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

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 forty–nine.

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.

 

 

What do Welshmen have to do with Polynesians?

 

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 20^th 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 6^thC AD.

 

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

 

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.