Jürg Wassmann

Number concepts without number lines in an indigenous group of Papua New Guinea.

Background The generic concept of number line, which maps numbers to unidimensional space, is a fundamental concept in mathematics, but its cognitive origins are uncertain. Two defining criteria of the number line are that (i) there is a mapping of each individual number (or numerosity) under consideration onto a specific location on the line, and (ii) that the mapping defines a unidimensional space representing numbers with a metric — a distance function. It has been proposed that the number line is based on a spontaneous universal human intuition, rooted directly in brain evolution, that maps number magnitude to linear space with a metric. To date, no culture lacking this intuition has been documented. Methodology/Principal Findings By means of a number line task, we investigated the universality proposal with the Yupno of Papua New Guinea. Unschooled adults did exhibit a number-to-space mapping (criterion i) but, strikingly, despite having precise cardinal number concepts, they located numbers only on the endpoints, thus failing to use the extent of the line. The produced mapping was bi-categorical and metric-free, in violation of criterion ii. In contrast, Yupnos with scholastic experience used the extent of the segment according to known standards, but they did so not as evenly as western controls, exhibiting a bias towards the endpoints. Conclusions/Significance Results suggest that cardinal number concepts can exist independently from number line representations. They also suggest that the number line mapping, although ubiquitous in the modern world, is not universally spontaneous, but rather seems to be learned through — and continually reinforced by — specific cultural practices.

“Hot” and “Cold”: Classification and Sorting Among the Yupno of Papua New Guinea

Abstract The authors advocate a combination of ethnographic and psychological methods: Cognitive processes and the social distribution of knowledge are to be studied not only through the collective representations derived from interviews with key informants, but through behaviour observations in everyday settings, as well as specifically designed tasks, in order to observe problem solving more directly. The collaboration between an anthropologist and a psychologist is illustrated in a study of classification among the Yupno of Papua New Guinea. Their world-view classifies everything into three states: “hot”, “cold”, and “cool”. Only experts (sorcerers) can manipulate these states. After an ethnographic description of this classification system, a sorting task was given to six samples of Yupno subjects. Only the sorcerers used the abstract category of “hotkold” explicitly; the other older adults used it implicitly through function, whereas schooling induced sorting by colour. These findings call into quest...

Person, Space, and Memory: Why Anthropology Needs Cognitive Science and Human Geography

Among the Iatmul of the Sepik River in Papua New Guinea, conflicts over the rightful possession of cosmologically significant names are decided by having the opponents and their supporters meet near the ceremonial stool (pabu) in the men’s house for a special debate. The thousands of secret sacred names of persons and places that may be involved are central to the ramified Iatmul mythological system, which is anchored in the landscape and which combines the past and present. Demanding elaborate feats of rhetorical skill and memory facilitated by localized mental representations, such encounters involve mastery of highly complex intellectual activities that draw on comprehensive knowledge of Iatmul myths of origin, clans, totems, migration, and settlement. This chapter first presents excepts from such debate and explains that an anthropologist’s understanding of this complex system requires insights into research on human memory and learning capacities as well as competence in indigenous concepts of local geography.

Landscape and Memory in Papua New Guinea

Amongst the Iatmul of the Sepik River, in the event of a conflict about the rightful possession of a name, the opponents and their supporters meet in the men’s house, in the center near the ceremonial stool, pabu, for the name debate. This is their most revered social form of intellectual discussion. For the Iatmul, the names are the centre of their ramified mythological system. Conflicts about land use, fishing rights, or rights to names are always about names or mythology.

Correction: Number Concepts without Number Lines in an Indigenous Group of Papua New Guinea.

Supplementary Figures 1 and 2 were incorrectly switched. The image currently appearing as Supplementary Figure 1 belongs with the title and legend for Supplementary Figure 2, and the image currently appearing as Supplementary Figure 2 belongs with the title and legend for Supplementary Figure 1. The titles and legends of the figures are in correct order.