Ethnostatistics

Studies of Mathematics as a Social Practice

Constructionist approaches to quantification highlighted conventional, culturally embedded, or arbitrary features to mathematical systems. Ethnomathematicians have outlined radically different mathematical systems such as Islamic geometry and Inca data structures. Ethnomathematicians have suggested that the earliest known mathematical objects may date back 37,000 years—a bone with notches that appear to be for counting. At 25,000 years old, the “Ishango Bone” appears to provide a table of prime numbers and a lunar phase calendar, suggesting to some that the mathematician may have been a woman tracking menstrual cycles.

David Bloor has developed constructionist arguments further and attempted to show how different forms of mathematics and concepts of number were fitted to different societies. For example, he argued that moves to a more continuous notion of number were associated with an increasingly involvement of mathematicians with problems of ballistics. The philosophers Ludwig Wittgenstein and Imre Lakatos both developed arguments that highlighted conventional elements to mathematics. Lakatos in particular attempted to bring philosophy of mathematics closer to history and sociology. He argued that mathematical proofs are not accomplished by formal procedures alone; historical studies of proofs show that they depend on a range of inexplicit or informal procedures.

There are profound debates over how far mathematics can be said to be invented or culturally contingent. For many ethnostatistical researchers, the issue is not whether mathematics itself is culturally contingent but rather how mathematics and various forms of quantification are built in different institutions and how they are distorted by social interests. For example, there is a range of studies in the tradition of radical statistics that explore critical issues such as the production of crime statistics to show increases in criminality or to show the effectiveness of severe punishment. These are not critical of statistical work as a principled project; rather, they are critical of particularly flawed or politically biased uses. In contrast, work in the sociology of scientific knowledge adopts a position of methodological indifference or relativism to the validity or correctness of statistical work and focuses instead on social questions of how it is produced and related to social organizations.

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