Monday, November 26, 2007

Base 4 - How?

A very well known Austronesian linguist wrote, in the An-Lang group:
"I cannot imagine what may have been the source of having '4' as a base for numeration."

I responded: The 1-4 numeral system is not so baffling when you consider that virtually all numbering systems began with finger-counting.
It just comes down to whether you consider the thumb part of the finger-count or not.
Different ways (and directions) in totting up fingers seem to have quite perceivable effects on the resulting number words.
Either way.
You might [ignore the thumb or] even emphasise it:
Bargam (Papuan) uses abainakinta (thumb) for 5.

The 'Papuan' Kewa of the PNG Southern Highlands have two number systems, a full body part tally (hand, up arm, over, and down the other side) giving a 47-cycle number system, used mainly by elders for massive gift exchanges, and a 1-4 cycle system for everyday stuff.
They're described at:
(The strange bit, that I still can't fathom, is how 7 = hand + 3 thumbs).
There's even a Papuan language (Kote, from Morobe Prov) that has a 22 cycle system, because they count both nostrils as well as their fingers and toes. (Wouldn't want to buy a dozen bread rolls from them, though).
There are more than a few Austronesian numeral systems that [seem to] show vestiges of an archaic 4 cycle system, with 8 at the end of the 2nd cycle, but most are now overlaid with a 10
In fact, they are rarer in New Guinea, with its multiple language families, and quite absent in Papuan languages west of there. They're not so very common elsewhere. (Except in California - where else?)
And there is even a suggestion of a vestigial trace of a 4 cycle system in Indo-European, in that *oktĂ´ is apparently the dual form of *kwetwores - Beeler (1964, p. 1). Common counting in dozens may be another vestige.
If the 6-9 numbers are simple 5+1, 5+2, etc, then 8 would include, somewhere, 3. If it's subtractive from 10, it would include 2. If it includes 4 then that indicates something
quite different.
If 9 includes a 1 morpheme, then it might be like 'sembilan' in Indonesian, or 'salapan' in Sunda, ie 1 from 10, or it could 'start again' from 8, which it would seem to do in the cases where 8 involves 4.
The next cycle, to 12, seems to have been mostly overlaid now by 10/teen systems.
Except, perhaps, in English, where 11 and 12 are 'irregular'.
Austronesian 4 cycles:

Formosa: Siraya, Thao, Favorlang/Babuza, Taokas, Saisiyat,
Atayal, Sedeq
- all show no. 8 inclusive of 4, then start again with 'something different', often including a 1 morpheme.

Enggano (which may not be An at all) - has an 8 related to 4.

Simba: Gaura Nggaura and Lamboya have 8 = pondopata ='x'.4 (or cognate) and banda' iha (or cognate) for 9.

Flores: Ende, Rongga, Lio and Nghada - have 8=2x4 and 'ta esa' (or cognate) for 9

Aru: Kola, Dobel, Ngaibor, Barakai, Tarangan West, Ujir - 8= karua and 9= ser, or tera (or cognates)

Keule, Wogeo, and Biem, offshore of E Sepik Prov, PNG, have straightforward and obvious 1-4 systems: Boiken, a neighbouring Papuan language shares this, but only in one offshore island dialect, near the An speakers. But the system may be related to nearby Vanimo, Rawo and Mountain Arapesh, Papuan languages, also with 1-4 number systems.

Ormu, Tobati/Yotafa and Kayupulau near Jayapura, have 'symptoms' of a 4 cycle. Adjacent to them is Nafri, the only member of the Sentani family to have a 4 cycle system.

Of all these, it seems only the Wogeo/Biem and Ormu/Yotafa groups may have existing neighbouring non-An languages with 1-4 systems. But those Papuan languages are very much in the minority themselves, so without more information there is no way of telling which way the influence went.

There are other languages that have a 4 morpheme in 8, but they seem to have a multiplicative system, with 6=2x3, etc, rather than a 1-4 cycle:

Wuvulu-Aua, in the Admiralties, has a strange (and very lonely) number system, analysed by Dempwolff (1905) as:
aiai : 1 - 1
gu-ai : 2 - 1
odu-ai : 3 - 1
gui-ne-roa : 2 - 2
ai-pan : 1 hand
ode-roa : 3 - 2
ode-ro-miai : 3 - 2 +1
vai-ne-roa : 4 - 2
vai-ne-ro-miai : 4 - 2 +1
(Almost all other Admiralties numerals show the unique Manus subtractive system).

'Motu' languages (under the 'tail' of Papua New Guinea) also (mostly) have a number 8 related to 4 (taura hani), and 9=8+1, but these also have 6='2'x3 (taura toi) with 7 = a 'regular' hitu, or ima ua =5/2 or 6/1 (karakoi ka pea). Quite mongrel systems.

Some of the Formosan number systems may be similar to this.

Or something else:
Makassarese: 8=7+1 - mystery in Sulawesi
but many languages in Borneo have 7= tudju (or cognate) and 8 = aya, hanga, or mai, followed by 9 = piah, jalatien, riqi (or cognates), which look as if they might just be 'start-agains'.

Cognates of 'hanga' for 8 also appear in the Solomons.

(I have no translations or even speculative etymologies for any of them, having 'discovered' them only yesterday, thanks to Anthony Jukes giving me the link to his excellent new Makassarese Grammar at: