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ssrn-id1076688 - More for Less An Introduction to New Ideas...

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1 More for Less: An Introduction to New Ideas in Mathematics, Physics and Economics This paper introduces ideas covered at greater length and in greater depth in the following three volumes, each of which is downloadable from www.michaelryan.org.uk New results on prime numbers There is such a thing as society: purposive contradiction, intervening duality and positive science More for Less 1. Overview Among ideas which are introduced here are: i) a new approach to the generation of integers; ii) the idea of a mathematical-physical dichotomy and its usefulness for describing and understanding mathematical and physical and economic phenomena; iii) fundamental roles for the ideas of duality and intervening duality in representing and explaining mathematical and physical and economic phenomena. The paper also explores methodological issues in mathematics and physics and economics. In that wider context a key theme is that, in distinction from mathematicians and physicists, economists do not just seek to model economies as relatively abstract mathematical and physical systems: they also seek to model the impact of economic agents, both upon elements of their mathematical and physical environments, and upon themselves and each other as economic agents. Much of what follows is motivated by these ideas, and especially by the fact that the focus of interest for economists is not only on abstraction and on professional consensus, but on gains which individuals by acting as individuals may make relative to themselves, each other and relative to a wider system. The challenge for economists, therefore, is that, in general, economic agents will differ with respect to their preferences and to their resources and that the very purpose of economic agents, when acting as economic agents, will frequently be to seek advantage for themselves and others stemming directly from these and other differences between themselves and other economic agents. A simple example may help here: if you have apples and don’t like apples and I have oranges and don’t like oranges it is very clear that there is potentially an advantage to both of us in exchanging these commodities with each other. It is not clear why there would be any advantage to either of us in seeking consensus – either theoretically (abstractly/mathematically) or actually (empirically/physically) on what are the attributes of an apple or what are the attributes of an orange. A fortiori it is not clear why either of us would be interested in persuading the other that their perception of the nature and/or merits of their commodity were – as they understood it – incorrect. In any case for each of us our gain from such an exchange would involve gains in knowledge of others’ preferences, gains in amounts of commodities which we prefer
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2 and gains by relinquishing commodities we do not prefer. At a deeper level, we would respectively gain from the difference between our prior perception of apples and of oranges, when we did not have them, and our perception (physical consumption?) of
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