Aparecida Vilaça and Fernando Codá Marques on Amazonian Mathematics

Feb. 11, 2020

On Thursday, February 6, the Brazil LAB and the Department of Anthropology hosted Aparecida Vilaça, Professor of Social Anthropology of Brazil’s Museu Nacional for the lecture ‘Forest Mathematics: Unstable Sets in Indigenous Amazonia.’ Fernando Codá Marques, Professor of Mathematics at Princeton was the discussant. 

Vilaça has carried out ethnographic research among the Wari’ people in Southwestern Amazonia, for over three decades with an emphasis on conversion to Christianity and schooling. Speaking to a standing-room only, Vilaça began her lecture by presenting a history of “mathematics in the contact zone” of the Amazon. Missionary inspired colonial and post-colonial accounts of the Wari’ have tended to see them, as indeed other Amazonian peoples as “betraying a poverty of numbers and numeracy”, Vilaça highlighted. In keeping with this, “teaching numbers to the Wari’ was part of the historical project of teaching them the word of God.” However, as the anthropologist’s long-term research demonstrates, for the Wari’ “solutions to math problems involve all the relationships not implicated in arithmetic.” 

Vilaça used a simple example to explain her point: every time the anthropologist asked one of her Wari’ interlocutors about how many grandchildren she had, she received a different response. Vilaça concluded this was because for the Wari’, “distributions of beings in categories depended on the relations they saw each other(s) in.” In terms of cosmology “Wari’ demonstrate no totality in making connections between objects and people.” On the other hand, contemporary conceptions of numeracy among the Wari’ (which draw on colonial and other missionary accounts) are leading the younger generations who are receiving formal education to view themselves as “poor in numbers.” Disregarding the cosmology of everyday life among the Wari’, evangelical education is failing to take into account the “complex play of perspectives” that construct the unity/solitude of ‘one’ among the Wari’ as contrary to the value of ‘one’ in Christianity.

In his response to Vilaça, Fernando Codá Marques underlined that while on the one hand Mathematics is based on the “rigour” of “standardization and results,” on the other hand “(the) innate sense of numbers that humans have is very approximate.” Codá Marques asked “do the Wari not have names for numbers higher than five because of their way of life being different from the Western world?” For Codá Marques “the effectiveness of ‘mathematics’ in the day to day world (or it’s lack thereof)” seemed to be a plausible factor that influenced the development of cosmologies of numeracy among the Wari’. 

The lively discussions that followed highlighted the conceptual tensions generated between ‘mathematics’ and ‘magic’, ‘numeracy’ and ‘cosmology’, ‘pespectives’ and ‘origins,’ leading to a series of rich provocations regarding how to the Wari’ people associate with the idea of ‘nothing’ and how do the Wari’ develop conceptions of time and temporality, notions of exchange and quantity, in the ostensible absense of numbers. In her concluding remarks, Vilaça added that it was owing to the “limitations of mathematical logic” that modern mathematical education was coming to be seen as an “impositions on the Wari” without adequately taking into account their “plural perspectives” on numbers. 

The event was part an ongoing partnership between the Brazil LAB and the Departments of Anthropology and Spanish and Portuguese with the Social Anthropology Graduate Program (PPGAS) of the Museu Nacional. This joint initiative has the support from the Provost Office and the Center for Human Values. The lecture was also co-sponsored by the Princeton Environmental Institute, the Program in Latin American Studies, and the Department of Spanish and Portuguese.