SCIENCE IN THE FOREST, SCIENCE IN THE PAST HBooksau Director Anne-Christine Taylor Editorial Collective Hylton White Catherine V. Howard Managing Editor Nanette Norris Editorial Staff Michelle Beckett Jane Sabherwal Hau Books are published by the Society for Ethnographic Theory (SET) SET Board of Directors Kriti Kapila (Chair) John Borneman Carlos Londoño Sulkin Anne-Christine Taylor www.haubooks.org SCIENCE IN THE FOREST, SCIENCE IN THE PAST Edited by Geoffrey E. R. Lloyd and Aparecida Vilaça Hau Books Chicago © 2020 Hau Books Originally published as a special issue of HAU: Journal of Ethnographic Theory 9 (1): 36–182. © 2019 Society for Ethnographic Theory Science in the Forest, Science in the Past, edited by Geoffrey E. R. Lloyd and Aparecida Vilaça, is licensed under CC BY-NC-ND 4.0 https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode Cover photo: Carlos Fausto. Used with permission. Cover design: Daniele Meucci and Ania Zayco Layout design: Deepak Sharma, Prepress Plus Typesetting: Prepress Plus (www.prepressplus.in) ISBN: 978-1-912808-41-0 [paperback] ISBN: 978-1-912808-79-3 [ebook] ISBN: 978-1-912808-42-7 [PDF] LCCN: 2020950467 Hau Books Chicago Distribution Center 11030 S. Langley Chicago, Il 60628 www.haubooks.org Publications of Hau Books are printed, marketed, and distributed by The University of Chicago Press. www.press.uchicago.edu Printed in the United States of America on acid-free paper. Contents List of Figures vii Preface viii Geoffrey E. R. Lloyd and Aparecida Vilaça Acknowledgments xii Chapter 1. The Clash of Ontologies and the Problems of Translation and Mutual Intelligibility 1 Geoffrey E. R. Lloyd Chapter 2. Inventing Nature: Christianity and Science in Indigenous Amazonia 15 Aparecida Vilaça Chapter 3. A Clash of Ontologies? Time, Law, and Science in Papua New Guinea 43 Marilyn Strathern Chapter 4. Mathematical Traditions in Ancient Greece and Rome 75 Serafina Cuomo Chapter 5. Is there Mathematics in the Forest? 97 Mauro William Barbosa de Almeida Chapter 6. Different Clusters of Texts from Ancient China, Different Mathematical Ontologies 121 Karine Chemla v Science in the Forest, Science in the Past Chapter 7. Shedding Light on Diverse Cultures of Mathematical Practices in South Asia: Early Sanskrit Mathematical Texts in Conversation with Modern Elementary Tamil Mathematical Curricula (in Dialogue with Senthil Babu) 147 Agathe Keller Chapter 8. Antidomestication in the Amazon: Swidden and its Foes 171 Manuela Carneiro da Cunha Chapter 9. Objective Functions: (In)humanity and Inequity in Artificial Intelligence 191 Alan Blackwell Chapter 10. Modeling, Ontology, and Wild Thought: Toward an Anthropology of the Artificially Intelligent 209 Willard McCarty Chapter 11. Rhetorical Antinomies and Radical Othering: Recent Reflections on Responses to an Old Paper Concerning Human–Animal Relations in Amazonia 237 Stephen Hugh-Jones Chapter 12. Turning to Ontology in Studies of Distant Sciences 255 Nicholas Jardine Chapter 13. Epilogue: The Way Ahead 267 Geoffrey E. R. Lloyd and Aparecida Vilaça List of Contributors 273 vi List of Figures Figure 1. Diagram for Euclid, Elements I.47, the so-called theorem of Pythagoras. Figure 2. Diagram for Hero, Metrica I.2. Figure 3. The symmetries inherent in the kinship terminology are illustrated as symmetries between the Jaguar and Puma moieties. Figure 4. The relationships between moieties and namesake sections are shown in formal terms. Figure 5. Euclidean proof of a theorem that Dedekind claimed Euclid could not prove. Figure 6a–6b. Process of multiplication and division with rods, according to Mathematical Canon by Master Sun. Figure 7. Rectangular diagram in the problem of the Pāṭīgaṇita. Figure 8. The entry for 17 x 17 kuḻi in the Eṇcuvaṭi. Figure 9. Three stages of the computational process. vii Preface Geoffrey E. R. Lloyd and Aparecida Vilaça The present volume stems from a workshop that the editors organized at the Needham Research Institute in Cambridge from May 31 to June 2, 2017. We observed that in recent years investigators in a number of dif- ferent disciplines have been questioning the ontological presuppositions of whatever branch of inquiry they are engaged in. The problems are particularly acute in two areas especially: (1) in the history of ancient sci- ence; and (2) in the cross-cultural ethnographic study of the knowledge and practices of living Indigenous peoples. In the case of the history of ancient science, one key question is how and why Greco-Roman and Chinese science in particular developed in the ways they did, a topic of particular importance in the context of the work currently undertaken at the Needham Research Institute and in the Classics Faculty at Cam- bridge University. In the case of Indigenous peoples, the focus is on the ontological clashes related to their contacts with Euro-Americans and the subsequent transformations brought by new political movements, insertion in the market economy, monetarization, Christianization and schooling, themes well-developed by the Brazilian and Cambridge or- ganizers and collaborators. The underlying problem in both types of case can be expressed like this. When different individuals, groups or whole societies evidently adopt markedly divergent views on the objects in the world around them, on the proper relations among humans and between humans and other living things, and on how knowledge on such matters is to be obtained, viii Preface what are we to say? On one view there is a single objective reality, cor- rect access to which is secured by philosophy, science and mathematics, which accordingly supply reliable criteria by which more or less accurate accounts are to be judged. In this view it is generally assumed that mod- ern Western science holds a privileged position, although this is often in ignorance of alternative traditions. It follows that this is one reason why it is so important to study science in such other cultures as China and in India. On the diametrically opposed view, there is no such single objective reality. Rather, we should allow that divergent knowledge and practices relate to different realities and that those who adopt and live by them should be seen as, in an important sense, inhabiting different worlds. Reflecting the aims of the workshop this volume brings together specialists from several different disciplines to tackle different aspects of these fundamental problems. Historians of mathematics examine the commonalities and the divergences in mathematical practices and concepts in different cultures separated in time or space or both, and they pose questions to do with the very framework within which the history of mathematics can be undertaken. The questions of the status of the objects that mathematics presupposes and the characteristics of the modes of reasoning it deploys are taken up, also, by those whose training is in computer engineering. Philosophers and historians of sci- ence here revisit the problems of mutual intelligibility posed by appar- ently incommensurable scientific paradigms. Anthropologists who have studied Indigenous cosmologies in the field comment on the problems of understanding they pose. Several who have direct experience of how both schooling and missionary activity effect Indigenous beliefs discuss how modern Western scientific ideas impact on the traditional ideas and practices of the peoples to whom those ideas are presented as correct solutions to the question of what reality consists in and how to investi- gate it. A particular feature of our approach is to stress the importance of intercultural knowledge exchange in the context of Indigenous and local understanding on biodiversity matters, an issue that has obvious potential consequences for policy-makers everywhere in the world as we face the more and more pressing challenges of climate change, the over- exploitation of natural resources and ecological degradation. Each of our participants brings a particular set of skills and experi- ence to bear, but all are united by the sense of the importance of the task. To achieve greater mutual understanding across peoples, cultures, religions and indeed across intellectual disciplines is as urgent now as it ix Science in the Forest, Science in the Past has ever been in human history. Past societies and contemporary ones alike are a precious resource contributing to this crucial goal. The aim of bringing together leading scholars in a wide variety of disciplines is to pool our expertise in a bid to throw light not just on current academic problems in each field (such as the ontological turn or the incommensu- rability of rival scientific paradigms) but also on issues of global practical concern. In the event not all of those who gave papers to the workshop were able to contribute chapters to this volume. But in rewriting our papers we have all been able to draw on the valuable points that were made in our wide-ranging discussions. The full list of participants in the workshop is as follows: Mauro William Barbosa de Almeida (Social Anthropology, Universidade Estadual de Campinas) Alan Blackwell (Computer Sciences, University of Cambridge Computer Laboratory) Matei Candea (Social Anthropology, University of Cambridge) Manuela Carneiro da Cunha (Social Anthropology, University of Chicago) Karine Chemla (Sinology, Université de Paris) Serafina Cuomo (Ancient History, Durham University) Giovanni da Col (Social Anthropology, SOAS, University of London) Marina Frasca-Spada (History and Philosophy of Science, University of Cambridge) Simon