Mathematics and real systems

The UK FSA’s Lord Turner, in the Turner Review of the financial crisis of 2008 was critical of the role of mathematics in misleading decision-makers about the possibility of a crisis. I have also found similar cynicism in other areas involving real complex systems. It seems that mathematics befuddles and misleads. (Or am I being unduly sensitive?)

In this INET interview Lord Turner provides a more considered and detailed critique of mathematics than I have come across from him before. (Unless you know different?) In defence of mathematicians I note:

  • His general criticism is that ‘sophisticated’ mathematical models were given a credibility that they did not deserve. But we do not judge a car on its engine alone. What mattered was not how mathematically brilliant the models may have been, but how they corresponded to reality. This was the preserve of the economist. If an economist declares certain assumptions to be true, the mathematician will build on them, yielding a model with certain behaviours. Normally you would expect the economist to reconsider the assumptions if the resultant behaviour wasn’t credible. But this didn’t happen.
  •  If the potential for crashes was a concern, no amount of statistical analysis based on data since the last big crash was ever going to be helpful. The problem was with the science, not the mathematics.
  • Turner is critical of the commonplace application of probability theory, extrapolating from past data, as if this were the only ‘mathematical’ approach.
  • Turner continually refers to ‘Knightian Uncertainty’ as if it were extra-mathematical. He does not note that Frank Knight was a Keynesian at a time when Keynes’ best known work was mathematical.
  • Turner refers to Keynes’ Treatise on Probability without remarking that it provides mathematical models for different types of Knightian uncertainty, or linking it to Whitehead’s (mathematical) work on complex systems.
  • In Whitehead’s terms, Turners criticism of mathematics is that it can only provide extropolations within a given epoch. But this is to ignore the work of Whitehead, Keynes and Turing, for example, on ’emergent properties’.

It seems clear that the economist’s assumption of ‘the end of history’ for economics led to the use of mathematical models that were only useful for making predictions conditional on the assumption that ‘the rules of the game are unchanging’. Is it reasonable to blame the mathematicians if some mistook an assumption for a mathematical theorem? (Possibly?) More importantly, Turner notes that the ‘end of history’ assumption led to a side-lining of economists who could work across epochs. They need to be revived. Perhaps so too do those mathematicians with a flair for the appropriate mathematics?

David Marsay, C. Math FIMA

See also: IMA paper, statistics blog.

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About Dave Marsay
Mathematician with an interest in 'good' reasoning.

5 Responses to Mathematics and real systems

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