Friday, 5 April 2019

Mathematician, heal thyself

I attended the second “Ethics in Mathematics” conference held at the University of Cambridge and organised by Maurice Chiodo. I had come across Maurice about twelve months ago when I was working with a Norwegian academic on the issue of ethics in maths. Maurice has developed into the Henry Oldenburg or Maurice Fréchet, though I suspect being a central node in a network is not as career enhancing for Maurice as it was for Oldenburg and Fréchet because the concern is ethics. In my experience mathematicians don’t really want to face up to ethical issues associated with their discipline.

Ethics in mathematics is a broad issue, and Maurice’s interests extend well beyond my focus. For example, there are significant issues of professional ethics (diversity of the profession; treatment of junior academics); incorporating ethics into the curricula (school, undergraduate, postgraduate) as well as the “ethical content” of mathematics and the use of mathematics in society (my interests).

The first hurdle in talking about ethics in mathematics is to clarify what is being talked about. Generally, “ethical behaviour” is taken to mean being “good”. But this does not stand up to examination since it is usually impossible to define what is being meant by good, for example the Mitchell and Webb sketch that has become an internet meme of David Mitchel as an SS officer asking the question “Maybe we’re the bad guys?” Socrates addressed the problem and saw a solution in being self-reflective: the SS officer asking the question is the start of ethics. Too often, the assumption is “I am a good person, therefore what I think is ethical”, all too often this results in people calling each other fascists.

I frequently refer to Gillian Tett’s Fools’ Gold as an account of ethical mathematical practice. Tett explains how J.P. Morgan came out of the 2008-2009 Financial Crisis because it used mathematics critically rather than blindly accepting the outputs of “black boxes”. I felt the approach Tett described was oddly discordant with the attitude of mathematicians. During the crisis, I co-ordinated a response from UK mathematicians, through the Council of Mathematical Sciences, to criticism of the use of mathematics in finance, this information was also passed onto the UK Science Minister of the time.

The standard response from (senior) UK mathematicians was along the lines that finance hadn’t used mathematics but abused it. The solution was to have “more” and “better” mathematicians. This was underpinned by some adopting a logical positivist line, attributed to Hume, that the role of mathematicians is to describe the world as it is, not as it ought to be. At the time I felt mathematicians were not examining the role of their discipline in the crisis; they were not behaving ethically. This was the start of my journey that transformed me from an “uncritical” (unethical?) mathematician to someone who feels mathematics is vital, so long as it is critical.

I was reminded of my experience in 2009-2010 at the conference when Maurice highlighted that of the hundreds of Cambridge maths faculty, only the two or three involved in organising the meeting were listening to the talks: UK mathematics (as distinct from statistics) seems disinterested in ethics, it does not wish to be critical. After making this observation, the session was on “Calling out bad mathematics”. There were two talks, on by Sam Marsh on issues with the valuation of UK academics’ valuation and the second about the use contemporary use of mathematics in support of “neo-eugenics” (“contemporary” because there is a long history of this). I had to come home and so was unable to participate in the discussion and what follows are the comments I would have made.

During the workshop I had made the point not to demonise finance, it is not intrinsically unethical (see the example in Fools’ Gold) though I did not comment in a discussion about funding sources that governments are rarely benign. I would have made this point in respect to Sam Marsh’s presentation. The pensions dispute is generally framed as academics (unionised workers) against the Universities Superannuation Scheme (agents of the bosses). What was pointed out to me by academic actuaries early on in the dispute was that the “gold plated” academic pension was doomed not because of the employers but because the UK Government’s “Pensions Regulator” was running a campaign to close these types of pensions because they were high risk if the sponsoring company failed. Academics do not tend to think universities will fail financially, the government takes a different view. As a result, the pension is not as sound, looking forward, as it appears. My question to Dr Marsh would have been “Where did the boss of the USS work before the USS”. The answer is, the Pensions Regulator. My point is, there was more in the USS valuation than the mathematics, the USS were enacting policy principles from the Pensions Regulator (a government agency), not necessarily the employers. This highlights that governments are not always paragons of virtue.

Clement Mouhout’s presentation highlighted the “abuse” of mathematics in support of eugenics. Mouhout categorised three types of “bad maths”: not being internally rigorous (not being valid); wrong application of axiomatic method (I interpret this as correct logic but incorrect premises); “math-science washing” (the area I am interest in). After I had left, a report on the discussion was
In the sense that mathematics cannot legitimate untrue theories, I agree. I am more concerned if the claim is mathematics cannot support “unpalatable” ideas. My concern is an issue I have with the use of mathematics to support left-wing ideology, not just right-wing ideology. My battle calling out mathematics was about a theory criticising finance. I have asked the authors to explain a saltus in their mathematical argument; their response was it has bee peer reviewed and they do not have to explain to me. I note this author/correspondent was on the editorial board of the journal who published the paper. Mathematics is unconcerned with politics, in this sense.

One issue that came out of Marsh's presentation and resonated with me was that people recognise the authority of mathematics and people will generally listen to mathematicians more than sociologists. Dr Marsh's experience, and confusion around the fact that the USS were unperturbed my criticism by mathematicians of mathematical ideas is that, while they might listen to mathematicians they might be more inclined to take notice of social scientists. I think this is a real ethical, in the sense that it relates to the "ethos", problem for mathematics: mathematics is authoritative, but widely irrelevant. The theories are rigorous, but vacuous.

This isn't a new issue, related to the widespread ignorance of expertise. In Feller's influential paper On the Theory of Stochastic Processes, with Particular Reference to Applications there is a rather innocuous discussion of the Pareto's law of wealth distribution (p 418). The Pareto Law is sometimes used to justify inequality (in a similar manner to mathematical models of race/sex being used to justify inequality) and is colloquially the "80-20" rule: 80% of wealth is held by 20% of the population. Feller raises the question whether the rule is valid in non-ergodic situations. This is substantive as it implies the 80-20 rule need not always hold, it is not natural. Economists do not worry about this mathematical concern.

What is the problem? I think the starting point is that mathematics is neutral, just as a rifle is neutral. There are a proportion of the population who believe mathematics is intrinsically evil (because it enables inhumane instrumental reasoning) just as there are a proportion who believe all firearms are intrinsically evil. There are those who feel that mathematics is intrinsically good, just as there are those who feel the solution to mass shootings is wider gun ownership. I tend to think mathematics is neither good nor evil but the use of mathematics an be ethical or unethical, just as a rifle can be used ethically or not. Mathematics is ethical if it is being used critically, meaning that those using it are being self-reflective in what they do. Mathematics is not ethical if it is being used instrumentally, that is used as a means to a pre-defined ends (justifying risky investments, closing pension schemes, eugenics, restraining finance).

Moreover, mathematicians need to articulate this and then take steps to be listened to in serious policy discussions. Politicians don't listen to mathematicians because mathematicians (as scientists) tell the politicians that their work is not political. This is a lie, mathematics is constantly being used to justify political ends, and a useless lie, in that it means mathematicians are not taken notice of by politicians when they challenge the instrumental use of mathematics.

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