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–

1kokopumitaranti

2assantilantesuhari

3pulpalipolipulipo

4katisamitisurupateste

5suruheratesarototonate

6aranterantesolosibarikotin

7kalikulusalintekorispul

8haparehoresulibande

9kokistekistepatoharitusa

10sapotopotokalintesosorina

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

The numbers 11–*ten- and-x*, where

11sapotopotokalintesosorinapukokopumitaranti

12sapotopotokalintesosorinapuassantilantesuhari

13sapotopotokalintesosorinapupulpalipolipulipo

etc.

Multiples of 10 are formed as *x-kure- tens*, where

20assantilantesuharikuresapotopotokalintesosorinasapotopotokalintesosorina

30pulpalipolipulipokuresapotopotokalintesosorinasapotopotokalintesosorina

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

36pulpalipolipulipokuresapotopotokalintesosorinasapotopotokalintesosorinapuaranterantesolosibarikoti

all the way up to

99kokistekistepatoharitusakuresapotopotokalintesosorinasapotopotokalintesosorinapukokistekistepatoharitusa

100bob

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.