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The gist of this, as I undestand it, has to do with problems that are easier to solve than to give a mathematical expression. This is certainly a good area for anthropology. There is a very interesting anthropological application of catastrophe theory in a book by Michael Thompson called 'Rubbish Theory'; this has always been a favourite of mine. In it Thompson looks at why certain objects are highly valued as antiques while others 'catastrophically' lose their value and become 'rubbish'. The answers require various kinds of models plus ethnographic description of people knocking through walls in their houses to make them more fashionable. Worth a look perhaps.
Huon, I agree, Thome's Catastrophe theory (CT) can provide not only pure qualitative insight, but also some kind of geometric imagination and intuitive description, expressed by Thompson. Today,CT is a part of more general KAM ( Kolmogorov-Arnold-Moser) theory of chaos, however, Thom's initial biologism and intuitive geometry cannot be forgotten. Even G.Soros in his attempt to use chaos theory to predict "superbubbles" in global economics cannot avoid Thom's-like intuitions, probably, because Soros's "intuitive reflexivity" is NP-incomplete problem...
Huon Wardle said:The gist of this, as I undestand it, has to do with problems that are easier to solve than to give a mathematical expression. This is certainly a good area for anthropology. There is a very interesting anthropological application of catastrophe theory in a book by Michael Thompson called 'Rubbish Theory'; this has always been a favourite of mine. In it Thompson looks at why certain objects are highly valued as antiques while others 'catastrophically' lose their value and become 'rubbish'. The answers require various kinds of models plus ethnographic description of people knocking through walls in their houses to make them more fashionable. Worth a look perhaps.
Michael, I am glad this is of some relevance - there is certainly a big gap between the imagination of anthropology and the mathematical elegance you are also seeking - personally I find Levi-Strauss earlier conjectures on kinship relatively convincing but his later myth work wildly tendentious. I have to admit also I am drawn to the geometric when it comes to this kind of thing - as are economists when they don't know what they are talking about; hence they draw big teleologically framed loops showing when a depressive 'cycle' is predicted to end (see the discussion on 'consumer confidence' in the economic anthropology group). What concerned me about your paper was that it consisted of two hypothetical actors whose wider beliefs remain unexplored as does anything to do with the wider conditions of their choices. How resilient are your models to the kinds of 'complex' (in a true sense of the word) phenomena empirically minded anthropologists might be interested in? I hope that the meeting between mathematics and anthropology is possible, but it would involve a very thoughtful examination of the language we use and our notions of what counts as relevant.
Michael Alexeevich Popov said:Huon, I agree, Thome's Catastrophe theory (CT) can provide not only pure qualitative insight, but also some kind of geometric imagination and intuitive description, expressed by Thompson. Today,CT is a part of more general KAM ( Kolmogorov-Arnold-Moser) theory of chaos, however, Thom's initial biologism and intuitive geometry cannot be forgotten. Even G.Soros in his attempt to use chaos theory to predict "superbubbles" in global economics cannot avoid Thom's-like intuitions, probably, because Soros's "intuitive reflexivity" is NP-incomplete problem...
Huon Wardle said:The gist of this, as I undestand it, has to do with problems that are easier to solve than to give a mathematical expression. This is certainly a good area for anthropology. There is a very interesting anthropological application of catastrophe theory in a book by Michael Thompson called 'Rubbish Theory'; this has always been a favourite of mine. In it Thompson looks at why certain objects are highly valued as antiques while others 'catastrophically' lose their value and become 'rubbish'. The answers require various kinds of models plus ethnographic description of people knocking through walls in their houses to make them more fashionable. Worth a look perhaps.
Well I have to admit a personal preference for your type 3. Are you trying to demonstrate that these 'societies' have ever existed/might exist or are they a new set of Platonic forms that, say, I might draw on in one of my thought processes in order to discard in the next?
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