Numbers in Arnhem Land: value and difference in a postcolonial mathematic

© 2011 Dr. Christian ClarkIn conventional accounts of mathematics and number there is nothing new to learn: difference and value always arrive internal to the accounts. Is there potential for alternative forms of mathematics, the potential for number to do more than name value? How might we learn to work with numbers that perform multiple valuations and how might we learn from number in situations that are constituted through difference? Can difference become more than what is left in the aftermath of 'our' values, and become a positive potential for learning new ways to value? These questions can only be understood and addressed through an empirical and philosophical re-conceptualisation of number, value and difference in situations constituted by difference. Numbers in Arnhem Land investigates the role of number and the ways in which it promotes a quality of oscillating value. Through an empirical investigation, number is understood as an event, an active and embodied relation or comparison done through and as difference. Numbers as event differenciate specific relations in collective life. Learning how number does value demands learning how number can articulate itself as relations that are multiple and open. The notion of oscillating value has value not as an abstract property of number, but a virtual quality. Valuations are the limits number approaches within the event. Understanding value as limits in this way allows numbers to play a full role in constituting collective life. Learning the potential of number through value demands an understanding of empiricism and ethnography that is also committed to difference as primary and irreducible in the encounter. Relational empiricism, as developed through this thesis, is not the measuring and valuing of worlds already ordered and valued (the forms of empiricism offered by both universal and relativist critiques), but the work of resonating differences, becoming sensitive to more tones, the audible and inaudible, through which new forms of collecting living and harmony may grow. Relational empiricism is an empiricism which is thoroughly experimental. Numbers in Arnhem Land is a post-colonial encounter. The analysis is located in between the Yolŋu ways of living in North East Arnhem Land and the dominant modes of living in Australia. It operates in between European thought and Yolŋu thought and in between the intellectual traditions of the academy and those of Aboriginal Australia. The problem for which this thesis works solutions is a problem of the postcolonial situation in contemporary Australia. Through engaging in an encounter through living 'in between', this project is itself performing and enacting relations. These relations are comparisons, the active holding together of difference in ways that sustain learning and participate in collective life in ways that are open and hopeful. In articulating number through difference, and feeling for ways into the resonances through which number operates as difference and through oscillating value, this thesis demonstrates a mode of learning value through a respect for difference. This thesis claims that caring for difference in such a way opens the way for a renewed and revived study of number and empiricism in the social sciences