A historian Joel Kaye has written widely on the development of science in medieval Europe. In Economy and Nature in the Fourteenth Century he presents a thesis that
In broad terms, the conceptual landscape that emerged in the fourteenth century resulted from a striking shift in the models derived to represent order and activity in the natural world: from a static world of numbered points and perfections to a dynamic world of ever-changing values conceived as continua in expansion and contraction; from a mathematics of arithmetical addition to a mathematics of geometrical multiplication, newly accepting of the approximate and the probable; from a world of fixed and absolute values to a shifting, relational world in which values were understood to be determined relative to changing perspectives and conditions; and from a philosophy focused on essences and perfections to one dominated by questions of quantification and measurement in respect to motion and change. Each of these new directions proved to be of great importance to the future of scientific thought.
Monday, 7 December 2009
Mathematics, Economics and Decision Making
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using mathematics
The 2009 Alan Tayler Lecture was delivered by Prof Lord Desai of the London School of Economics and Political Science at the University of Oxford on 30 November.
I did not attend the lecture, but I understand that Lord Desai called for economists to use more sophisticated modeling techniques - i.e. not to rely on single-factor linear models when trying to understand the economy. Makes sense to me.
I shall try and get a copy of the talk.
I also recently attended a talk by Prof Lord Skidelsky who was talking about Keynes, and publicising his book Keynes: The Return of the Master. A key point made by Skidelsky was Keynes belief in "irreducible uncertainty". From the perspective of maths, there is nothing controversial in Keynes is position, the Fundamental Theorem of Asset Pricing, in noting that there are infintely many martingale measure in an incomplet market, makes the same point. As a Russian mathematician has pointed out to me, when economists talk about "rational expectations", ask them under which measure they are calculating the expectation.
I did not attend the lecture, but I understand that Lord Desai called for economists to use more sophisticated modeling techniques - i.e. not to rely on single-factor linear models when trying to understand the economy. Makes sense to me.
I shall try and get a copy of the talk.
I also recently attended a talk by Prof Lord Skidelsky who was talking about Keynes, and publicising his book Keynes: The Return of the Master. A key point made by Skidelsky was Keynes belief in "irreducible uncertainty". From the perspective of maths, there is nothing controversial in Keynes is position, the Fundamental Theorem of Asset Pricing, in noting that there are infintely many martingale measure in an incomplet market, makes the same point. As a Russian mathematician has pointed out to me, when economists talk about "rational expectations", ask them under which measure they are calculating the expectation.
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