Display of Oksapmin body-counting system from thumb (1) around upper periphery of body to pinky (27) and then looping to wrist (28).
Man in 1978 displaying the ending of a count showing fu gon a! (with fist), a completion of all of the body parts.
A traditional man displaying body part positions in the Oksapmin 27-body part counting system
A boy hunting with bow and arrow (1978).
A child's display of Oksapmin's 27-body part counting system.
This video captures part of a purchase of tinned fish at the Baptist mission trade store in Tekin in 1978. The customers are making successive requests and payments of the fish.
A scene from the mission trade store in 1978.
You have 16 pigs; you give seven away; how many left? The 4th grader begins his solution of the problem with the ear-on-the-other-side (16). He indicates that this (ear (16) is given away, and corresponds to the thumb (1); the eye on the other side (15) is given away, and that corresponds to the index finger (2); the nose (14) is given away, and that's the middle finger (3)... the child proceeds to the shoulder (10) is given away and that's the forearm (7), leaving biceps (9), the answer. In the Cultural Development of Mathematical Ideas, this approach is refered to as a "double enumeration" strategy. Children are not taught the approach; it's an approach that emerged as Oksapmin children made efforts to make sense of the mathematics taught in school in the post-colonial approach to schooling. (1980)
The teacher presents the class with an arithmetic problem. Note that some children begin to solve the problem using the body counting system. During this era, teachers were not from the Oksapmin area and knew little about indigenous knowledge systems of the community. (1980)
This film was taken in 1980. The man interviewed is a trade store owner who has developed new ways of using the body part counting system to solve arithmetic problems. He is presented with the problem that he has one kina and sixty toea and spends seventy toea. In the video, he represents one kina sixty toea as 16, distributing the value as shoulder (10) and wrist (6). Then from the side for which he has registered shoulder (10), he indicates that he spends the equivalent of seven or forearm (7). To solve the problem, he the "moves" the remaining body parts from the shoulder side to the side registering wrist. First he moves the elbow (8) to the forearm (7); then the biceps (9) to the elbow (8) ; he finally moves the shoulder (10) to the biceps (9). Biceps (9) then is the solution of the problem. In the Cultural Development of Mathematical Ideas, this approach is refered to as a "halved body" strategy. The man was not taught the approach; it's an approach that emerged as Oksapmin people engaged in novel practices of economic exchange with currency. (1980)
The man is presented with eleven kina as shown on the left. He examines the currency and states their value as hanen fu hama doba temsi tana. The more or less literal meaning of the expression is conversational number word 5 (hanen) double (fu) and on the wrist (6) (doba (6th body part) put the flat with hole (temsi tana, the expression for the one kina coin or the value of one kina).
The video shows an elder counting six stones using the body counting system. The count proceeds tipana (thumb (1)), tipnarip (index finger (2)), bumrip (middle finger (3)), hadrip (ring finger (4)), hathatah (pinky (5)), dopa (wrist (6)). The suffix -hai indicates a cardinal value, hence the answer, dop-hai (wrist (6)-CARDINAL).
The video shows an elder counting eleven stones using the Oksapmin body counting system. The count proceeds tipana (thumb (1)), tipnarip (index finger (2)), bumrip (middle finger (3)), hadrip (ring finger (4)), hathatah (pinky (5)), dopa (wrist (6)), besa (forearm (7)), kir (elbow (8)), towat (biceps (8)), kata (shoulder (10)), gwer (neck (11)). In the video, the man points to his neck (off camera) to indicate the total.
This man is finishing his count of 29 stones using body part names. When he finishes, he states the cardinal value, tit fu gona it was besa tit si. One loose translation of the expression is, the completion of all 27 body parts of the count (tit fu gona) and then counting back around to the forearm.
The man refers to the five-kina note as "faiv kina." The expression is borrowed from Tok Pisin. There are other Oksapmin expressions for the faiv kina note, but there is great variability in the community in its Oksapmin name. In the interview, the man reflects on an Oksapmin expression for the note, but doesn't provide one.
Men who are paying Oksapmin people for their vegetables (that have been exported to the Ok Tedi mine in Tabubil).
The man calls the twenty-kina note "kat-hai fu." The expression translates as "shoulder" ("kata" is the 10th body part in the Oksapmin counting system) and "double" or "two kina notes" ("fu").
The man identifies the two-kina note as "wan faun tana." Part of the expression is borrowed from Tok Pisin. "Faun" in Tok Pisin refers to the now-obsolete Australian pound, and "wan" is the Tok Pisin equivalent "one." "Tana" is the Oksapmin word for a flat object. "Faun" is an expression used generally in the Oksapmin community to refer to a two-kina note.
The man is presented with one kina and ten toea in the form of two 50 toea coins and one ten toea coin. Because of a prior history detailed in the book, the value of 10t is treated as a unit. The man represents the value as gwer or neck (11th position) in the Oksapmin body part counting system, the equivalent of eleven 10 toea coins.
The video shows an elder responding to a question about the name for the 50-toea coin in the Oksapmin language. He responds "gangasi" (literally "cornered" but used conventionally for the 50-toea coin) OR hanen gona (the conversational number word, "five"). Note: The 50-toea coin is the only token with corners.
This woman is displaying the Oksapmin 27-body part counting system (see figure at left). In the video, you will see her enumerate body part names beginning with the thumb on one hand (1) proceeding up to the nose (14) and down to the little finger on the other side of her body (27). At the end of the count, as has been standard practice, she exclaims a fists raised "tit fu!", indicating that she's completed all of the body parts of the system.* Similar 27-body part systems have been used traditionally throughout the larger Mountain-Ok region of central New Guinea (see map below). Note the direction of the count is arbitrary and meaning is linked to the act -- the woman is using a right-to-left trajectory whereas the upper left schematic shows the opposite direction. Traditionally, if people need to count beyond the 27th body part, they loop back to tan dopa (28), or the wrist on the other side (28th position).
Traditional uses of the system did not involve arithmetical functions. With the introduction of currency and people's engagement with economic exchanges with currency in tradestores, some Oksapmin people elaborated arithmetical functions for the system. To observe a tradestore owner using the body system to accomplish an arithmetical problem, go to the following link: Oksapmin tradestore owner solving 16-7=?
Schooling was another context in which Oksapmin elaborated arithmetical functions for the system. To observe a fourth grader constructing an arithmetical function for the body system, go to the following link: fourth grader solving 16-7=?
*Although the woman labels every body part with its appropriate body part name, she inadvertantly skips one body part in the system - tan kata (18). Tan kata (18) means shoulder-on-the-other-side (or the 18th position)).
This Oksapmin man (2001) was shown twenty-one kina worth of Papua New Guinea currency and is representing that amount in the Oksapmin language. He indicates his shoulder (10) or kat(-hai) (pointing to shoulder) doubles that value with reference fu and then indicates that he places one kina coin temsi tana (flat with hole) at his neck (11), for a total of twenty-one kina.
One morning in 2001, children arrived at the elementary school classroom, but their teachers were away. As a group, they were eager to display for me the Oksapmin 27-body part counting system.