Austronesian Counting

Tuesday, June 24, 2008

Kokota – one of the most bizarre numeral systems attested for an Oceanic language

Filed under: Uncategorized — richardparker01 @ 11:42 am

Robert Blust, perhaps the most  influential Austronesian linguist today, said this about the Kokota (Ysabel Island, Solomons) counting/numbering system:

“The numeral system, while basically decimal (1: kaike, 2: palu, 3: tilo, 4: fnoto, 5: yaha, 6: nablo, 7: fitu, 8: hana, 9: nheva, 10: naboto), contains only one clear reflex of the POC numerals (fitu < POC *pitu). Most strikingly, the higher numerals from 20 to 60 have been constructed on the basis of alternating decimal and vigesimal principles, the former occurring with odd multiples of ten and the latter with even multiples, though this has been obscured by historical change: varedake ’20’, tulufulu ’30’ (< POC *tolupuluq = 3 x 10), palu-tutu ’40’ (= 2 x tutu, a morpheme that does not occur earlier in the numeral system, but with the implied value ’20’), limafulu (< POC *limapuluq = 5 x 10), tilo-tutu ’60’ (= 3 x tutu). The numerals 70-90 are decimal-based multiples of salai, a morpheme with the implied value ’10’ that does not occur earlier: fitu-salai ’70’, hana-salai ’80’, nheva-salai ’90’. There are separate morphemes for ‘100’ (gobi) and ‘1000’ (toga).

This must surely rank as one of the most bizarre numeral systems attested for an Oceanic language, and naturally raises questions about possible past contact influences”.
Blust, Robert. “John Lynch, Malcolm Ross, and Terry Crowley. 2002. The Oceanic languages.” Oceanic Linguistics 44.2 (Dec 2005)

The languages of Ysabel form a dialect chain until they meet up with a different language group in the SE corner: All, except Bughotu, are currently grouped as Meso-Melanesian. Bughotu belongs to the Central East Oceanic grouping.

Languages

1

2

3

4

5

6

7

8

9

10

20

Kia, Zabana

kaike

pa lu

lito

rodana

gaha

onomo

vitu

hana

legha ha

tazo

Laghu (almost extinct)

kaike

palu

lito

fotho

gaoha

onomo

fitu

hana

legha ha

kuboto

 

Kokota 

kaike

palu

tilou /  tilo

fnotou

gaha

nablo

fitu

hana

nheva

na boto

varedaki

Zazao, Kilokaka

ka’isa

phea

thilo

fno’to

gaha

hna’blo

fitu

hana

hne’va

bo ‘tq h’

 

Blablanga

kaisa

phea

thilo

fati

glima

hnablo

fitu

hnana

hneva

na botho

Cheke Holo, Maringe, Hograno

kaha /  kaisei

pea / phia

thilo

fati

falima /  glima

famno /  namno

fitu

hana /  nhana

heva /  nheva

botho /  nabotho

varadaki

Gayo, Gao

tasa

phalu

tholu

fati

falima

famno

fitu

fehu

fahia

fa botho

Bugotu, Bughotu

keha

rua

tolu

vati

lima

ono

vitu

alu

hia

sa lage

tutugu
tutu

The Ysabel Island 1-10s, viewed as a complete set, show that some reflexes of POC 1-10 can, at least, be recognised. 

The first 7 languages are from the NW of Ysabel, where they form a chain of language ‘bands’, spanning the relatively long, narrow island, from north to south, all in  the Meso-Melanesian language grouping.

Several of them use na botho for 10, instead of a reflex of proto-Oceanic *sa nga puluq.

Botho means ‘closed’, or ‘shut’; a very obvious term for the two closed fists that mark 10, after counting two hands by bending fingers, one by one,  down to the palm.

Bughotu, the last language, from the SE tip of the island, is from a completely different grouping, Central Eastern Oceanic. It is clearly more ‘conservative’ of the POC terms than the others.

But Bughotu was also used as a missionary ‘lingua franca’ in the 19thC, and this may be how some of its higher numbers ‘leaked over’ into Cheke Holo and Kokota, as shown below:

Analysing only the numbers 1-10 is not enough. To understand a number system properly, you must include the higher numbers, if any existed.

A common assumption, that a special word for 10 demonstrates a fully decimal system is simply not true.

Sometimes, in undeveloped number systems, a special word for 10 denotes only a ‘top number’ before counting the toes, using the same words again, until a special word for 20 marks the full set. But, in some recorded systems, yet another ‘top number’ kicks in at 15, to show when the left toes turn to the right, as in this example from Vanuatu:

 

5

6

7

8

9

10

11

15

20

South-East Ambrym

 

lim

te he tisav

lu he tisav

tol he tisav

hat he tisav

hexalu

tei e le       

le tei bus  

hanu tap

 

hand

1- (second hand)

2– (second hand)

3– (second hand)

4– (second hand)

‘something’ – 2

one on leg

leg 1 finishes

whole person

 

Anomalies in the Kokota  decades

 

 

10

20

30

40

50

60

70

80

90

100

Kokota 

na boto

varedaki

tulufulu

palututu

limafulu

tilotutu

fitsalai

hanasalai

nheva salai

gobi

Cheke Holo

botho /  nabotho

varadaki

tolufului

phiatutu

glimafului

thilotutu / namnosalei

fitusalei

nhanasalei

nhevasalei

kaisei gobi

1 hundred

Bughotu

sa lage

tutugu /
tutu

tolu hanavulu

e rua tutugu

e lime hanavulu

tolu tutugu

vitu hanavulu

vati tutugu

hia hanavulu

hathangatu

The Kokota decades show every symptom of having been adopted, or imposed, from somewhere else. They break one of the very first ‘elementary rules’ of true decimalisation; that they should be a clear, simple system of multiples of 10. They are not.  

Nobody innovates a system, for their own use, where they have to memorise more than a few new words to apply to the original 1-10, and 20.

Part of the reason for the modern dominance of the pure decimal system, worldwide, is that it is very simple to construct a higher number using only the first 10 number words, together with a single made-up word for each following power levels. So a number like 1,236,549 can be easily spoken as ‘one million (106), two hundred (102) and thirty six thousand (103), five hundred (102)  and fortynine.

The highest numbers that can be spoken are limited by the words you have available, so for instance, if your highest number word is 20, you’re subject to a theoretical Limiting Number of 400 (=20×20).

So, it looks as if Bughotu had a simple and limited vigesimal system, with a morpheme (hangavulu) borrowed from another South Solomonic language, probably Nggela, its neighbour, to denote 30 and and other odd-numbered decades.

Note that (hangavulu) is used as a single word, which can be multiplied, not a direct reflex of POC *sa-nga-puluq, meaning 1-10, so that POC 20 = *rua-nga-puluq.

In Bughotu, 30 is tolu-hanavulu, literally translated as: 3-1-10.

This loss of the logical meaning of *sa nga puluq (or its derivatives, hangafulu, tangavulu, etc) is very common as far to the west as the Bird’s Head of New Guinea, and throughout the Oceanic language group. I have termed it ‘Tautological Ten’.

So, when we turn to Kokota and Cheke Holo, and find their use of a reflex of *sa nga puluq (in only two odd-numbered decades) does ‘follow the rule’ (they seem to be using the –fulu portion of the morpheme ‘correctly’) this must arouse suspicions.

To find they, later on, utilise an apparent borrowing, salai, from Bughotu sa lage (remember that is from a separate language group) for 70, 80, and 90 almost proves there’s been some monkey-business.

I suspect this occurred when many Solomon Island number systems were standardised after the onset of literacy and formal education that arrived with missionaries in the late 19thC.

Often, languages, as they perceive a need for higher numbers, adopt a completely new borrowed system, as Embaloh is now doing in Borneo, Swahili did in East Africa, and Hausa did in West Africa. Each of these has adopted parts of their number systems from more ‘prestigious’ groups.

Usually, in an original vigesimal system, the counting goes up to 20 (1x ‘20 unit’) then repeats the cycle until the second 20 2x ‘20 unit’).  So, the counting of fingers goes up to a ‘top number’, 10, and the counting of toes up to another, usually glossed as ‘one man’ or ‘fingers-and-toes-finished

A very simple economical system, with their original 10 showing up on odd-numbered decades, is shown in this language from the western end of New Guinea:

 

10

20

30

40

Dusner
SHWNG

sampur

snontujoser
(20×1)

snontujoser e sam-pur

(20+1×10)

snontunoru
(20×2)

 

Higher Numbers Still

In normal counting, the Dusneri don’t seem to have gone much further. Dusner has utin for 100, (or more probably, for a ‘very large number’) but no known larger numbers.

Many pre-literate cultures standardised and formalised their number systems, but usually only if they had a special need for higher numbers.

Babylonian – taxes and astronomy,

Yele – shell money,

and many Papua New Guinea Highlanders – body-part tallies to demonstrate shares of huge feasts, etc.

But, in interpretations of pre-literate number systems, modern scholars have gone much further, pinpointing certain words, and offering very precise translations of the modern usages, perhaps unjustifiably:

 

100

1000

10000

Kokota 

gobi

toga

mola = 1 million

Cheke Holo

kaisei gobi

1 hundred

kaisei thoga
1 thousand

feferi = very large number

Bughotu

hathangatu

toga

mola = 10,000

feferi = 100,000

In Kokota, gobi (100) may be related to goba – fat (obese), but probably without the same pejorative sense that we see n that description .

gobi (100) in nearby Nggela (related to Bughotu) is a specific measure – 10 canoes (or perhaps 10 canoe-worths of warriors?) (Codrington via Ivens)

         toga (1000) – also means many in Kokota. Datau toga = paramount chief , tehi = many, and togatehi = a great many or perhaps an emphatic combination

         feferi represents an uncountable large number in Cheke Holo, but, translated as a precise 100,000 in Bughotu

         mola is a common word in the Solomons for a ‘vast number’.
In some languages it has become standardised as 10,000, but in other cases, like Kokota, it now means ‘million’.
In Nggela, mola is the term for ten baskets of canarium nuts. This is not to suggest that someone once actually counted out a thousand nuts, then created a standard basket for them, as a measure, but that the word was appropriated at contact, and with the onset of literacy and decimalisation, to denote a more precise number.

Kokota certainly has a bizarre counting system, but I hope this post clarifies, a little, why that is so.

 

 

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What do Welshmen have to do with Polynesians?

Filed under: Uncategorized — richardparker01 @ 8:22 am

 

It’s very difficult to convince Austronesian linguists that An numbers didn’t actually spring, fully-formed, as miraculously decimal systems in proto-Austronesian, or proto-Oceanic, at the latest, 3500 years ago. (It was just as difficult to convince Indo-Europeanists that this didn’t happen, either, but at least they’re coming round, now).

After all, if you collect large sets of cognate words from daughter languages, and then reconstruct them, using the phonetic rules you’ve already found by reconstructing other words, and end up with a very obvious decimal set, from 1-10, you make the most obvious deduction; it must always have been that way. Well, it wasn’t.

 

Vigesimal numbering, at least in the basic stages, occurred worldwide, simply because 20 is the logical end-point to counting first your fingers, and then your toes. At 20, you’ve got a higher unit, so you can memorise it somehow, and start again to count up to 20 again. Now you’ve got two higher units. Remember them, and then do it all over again. At the end, you will have x higher units, and an exact number left over.

At each count of twenty, you simply score a stick, or run your hand down your shepherd’s crook to another readymade score.

Right up to the 20th century, shepherds around England were using a ‘shepherd’s score’ to count their flocks. The system was adapted from the old Briton, or Brythonic number system, which itself evolved into separate languages (Welsh, Cumbric, Cornish and Breton) when the British were split up and forced west by the rude Anglo-Saxons in the 6thC AD.

 

Here’s an example of just one of these shepherds’ systems, compared with the old Welsh vigesimal system, that also persevered until the 20thC

 

Old Shepherds’ Score

1

2

3

4

5

6

7

8

9

10

Lincolnshire

yan

tan

tethera

pethera

pimp

sethera

lethera

hovera

covera

dik

Welsh

un

dau, dwy (fem)

tri,tair (fem)

pedwar, pedair (fem)

pump

chwech

saith

wyth

naw

deg

 

 

 

 

 

 

 

 

 

 

11

12

13

14

15

16

17

18

19

20

Lincolnshire

yan-a-dik

tan-a-dik

tethera-dik

pethera-dik

bumfit

yan-a-bumfit

tan-a-bumfit

tethera-bumfit

pethera-bumfit

figgot

Welsh

 

 

 

 

 

 

 

 

 

un ar ddeg

deuddeg

tair ar ddeg

pedair ar ddeg

pymtheg

un ar bymtheg

dwy ar bymtheg

deunaw

pedair ar bymtheg

ugain

 

So these (almost certainly illiterate) shepherds adopted a counting system from a different language (or kept it, because they were lower-status Brythons left behind) in an interesting way. They didn’t even consider applying the logic inherent in the original system, but used made-up, but memorable, rhyming nonsense words instead.

Also, young mothers started using these rhyming words as lullabies. Hence ‘counting sheep’ to go to sleep. And when they grew older, they used the same tally words to count stitches in knitting. And children still use them in counting out games.

 

But there’s more of interest in the Welsh counting system, and some details that might reveal its real roots.

The counts through from 20 to 100 are very practically based on 20s – vigesimal. From 20 to 40 you go up again to 10 – deg ar hugain- and on, to deugain (2 ugains). But, at 50, the new word is hanner cant (half hundred). So now you’ve got three lots of higher units – 20s, 50s and 100s. With those higher units, you can go a long way; you could count yourself to sleep for a fortnight.

 

Old Welsh vigesimal system

10

20

30

40

50

60

70

80

90

100

deg

ugain

deg ar hugain

deugain

hanner cant

trigain

deg a thrigain

pedwar ugain

deg a phedwar ugain

cant (cannoedd)

 

But there are a few other subtle clues in the Welsh counting system to the real history of Celtic systems:.

          at 15, the count starts again 15+1, 15+2, up to 20. This isn’t unusual; many languages reach the end of counting the first lot of toes, and then start out again with the second lot, ending up with ‘whole man’. What is unusual here is that the first lot of numbers (up to 10) isn’t applied to counting the teens.

         but then Welsh counting also does something else a bit strange. 18 is deunaw, (two nines) for some strange reason.

         In Breton, a closely related language (fleeing Brythons doing the very opposite of Dunkirk) 18 is tri w’ech (three sixes).

Why? These may be fossils of an archaic system of counting in threes, not fives.

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