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ABSTRACT
This essay investigates the practical ways that artists and craftspeople cultivate mathematical sensibilities through their practical immersion in making and problem-solving. Mathematical sensibilities refer to skilled kinds of perception and heightened levels of attention and discernment regarding the qualitative properties of an object or composition, such as its shape, proportion, balance, symmetry, centredness, alignment or levelness. It also includes an ‘intuitive’ quantitative sense of volume, mass, weight, thickness and dimension. The objective of the investigation is not to describe the ways that a maker’s existing knowledge and training in formal mathematics is put into practice, but rather to elucidate the ways that their practices of making produce kinds of ‘non-formalised’, context-dependent mathematical understanding and knowledge. The starting point for exploring embodied mathematizing is therefore not from the cognitive or neurosciences, psychology or formal mathematics, it is argued, but rather from a phenomenological approach – ‘an opening on the world’ – that attends to person, materials, tools and other physical and qualitative features that make up the total environment in which activity unfolds.
Acknowledgements
My thanks to Willard McCarty, Elizabeth de Freitas and Roy Dilley for their generous feedback and suggestions on an earlier draft of this essay. I am indebted to Elizabeth for her inspiring presentation at the Beyond Perception symposium organized in Aberdeen in honour of Tim Ingold. It enthused me to examine embodied mathematics in a more dedicated way.
Disclosure statement
No potential conflict of interest was reported by the author.
Notes on contributor
Trevor H. J. Marchand is Emeritus Professor of Social Anthropology at the School of Oriental and African Studies (SOAS), London; recipient of the Royal Anthropological Institute’s Rivers Memorial Medal (2014), and consultant for ICOMOS. He trained as an architect (McGill), received a PhD in anthropology (SOAS), and qualified as a fine woodworker at London’s Building Crafts College. Marchand has conducted fieldwork with craftspeople in Nigeria, Yemen, Mali and London. He has published extensively, directed documentary films and curated exhibitions for the Smithsonian (Washington, DC), the RIBA (London), Brunei Gallery (London), Museum of Oriental Art (Turin) and the Pergamon Museum (Berlin). Marchand works as an independent researcher and writer. His forthcoming monograph is titled The Pursuit of Pleasurable Work.
Notes
1 In fact, a CEGEP (Collège d'enseignement général et professionnel) diploma. CEGEP is a publicly funded pre-university college system unique to the Canadian province of Quebec.
2 I also learned that the linearity of spoken language fails to capture the dynamics of skilled practice, which characteristically entails the synchronous enactment of numerous cognitive, perceptual and motor activities. In short, the master masons could not effectively or efficiently explain what it is they know how to do. In my later explorations of this subject (Citation2010), I developed a theory of motor-based concepts grounded in Fodor’s theory of informational atomism (2003; see Fodor Citation1998), and a theory of embodied communication, which builds upon the linguistic theory of Dynamic Syntax (Kempson, Meyer-Viol, and Gabbay Citation2000)
3 ACAVA, the Association for Cultural Advancement through Visual Arts, is an educational charity providing studios for more than 500 artists in 20 buildings, mostly in London.
7 With reference to Hutchins (Citation1995), Bender and Beller define distributed cognition as the interactive processing of internally and externally represented information. The result of that interactive processing allows cognition to be off-loaded into the environment through social, material, embodied and technological means, thereby alleviating the workload performed by memory retrieval.
8 The approach I am advocating does not in any way discount valuable learning about skilled activity that can be gained from the cognitive and neurosciences or from mathematics, but rather it insists on fieldwork as the starting point and a method and analytical framework that takes stock of the total environment, as it has been defined here.
9 Thanks to Elizabeth de Freitas for this prompt.
10 On reflection, I recognize that my question presupposed a specific function for Andrew’s flag and possibly induced the artist to create a connection between it and some other entity. On his own accord, however, he conceptualised all of the individual projects he created during our time together at ACAVA as forming part of a single installation, centered on ‘Table with People Eating’.