some notes on numbers

Thu Jun 21 02:19:10 UTC 2007

my personal favorite numeral system (after Skou and Kanum) is the
Skou-family language that counts:

1     1
2     2
3     2+1
4     2+2
5     2+3
6+   many

Arop and Sera from Sissano have more elaborate numbers, in my 2000
data; the Arop weren't all wiped out in the tsunami. Even excluding
the large number of people living in Vanimo and Aitape, there were
about 6 survivors from the village.

-Mark

On 6/21/07, an-lang-request at anu.edu.au <an-lang-request at anu.edu.au> wrote:
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>    1. Numbers yet again - Re: New Book from SIL PNG  (Richard Parker)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Tue, 19 Jun 2007 23:31:57 -0700 (PDT)
> From: Richard Parker <richardparker01 at yahoo.com>
> Subject: [An-lang] Numbers yet again - Re: New Book from SIL PNG
> To: an-lang at anu.edu.au
> Message-ID: <200489.29255.qm at web50205.mail.re2.yahoo.com>
> Content-Type: text/plain; charset="iso-8859-1"
>
> Glen Lean's data is held by the Glen Lean Ethnomathematics Centre at Goroka University, PNG.
> http://www.uog.ac.pg/glec/thesis/thesis.htm
>
>   There is a link on the website to the full database, but currently there's a glitch that prevents access. That should be repaired in Aug or Sept.
>
>   Dr.Kay Owens is very kindly emailing me with batches of a couple of volumes of data every other week. They are very detailed and take a bit of digesting, but are invaluable.
>
>   They're available, as they come to me, for anyone interested. I would request, politely, that others don't barge in, and upset the flow.
>
>   I really don't blame Glen Lean for using old records rather than his own primary sources. He did some field work in the 70s, and was adopted into the Tolai (New Britain). He later set up a questionnaire system, with local chiefs and priests, for current number names (CSQs in his docs), but often the systems were already going out of use, in favour of Tok Pisin, even as he collected data.
>
>   Comparing the older documents with the newer CSQs gives a very good idea of the interim language changes. Some were very stable, and others quite fluid.
>
>   Glen wasn't so concerned with the linguistics of the number systems, as with the mathematical logic of them, but his papers usually give glosses of words used in constructing the numbers, which are invaluable.
>
>   The old documents preserve a lot. I know of only one An language that had only 2 words, 1 and 2, for their entire counting system (Arop Sissano - N New Guinea).
>
>   Both villages, Arop and Sissano, of c2000 inhabitants each, were completely wiped out by the tsunami of 1998.
> See John Terrell's comments at:
> http://www.archaeology.org/9811/abstracts/pacific.html
>   =====================================================
>
>   Re hands and number systems:
>
>   Harald - I wasn't very clear - there usually seems to be a sharp break between 1-5 and 6-9, but not in the first hand count. Foot morphemes are often used in counting the 'teens, and 'whole man' is frequent for 20.
>
>   In some Papuan body part tallies, they go the whole hog - fingers first, then up the arm, round the head, and down the other side, to end up with number systems of base 27, 35, or whatever, but few of these are in contact with Austronesian languages.
>
>   The evolution of the number systems, from simple 1 & 2 words only
>
>   - to 1,2,3,hand, hand+1,2,3, 10=2 hands
>
>   - to a full decimal system where 5 is no longer directly related to hand, and ten is a stand-alone numeral, 20 is 2 tens, and not 'whole man', is traceable.
>
>   And that evolution story does carry a lot of useful information.
>
>   eg: many Vanuatu languages still retain hand+1,2,3,4 for 6-9, so those islands must have been first settled before the full An decimal system was conceived. It's possible, even, to detect sequential waves of Vanuatu settlement as the number systems grow more sophisticated.
>
>   There's an alternative, of course, that they were too stupid, or too conservative, to accept a simple new system brought in by Austronesian-speakers ready-equipped with the PAn decimal system.
>
>   A third alternative could be that the uses to which counting was put didn't justify more sophisticated systems. Local people here on Siargao island use An numbers for counting things, and measuring, but Spanish ones for money and time. The higher,less-used numbers are going first, but isa ka gatus is still used for measuring depths (fishing), in preference to syento.
>
>   (I'm becoming aware that studying these number systems is much more complex than a simple analysis of morphemes and numbering systems. We tend to split off and specialise in maths or linguistics or ethnology, but they're very intertwined, and perhaps they could use a little more miscegenation).
>
>   Polynesians, who arrived on empty islands with a ready-made decimal system, had the means to develop number systems up into the millions, and have done so.
>
>   For the source of island settlements, there may be clues in number words used elsewhere.
>
>   Here's a fairly basic An system, Dawawa - Milne Bay, PNG.
>
>   1....tegana
> 2....rabui
> 3....rabui tega  (2,1)
> 4....rabui be rabui (2,2)
> 5....nima tegana yakovina (hand 1 finished)
> 10...nima rabui yakovina (hand 2 finished)
> (No numbers available for 6-9)
>
>   Abui, abu, and abuti are 2 in Mountain Koiari, Koita, and Grass Koiari, all Papuan speakers, but some 200 miles west, over the mountains of the Papuan bird's tail, near Port Moresby. No other number word morphemes in those languages resemble anything in An.
>   Perhaps r(u) abui, l(u) abui, are combo An/Pap mixtures.
>
>   Rabui/labui for 2 is very much like the connector laB or leB in 6-9 in many Vanuatu languages.
>
>   Near to Dawawa, Boianaki (An) has progressed a bit:
>   1....sago or saukava
> 2....rua
> 3....aroba - innovation - named number 3
> 4....rua ma rua
> 5....meikovi
> 6....kumaneva sago
> 7....kumaneva rua
> 8....kumaneva aroba
> 9....kumaneva rua ma rua
> 10...ima rua (ikovi) - hand 2 or 'finished'
>
>   By the 'Boianaki' stage, number 3 has become a monomorpheme, with no very obvious etymology, but it could well be a-2-ba, or 2+.
>
>   So a similar etymology could then apply to PAn 3 *telu = to-2. (The morpheme lu, or ru seems more common than du as 2, though Nelemwa, in New Caledonia, right at the end of the chain, apparently uses du, lu, and ru interchangeably).
>
>   Boianaki 6-9 has a different morpheme, kuma-neva, than nima=5, and I'm assuming, so far, that this is related to 'fist' or 'knuckle', and neva to hand. Kumo is fist in Cebuano.
>
>   Nevera, Bari, nar, nëvëren are words for hand or arm in some Vanuatu languages, and a related morpheme is used in hneva=9 in the Solomons.
>
>   yari, Bar, Beri, kuver, are variants for 4 in some Vanuatu languages.
>
>   Rempi (Pap), Gedaged (An) Wagi (Pap) Panim (Pap) Bilbil (An) are neighbours on the N New Guinea coast. Their names for 4 go: walik, pal, varos, woalai, pali, waloso. None of the other words in their 1-10 number names correspond between An and Pap in any way. So who lent to who and why?
>
>   Except for one example - Wagi's evel-leplep = 10, is remarkably similar to SW Tanna's kelkelep kelkelep. SW Tanna is way at the bottom of Vanuatu, 1800 miles away.
>   ==================================
> Non-hand morphemes:
>
>   Papuan languages Bargam, Wagi, and Panim, all TNG Madang-Adelbert, and close(ish) to each other in Morobe, N PNG, use  abainakinta, tanigole, mamagai as a 'thumb' morpheme for 5. Neighbouring An languages use a variant of nima (hand).
>
>   Waffa, another Papuan language further east, sometimes uses 'eero ivo'= 5th finger, for 5, but also a more usual yaaku sai-vai = hand-half-it is.
>
>   The Wagi tanigole, thumb, seems remarkably cognate with Malay tangan, hand.
>
>   But not teeth - definitely not....so far.
>
>   Some of the Alor Pantar Papuan number systems have an unusual subtractive system, as developed in Manus Island, 1500 miles away. ie 6-9 goes 3,2,1, not 1,2,3
> ===============
>   regards
>   Richard
>
> PS I've just been reminded by Laurie Reid that most professional linguists are VERY busy, and perhaps I should just buy a couple of Teach-Yourself-Linguistics books, and find out for myself. The last book I ordered took 18 months to be delivered.
>
>   This discussion forum is more or less empty, except for my little piping voice. It's been very usefully active in the past, and it is certainly helping me now.
>
>   If I ask a stupid question, I really don't demand or expect an immediate answer.
>
>   But the stupid questions are there on record, and if someone suddenly makes a connection, and contacts me, then I'm more than grateful for any help.
>
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