At a time when there is an emphasis on inter disciplinary research, it is not that useful to divide science into separate categories. However one distinction that, as a mathematician, I find useful is between Romantic and Enlightenment science. Enlightenment science is concerned with the universal, and is developed by collaborative analysis, and, to facilitate both the collaboration and analysis, mathematics plays an important role. Romanticism emerged in the second half of the eighteenth century and dominated British and German culture in the following half-century. Romantic science emerges out of senses trying to understand the whole, rather than the parts, sentiment over reason, and is often the result of an individual genius's struggle, frequently against dark forces.
The archetypical romantic scientists are Alexander Humboldt, Lewis and Clark and Darwin, who developed science through exploration. The archetypal romantic mathematician is Galois, whose career was hindered by his reliance on intuition rather than the clear proof favoured by the French Academy and a myth has grown up around him that he did his most significant work the night before he was killed in a duel over a love affair.
I have been thinking a lot about the transformation from Enlightenment to Romanticism, because there seems to have been a massive change in the relationship between science and finance in the first half of the nineteenth century, at the time that Romanticism dominated culture.
I thought about this distinction after listening to Dylan Evans promoting his book Risk Intelligence on the radio. Evans defines Risk Intelligence as the "ability to estimate probabilities accurately" (0.24 on audio), such as the chance a horse wins a race (0.52). Evans goes on to make the point that our educational system does not train people in making decisions under uncertainty (1.29), what he calls a "twilight zone" (1.40). Further on he explains that because finance (2:57) became to rely on mathematical models and the "intuitive gambler types were edged out and as a result Wall Street haemorrhaged risk intelligence" (3:35), and this transformation was partly responsible for the failures of finance.
One point I would agree with Dr Evans on, that there needs to be an effort to get concepts around uncertainty onto school curricula. In fact, at the "Credit Crisis Five Years On" meeting recently I asked Andy Haldane if he felt the Bank of England had a role to play in helping shape curricula in this way. I think there are significant issues with Evans' view that the chance of a horse winning a race can be estimated accurately, Knightian uncertainty / Keynes' irreducible uncertainty' spring to mind. However, my main concern is in the claim that it was the use of mathematics that was partially responsible for the failures of finance.
It struck me that in the interview, Evans seems to be endorsing Romantic Science, there is an emphasis on "intuition" over mathematics in what he says and reference to "twilight", the darkness that is a feature of Romanticism. But just because Risk Intelligence might be a Romantic idea, doesn't mean to say it is dangerous. The danger with a concept like Risk Intelligence is the emphasis on there are some people who are "good" at risk, there is a link to that other idea that emerged out of Romanticism, the idea of genius, and that mathematics is a hindrance, not a help, in finance.
Why is mathematics important in finance? It goes back to why Fibonacci's Liber Abaci was a publishing phenomena at a time when books were hand copied - the mathematics it described enabled merchants to write down, disseminate, discuss and improve their financial models. This is the point of mathematics, whether in physics or finance, and why mathematics is such an important part of Enlightenment science but missing from the Romantic: Enlightenment science is collaborative and needs a common language, and its arguments are written in that language, mathematics.
The problem with modern finance is not in the mathematical models, but in that the models were an end in themselves and not a means for developing a consensus, understanding, knowledge about finance. Banks employed geniuses to develop these models in house that they kept secret, or, they bought black boxes that had been created by geniuses elsewhere. When mathematicians, such as Phillipe Artzner and Freddy Delbaen or Michael Gordy, shone a light on the some of the leading industry models, their illumination was blocked by the towering geniuses, the "masters of the universe", working in banking.
When you read the book, rather than listen to the interview, the issue of mathematics in finance is not as significant. In fact, the whole book rests on a mathematical model of RQ (compare with IQ or Samuelson's "Portfolio IQ", "PQ"), which is implemented on-line for you to test your own RQ.
Evans claims the motivation behind RQ is a 1986 paper Ceci and Liker where RQ is identified as a type of intelligence uncorrelated with IQ. Unfortunately, Ceci and Liker's science was not up to much, and within two years this key result was overturned by better analysis. In fact "RQ" seems to be highly correlated to "IQ". Evans argues that Banking regulation should involve measuring the RQ of bankers. The problem is anyone can "game" RQ (when I did the test I got a very high score of 80 because I realised immediately what was going on).
Having laid the basis of RQ Evans attempts to describe how you can improve your RQ, which boils down to understanding the limitations of what you know. This does not strike me as particularly novel, and might be labelled as "science", which has been described as "organised scepticism".
In fact, Evans' criticism of maths in finance turns out to be more a criticism of calculation in finance, and this has been addressed more tangentially, but more eloquently, by the philosopher Richard Sennett in The Craftsman. Sennett makes the point that we can all be craftsmen in the modern age, if we learn a craft. Developing RQ seems no different from becoming skilled in understanding risk. What is important in becoming a craftsman is hard work in a social context (crafts were traditionally regulated by a guild) and this is why I feel RQ is not simply a banal idea but a dangerous one.
The Romantic Evans seems to believe in an intuitive genius that can be developed outside of the workshop, I think this is dangerous because I believe the solution to banking's problems lies in open discussion and debate about the risks and rewards of finance (i.e. science), and that good bankers are skilled craftsmen who have learnt their trade by spending hours developing their skill in the work place. If something has happened in finance over the last 25 years it is that banks have not been recruiting schoolboy apprentices (I knew three people who left school to go into finance, one to a Bank of England apprenticeship) who they train up over five years, but have been recruiting staff "off the shelf" out of universities and assuming that these academically trained men and women have the right skills for banking. Or they have recruited ready-made business experts such as Andy Hornby and Fred Goodwin.
Dylan Evans's central argument, that people who are gifted in making risky decisions can be identified and hired to run finance, relegating the need for good ethics, is dangerous.