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What are concepts in considering maths as a cultural practice?

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I’m going to start working in the question ‘what is a concept?’ It is one thread weaving through the debate about method and metaphysics that is going on in a number of places at the moment. But I want to begin with the project called Maths as a Cultural Practice. It is a project between the Yolngu Aboriginal Consultant’s Initiative and SiMERR (Science, Information and Communication Technology, and Mathematics Education for Rural and Regional Australia) whose main event was a workshop at Charles Darwin Uni in 2007 (details and reports can be found here). This was the first time I was part of an explicit knowledge work with Yolŋu.

The website states: ‘The Yolŋu Aboriginal Consultants Initiative is searching for a variety of ways in which we can represent workshop outcomes’ and that the website is part of this way finding. One element of the website is the page entitle ‘Key Concepts’. It looks like this and click the image to go the real thing.

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To many people it may look like a glossary of terms; Yolŋu matha terms and phrases in alphabetical order on one side, expanded English definitions on the other. In this case, the reasoning behind it might be thus: ‘in order not to loose too much in language translation we are keeping the Yolŋu words in the main text and providing a glossary in English for you to turn to to find out what the words mean.’ There could also be the justification that keeping Yolŋu language at the fore is politically important for reminding people that there are many Indigenous languages in Australia, most of which are threatened, and that these are fundamental to the survival of indigenous knowledge, philosophy and culture. The front page of the project brings our attention to the important of Yolŋu Matha:

‘Yolŋu Matha – Most of the workshop was conducted in the various Yolŋu languages (matha) which belong to the consultants. Yolŋu languages have special characters. We have only used the special character ŋ on this website. The other characters have been reduced to the nearest English equivalent.Feedback on this website and our work is welcome. Please see the Resources page.’

It is not an oversight that this section does not bring our attention to the ‘Key Concepts’ page. This is because this page is not a glossary of terms. It is NOT a list of words and their meanings. It can be read and used as a glossary (and in some ways it is important that it is *also* a glossary), but by naming it ‘Key Concepts’ and not ‘Key Words’ the authors of the site specifically attempt for this not to be the case. So, how would we take this page as one constituted by key concepts? What understandings of concepts might we have for this task?

Nick Gane has recentḻy considered this question as it might be posed more generally for the social sciences in “Concepts and the `New’ Empiricism” (2009). Articulating the Deleuze inspired ‘new empiricism’ Gane presents concepts and conceptual work emerging from empirical work, in which empirical data ‘characterized by difference and singularity’ presents challenges to thought which provoke conceptual work (amongst other things). Conceptual work, here understood as the design of concepts, can be that of classification, commodification and pedagogy. So just to return to the ‘Key Concepts’, we can easily see how they might do classificatory work as a glossary for example, or they might do commodification as rendering Yolŋu knowledge as consumable and tradable in the academic-research-consultancy market place. But how might they do pedagogical work? Let’s return to Nick.

Pedagogical work produces concepts as ‘experimental tools that are born out of tensions between the empirical world, for Deleuze, the realm of ‘pure difference’, and ‘philosophical thought’ (p86). Moreover, ‘concepts are never forged in abstraction as they always come from somewhere, but at the same time they are never ready made’ (p86). Concepts are not backward looking (seeking to represent some prior or always existing real) but are future looking. They create an event and are in the business of becoming, creation and dealing with what is possible (and here I understand Gane to mean what is possible not in an imagined world or in any abstracted knowledge but possible in the world). Gane points out two paradoxes that he sees, and apologies for the next bit as I try to avoid getting completely confused by Deleuze and Guattari’s terminology (maybe there is a glossary of their concepts somewhere!). One, he says concepts are ‘intensities’ implying they are not already involved in an external state of affairs, even though as we read earlier ‘concepts come from somewhere and are not ready made.’ Second, quoting Deleuze and Guattari, the ‘concept is an incorporeal, even though it is incarnated or effectuated in bodies’ (p87).

So, in the sense that concepts are never ready made, the concepts above were not simply ‘picked’ from Yolŋu philosophy or Yolŋu heads. But they do come from somewhere, in this case, a bi-cultural research project trying to account for itself on a website. This is consistent with Gane’s argument that concepts in the new empiricism are ‘a process which poses problems to thought and forces it [to] account for itself’ (p89). Later on, quoting Deleuze again, a concept is ‘not a description of reality but aims to give unambiguous means of expression to such a description’ (p91). I could interpret this as saying, reality and its description are one and the same, so what conceptual work does it gives ‘unambiguous means of expression’ to this.

In the second half of the paper, Gane goes onto to consider five topics that are specifically to do with research method: Concepts and empirical reality, Concepts and problems, Pedagogy of the Concept, Networks of Concepts, Concepts as Multiplicities. While Gane specifically draws attention to the connection between Deleuze and Weber, the latter two section on networks and multiplicities show some obvious inspirations from Actor-Network Theory, material semiotics and other related approaches.

In ‘Concepts and empirical reality’, Gane argues that concepts can create a stability and take a slice of the flux empirical reality. Concepts and problems suggests that concepts first come from problems of thought and the pedagogy of the concepts holds the concept as a ‘heuristic’ device or ‘means’ that simultaneously invents and discovers in its engagements with reality. That no concept is isolated, but is related to many other concepts and that no concepts is singular but internally differentiated shows that concepts live and behave semiotically.

Questions: What is the difference between concepts and conceptual work? Are concepts any ‘thing’ with which we do conceptual work. If numbers are concepts, can they be multiple, networked etc?

Gane, N., 2009. Concepts and the `New’ Empiricism. European Journal of Social Theory, 12(1), 83-97. Available at: http://est.sagepub.com.ezp.lib.unimelb.edu.au/cgi/content/abstract/12/1/83.

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