Group Actions and Mathematical Cognition. Sand Drawing in Vanuatu through the lens of Ethnomathematics and 4E
Bibliographic record
Abstract
In Vanuatu, artists perform symmetrical figures on the ground using one finger, without lifting it off the ground, without retracing lines, and returning to the starting point. This cultural practice paves the way for a dialogue between ethnomathematics and cognitive sciences, two fields that have remained far apart until now. We present new evidence of mathematical abilities that go beyond classical numerical concepts and Euclidean geometric concepts, and in particular the concept of group actions, which has so far been underexploited. Based on ethnographic research, we propose a mathematical model that offers a rigorous framework for discussing the cognitive processes of creation and memorization. We then open an unexplored avenue by combining this ethnomathematical analysis with the 4E cognition approach. We suggest that this kind of interdisciplinary effort, based on holistic observations of societies with an oral tradition, could form the basis of alternative research methods for understanding what makes human beings, in all their diversity, capable of mathematical ideas.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.003 | 0.012 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".