Science, politics, mathematics and finance

I went "offline" over the Christmas break and so missed the fallout of Brian Cox and Robin Ince's article in the New Statesman Politicians must not elevate mere opinion over science.  The essence of C&I's piece is that science exists as an "adjudicator above opinion", but C&I's "science" is narrowly defined, "science is a process, a series of structures that allow us, in as unbiased a way as possible, to test our assertions against Nature", essentially science is the set of phenomena that does not involve human interaction. They go on to say that

Science is the framework within which we reach conclusions about the natural world. These conclusions are always preliminary, always open to revision, but they are the best we can do. It is not logical to challenge the findings of science unless there are specific, evidence-based reasons for doing so. Elected politicians are free to disregard its findings and recommendations. Indeed, there may be good reasons for doing so. But they must understand in detail what they are disregarding, and be prepared to explain with precision why they chose to do so. It is not acceptable to see science as one among many acceptable “views”. Science is the only way we have of exploring nature, and nature exists outside of human structures.

 This is a well structured argument.  The five sentences are hard to disagree with, the paragraph gets our agreement, then it hits us with more controversial comments that to disregard scientific advice requires precise explanation.  The final clause is telling "nature exists outside of human structures".

The problem I have with this assessment is that C&I claim science is essential in areas such as climate change, vaccines, GMOs and evolution.  Now, apart from evolution, all these topics involve human interaction with nature: the issue about climate change is whether it is human induced; vaccines and GMOs are essentially   compounds synthesised by humans and placed into "nature".   While nature exists outside human structures, vaccines, GMOs and human-induced climate change cannot.

Brian Cox has Tweeted "Reviewed criticism of @robinince and my Christmas New Statesman, and concluded none is scientifically valid - so still time to get it :)".  This gets to the heart of my problem with the C&I argument - they define what is "scientific" in such a way that it becomes impossible to argue a case against them "scientifically".

As a mathematician working in relation to finance, why should I care?  Between 2006-2011 I was the "RCUK's Academic Fellow in Financial Mathematics", the Academic Fellowship scheme was initiated by the UK government in the aftermath of the MMR vaccine fiasco and the problems with the introduction of GMOs to establish 800 scientists who would act as advocates for their discipline in the event that discipline became a subject of the news.

In September 2008 I contacted the RCUK, my funders, about "what should I do", given that the world was in the grip of the Credit Crisis, the RCUK advised I contact the Science Media Centre,  a publicly funded “venture working to promote the voices, stories and views of the scientific community to the national news media when science is in the headlines”  to facilitate communication between mathematicians and science journalists on the credit crisis.  I sent an e-mail to the SMC but did not here anything back.  After I had been asked to appear on the BBC's Newsnight programme to discuss the science behind the Crisis, I phoned the SMC about my earlier contact.  The SMC had decided that the Credit Crisis was not a science story, and therefore beyond their remit. This was really annoying because a highly political Press Officer, Fiona Fox, with no scientific credentials was telling me, someone who had a Physics BSc, had worked in a technology based industry, had a PhD in applied probability and was an established academic,  what science was.  The following February, I was contacted by the office of the Science Minister who asked me to collate the views of mathematicians n the Credit Crisis, they asked if I had any support from the SMC and I recounted the tale.  Later that day I was contacted by the SMC to sort things out - some four months after the damage had been done. (see also one of my first posts Was the Credit Crisis a Science Story)

This experience with Ms Fox revealed to me some serious issues with British science.  There are a hard-core of scientists, a vocal minority, who are convinced science is undervalued, because it is under-funded and the country is not run as a technocracy.  They often complain that they are not taken seriously by society, while simultaneously withdrawing from addressing issues that are of concern to society: true science is about cosmology or particle physics, not about obesity or poverty.

What is perplexing is that, as many sociologists have pointed out, is that, for the likes of C&I,  the one area that should not be open to rational examination (i.e. science) is their beloved "science".

Now lets get to the maths and finance.  C&I are famous for being the presenters of the award winning BBC Radio Show The Infinite Monkey Cage.  The title is an oblique reference to the idea that if you collect an infinite number of monkeys and typewriters  they will eventually come up with the works of Shakespeare.  To be precise, they will almost surely (a.s.) come up with the works of Shakespeare.  The term a.s. is mathematical, a physicist like Cox would not worry about it, and it means that it is not certain that the monkeys would come up with the works, just that it is highly probable - the two are not the same as any financial practitioner is regularly reminded.

This distinction between a.s and certainty plays an important role in the philosophy of mathematics, in particular intuitionism or constructivism.  L.E.J. Bouwer argued that  statements like "there are a sequence of 100 9's in the decimal expansion of pi" (which as an irrational number has an infinite number of digits) can neither be proved to be true or false, in mathematics we cannot rely on the Law of Excluded Middle that assumes propositions are either true of false. If we cannot rely on truth/falsity of mathematical statements that apply to continuous phenomena (which involve infinite sets), then how can we rely on scientific statements to be true or false?  The issue is that many of the scientists who worry about public disregard for science often do not undertake a rational assessment of the "scientific method" that they are so reliant on, and dismiss any questioning of it as "un-scientific" because it implicitly considers science as a human construct (which is the essence of  my paper on Ethics and Finance).  The story of Brouwer and the LEM is particularly pertinent here because Brouwer took a constructivist approach because he was a Marxist - it was a political act.

Brouwer was not isolated in his distrust of non-constructivist theories, Poincare, Borel and Lebesgue were equally circumspect of the approach.  Again, what is pertinent here is that both Poincare and Borel were mathematicians who took an active role in political life and contemporary culture, they did not withdraw into academic cloisters and complain about society's disinterest in science.

Now the finance.  C&I base their science on observation, data, and the predictive models constructed on the basis of the data.  However there appears to be an assumption that "science" will come up with the right models, modulo the approximation problem, given the data.  However this approach makes some omissions: what data is collected and why (science does not work by collecting reams of data in the hope something will drop out), data analysis is subjective (is climate data a hockey stick or a bath - see McIntyre&McKitrick, what does the data say?), models are human constructions.

Making these observations does not seem relevant to C&I, but they are crucial in  modern finance,  an arena of people competing to select and interpret data and develop the best models.  It is a microcosm of good science, and for this reason it should be taken more seriously by the scientific establishment.  Not least because modern finance is more relevant, and therefore more interesting, to the public than cosmology or theoretical physics.