Friday, 27 June 2014

Academic metrics and market mechanisms: heaven or hell

This post is a draft of my contribution to the 'Independent review of the role of metrics in research assessment' being undertaken by the Higher Education Funding Council of England and Wales (I will think about it over the weekend).

As a mathematician I felt my views were covered in the submission made by Prof David Speigelhalter  that he has disseminated. I did not intend to make any further comments until I read the views of Prof Steve Fuller . Specifically, as a Financial Mathematician I believe I can offer some insights on the approach Prof Fuller puts forward.

Prof Fuller’s argument was interesting to me because he starts by considering the clustering of ‘networks’ that some bibliometrics identify; he refers to the clusters as fiefdoms. Since metrics identify these fiefdoms they are useful, he also implies that work that creates connections between fiefdoms/archipelagos should be highly valued. I agree with this observation, and so my main recommendation would be to develop bibliometrics that asses how research facilitates connections on the basis of complex graph theory (as distinct from crude statistics). As a Financial Mathematician  I am interested in this area because, since the Financial Crisis, the Bank of England has been encouraging mathematicians to start analysing the financial system as a complex network, with little success that is reflected in the general immaturity of the science (though research is emerging).

My concerns with Prof Fuller’s approach begin with this comment
More specifically, academics should be trained to think about their citations as investments under conditions of scarcity — that is, exactly like a capital resource.
and develop with
To be sure, in the end, we will need to admit upfront that the move to citations is a move to integrate a proper conception of markets into the internal dynamics of academic knowledge production.
As a financial mathematician who has worked in markets I have a deep commitment to markets but what I wish to highlight in Prof Fuller’s argument (as disseminated) is that it is not clear what is meant by “a proper conception of markets”.

Since the Financial Crisis there has been increasing interest in what is a “a proper conception of markets” and an emerging (minority) consensus that the current conception is flawed and the Financial Crisis of 2007-2009 and subsequent crises of ethics are the consequences of this flawed conception. One line of thought in this emerging consensus is that the ‘good internal’ to markets is not profit maximisation under scarcity, following from Robbins definition, but the distribution of credit in the presence of uncertainty to support social cohesion, closer to Maynard Keynes conception.

I would suggest that Fuller’s focus on citations is analogous to a naive financier's focus on money. I would argue that the focus of HEFCE should be the less tangible concept of ‘knowledge’, just as a good financier is concerned with ‘credit’. I believe this observation is a markets focussed corollary to the comments made by Meera Sabaratnam.

That is as much as I will say in the submission.  There is some context that comes from this response from Brad DeLong on initiatives to change the economics curriculum in the UK.  Prof DeLong states
I think that modern neoclassical economics is in fine shape as long as it is understood as the ideological and substantive legitimating doctrine of the political theory of possessive individualism.
This is really interesting since the term `possessive individualism' was coined by the Canadian political scientist C.B. Macpherson  in a critique of the identification of democracy with markets.

DeLong implies that to challenge mainstream neoclassical economics is to challenge the ideology of possessive individualism.  Central to my work is diminishing the role of "max U" in finance and replacing it with reciprocity in the face of uncertainty, which I believe is challenging the ideology of possessive individualism.

I am becoming obsessed with the relationships between finance, science and democracy.

Thursday, 19 June 2014

Rethinking the finance curriculum

Emerging in the wake of the Rethinking Economics movement is Rethinking Finance, and it looks as if Rethinking Finance is going to place some emphasis on the finance curriculum, just as Rethinking Economics , as a student organisation,  has.  @NeilLancastle, one of the organisers of Rethinking Economics asked me for my views on the finance curriculum, with reference to a review published by the CFA Institute Research Foundation.

As a lecturer in finance (derivative markets and pricing to actuarial undergraduates and MSc students) two things are in my mind.  Firstly students have little interest in and less conception of the nature of money.  I think this is peculiar given they have made a commitment to working in finance which is concerned, principally, with money (OED 7: finance (n); The management of money, esp. public money; the science which concerns itself with the levying and application of revenue in a state, corporation, etc.).

More relevant to the students I work with, who approach finance mathematically, there is virtually no ability to critically reflect on what they are told.  This was emphasised a few months ago with our MSc cohort in Quantitative Financial Risk Management, which is notorious for testing maths graduates with qualitative approaches to risk.  We arrange for the students to address problems set by business, and this year a problem was set by an asset manager and the question related to the value of active fund management.  The students, universally, answered the question on the basis of the guidance and literature that the asset manger provided: they were a series of presentations suitable for a stock pickers' benevolent fund. All the presentations were scholarly weak, but the question the academics, as examiners, had to address was whether it was fair to penalise the students when we do not train them to be critical of published research.  In developing mathematicians, the truth is the truth.

What struck me when comparing the CFA's proposals (p 73) with those from a conference sponsored by the Royal Economic Society reported in 2013 was a similarity.  The RES highlights
There was broad agreement that students need:
  • Greater awareness of economic history and current real-world context;
  • Better practical data-handling skills;
  • Greater ability to communicate economics to non-specialists;
  • More understanding of the limitations of modelling and current economic methodology;
  • A more pluralistic approach to economics;
  • A combination of deductive and inductive reasoning.
where as the CFA
asked sources what subjects they believed should be reinforced in or added to the curriculum. ..., as follows:
• macroeconomics,
• a historical perspective on macroeconomics,
• the history of financial markets and economic history,
• behavioral finance,
• statistics beyond the use of the normal distribution,
• risk management, and
• ethics.
The key overlap seems to me to be in

  • a historical perspective [this would lead to] 
  • pluralism
  • practical tools
  • a synthesis of facts with values 
Focusing on the CFA report I noticed a tension captured by the final sentence of this paragraph spanning pp 1-2

Is our “science” merely an idealized rational construction that ignores market realities? If so, exactly what should we be teaching students of finance whose objective is to manage other people’s money? Is an alternative science based on observations available (or in progress)? Or does our current knowledge of economics and finance have to be removed from the realm of science altogether and placed on a par with the social sciences? (my emphasis)
I think what this highlights is a lack of clarity over what is meant by 'science' (in what sense are social sciences removed from the realm of science?).  Because there is this lack of clarity, I think it is difficult how to answer the questions posed.

I don't think this lack of clarity about science is a particular feature of the CFA or finance more generally, I think it is a common problem that makes resolving these sorts of issues hard.

Labelling different disciplines as 'science' or 'not science' and be problematic.  I tend to use the term 'human sciences' to emphasise an equality of status between history (human), economics (social), biology (natural), physics (physical) and statistics (mathematical).  However I do think it is sometimes helpful to use the classical distinctions of episteme, phronesis and techne.  The work-place is often associated with techne, the university, especially in the context of research,  with episteme.  These terms could apply equally well to all disciplines and professional bodies, such as CFA, should be concerned principally with phronesis.

This train of thought might suggest that I think academics do not involve themselves with phronesis, this is not the case.  I feel that academics place too much emphasis on episteme at the expense of helping students in developing phronesis.  This is demonstrated by graduates leaving university with a sense that they know the truth but completely lacking in practical skills.

These comments encapsulate my criticism of the first part of the CFA report.  The second part of the report focuses on six aspects of investment management, namely

  • diversification,
  • optimization-diversification formalized,
  • the CAPM and similar models,
  • the efficient market hypothesis,
  • risk measurement and risk management, and
  • crises.
What strikes me is the implication of the report (all be it corrected in a footnote) that diversification started with Markowitz, on this basis optimization is mean-variance portfolio selection that, in synthesis with neo-classical economics,  leads to CAPM.  What this account (and presumably the CFA syllabus) lacks is a historical perspective.  Diversification existed long before Markowitz and the success of mean-variance portfolio selection was a much because of its mathematical tractability, rather than its 'financial' sense.  Given that the CFA is keen to promote behavioural finance, a key object of behavioural finance are S-shaped utility functions, it is therefore worth noting that these were first identified in 1948 in the collaboration of an economist (Milton Friedman) and a statistician (Jimmy Savage).  The apparent omission of this work from the CFA syllabus, probably because of the problems of optimising S-shaped utility curves is  "massively difficult", highlights the main problem with the syllabus: it tells a simple story rather than preparing candidates for practice.

A similar issue exists with risk management.  Again this is an old practice that has been incorporated in to actuarial science for hundreds of years but is presented as being a modern science.

My work sees EMH as being an expression of justice in exchange, so EHM can be retained even if the focus of finance switches from individual profit maximisation in a competitive arena to reciprocity in support of social cohesion.  This work has initiated a switch in my own research from focussing on stochastic control to exploring complex network theory in order to better understand crises.

What links all these six themes is the importance of a historical context.  I often remark that for financiaers to justify fat fees they need to convey the impression that they are addressing novel problems.  I think if you consider the history of finance you soon come to realise that the problems and technologies are persistent, it is the culture that changes.

Section 3 of the CFA report moves on to consider the teaching of finance in reference to the topics discussed.  In section 4 it asks what is missing from the current curriculum and comes up with the seven topics listed earlier.

The first suggestion is the need for more macroeconomics.  But what does this mean?  Macroeconomics is usually concerned with aggregate parameters - GDP, unemployment, inflation, savings and investment rates, etc. -and the simple relationships between these parameters.  The standard models they work with - Aggregate Demand - Aggregate Supply, Investment Saving–Liquidity Preference Money Supply - don't seem that useful to financiers.  What I think is more useful is the presentation of money (and finance) as an integral part of a highly connected economic system; the relations between interest rates, exchange rates, prices, demand, supply, confidence, uncertainty.
This observation ties into the second suggestion: the need to take a historical perspective on macro-economics.  This should highlight the relationships I mention.

The third suggestion is, to my mind, critical for the CFA syllabus: The History of Finance/Financial Markets.  The report lists a number of texts, I would add Geoffrey Poitras' The Early History of Financial Economics, 1478-1776: From Commercial Arithmetic to Life Annuities and Joint Stocks.  I would also support strongly William Goetzmann's comments that
Studying the how and why of financial institutions, markets and instruments forces us to understand modern finance in the broader context of human lives. It provides a framework for understanding how finance can make the world better and what kinds of possibilities and problems can emerge. 
 I think this: disseminating the role finance has played in stimulating the development of science and democracy; should be a core priority of the CFA, as the principle professional body.  This is an emphatic statement but having met Richard Seaford recently, who argues that the origins of Greek philosophy are in money, combined with my knowledge of the impact of finance on European thought in the thirteenth and seventeenth century, I think this is an important story untold, to the detriment of financiers and their practice.

I have been told that there is a trend in business schools (and the like) to shift from focusing on a narrow definition of finance to evolving into research/teaching establishments that place finance at the centre of an multi-disciplinary constellation.  I understand this is the ethos at Copenhagen and Vienna.  In this setting it is hard to see how behavioural finance does not become integral to finance as a whole.

From this starting point, Behavioural Finance follows as well as the Ethics issue.  I must admit that I feel the CFA is weak on ethics, its Code of Conduct appears to me nothing more than "don't break the law".  Ethics is much more than this.  The Governor of the Bank of England recently highlighted the issue in a speech where it is pointed out that , in the past
 Bank leaders created cultures around a simple principle: if it’s legal and others are doing it, we should do it too if it makes money. It didn’t matter if it  as the right thing to do for the customer, community or country
 The rational approach to ethics is to place it in a cultural context, this is only really feasible if the theory of finance is placed in a cultural context.

Finally, since 2007 I have perceived a convergence of asset and risk management practices, locally this is characterised by Standard Life's GARS fund.  My suggestion to the CFA is to re-structure "Modern Portfolio Theory" as "Risk Management" with Markowitz, and its successors, being one approach where risk is managed by minimising variance of returns.

In summary, my syllabus structure would be
  1. The nature of money (macroeconomics and more)
  2. The purpose of finance (history and ethics)
  3. The practice of finance (behavioural, risk and asset management)
  4. Tools and techniques (optimisation, statistics)
and my closing comment is that it would take at least seven years for a apprentice Merchant Adventurer or Mercer to become a freeman in the sixteenth century.  That is seven years of on-the-job training.  Students today believe they are qualified after a degree and maybe 3 years preparing for CFA I, II, III.  Actuaries can expect to be fully qualified after one of our 4-year degrees and 2-3 years on the job training.  I am not convinced that the contemporary training is as good as the medieval training (in relation to contemporary complexities).  I also believe, as does Mark Carney, that banking needs to be professionalised by "building a sense of vocation and responsibility" like the law, medicine, accounting and insurance.  I think the CFA should take a central role in advocating this.


Friday, 13 June 2014

Reciprocity and the difference between usury and interest

At the IASH meeting on the Human-Business interface I attended last week, Michael Northcott discussed the relationship between capitalism and sustainability.  Michael is an authority on both subjects, having written on environmental ethics and debt.  At the end of Michael's presentation I made the point that theologians distinguished interest ad usury in the past, a distinction that was missing in Michael's discussion.

Usury derives from the Latin usus, meaning 'use',  and referred to the charging of a fee for the use of money.  Interest comes from the Latin interesse, meaning 'compensation for loss', and originated, in the Roman legal codes as the fee someone was paid  if they suffered a loss as a result of a contract being broken.  So a lender could charge interest to compensate for a loss, but they could not make a gain by lending.

It is easier to understand this distinction with a simple example.  A farmer lends a cow to their cousin for a year.  In the normal course of events, the cow would give birth to a calf  and the cousin would gain the benefit of the cow's milk.  At the end of the loan, the farmer could expect the cow and the calf to be returned.  The interest rate is 100%, but it is an interest since the farmer, if they had not lent the cow to their cousin, would have expected to end the year with a cow and a calf.  Similarly, if the farmer lent out grain, they could expect to get the loan plus a premium on the basis that their cousin planted the grain, he would reap a harvest far greater than the sum lent.

Because money is 'barren', unlike land or labour it could not 'produce' anything.  As a result, money can have no intrinsic value, other than its use to facilitate exchange, and so charging for the lending of money is essentially selling something that has no value.  Thomas Aquinas argued that
To take usury for money lent is unjust in itself, because this is to sell what does not exist, and this evidently leads to inequality which is contrary to justice.
So, usury contradicts 'natural law'.  Even if you could convince the canon lawyers that you were, in fact, selling something that did exist, the theologians might argue that usury was an affront to God because, since money was barren, the usurer was charging for time, and "time was God's exclusive property''.

In theory, this is all very clear, in practice there was still the question of where the dividing line between usury and  interest was and almost everyone who was handling money was looking to charge as much interest as was permissible.

Around 1236, an English professor of canon (church) law, Alanus Anglicus,  argued that usury did not exist if the future price of the good was uncertain in the mind of the merchant.  These theories became established in the medieval legal system between 1246 and 1253 by Pope Innocent IV, a former professor of law at Bologna.  Not only could a merchant adjust the 'just price' to cover their labour and expenses, but also they could also adjust the price to take into account the risk they bore,  called an aleatory contract, from the Latin word alea for chance.  In establishing this principle, a Catholic jurist initiated the scientific study of financial risk.

Today, financial economics models interest through a force of interest, r, and so the value of a loan of  X0 at time t = 0 would be repaid by an amount XT given by
This implies that the repayment amount Xt is the solution to the most basic differential equation,

that is, Xt grows at a constant rate r. This links to Piketty’s thesis that capitalism induces inequality because r, the return on money, is greater than g the growth rate of the economy. This is conventional economic theory.

I argue that at the heart of financial economics is not growth but reciprocity, so how do I account for interest?

 In 1837 Poisson wrote Recherches sur la probabilité des jugements en matiére criminelle et en matiére civile (‘Research on the Probability of Judgments in Criminal and Civil Matters’). Despite its title, most of Possion’s book was a development of ‘probability calculus’, and according to the historian of probability, Ivo Schneider, after its publication “there was hardly anything left that could justify a young mathematician from taking up probability theory”. The heart of Recherches was a single chapter on determining the probability of someone being convicted in a court, by a majority of twelve jurors, each of whom is “is subject to a given probability of not being wrong” and taking into account the police’s assessment of the accused’s guilt. In order to answer this problem, Poisson needed to understand what has become known as the ‘Law of Rare Events’, in contrast to the Law of Large Numbers. Poisson’s starting point was the Binomial Model, based on two possible outcomes such as the toss of a coin, or the establishment of innocence or guilt. De Moivre had considered what would happen as the number of steps in the ‘random walk’ of the Binomial Model became very large, with the probability of a success being about half. Poisson considered what would happen if, as the number of steps increased, the chance of a success decreased simultaneously, so that it became very small.

On this basis, Poisson worked out that if the rate of a rare events occurring, the number of wins per round, was r, then the chance of there being k wins in n rounds was given by  
the Poisson distribution. Apart from being one of the key models in probability, along with the Binomial and the Normal, the Poisson distribution has an important financial interpretation.
Consider a banker lending a sum of money, X0.  The banker is concerned that the borrower does not default, which is hopefully a rare event, and will eventually pay back the loan. Say the banker assesses that the borrower will default at a rate of r defaults a day, and the loan will last T days. The banker might also assume that they will get all their money back, providing the borrower makes no defaults in the T days, and nothing if the borrower makes one or more defaults. On this basis the bankers mathematical expectation of the value of the loan is
E[loan] =   (Probability of no defaults × X0) + (Probability at least one default × 0)
we can ignore the second expression, since it is zero, and for the first, using the Law of Rare Events, the probability of no defaults is given when = 0 we have that (rT)0 = 1 and 0! = 1, so
E[loan] =  X0e-rT.

So the banker is handing over X0 with the expectation of only getting X0e-rT < X 0 back. To make the initial loan amount equal the expected repayment, the banker needs to inflate the expected repayment by erT ,
 That is, the repayment amount needs to be
.

We can interpret interest in two ways, as a means of "growing" ones wealth, which would be usurious in the Scholastic sense, or as a compensation.  If it is a compensation the wealth is not expected to grow, that is, Piketty's whole argument becomes somewhat meaningless.

Michael Northcott argued that the Christian prohibition on usury/interest was related to an intent to inhibit human bondage and he noted that contemporary Islamic finance still prohibited the charging of interest.  There in lies a counter argument to the interest equates to slavery claim, it was capitalist Britain that led the way in the emancipation of slavery, Islamic jurisdictions retained slavery into the second half of the twentieth century.

I agree with Michael that usury is a form of bondage, but I do not agree that the charging of interest is usurious, particularly if the interest is determined on the principle of balanced reciprocity.  The problem contemporary finance faces is that it emphasising economic growth over social cohesion, the distinction between usury and interest is obscured.

Wednesday, 11 June 2014

Fairy dust sprinkled from ivory towers

On the basis that the "impact agenda" is important I thought it worth while responding to Paul Krugman, who seems to think I'm a bit of an idiot ("what I assumed was obvious apparently isn’t to everyone").  That might well be true but let me try and justify my statement that
Krugman seems to believe that by sprinkling the fairy dust of incentives over society the emission busting new technologies will emerge.
The "fairy dust" analogy actually comes from the Disney film The Pirate Fairy (released as Tinkerbell and the Pirates in the UK) which I saw as I am blessed with a 3 year old daughter.  After seeing it I tweeted
The plot is an inquisitive fairy, Zarina, causes havoc when an experiment goes wrong and leaves the fairy kingdom and her friends.  She returns and steals the fairy dust having fallen in with a bunch of pirates.  When the pirates have harnessed the power of the stolen dust they lock her up.   Zarina is rescued by her friends, the pirates are defeated (it is a prequel to Peter Pan, and there is a baby crocodile) and the fairies "live happily ever after".  Not expecting much I found an allegory for how science goes wrong when disconnected from society.  This is, no doubt, further evidence that I am an idiot. Alternatively it might be evidence that I am committed to the idea of science in the service of society, not its sovereign.

Because he thinks I am a bit ignorant, Krugman assumes I believe new technologies need to emerge to resolve the problem of carbon emissions.  He argues
I was talking about the fact that at any given time we have a choice of already existing technologies. You can drive a conventional SUV, but you could also drive a hybrid, or for that matter a smaller vehicle that, say, emits half as much carbon as the SUV while providing services that are a lot more than half of what the SUV would provide. You can generate electricity using a coal-fired plant, but you can also use a gas-fired plant, a wind turbine, or solar panels.
In a sense, so was I.

I have been involved in published research on modelling incentive structures to trigger investment in the UK's generation capacity to maintain an acceptable level of security of supply.  The UK energy market was de-regulated in the 1990s in the expectation that the privatised industry would deliver lower retail prices.  This it did, but at two costs.  Firstly UK energy prices are volatile, which is a problem for retail consumers who have a preference for "fixed costs".  More important for the UK's energy supply is that the privatised business has taken rents but is not regenerating generation capacity and there is a real concern that the industry will fail to meet future demand, from whatever sources.  My intuition based on my research is that the liberalised market in the UK has not been a success, and the industry would have been better managed as a state monopoly.  This is the consensus in the EU where ambitious plans to liberalise Europe's energy industry have been quietly dropped.  At the moment the public opinion of the UK energy industry is on a par with their opinion of investment banking, and this morning the news was full of concerns over the industry.

I am currently working on a research project to develop a methodology that can evaluate the effect that different power storage technologies will have on the UKs power system.  These storage technologies are needed because wind power generation is intermittent and cannot  be relied upon to deliver power when and where it is required.  Texas is famous for having installed a lot of wind generation capacity, unfortunately this does not produce power on hot, still, still summer days when the Texan people want their air conditioners on.  Existing technologies to resolve the problem, such as new transmission lines, are costly, as reported by the New York Times as long ago as 2008, and were still an issue in New England last year.  A focus of UK Energy research is to develop storage technologies that enable the integration significant (intermittent) renewables, which is a more robust solution than relying on transmission (the UK has less of an issue with power transmission that the US, a result of the system having been developed by a single state body).  Without these technologies it is unclear how wind-power can significantly replace carbon intensive generation.  Suggesting it is a "done deal" and simply a matter of incentives that renewables can replace conventional generation is a dangerously mis-leading since it creates false expectations; dreams deferred.  I recall hearing of research that identified a  link between the proliferation of reported "cures for cancer" and a decline in trust in medical research, since the public experience is that cancer is not "cured".  The public like scientists but they also want honesty from us.

The impression I wish to convey is that the claim that
You can generate electricity using a coal-fired plant, but you can also use a gas-fired plant, a wind turbine, or solar panels.
is a bit glib.  The technologies exist in theory but do they do so in practice?  This is nothing new, those with access to academic journals could have a look at a special edition of Energy Policy (Volume 38, Issue 7,in particular the editorial and Market protocols in ERCOT and their effect on wind generation). I suggest that there is evidence that my original claim is sound.

Krugman makes things somewhat worse for himself when he argues that
You can drive a conventional SUV, but you could also drive a hybrid, or for that matter a smaller vehicle that, say, emits half as much carbon as the SUV
Just as the UK preceded the US in liberalising its energy markets, it has developed economic incentives to encourage people to switch from high carbon emitting vehicles to low carbon emitting vehicles, principally through two mechanisms, the fuel price escalator (since 1993, a Conservative initiative) and car tax differentials (since 2005).  The fuel price escalator is controversial and anyone who is interested in the details, and why I am sceptical of the "fairy dust", they could read a Parliamentary briefing on the UK debates.  To get a gist of the issue, and why there is broad support for the suspension of the escalator even amongst parties with strong "green" credentials such as the SNP and Liberal Democrats, consider the situation of a low-skilled worker living in rural Britain.  During the down-turn such people were liable to have to travel 50+ miles to work and earn a living  and could only rely on private transport.  If they did not have wealth they typically buy second hand, old,  "dirty" cars; they do not have the resources to "choose" to buy a clean, low cost, hybrid -UK car prices are clever, the price of "workaday" cars often reflects their present value; if a car has low running costs it is usually more expensive to buy.

In reality the poor do not really have choices.  One is reminded of Rousseau's recollection
 of a great princess who was told that the peasants had no bread, and who responded: "Let them eat brioche."
Academics do themselves no favours by offering unworkable solutions.  I am committed to carbon reduction - I spend time researching technical solutions - but I am also committed to helping those in "energy poverty".  If intellectuals spend time telling the public what they out to or ought not do without considering how those commandments affect others with less influence, they will lose the public's confidence.  If science is to maintain its high status I think it should be wary of ascribing criticism to "a toxic mix of ideology and anti-intellectualism".

There is a story that John Dewey's philosophy was inspired by being forced to spend time talking to "regular people" on a broken down train.  Along with the other pragmatists he argued that
The value of any fact or theory as bearing on human activity is, in the long run, determined by practical application - that is by using it for accomplishing some definite purpose. If it works well - if it removes friction, frees activity, economises effort, makes for richer results - it is valuable as contributing to a perfect adjustment of means to end. If it makes no such contribution it is practically useless, no matter what claims may be theoretically urged on its behalf.
I remain to be convinced that the important problem of carbon emissions can be resolved by economic incentives, the story is more complex and should be treated with respect.

Monday, 9 June 2014

Dogmatic Indifference

Last week Roger Pielke Jr had a letter to the FT published where he questioned the effectiveness of a carbon cap in China.  Paul Krugman responded to Pielke's letter with a post where he claims that
the letter offers a teachable moment, a chance to explain why claims that we can’t limit emissions without destroying economic growth are nonsense
 I am neither a climate scientist not an economist, but none the less I will offer my opinion on the debate because I think it offers a "teachable moment" of the perils of dogmatism in policy formulation by relating this discussion to my reflections on a meeting I had attended, hosted by the University of Edinburgh's Institute for Advanced Study in the Humanities, as the debate was going on.

Pielke based his argument on the "Kaya identity".  What is interesting as a mathematician is Pielke is talking about an "identity" not a "model".  For example E=mc^2 is a model (or definition), and identity is a stronger statement, basically what is on the left hand side of the equation is identical to what is on the rhs.  The Kaya Identity is a straightforward tautology, the lhs is "CO2" (carbon dioxide emissions) the rhs is
P * GDP/P * E/GDP * CO2/E
Noting that "P" (population) "GDP" and "E" (energy consumption)  are all in the numerator and denominator the rhs can be re-written
1*1*1*CO2.
The analytic value of the Kaya Identity is that it decomposes the human impact on the environment into three factors: population, affluence (GDP/P) and technology (CO2/GDP) which is divided into "Energy Intensity" (E/GDP) and "Carbon Intensity" (CO2/E).  Pielke's argument is that by fixing "CO2" (the rhs) implies that for GDP/P (affluence) to go up there needs to be reductions caused by technological changes (Carbon and/or Energy Intensity go down). This seems like a sound argument to me, but I am no expert.

Krugman's response to Pielke's letter is
This is actually kind of wonderful, in a bang-your-head-on-the-table sort of way. Pielke isn’t claiming that it’s hard in practice to limit emissions without halting economic growth, he’s arguing that it’s logically impossible. So let’s talk about why this is stupid.
The point to note here is that Pielke is not arguing that it is "logically impossible to limit emissions without halting economic growth" he is arguing that it is "logically impossible to limit without halting economic growth or creating new technologies".  Perhaps because Krugman is an economist he is overlooks the need to create technology here, physical things that have tangible effects.  Krugman goes on to say
Yes, emissions reflect the size of the economy and the available technologies. But they also reflect choices – choices about what to consume and how to produce it, choices about which of a number of energy technologies to use. These choices are, in turn, strongly affected by incentives: change the incentives and you can greatly change the quantity of emissions associated with a given amount of real GDP.
and at the end of the piece
 Let me add, by the way, that Pielke’s fallacy here – the notion that there’s a rigid link between growth and pollution – is shared by some people on the left, who believe that saving the planet means that economic growth must end. What we actually need is a change in the form of growth – and that’s exactly the kind of thing markets are good at, if you get the prices right.
What strikes me is that Krugman seems to believe that by sprinkling the fairy dust of incentives over society the emission busting new technologies will emerge.  This is a bit too deterministic for me.  Furthermore there is a blind faith in the power of markets.  This is problematic for a number of reasons, firstly European Cap and Trade policies are widely regarded as a failure, though market advocates would point to a problem of design (Fac me bonum, deus meus, sed noli modo-Give me chastity and self-control, but not just yet).

There is a more problematic criticisms of market mechanisms; their morality. Cap and trade enables a polluter to pollute by paying a penalty - they are in effect the indulgences that the Medieval church was criticised for.  The problem is that CO2 emissions in Europe, China or America have the potential to impact on the well being of future generations in Africa or Indian or Pacific Islands.  It is not clear how the payment of the penalty by the polluter will mitigate the suffering of the people affected by the pollution.  The operators of Heathrow airport benefit from the operation of the airport, the people living around the airport do not benefit from it.  The question is: are we entitled to buy and sell permits to pollute? in the same sense as are we entitled to buy and sell humans?

Krugman might baulk at the comparison, but Michael Northcott, the Professor of Ethics at Edinburgh, might not. Northcott gave a presentation at the IASH meeting where he made a case against capitalism because capitalism insisted on GDP growth at the lowest cost, which resulted in pollution.  Northcott builds his argument, in part at least, on Political Theology.

Since I base my arguments for seeing markets as centre of communicative action on rejections on two key components of Political Theory, Schmitt's views on sovereignty and Adorno's criticism of modernity, it is unlikely that Northcott and I will agree.  It is not peculiar for Northcott, as a minister of the church, to be attracted to Schmitt's neo-Hobbesian attitudes that the sovereign's authority has precedence over the (liberal) law, since he will believe in the sovereignty of a god.  My work on the nature of the markets rests heavily on Cheryl Misak's Truth, Politics and Morality, which is an explicit rejection of Schmitt in favour of liberal pluralism.  Another basis of my work is Habermas' rejection of the negativity towards modernity in the Dialetic of the Enligthenment.

Krugman and Northcott agree on the policy: that carbon emissions should be capped, but they do so from very different ideological positions.  Northcott from the theological dogma of "thou shalt not because I speak with the authority of a transcendental god", Krugman from the economic dogma "thou shalt not because the market will deliver us from evil", but both dogmas are in opposition to each other.  This dissonance, I believe, enables those who oppose climate change mitigation policies to focus on the ideology underpinning the justification for carbon caps rather than the factuality of the dangers of carbon emissions.

Another speaker at the IASH conference, and the person who invited me to attend, was Paolo Quattrone.  Paolo shares, from the perspective of accounting, my view (ideology, if you like) that
financial markets are, and should be treated as,  centres of communicative action with the purpose of achieving a consensus on the ‘just’ price of assets in an uncertain world. In this framework, markets should operate on the basis of norms of discourse, such as reciprocity, sincerity and charity. My argument focuses on a discussion of how the norm of reciprocity is deeply embedded in the Fundamental Theorem of Asset Pricing, the foundational theory of mathematicians working in finance. A key conclusion is that, in this framework, mathematics provides the discursive language, rather than being a truth-bearer. 
Paolo has researched Jesuit accounting practices where the financial accounts were a tool for reflection, rather than  a statement of fact.  This approach was a feature of Italian accounting practices (GAAP) until there was global standardisation of GAAP and meant that in the 1960s Italian accounts involved facts, based on market prices, and less certain valuations based on judgement.  The emphasis of the accountant was to reflect on the less certain aspects of the accounts.  Today there is an emphasis on "objective" market prices, and where these are unavailable "model" prices.

Paolo also highlighted a feature of Jesuitical practice; that the Jesuit must be "indifferent".  The immediate interpretation of this is that the Jesuit does not care, but Paolo explained it meant that the Jesuit had to be "rational" "in difference".  That is, the Jesuit had to be concious of the different ideologies around them and come to a judgement on the basis of this conciousness.

I think this "in-difference" concept is important for scientists in the climate debate.  It is not the same as "apolitical", since arguing for climate change mitigation actions is arguing for policy, which is political. The role of the scientist should be that of the "indifferent" questioner who challenges the claim, irrespective of its ideological basis.   In this respect Pielke, in challenging the assumption that a carbon cap would work, is playing the correct role of a scientist.

This is important because in a liberal democracy policy decisions need to be justified.  This is not the same as a majority needs to accept a policy, my understanding is that around 60% of the population of western democracies accept the need for climate mitigation policies, but a small minority challenge them.  For the policies to be "democratically valid" they need to be justified to the minority not accepted by the majority.  The opening quote to Karl Popper's The Open Society and Its Enemies is from Pericles
Although only a few may originate a policy, we are all able to judge it. 
It is against the Open Society to condemn challenges to policy.

Cheryl Misak's justification for liberal democracy is because it is through deliberation that the best decisions are arrived at.  Pielke is challenging the claim that carbon caps will lead to a better society because it demands the policy is justified (deliberatively). In challenging it, those who advocate the cap must respond to the criticism, not reject the criticism on the basis of divine or economic authority.  If they do not respond the public cannot be sure that the policy is the "best" policy and doubt will prevail.

I note that Krugman appears to have stepped back from his position last week. Interestingly, he, like me, identifies the issue as being "ideological", but I suspect he sees himself as being a "scientist" and above ideology.
What makes rational action on climate so hard is something else – a toxic mix of ideology and anti-intellectualism.
and then at the end of the piece
 The fact that climate concerns rest on scientific consensus makes things even worse, because it plays into the anti-intellectualism that has always been a powerful force in American life, mainly on the right. It’s not really surprising that so many right-wing politicians and pundits quickly turned to conspiracy theories, to accusations that thousands of researchers around the world were colluding in a gigantic hoax whose real purpose was to justify a big-government power grab. After all, right-wingers never liked or trusted scientists in the first place.
So the real obstacle, as we try to confront global warming, is economic ideology [I take this to be market libertarianism] reinforced by hostility to science. In some ways this makes the task easier: we do not, in fact, have to force people to accept large monetary losses. But we do have to overcome pride and willful ignorance, which is hard indeed.
 On the one hand Krugman be-moans the anti-intellectualism of America, but I see America's scepticism towards academic (and theocratic, plutocratic, aristocratic) authority as part of the bed-rock upon which its democracy is built.  The vast majority of the public respect and admire science and scientists, but there is also a legitimate concern that cloistered and wealthy academics are imposing un-justified policies on the public.

The evangelical right might ask "What would Jesus do?", maybe the academic left could similarly ask "What would Pierce/James/Dewey do?" when faced with a doubtful public minority.

Wednesday, 28 May 2014

Scientific facts and democratic values

I spoke at the Circling the Square conference last week, keeping closely to the text I put up before I went to Nottingham.  The most significant change was that I ended with a comment on a claim made by an experimental physicist (hereafter labelled as "EP")   the previous day that "E=mc2 is a fact" and was on the following panel where he argued that "Science is  not democratic".  I want to explore these two points.

As a mathematician, E=mc2 looks like a model, and I come from a tradition that lives by the aphorism that "all models are wrong".  But this is simplistic, a better argument is presented by Poincare, who is an authority I suspect that EP would be reluctant to dismiss with the confidence that they dismiss sociology.

Poincare is difficult to read, because his approach is to take ironic positions that he then dismantles.  In Chapter 6 of Science and Hypothesis he does this with the playful statement
The English teach mechanics as an experimental science; on the Continent it is taught always more or less as a deductive a priori science.  The English are right, no doubt
He then proceeds to cast doubt on that indubitable statement.  Poincare notes that the issue is that
treatises on mechanics do not clearly distinguish between what is experiment, what is mathematical reasoning, what is convention and what is hypothesis
Over a hundred years on physicists are still unclear about these things, something that annoys sociologists.  Later, in Chapter 8, Poincare untangles the difficult concept of energy, and it is in this context that I asked the question "Is E=mc2 a definition", if this is the case and we associate facts with definitions we are close to Nominalism.

In response, the EP raised a cup as if to drop it and the claim was made that it will accelerate at 9.81.. m/s2 and this was a fact, known within definite errors.

A fact with error bars on it, mmmm.  Not convincing.

The point is this fact, even with error bars, is dubious.  I worked in the oil industry and one way of prospecting is to search for gravity anomolies, that is to make money by looking for where the model fails.

Thus far EP has failed to justify to me that physics is based on facts, but I still believe in physics.  What is my reasoning.

In Chapter 7 of Science and Hypothesis Poincare asks the reader to imagine a planet that is covered with thick clouds, so much so that they cannot see the stars.  He then argues that, at some point, a Copernicus will "come at last'' to the planet and would argue that
 It is more convenient to suppose the earth turns round, because the laws of mechanics are thus expressed in much more simple language. 
and then he goes on to say
these two propositions "the earth turns round,'' and "it is more convenient to suppose that the earth turns round,'' have one and the same meaning
This statement was picked up by a mathematician and  philosopher, Edouard LeRoy. LeRoy was a friend and follower of the philosopher Henri Bergson, who is associated with philosophical irrationalism and  LeRoy believed that science "can teach us nothing of truth; it can only serve as a rule of action'' and, following Bergeson,  "the intellect deforms all it touches'' and is a version of Nominalism.  Poincare was forced to write his second book The Value of Science  where he clarifies his earlier work and argues, passionately, for the value of science.

Poincare starts by arguing that science is not simply a 'rule of action' in the same way that there are rules to a game,
[If science has] a value as `recipes' have a value, as a rule of action, it is because we know they succeed, generally at least.  But to know this is to know something and then why tell us we know nothing?
He then goes on to distinguish a 'crude fact' from a 'scientific fact'
The scientific fact is only the crude fact translated into a convenient language. 
Poincare observes that the convenient language could be French or German (or  Euclidean or non-Euclidean geometry), but the point is that, in science at least, a French speaker could come to understand German, "because there remains between the French and Germans something in common, since both are men''.  The nominal language that scientists use is only a convenient veneer on the universality of science.

Poincare then goes on to answer the fundamental question: What is science? and offers the following
 it is before all a classification, a manner of bringing together facts which appear separate, though they were bound together by some natural and hidden kinship.  Science, in other words, is a system of relations.  Now, ..., it is in the relations alone that objectivity must be sought
followed by
 Therefore when we ask what is the objective value of science, that does not mean: Does science teach us about the true nature of things? but it means: Does it teach us about the true relations of things? (my emphasis)
The equivalence of the statements "the earth turns round,'' and "it is more convenient to suppose that the earth turns round,'' is a consequence of the relativity of space.  To state that either "The earth turns around'' or "The earth does not turn around'' only has meaning if space absolute, and not if science is about relations of things.

Having set the scene with Poincare, to entice the EP in,  I will run forward to modern philosophy.  Susan Haack gives us the metaphor of knowledge (scientia) as a crossword puzzle, we answer some clues and infer others.  For example if in my crossword I see the letters "f_l_c_t_" I am justified in filling in "felicity" (without referring to the crossword clue), just as a physicists are justified by filling in "E=mc2" in science.  But, if I find the answer that gave me the "l" is wrong, I have to re-visit "felicity"; it could be "ferocity" or "frascati".  Metaphorically, my issue with multiverses is that I feel physicists are solving  the clue with "fulocite" (rhymes with "full of ..."); inventing a meaningless word to fill in the blanks.

Haack is not immediately interested in the natural and physical sciences, her main concern is the law and how science influences legal judgements (which is itself related to the topic of the conference).  The reason Haack, Poincare and I take this line in knowledge is that we want science to take a central role in policy making.  This implies we cannot be exclusive in our definition of science as that which relates to nature.

What I mean by this is I believe it is equally justified to claim the "E=mc2" and that "Raping three year olds is wrong" and I need to have a framework that acknowledges the equivalence of these claims.  The reason I use an extreme example is that the question of raping children is clearly predominantly a moral question, so what I am claiming is that my intellectual framework needs to be equally robust in supporting "facts" as "values".  I cannot immediately justify either claim, I rely on a confidence that I can discover robust justifications.  Furthermore, I would conject that the proportion of the British population who reject both claims is similar, and more controversially that there is an overlap in the groups.  My basis for the second claim is in the recognition of a link between emotivism, that moral statements are essentially emotional, in moral philosophy and relativism in philosophy more generally.

Now the sting in the tail:  emotivism is closely related to logical positivism, notably through the work of A. J. Ayer.  I see a connection between logical-positivism, that the only truths are those that can be verified through experimentation, with emotivism, that moral statements are propositionally empty,  with relativism, that there can be no absolute justification for a claim.  If you take the logical positivist out of the laboratory their position, for me, becomes untenable and relates to the relativists they typically despise.  N.B. Do not quote this argument in a 101 Philosophy paper.

Why do I care?  Why do I need to employ a framework that acknowledges the equivalence of the claims?  The reason is that, like Haack and Poincare,  I believe that scientists have a role in policy.  I finished my statement at the conference with the hyperbole that the Credit Crisis was caused by people who are committed to the idea that E=mc2 is a fact.  Let me explain.

Since the 1980s investment banks have been actively recruiting, at an increasing rate, graduates from science, technology, engineering and mathematics backgrounds.  The reason was the increasingly quantitative nature of finance.  This was not new, there has always been a strong relationship between science and finance that had become overshadowed between 1914 and 1970 when states set exchange rates deterministically.  Finance gained much from these graduates, but they came with baggage, they believed in the truth-bearing nature of mathematics and did not recognise an ethical dimension of the equations they employed.  As the Financial Crisis Enquiry Commission reported, the Credit Crisis was a result of "a systemic breakdown in accountability and ethics".  It was not the mathematics that was wrong it was the moral context in which they were used. In response,  my work since 2010 has centred on un-covering the ethical dimension of the abstract mathematics employed in finance.

Something that struck me at the Conference was the extraordinary status of finance and economics.  I plan to explore this in a future post - I need to check what people actually said on the recordings rather than rely on what I think I heard - but for the benefit of those who were not their it came up a number of times that no-one, from the Parliamentary Office of Science and Technology, the government's scientific advisers, academics and so on, challenge the basis of financial decisions.  This is extraordinary because modern policy decisions are based primarily on economic arguments.    For example, the Stern case for taking action today to mitigate uncertain climate change in the future rests on taking an unconventional financial position.  As economists are reluctant to take this position, there is never an economic case in favour of many mitigation strategies.  In un-covering the ethical dimension of the abstract mathematics employed in finance I present a case for Stern's position.  If there is no questioning of the financial basis of policy decisions, most of the discussion about scientific advice is redundant.

As something of an aside, but an issue that came up at this conference and after the Mathematical Cultures meeting is the widespread belief that the root of science's problems is "neo-liberalism".  I have explained a number of times that "neo-liberalism" is a technical term relating to a synthesis of statist and classical liberal policies.  The financialisation of academia, taking it from public to private control,  is a return to "liberal" policies.  There seems to be a reluctance to associate what is bad with policies that originate, in part,  with Bentham and Mill.  One academic responded "Well at least we've never had "liberal" governments then".  The problem is we have.  The British policy of Russell's government in response to the Irish Famine from 1846 was classically liberal and perceived as being "scientific" (in accordance with Mill's conception of political science) at the time.  Peel's Tory policy had been both less liberal and motivated by Christian charity and is usually perceived as humane, but flawed.

This leads me on to the second statement by EP: Science is undemocratic.  Given that I had made the point that, as a bystander, I think that the climate debate has degenerated into one of seeing which camp can have the most peer-reviewed papers published, suggests that we are in agreement.  Maybe, but not in how to present the case.  I argue that the issue is inside academia - it is about getting papers published, EP suggests the problem is outside the academies, in the public space.

Claiming "E=mc2 is a fact" and "Science is undemocratic" are both problematic: the first is open to challenge, as I have done, and if it looks invalid it undermines subsequent claims.  The second raises in the hearers mind, if it is not democratic, what exactly is it: technocratic? plutocratic? theocratic? In my work I identify a correspondence between good scientific, democratic and commercial practice.  I build this case on Cheryl Misak's Truth, Politics and Morality, which, according to the publisher, "argues that truth ought to be reinstated to a central position in moral and political philosophy": nothing woolly there.  Misak's argument is essentially that if we are to arrive at something we can call truth we must put our claims up to be challenged; this is the democratic ideal.  The very fact that EP embarks on an admirable crusade to challenge published work demonstrates that they advocate that science is democratic: they are rejecting the autocratic authority of the journal and the peer review process.

Poincare suggested that what distinguishes the scientist is their ability to ask the right questions, not their ability to deliver the right answers.  My feeling towards the end of the Circling the Square conference that academics seem to be becoming very introspective.  When EP claims that "Science is undemocratic" they are talking to other academics, not to the broader public. The discussions focussed on climate science, particularly geo-engineering and the badger cull.  As Sheila Jasanoff pointed out, the academics' main mechanism for affecting climate policy, the IPCC,  has failed and we should move on to thinking of something workable while someone else pointed out that public opinion on the fate of British badgers was clear: we don't care.  I was left thinking that academics are fighting amongst themselves over the scraps under the table, when the juicy joint has been left unguarded on the table.  All this was going on while  a significant portion of the European public was going to the polls and giving the establishment, of which publicly funded academics are part, a significant vote of no confidence.

Sunday, 25 May 2014

Piketty and the problems of data interpretation

I have not read Piketty, but like many in my position I will not let that stop me talking about the debate of his book focusing on data interpretation.

After leaving university I worked for a number of oil industry related consultancies, the formative time being spent with a firm that made their money by providing expert witness testimony in legal disputes around the revenue split from oil fields that crossed legal, often and lucratively international, boundaries.  The charismatic founder of the consultancy, a Napoleonic Inverness-ite, liked to tell the junior technical staff that lawyers started with a case and gathered the evidence, where as scientists gathered the evidence to build a case.  Now that I am older I wonder if this was more nuanced than I imagined in my twenties: scientists will gather evidence in order to answer the question at hand, they do not, as Francis Bacon seems to suggest, just gather the data and watch the science precipitate out of it.

In the early '90s the firm realised that there was money to be made in 'data management': collating the information on an oil reservoir, cleaning it up and delivering it to oil companies for their technicians to interpret.  The boss was happy to provide this service for paying customers, but for the consultancy work of his firm, the interpreters gathered and cleaned up the data.  The reason for this is that in the process of collating the information the interpreter develops deep tacit knowledge of strengths and weaknesses in the data that goes on to  inform the interpretation.  Most data sets are incomplete, clearly contain errors and in the process the interpreter needs to make judgements about how the data is manipulated to make it coherent.  Understanding this helps in the analysis.

The Financial Times has identified manipulations in Piketty's data set, and no doubt the journalists who did this felt they were on to a significant scoop relating to the intellectual phenomena of the year.  I think this highlights the journalist's unfamiliarity with the scientific process rather than problems with Piketty's work.  I am immediatley reminded of Pierce's pragmatic metaphor of science: it is a cable not a chain.  What this means, is that a chain fails when a link breaks where as a cable can suffer the breakage of a number of strands before it fails.  The evidence is the Forth Road suspension bridge that has microphones attached to its ageing cables counting the strands that have broken to inform on its integrity.

The FT journalists were able to identify the issues with the data because Piketty had made so much data available for review. It is difficult to criticise his science because of this basic fact.  The FT has raised doubts about the data, and he has responded with a justification, the justification that as someone experienced with interpreting data, I would expect.  Again his science is difficult to fault.  If we are going to claim that because he had to clean up the raw data, his conclusions are unsound, we need to be prepared to write of the vast majority of science, ancient and modern.  I would start with the discovery of the Higgs Boson, for example.  I think the UK (and possibly US) are in the midst of a real crisis of science because of the obsession we have with "the data" at the expense of the process (see my previous post).

I have not read Piketty's book but I will, I will do so on the basis that I am dubious about his conclusions and I base this doubt on an intuition that he believes that capitalism inevitably leads to wealth inequality.  I see this is a marxist (as distinct from Marxist) interpretation that rests on a sense of determinism.  I believe that capitalism can take on many characters, just as eating is done differently in East Asian and West European cultures.  In this respect we can construct a capitalism that does not lead to wealth inequality. (Of course, this may rest on how capitalism is defined, if it is defined on the basis of profit maximisation rather than market exchange, there is no hope for capitalism, in my opinion).

Wednesday, 14 May 2014

Is it robust knowledge or make believe? Evidence, uncertainty and the role of values.

I am participating in the "Circling the square:Research, politics, media and impact" conference next week and I am collecting my thoughts.  This is a preview of my opening statement.

A few years ago I attended a meeting on the applications of mathematics to "energy problems" sponsored by the Engineering and Physical Sciences Research Council and the London Mathematical Society.  During one of the presentations a British Nuclear Engineer noted that in France they do not employ probabilistic arguments in favour of nuclear power because probabilistic arguments are too advanced for the public.  Two people who did not snigger at the ignorance of the French were myself and the senior probabilist at the University of Oxford.  We understood the French position: mathematical probability is a branch of mathematical analysis.  The British, by and large, associate probability with statistics, counting things and calculating relative frequencies.

The difference is captured in the different words we use for the English mathematical term 'expectation', the French use the word espérance, with the literal translation of hope.  Since the Latin root of expectation is associated with waiting, and in the past 'expect' and 'wait' have been used synonymously (i.e. Dickens's Great Expectations), we can infer that there is a tendency for the English speaker to anticipate a mathematical expectation, where as a French speaker merely hopes for it.   Similar issues exist within English for the words 'risk' and 'uncertainty'.  An economist will usually interpret a risk as calculable chance, a physicist might view an uncertainty as an error rather than something undependable.

I sometimes distinguish mathematical probability from statistics by using the analogy of hope (Spes, Elpis) and faith (Fides, Pistis).  Most theologians agree that faith is necessary because there is doubt: statistics is a necessary part of science because our results are doubtful.  Statistics provides a justification for our doubtful claims based on what has happened in the past.  Probable also implies provable and true, but where as statistics has an empirical angle, probability has a more metaphysical aspect.  This was exemplified in the medieval genesis of probability in the context of jurisprudence where conscience and moral certainty were key issues, issues that were still important in Bernoulli's The Art of Conjecture and through the eighteenth century discussions of the Petersburg game.  They disappeared in the post-Laplacian conception of probability.

One of the original purposes of probability was to price contracts and it did this by considering ratios, on which justice is based, this is present in Aristotle's Nicomachean Ethics.  The word 'rational' is derived from 'ratio' and is associated with reasons and accounts: justification.  Mathematical probability emerged in the mid-seventeenth century as a result of centuries of discussion around the morality of commercial contracts.  When Huygens coined the term expectatio in the first treatise of probability he did so in to context of establishing the fair, or just, price of a contract.  If we win £10 on a head and £2 on a tail the expectation of the coin toss, its fair price, is £6. We can not 'expect' to win £6 because it will never happen.  I argue that this ethical dimension to probability is still implicit in Financial Mathematics, but not recognised.

My main point is, the mathematics of probability and statistics exist because we need to justify our claims.  My secondary point is that historically, there was an explicit moral dimension to the process of valuation that became obscured in the nineteenth century, at the same time as episteme came to dominate discourse (before Foucault).

If the question was "Is it episteme or make believe?"  I think the question would be wrong.  Firstly the dichotomy is false.  It is not a choice between "scientific" or "true knowledge"  and "make believe" it is a problem of deciding on the best course of action in the uncertain, undependable, world outside a controlled laboratory.   Aristotle distinguished  episteme, passive knowledge from phronesis, active thinking and I think the issue pertinent to "Research, politics, media and impact" is robust thinking rather than just robust knowledge.  The antonym of "make believe" is not "true belief" but "justified belief" and, it is my opinion, that science should focus on the manner of its justifications rather than its results.

 Re-emphasising  phronesis, with the aim of good, virtuous, living, might be worth considering in light of our experience of the Financial Crisis, which highlighted that scientific knowledge is not as robust as many of us would like to believe.  For example, most of the research in Financial Mathematics has been focused on establishing the "true" price of a contract, some of my work is about re-orientating the discipline to focus on the principles that make thinking robust, given that we cannot rely on certain knowledge in an uncertain world.  For example, I argue that the origins of Financial Mathematics are in the synthesis of the virtues Faith, Hope and Charity (Caritas, Agape).  I am not alone in thinking this way, Rethinking Economics argue that
It is clear that maths and statistics are crucial to our discipline. But all too often students learn to master quantitative methods without ever discussing if and why they should be used, the choice of assumptions and the applicability of results.
I interpret this as it is not the tools of mathematics that are important, but how they are employed.  This observation is as pertinent to most students and their teachers.

My motivation for these comments originates in a conversation I had before the crisis about the use of mathematics in finance.  Basically  mathematical models were being used as rhetorical devices: if a trader had a "better" model than the risk manager, they could do what they wanted to; the trader didn't necessarily believe the model but justified their actions.  This idea emerged in the Bank of England's testimony to the Parliamentary Commission for Banking standards
unnecessary complexity [of mathematical models] is a recipe for […] ripping off […], in the pulling of the wool over the eyes of the  regulators about how much risk is actually on the balance sheet, through complex models. 
The existence of a model was enough, there is no understanding of how it works, how it justifies.

More generally I sense a connection here to issues around, for example, climate science.  As a bystander I feel that the climate debate is one of which camp has the larger collection of peer reviewed papers wins.  There seems to be little rational discourse of making a claim, challenging a claim, justifying a claim.  The claim, if published, stands as a fact. The problem is that while many academics are judged on their ability to create facts, a collection of facts is no more science than a collection of bricks is a house.  Le savant doit ordonner, the role of the academic is to turn the facts into `science'.

Friday, 9 May 2014

Objections to Objectivity

I start with a warning that this is a synthesis-in-development of some thoughts about mathematics, economics, objectivity and justification.  As a work in progress it might be a bit incoherent.  I have been thinking about "justification" having read Cheryl Misak's Truth, Politics and Morality on the advice of the pragmatist Matthew Festenstein when giving me feed-back on my Reciprocity paper.  Matthew had identified a relationship between the influence on seventeenth century commerce on politics (his field) and finance (my interest) and given it takes place in the seventeenth century there is a third node: science.

Following reading Misak I went to Susan Haack's Putting Philosophy to Work that discusses science in the context of pragmatism.  Misak and Haack got me thinking that fundamental to the pragmatic conception of politics and science, and by induction, finance, is the idea that in making a claim you put it up for criticism, if there is no criticism the claim passes but if it challenged the claim needs to be justified in a discursive manner.  Eventually a consensus is reached.  The problem for philosophy is under what conditions can the consensus be regarded as truth.  Clearly a "democratic" conception that 51% signifies truth is inadequate, and this opens the door to wondering if 90% of "scientists" signifies truth or if the "market" determines truth.

With this in mind I attended a workshop on Mathematical Cultures during which Norma Beatriz Goethe gave a talk on Leibnitz.  What caught my attention was in the pre-amble Norma discussed how in the mid-seventeenth century there was a tradition of representing the scientist as a spectator at a theatre, with nature being what occurred on the stage.  This was interesting to me because one of the cornerstones of pragmatism is the rejection of the Cartesian belief that the scientist can be an objective observer of the world.  This is a reasonable working hypothesis for the physical sciences, but begins to break down in the natural sciences (the "anthropocene"), is dubious in the social sciences and untenable in the human sciences.

However, what really caught my attention was an illustration in this vein which had the "scientist" in a room that enabled them to eavesdrop on those around them, with massive "hearing horns" and spyglasses observing activities in a public space.  What struck me was a correspondence between these prototypical conceptions of science, the scientist as the observer, and recent crises of mathematicians working for security services monitoring the public's activity.

My talk, in order to justify its place in a discussion of Mathematical Cultures, centred on financial mathematics as a language to facilitate discourse rather than the more popular conception as the key to unlocking the secrets of financial markets.  A concern I share with many applied mathematicians - and regulators - is that contemporary financial mathematics has become too complex to be useful.  However, more pertinent is the fact that research mathematicians might become irrelevant because in the markets there seems to be a paradigm shift away from sophisticated models to simpler models that incorporate  CVA - a basic accounting tool abhorrent to a PhD trained quant.  Though I am sure us mathematicians could, given time, make CVA incomprehensible to the uninitiated as well.  I note with interest that Mark Davis (my mathematical grandfather) is questioning mathematicians' objections to VaR as a risk measure and re-poses the mathematical question: "Instead of asking whether our model is correct, we should ask whether our objective in building the model has been achieved."  I suggest we can interpret this as a statement that we do not require objective justification for the validity of the model, rather we need a subjective, i.e. relative to our aims, assessment. The mathematician is an actor on the stage of finance.

Twitter alerted me to two posts by @MarkThoma.  One from last year makes the observation that
We like to think or ourselves as scientists, but if data can’t settle our theoretical disputes – and it doesn't appear that it can – then our claim for scientific validity has little or no merit.
while one from yesterday is titled 'Pretending To Do Something Like Science'??? and is a quote from Paul Krugman
Were the freshwater guys always just pretending to do something like science, when it was always politics? Is there simply too much money and too much vested interest behind their point of view?
Both these posts, and Mark's presentation, (implicitly) ask the question "what is science", a question that dominates much of my thinking as a "scientist" working in finance.

With regard to Mark Thoma's 2013 post, Poincare was always sceptical of the Anglo-Saxon obsession with "facts", "facts are to science what bricks are to houses: a collection of facts is no more science than a pile of bricks is a house".  In this setting mathematics has the role of mortar or cement, identifying the relationships between facts and linking them together.  Something else I learnt from Poincare is that mathematics is essential when you cannot perform an experiment: Higgs' mathematics being proved by the Large Hadron Collider is an example.  This is why mathematics is essential for economics and finance: because we cannot experiment in economics because the system is so dynamic we need a way of disentangling the myriad of facts that we are presented with.

The main point of the 2013 post is that economic mathematicians cannot agree on "one model" for the economy.  I would suggest is that Thoma is wishing to place economists in the audience where they can objectively deduce the "true" model for the economy that enables its control.  I would suggest a better aim is to follow Mark Davis' lead and evaluate different models on the basis of the aim in mind, different aims will require different models, but now single model can accomplish multiple aims.  Anyone who recognises Mark Thoma's predicament could do worse than read three of Poincare's essays: "The Mathematical Sciences" and "The Objective Value of Science" from The Value of Science and "The Scientist and Science" from Science and Method.

I think Paul Krugman's frustration with the "freshwater guys" more troubling because it is a symptom of a general degradation of science.  I worry that scientific discourse has degenerated into the accumulation of publications.  For example. I have been critical of an important (because it is cited) paper on financial stability.  My issue is that the authors - physicists - construct a discrete-time/finite state economy that they show becomes unstable when the number of assets traded is four times the number of possible states.  Cramer's Rule tells me that as soon as the number of states equals the number of assets, the economy becomes deterministic (it is 'complete'). One of the authors responded to my criticism, which was nice.  But what troubled me was this attitude
As for any paper, there is a time to defend it, which is when it is submitted to a journal and it goes to the referees. Once published, it should defend by itself. 
This implies to me that the author believes that a claim is "justified" if two or three (like minded) individuals   agree with what is claimed.  My criticism need not be considered, and if I have a criticism I should not raise it publicly, but privately.

I think beliefs like these are at the root of Krugman's concern.  If my friends and I can come up with a coherent set of claims that we can get peer-reviewed and published, they justified. I do not have to justify my claims to criticism, particularly external criticism.  This is not a problem of economics but much of what is currently perceived as science: it is a feature of the climate debate and pharmaceutical research.  It is damaging to science but corrosive to society as a whole where politics is dominated by the sound bite and "fact" with little effort or interest of many politicians to justify themselves.  I believe the popularity of UKIP, the 'Tea Party' and Front National are the consequences of  mainstream political leaders to justify their claims in any meaningful way.

My objection to objectivity is that it elevates the scientist to a position of authority that cannot be challenged by non-scientists, or scientists that you do not disagree with.  Suggesting that scientists accept they acknowledge they are on the stage diminishes their authority, they become fallible, but in doing so I think we can actually solve problems rather than fail to control situations.

Tuesday, 29 April 2014

When being wrong is right

I attended the Mathematical Cultures workshop/conference a the London Mathematical Society at the start of the month where I presented Is fairness a mathematical concept in the context of how the culture of mathematics contributed to the Financial Crisis.  Specifically, I began my talk with this quote from the UK's Parliamentary Commission on Banking Standards Report (Volume 2)
89. The Basel II international capital requirements regime allowed banks granted “advanced status” by the regulator to use internal mathematical models to calculate the risk weightings of assets on their balance sheets. Andy Haldane described this as being equivalent to allowing banks to mark their own examination papers.  A fog of complexity enabled banks to con regulators about their risk exposures:
[...] unnecessary complexity is a recipe for […] ripping off […], in the pulling of the wool over the eyes of the  regulators about how much risk is actually on the balance sheet, through complex models
 (my emphasis) 
and I ended it with this clip from a 1999 BBC science program on Black-Scholes-Merton and the collapse of LTCM (the speaker is Paul Samuelson) (the clip starts at 12:20 in the original programme)

 

My observation is that there is a culture of mathematics being a magical language that unlocks the secrets of the universe.  This is captured in many popular representations of mathematics: in  Darren Aronofsky's film Pi, that links maths, kabbalah and finance

the Da Vinci Code

Marcus Du Sautoy's The Code


even Simon Singh's book on the Simpsons

(for those who don't want to buy the Simpson's book, there is a long standing web-site)

On Saturday, I listened to Bridget Kendall's show 'The Forum'.  Kendall is well known in the UK for having been the BBC's Moscow correspondent during the 1991 coup and rise of Boris Yeltsin, and then the BBC's Washington correspondent.  Less well known, she is the daughter of Britain's most important probabilist of the twentieth century, David Kendall, and her brother is a probabilist at Warwick - I suspect she has a good grasp of mathematics.

Kendall begins the programme by asking Max Tegmark, an MIT cosmologist, about the idea of "maths as a kind of key" in this excerpt starting at 2:35 of the programme.  Tegmark is committed to mathematical realism and believes that ultimately, mathematics enables us to "ultimately predict the future" (at 0:55 in the except, 3:30 in the original).

I see a strong connection between Haldane's criticism of the use of maths in finance and Samuelson's and Tegmark's mathematical realism.  To paraphrase William Tait's description of mathematical realism:
A mathematical proposition  is about a certain structure, financial markets. It refers to prices and relations among them. If it is true, it is so in virtue of a certain fact about this structure. And this fact may obtain even if we do not or cannot know that it does.
The maths makes the financial theory true.

Following the meeting Heather Mendick shared a post where she contrasts Will Smith being constrained by the mathematical fact that 2+2=4,

with Orwell's presentation that "Freedom is the freedom to say that two plus two equals four".

Heather sees Smith's approach as being an example of "extreme neoliberalism", (I think she means extreme liberalism), but I argued that there is a connection between Orwell's "freedom" to claim 2+2=4 in the context of empiricism and Will Smith's (I assume, metaphorical) rejection of 2+2=4 as a rejection of imposed authority.

What struck me when listening to The Forum was how the discussion developed immediately after the except above.  In this excerpt, starting at 3:41, Kendall asks Tegmark to explain how  accepting the rules of mathematics leads to a belief in parallel universes.  I have recently shared my views on multi-verses, and my belief is that they are a fiction resulting from an incomplete understanding of the mathematical physics.  Tegmark supports my view that multi-verses are a mathematical consequence but his Platonism forces him to believe in multi-verses.  In this context, comparing Will Smith to Max Tegmark, who is wrong in rejecting mathematical truths.  We all recognise Smith is wrong, even probably Smith, but at the same time it is difficult to reject what Tegmark argues, despite the fact that Kendall comments that to the "unititiated" it all looks like make-believe (at 2:30 in the except, 6:11 in the original).

We label Smith as "ignorant" for presenting the claim that 2+2=5 in the context of advocating people reject the status quo, but we are expected to believe in multiverses.  Haldan'e criticism (probably) referred to the London Whale, where by presenting mathematics traders at J.P. Morgan reduced the liability of a portfolio from $22 billion to $13 billion (I may be inaccurate here, but the order of magnitude is correct).  To the "uninitiated" it all looked like make believe, but, like multi-verses, it carries the authority of mathematics.

Something that always appealed tome about science is its iconoclasm: science is right because it is happy to destroy its icons and move on.  We criticise Smith but venerate Galileo for rejecting the Ptolomaic system, despite the fact he the Dialogue is spectacularly wrong on the tides (e.g. Aiton, Brown).  Galileo is wrong, as the Inquisition realised, but he was right.

If economics is real in the Platonic sense, and can be described by exact mathematical equations, it will eventually grind to a halt.  This was the concern of many economists in the first half of the twentieth century, Knight, Keynes and the Austrians all agreed on the significance of uncertainty and unpredictability in determining economic affairs.  The organiser of the Mathematical Cultures conference, the philosopher Brendan Larvour, remarked
a repsonse was
My response is that Piketty, a French economist, is mathematically sophisticated, but in a different way to that of the realists/Platonists like Samuelson and Tegmark.  My disquieting suggestion is that in order to prevent Financial Crises we really need to examine how tenable mathematical realism, and the science built on this basis, is.

PS A Tweet from a French mathematician quoting another section of the Guardian