Some Aspects of the Counting System of Nappaholihok

Darren Traming
Research Student in Mathematical Linguistics
University of Ledworth

A feature of counting systems in general is that if the number of letters used to write a given number is tallied, and this is repeated with the number so found, the process will eventually converge to either a single value (e.g., four in English) or a cycle (e.g., trois, cinq, quatre, six in French). In Nappaholihok, a language of Papua New Guinea, the situation is more complex, as explained below.

According to the oral history of the Nappaholi people, their ancestors once suffered a humiliating defeat when their chief counted the enemy warriors, saw that he was outnumbered and lost heart. In order to prevent such a thing happening again, the Nappaholi devised a counting system so complex that they would never again have time to count their enemies before joining battle.

The numbers 1–10 are as follows (written in Neil de Veratte’s romanisation)

1

koko­pumi­taranti

2

ass­anti­lante­suhari

3

pul­pali­poli­pulipo

4

kati­samiti­suru­pateste

5

suru­hera­tesa­roto­tonate

6

aran­teran­teso­losi­bari­kotin

7

kali­kulu­salin­teko­rispul

8

hapa­rehore­suli­bande

9

koki­stekis­tepato­hari­tusa

10

sapo­topo­toka­linte­soso­rina

Despite the best efforts of extreme morphologists to analyse them, these appear to be indivisible roots.

The numbers 11–19 have the form ten-and-x, where and is represented by the affix pu (found only in this context), thus

11

sapo­topo­toka­linte­soso­rina­pu­koko­pumi­taranti

12

sapo­topo­toka­linte­soso­rina­pu­ass­anti­lante­suhari

13

sapo­topo­toka­linte­soso­rina­pu­pulpalipolipulipo

etc.

Multiples of 10 are formed as x-kure-tens, where kure appears to be related to a word for bag. Note that ten is pluralised. Nappaholihok plurals are historically derived from reduplication, but in most cases have undergone phonological reduction, for example *wugwug ⇒ *wubug ⇒ *wuvug ⇒ wuvg. However, as numbers are so frequently used, the reduplication has remained completely regular, hence

20

ass­anti­lante­suhari­kure­sapo­topo­toka­linte­soso­rina­sapo­topo­toka­linte­soso­rina

30

pul­pali­poli­pulipo­kure­sapo­topo­toka­linte­soso­rina­sapo­topo­toka­linte­soso­rina

These two mechanisms combine as may be expected, e.g.:

36

pul­pali­poli­pulipo­kure­sapo­topo­toka­linte­soso­rina­sapo­topo­toka­linte­soso­rina­pu­aran­teran­teso­losi­bari­koti

all the way up to

99

koki­stekis­tepato­hari­tusa­kure­sapo­topo­toka­linte­soso­rina­sapo­topo­toka­linte­soso­rina­pu­koki­stekis­tepato­hari­tusa

100

bob

When the process of counting letters is followed, we find that this converges to the sequence:

pulpalipolipulipo, sapo­topo­toka­linte­soso­rina, suru­hera­tesa­roto­tonate­kure­sapo­topo­toka­linte­soso­rina­sapo­topo­toka­linte­soso­rina, aran­teran­teso­losi­bari­kotin­kure­sapo­topo­toka­linte­soso­rina­sapo­topo­toka­linte­soso­rina­pu­koki­stekis­tepato­hari­tusa, koki­stekis­tepato­hari­tusa­kure­sapo­topo­toka­linte­soso­rina­sapo­topo­toka­linte­soso­rina­pu­koki­stekis­tepato­hari­tusa, bob.

Early works on Nappaholihok seldom mention its remarkable counting system, and many propagate the myth that persists to this day that the Nappaholi count one, two, many. It appears that when the Nappaholi initially explained their counting system, explorers simply did not believe them.

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