixes use the more complicated sounds of the inventory of your proto-language, you still have a problem since this goes against the trend in languages we observe throughout the world, a reason that Allen Bomhard used to reject Illich-Svitych's reconstruction of Nostratic (e.g. Illich-Svitych and Dolgopolsky reconstructed the 2ps pronoun starting with the symbol *ṭ-, an ejective rather than its plain counterpart). This is how Occam's Razor works. In all aspects of our theory, we must abide by the simplest answer possible. Whenever you hear an argument like "Yeah, but, there's this language in some remote part of Africa with 30 speakers that uses a really rare sound or does something else that's really rare just like in my theory!" then you know that you're not dealing with someone in their right mind. Occam's Razor avoids unnecessarily exotic solutions at all times and teaches us to not confuse "minute possibility" for "convincing probability". For example, Klallam is certainly an existing spoken language, but there's also no doubt that its sound system and consonant clusters are very rare. So Klallam is something that your proto-language should not look like until you have solid proof (i.e. numerous regular sound correspondences) to back it all up.

By searching in the Tower of Babel's North Caucasian database for words beginning with sibilants, we get the following screwy search results. As of today, only one word with plain *z- in initial position is to be found, namely the first person pronoun claimed to be *zō, despite the fact that there are two instances of *ź- and *ž-. This means that plain *z- is outnumbered 3 to 1 by the comparatively more exotic counterparts with palatalization, labialization, clusters, etc. Even worse, there are only two instances of plain *s- among twelve roots starting with unvoiced sibilants. So plain phonemes are in the minority, as we would find if we were reconstructing a science-fiction language. Consistently, Starostin's North Caucasian defies any rational structure or common sense and a perfect example of diacritic overkill.

3. Make pages and pages of "correspondence tables" They're sure to impress your family members!

"Correspondence tables" are lists of sounds in the daughter languages of a hypothetical proto-language proposed to prove regular correspondence and thus genuine relationship. So we can say that Germanic *θ often corresponds to Latin t as Jacob Grimm remarked upon in 1822 showing that Germanic and Latin are part of the Indo-European family of languages. However, language isn't that simple and far more often than not, there are numerous exceptions to such simplistic equations. For example, the word 'eight' is octo in Latin and yet *ahtōu with a *t in Germanic. This is because the stop fails to be weakened to a fricative after another stop. What good then are correspondence tables when we can save time and space by actually describing sound changes and their processes? For some reason, Nostraticists and other longrangers like to use these at every turn, as does Sergei Starostin. These childishly repetitive tables simply waste pages and pages of paper and bandwidth without being terribly informative, but it's certainly an excellent way to make your book look thicker and impress your family.

4. Remember: All critics are conspiring against you! Beat dead horses to death and if you can't win, punch them!

You may find that your theory isn't gaining the kind of press that you had hoped and quite a few may be noticing several flaws in your theory. You may not have a single factoid in your favour to form a coherent rebuttal. This is when you bring out the big guns: ignorance combined with non sequitur. This tactic must be handled delicately however. You could try attacking your critics on the personal level, whether that be through the direct use of swearwords or through subtle mockery of your opponent. However this is a desperate last resort, more common on Yahoo! Forums or Youtube. It looks more professional however to simply ignore critics altogether while overpraising the capabilities of yourself and your associates. Using a plethora of unnecessarily sesquipedalian, multipolysyllabic megaterminology, such as "lexicostatistical", is a great tactic to conceal the weaknesses of your theories, as is treating your conjectures as proven facts in any of your publications so as to not bog down your important work with silly things like justification or common sense. Remember, all critics don't know what they're talking about. Their valid criticisms are just a devilish trick of theirs to throw you off-track and pull you off of your hobby horse.

NOTES
^[1] Note that this pdf incorrectly cites TLE 295 in reference to a word zar when in fact it's properly TLE 275. Furthermore, automatically assuming that zar and śar are the same word purposely ignores phonemic distinctions in order to stroke one's pet theory. The instance of huθ-zars declined in the genitive case (TLE 191) has absolutely nothing to do with zar and everything to do with the fact that a dental stop plus the initial sibilant of attested śar (TCort ii) yield z /tʃ/ in this one particular instance. It's all quite understandable once one puts in the time and effort learning the basics of Etruscan phonetics.
^[2] See Krishnamurti, Comparative Dravidian Linguistics: Current Perspectives (2001), p.250 [click here]
^[3] Visit Mark Rosenfeld's humorous but rational article on the Proto-World language and its associated failures in reasoning: Deriving Proto-World with tools you probably have at home. One of the most poignant criticisms towards the proposals of Merrit Ruhlen and Joseph Greenberg (R&G) that I appreciate here is: "R&G really gain the benefit of obscurity here: how many of us can determine whether they are (unconsciously) playing the same kind of tricks with Tfaltik and Guamo as I am playing with Chinese and Quechua here?" This criticism is equally applicable to Starostin's theory of North Caucasian and his Tower of Babel project where a similar "benefit of obscurity" is being used against his readers.

UPDATES
(Feb 14 2008) My entry The hidden binary behind the Japanese numeral system exposes another flaw in Starostin's reconstructions concerning the origin of Japanese numerals.