Be Together. Not the Same. Can maths address big data in banking

I recently attended the Alan Turing Institute summit on Data Analytics for Credit Risk and left wondering if statistics is well placed to address the problems of big data and if there were skills in the humanities that were more appropriate.  It also lead me to wonder if the neo-classical synthesis' criticism of institutional economics for not being able to deliver predictive theories is reasonable.  I end up arguing that bankers should build their businesses on the human and social sciences,  not an algorithm driven mathematical science.

While some of the presentations have been released the ones really relevant to forming my opinion are not (yet?) available, and so I will not attribute un-released sources and will present my own inferences of what was said.

Dan Kellet mentioned that geographers sometimes made better (big data) modellers than statisticians, this was at first interesting.  Then another speaker highlighted how a talk at Tate Modern in Liverpool helped him understand a central problem of big data.  He recounted how a photograph of a beach, or a desert, suggests that, from a distance, the sand is uniformly coloured,  but close up you see that every grain has a different colour, from white to black.  Another presenter had given two sequences of similar bank transactions, showing an increase in grocery spending, switching from economy to premium vendors, and a simultaneous increase in cash withdrawals at the weekend.  However,  while the changes looked similar at the start then ended at opposite ends of the spectrum, one customer proved to be a good credit risk the other a bad one.  The explanation is that one set of transactions was  indicative of the starting of a long term relationship and the other of the ending of a long term relationship.

The problem faced by bankers presented with data is not so much one of identifying outliers, as is the case with classical statistics.  The decision whether or not to lend to a heroin addict, an outlier, or a Quaker heiress, a different outlier, is easy. what is needed is to pick out the white and black grains of sand from a distance. However, the whole purpose of classical statistics is to blend the different coloured grains of sand into a single hue, represented by a 'statistic'; the opposite of what is needed.

Of course, most statisticians don't  believe the classical statistics of means, variances and p-values, is going to answer the bankers problem. The solution lies in statistical inference.

A classical statistician, employing frequentist probability,  would observe the tossing of a coin and advise on the chances of it coming up a heads, or observe mortality statistics and advise on an insurance premium, or advise on the ability of an opinion poll to predict an election.  Statistical inference, based on subjective probability, could asses the probability that I voted a particular way in an election, or that I died because I smoked.  The most topical use of Bayesian inference is in Amazon's and Google's predictive modelling to make recommendations.

However, I have never bought a book on the basis that Amazon recommended it to me.  I am not convinced that much can be inferred on the basis that in a order I purchased Brandom's Making it Explicit and Scarey's Cars Trucks and Things that Go .  The algorithm needs 'colour' added to the data, and this is Google and Facebook's advantage in holding information on my interactions (that I am an academic with young children) and interests.

The challenge facing banks is summed up in Google's Android catchphrase "Be together. Not the same" highlighting the heterogeneity of people connected together in a community.  While there are statistical methods that are able to cluster people, the input to these algorithms is a small collection of parameters and the clusters coarse; I am to be convinced that it is worthwhile for Amazon to actually figure out what to recommend to me based on my transaction history and the banks are already struggling with how to improve their decision making based on 'colourless' data.

The repeated references at the summit, however tangential, to the human and social sciences got me thinking.  Statistical techniques, developed to reduce the distributed mass to a point and then identify ‘outliers’, is irrelevant to the challenge of interpreting huge quantities of data.  The modern challenge is, given a mass of information, that looks homogeneous from a distance, to identify similar entities dispersed in the mass.  Hence, extracting value from ‘big data’ requires the repeated study of special cases from which general principles can be deduced, skills typically associated with the humanities.  The distinction is reminiscent of the difference in Quetelet’s and Le Play’s approaches to social science in the nineteenth century.

An explosion of data collection in the after 1820 enabled a number of people to observe that certain 'social' statistics, such as murder, suicide and marriage rates were remarkably stable.  Quetelet explained this in terms of Gaussian  errors. L'homme moyen, 'the average man', was driven by 'social forces', such as egoism, social conventions, and so on, which resulted  penchants, for marriage, murder and suicide, which were reflected as the means of social statistics.  Deviations from the means were as a consequence of the social equivalent of accidental or inconstant physical phenomena, such as friction or atmospheric variation.

These theories  were popular with the public.  France, like the rest of Europe, had been in political turmoil  between the fall of Napoleon Bonaparte in 1813 and the creation of the Second Empire in 1852, following the 1848 Revolution.  During the 1820s there was an explosion in the number of newspapers published in Paris, and these papers fed the middle classes a diet of social statistics that acted as a barometer to predict unrest.  The penchant for murder implied that murder was a consequence of society, the forces that created the penchant were responsible and so the individual murderer could be seen as an 'innocent' victim of the ills of society.

 Despite the public popularity of 'social physics', Quetelet's l'homme moyen  was not popular with many academics.  The term 'social physics' had, in fact, been coined by the French philosopher, Auguste Comte, who, as part of this overall philosophy of science, believed that first humans would develop an understanding of the 'scientific method' through the physical sciences, which they would then be able to apply to, the harder and more important,  'social sciences'.  When Comte realised that Quetelet had adopted his term of `social physics', Comte adopted the more familiar term, sociology for the science of society.

From a technical standpoint, Quetelet had based this theory on an initial observation that physical traits, such as heights, seemed to be Normally (Gaussian) distributed.  The problem was that, apart from the fact that heights are not Normally distributed ( Firstly the Normal distribution is unbounded, and so there is a positive probability of someone having a height of 5 metres or even -3 metres.  Secondly, and contradictory, , the incidence of giants and dwarfs in the real population exceeds the expected number based on a Normal distribution of heights.  Quetelet was confusing `looks like' with `is'.).  Also,   since murders and suicides are 'rare', there can be little confidence in the statistics, and many experts of the time, including Comte, rejected Quetelet's theories on the basis that they did not believe that   'laws of society' could be identified simply by  examining statistics and observing correlations between data  and even Quetelet, later in life counselled against over-reliance in statistics.

Beyond these practical criticisms there were philosophical objections.  The  l'homme moyen was a `statistical' composite of all society and who was governed by  universal and constant laws.  L'homme moyen was nothing like the Enlightenment's l'homme eclaire, the person who applied rational thinking to guide their action, thinking that was guided by science and reason and not statistics.  The decline of Quetelet's theorems in Europe coincides not just with the political stability of the Second Empire, but with a change in attitude.   The poor were no longer unfortunate as a consequence of their appalling living conditions, but through their individual failings, like drunkenness or laziness.    The second half of the nineteenth century was about 'self-help' not the causality of  'social physics'.

The early criticisms of Quetelet did not come from the innumerate, one of the severest critics of Quetelet was a famous mining engineer, Frederic Le Play, a graduate of the Ecole Polytechnique and the Ecole Nationale Superieure des Mines, centres of French rationalism and mathematics.  Le Play felt that  the direct observation of facts  was achieved by the scientist, a trained specialist, closely observing phenomena,  families for example, not by clerks trawling through reams of data. LePlay was not alone in his approach, but part of a much broader movement that dominated German and British science for the first half of the nineteenth century, Naturphilosophie or Romantic science.

Modern science is associated with objectivity, scientists should extract themselves from the world in order to be able to identify the 'truth', perfect knowledge. This objective was the motivation for Laplace's analysis of errors.  While the Revolutionary French pursued truth, in Prussia, Immanuel Kant asked whether objectivity was ever really possible, and, primarily in Germany and empiricist Britain, these doubts evolved into a 'Romantic' view of science, Naturphilosophie.  If Laplace championed Newton's mechanistic view that the universe was a giant clock, the Romantics saw it  more as a complex, 'living' organism and looked to discover universal principles by observing individual subjects.  Two key figures of associated with Romantic science are Charles Darwinand Alexander von Humboldt, both of whom explored the world, literally, travelling thousands of miles and observing nature in the raw.

The impact of  Naturphilosophie on English science is discussed in Richard Holmes's book, The Age of Wonder.  Holmes describes the period as a "second scientific revolution'', but in one way it was a counter-revolution, with  a rejection of the mathematisation of science that had taken place in first scientific revolution and a return to Aristotelian methods of observation and qualitative description.

Possibly the most important legacy of Naturphilosophie was a shift in emphasis in science from considering the world 'as it is' to trying to understand 'how it changes'.  Darwin is the best known example of this shift, biology was not just about the classification of living species but about trying to understand how the diversity of life had come about.

There was a problem with Romantic science: Was it objective?  As Patricia Fara explains

 Victorian [i.e.1837-1901] scientists were appalled to think that subjectivity might lie at the very heart of science. .... Scientists were exhorted to exert self-discipline and behave as if they were recording instruments producing an objective view.

It was in this context that Quetelet's quantitative methods re-emerged in Britain.  In 1850, Sir John Herschel, one of the key figures of the Age of Wonder, reviewed Quetelet's works and concluded that the Law of Errors was fundamental to science. In 1857, Henry Thomas Buckle published the first part of a History of Civilisation in England, which was  an explanation of the superiority of Europe, and England in particular, based on Quetelet's social physics.  Sir Francis Galton combined the work of his half-cousin, Charles Darwin, with that of Quetelet to come up with a statistical model of Hereditary Genius in the 1870s and in the process introduced the concepts of 'reversion to the mean' and statistical correlation. At the start of the twentieth century Galton's statistical approach, was championed by Karl Pearson who said that the questions of evolution and genetics were "in the first place statistical, in the second place statistical and only in the third place biological'', and the aim of  biologists following this approach was to "seek hidden causes or true values'' behind the observed data processed with statistical tools.

Le Play's approach of synthesising a coherent narrative out of hundreds of special cases was forgotten.  The methodology was related to the historical schools of economics and institutional economics.  This ethos seems to have been smothered by the reductionism of modern science.

On the morning of the Monday following the Turing summit I listened to Helga Nowotny being interviewed about her new book, The Cunning of Uncertainty where she notes that we have evolved to identify cause and effect, not connections that lead to complexity and result in uncertainty (around 16:20 on the podcast).  She then argues that there is no (economic) Theory of Innovation, all we have is case studies of innovation.  Case studies are not bad, but describe a specific set of circumstances in a specific context.  In this set up we are unable to create a predictive theory but this does not mean a thoughtful person cannot direct innovation, but it does imply we cannot create an algorithm to produce innovation.  I thought Nowotny here was saying something relevant to economics, is it right toscorn the historical/institutional schools for delivering only case studies and not theories.  Of course, most vernacular training comes from case studies and few practitioners value theory.

At this point one might ask, but what about "machine learning", surely an algorithm that learns could resolve the problems of big data.  However, machine learning in banking is a problem.  The "acid test" of a credit system is, apparently, that it delivers an audit trail as to how a specific decision was made.  The decision needs to be able to be justified.  The nature of machine learning, apparently, makes the task of justification difficult. As the machine learns the algorithm changes and the response to a  set of inputs is unstable and it becomes difficult to follow the "learning machine's train of thought".

Now let us assume that an algorithm could be created that could make audit-able lending decisions by employing Bayesian techniques in conjunction with social media data.  This seemed to be the utopia some of the bankers at  the summit aspired to.  But  one wonders if the legal barriers imposed in the UK and US preventing the synthesis of social data and lending decisions were removed, the result would be that the experts at this synthesis, Google and Facebook, would be better placed to become banks than banks to become data mongers.  The banks, as we know them, would fast disappear; the gods punish us by giving us what we pray for.

Is there an alternative for banks.  I think so, go back to basics.  Treat customers as individuals, not data points on a 50-dimensional space, employ staff who develop narratives around customers from which they can create an intuition about lending.  Old fashioned banking based on the human and social sciences, not an algorithm driven mathematical science that even if it was possible could well lead to their demise.

Building real markets for the good of the people

The Bank of England is seeking to build an 'Open Forum' Building real markets for the good of the people. I am participating in this forum and here I seek to address the questions

• Are reforms creating the soft and hard infrastructure to ensure FICC markets are effective and  retain their social licence?
• Where has too little been done?  In some areas, might reform have gone too far?   
• Does the reform agenda form a coherent whole or are there gaps and inconsistencies?
• How should the programme of reform be made dynamic and adaptive to current and future innovations in markets?

In summary I believe the reforms focus on specific actions but do not address fundamental issues around how markets are perceived. This reflects the Bank’s desire to deliver concrete proposals to solve a range of specific problems. The risk is that the reforms tackle situations already identified and are not robust to new phenomena.

The basis of my argument rests on a matter of fact: two hundred years ago banking, and commerce generally, was  conceived of as being conducive to social order; today it is generally perceived as socially destructive.  Before the nineteenth century, in theory, the primary concern of markets was fairness in exchange.  Through the nineteenth century this concern was replaced by profit maximisation.  I would assert that contemporary market malfeasance is a result of this transformation; practices become justified by a consequentialist argument that profits, however generated, are ultimately beneficial to society.  

The Bank and market regulators seek to correct market misconduct, in the main, by creating new rules and regulations; a deontological response.  The weakness of this approach is that rules and regulations, necessarily, relate to specific situations and so are slow to evolve to new technologies.  

Both consequentialist and deontological moralities rely on predictability, something rarely encountered in markets.  Consequentialism rests on an assumption that we are able to calculate the consequences of our actions and deontology that we can identify the set of possible situations that need proscribing.  In the presence of uncertainty the ethicist should turn to character, or virtue, based morality.  The Fair and Efficient Market’s Review recognises this and highlights the need to improve standards, professionalism and accountability, issues of character while the 3 ‘pillars’ of Basel reflect deontological (Pillar I) , character (Pillar II) and consequentialist (Pillar III) approaches.

I believe that the Bank will struggle to actually deliver its objective of ‘Markets for All’ so long as market participants are taught to adhere a consequentialist ethic to maximise profits while the regulator focuses on developing rules to restrain these instincts.  Alongside the work on strengthening rules and regulations in order to deliver ‘Markets for All’ I assert that the Bank of England must undertake a programme of work focussing on the culture of banking.

Character is developed through practice in the context of a culture.  This is reflected in the meaning of the Greek word at the root of ethics and the Latin word at the root of morality, both relate to practice.   Thirty years ago many bankers, including Bank of England employees,  started their careers directly from school as apprentices, learning their trade in practice.  Today, the majority of City bankers will have gone through an academic training  rooted in a consequentialist ethic and built on profit maximisation in the presence of scarcity.

While many see the decline in commercial ethics as being a recent phenomena, Milton Friedman, Reaganomics and Thatcherism are often mentioned, I point to the 1950 English Trust Law case, Buttle v Saunders ([1950] 2 All ER 193), where in the High Court ruled that the fiduciary duty to maximise a client’s profits superceded any conception of commercial ethics, such as ‘my word is my bond’; introducing the practice of ‘gazumping’ into English commercial practice.  I also highlight that at this time, because of the Bretton-Woods system,  exchange rates,  and hence interest rates and commodity prices, were fixed.  That is, in 1950  the FICC markets were broadly predictable and in this environment the ideology of profit maximisation, formulated in the academic sphere, came to dominate financial practice.   

I have argued that the current perception of markets as being competitive arenas designed to maximise profits is misguided.  A truer conception of markets is as a response to radical uncertainty and that markets are forums, centres of discourse, where the aim is to reach a consensus on prices.  This position is developed on the identification of reciprocity (fairness in exchange) as being deeply embedded in contemporary financial mathematics and reflects the origins of mathematical probability theory being in the ethical assessment of contingent contracts.  Reciprocity, I argue, is a key  ‘norm of market discourse’, along with charity and sincerity.

My case is based on the view that in the aftermath of the Enlightenment instrumental mindsets that sought to optimally achieve predetermined ends in the context of an underlying need to control external events emerged and dominated science.  This approach is founded on an assumption of predictability, that emerged in the nineteenth century, and that fails in the face of radical uncertainty.  

Integral to my case is the view that western commercial practice has driven the development of both western science and western democracy.  The explanation is that society learns about discourse in the marketplace, and discourse is at the basis of both democracy and science.  Greek commerce was uniquely based on money and delivered a unique approach to science and politics.  The commercial revolution of twelfth century Europe ended feudalism and resulted in Europe's mathematisation of physics.  Thomas Gresham and Simon Stevin preceded Isaac Newton and Christiaan Huygens. This turns table on the conventional standpoint that commerce is built on science and democracy and emphasises the merit of markets.  

On this basis, my responses to the questions presented are as follows.

• Are reforms creating the soft and hard infrastructure to ensure FICC markets are effective and  retain their social licence?

I cannot see (perhaps based on ignorance) initiatives to address the ‘soft’ infrastructure to the same extent as there are initiatives to address the ‘hard’ infrastructure.  I am not surprised by this given Bank’s desire to deliver concrete actions to solve a range of specific problems, but I think the bones of the hard infrastructure are useless without the meat of the soft infrastructure.

• Where has too little been done?  In some areas, might reform have gone too far?   

I cannot find a clear vision of how the culture of Banking will be improved.  There is a commitment to making the rules and regulations stronger but it is assumed that everyone agrees on what a market is and why it exists.  I believe the Bank should bring clarity to this fundamental issue.  As long as a market is seen by some as a panacea while others see it as demonic the ultimate objective of  markets regaining their social license will be at risk.  I believe the ‘Open Public Forum’ needs to deliver a generally accessible and widely agreed understanding of the role of markets.

New financial technologies, such as crowdfunding, peer-to-peer lending and alternative currencies, are characterised by their distributed, non-centralised, nature.  My case that markets are forums for achieving consensus is more sympathetic to these new technologies than the conventional approach that markets are to maximise profits. The new financial mechanisms have been reviewed by regulators.  There is concern that regulators will force the emergent mechanisms to mimic existing structures, which are profit maximising, destroying their beneficial distinctiveness and the FCA consultation was debated in the UK Parliament (18 December 2013,  `Crowdfunding and the FCA').  and during the debate it was observed that the UK has the potential to be the global leader in crowdfunding  because the US SEC has over-regulated it and “strangled the baby at birth''.

• Does the reform agenda form a coherent whole or are there gaps and inconsistencies?

I don’t think the reform agenda is incoherent and implicit in the agenda is a desire to address the culture of banking.  However I do not think this is explicit and so will be lost.

• How should the programme of reform be made dynamic and adaptive to current and future innovations in markets?

I would argue that the Bank should promote dialogue and research on the how markets are perceived. Whilst finance is in the midst of an ethical crisis it is also undergoing significant change driven by technology and there is significant public interest in finance, unprecedented in recent history.  Because markets are intrinsically unpredictable and it is impossible to identify how they will evolve, what is needed is to harness this interest in honest discourse about how markets should develop.  

Finance, science and democracy are all failing to deliver a robust consensus on important issues, can finance return to its ethical roots and teach the other domains how it is done?

Does the hidden hand need to hold a stake in society?

As the father of a four year old daughter, I have been to the cinema to see the the Disney film, Tinkerbell and the Pirate Fairy.  When I took my daughter to the cinema I had taken an mp3 player as I anticipated I would need a diversion, however I became engrossed in the film.

The film tells the story of how a 'fairy scientist', Zarina,  undertook an experiment, which went wrong.  In response, Zarina left the fairy kingdom, taking pixie dust, and got involved with the young Captain Hook.  Hook had convinced Zarina that they were a team, but in fact the pirate was using the fairy so that he could use Zarina's knowledge of pixie dust to get his ship to fly in order that he could become the most powerful pirate. Eventually, other fairies, led by Tinkerbell, rescued Zarina, by showing who her friends really were, and she was bought back into the fairy-fold.

I saw the film around the time I spoke at the Circling the square: Research, politics, media and impact conference last year and there was coverage of the idea that U.S. high tech firms were considering going 'off-shore' so that they would escape regulation.  On the face of it, there seemed to be a connection between Captain Hook and the Seasteading Institute or Andreessen Horowitz.

These thoughts returned to me while reading Albert Hirschman's The Passions and the Interests: Political Arguments for Capitalism before Its Triumph on the advice of @tcspears.  From the back-cover

In this volume, Albert Hirschman reconstructs the intellectual climate of the seventeenth and eighteenth centuries to illuminate the intricate ideological transformation that occurred, wherein the pursuit of material interests - so long condemned as the deadly sin of avarice - was assigned the role of containing the unruly and destructive passions of man. Hirschman here offers a new interpretation for the rise of capitalism, one that emphasizes the continuities between old and new, in contrast to the assumption of a sharp break that is a common feature of both Marxian and Weberian thinking.

Hirschman begins his story with Machiavelli and highlights the following paragraph in Chapter 15 of The Prince

But since it is my [Machiavelli's] object to write what shall be useful to whosoever understands it, it seems to me better to follow the real truth of things than an imaginary view of them. For many Republics and Princedoms have been imagined that were never seen or known to exist in reality. And the manner in which we live, and that in which we ought to live, are things so wide asunder, that he who quits the one to betake himself to the other is more likely to destroy than to save himself; since any one who would act up to a perfect standard of goodness in everything, must be ruined among so many who are not good. It is essential, therefore, for a Prince who desires to maintain his position, to have learned how to be other than good, and to use or not to use his goodness as necessity requires.

In 1532 Machiavelli appears to be making precisely the same point as behavioural economists make today, it beggars the question: what progress have we made in almost 500 years?

 Hirschman identifies this passage as the start of the 'fact-value dichotomy' that features in Hobbes, Spinoza, Rousseau and, most famously (for English speakers?) in Hume. It reminded me that during the Enlightenment, when the consensus was on the dominance of the passions,  today  the fact-value dichotomy is invoked to ensure policy is guided by positivist, 'rational', arguments.

Before the nineteenth century the view was that humans, as they really are, are governed by their passions (in particular, lust, the excessive passion for love; pride, the excessive passion for honour, and avarice, the excessive passion for wealth) and during the seventeenth century there was discussion of how a damaging passion can be harnessed by another passion: a person sublimates their adulterous lust by their desire to be honoured.

Hirschman notes that these thought processes originate in political theory, where the entity in question is the state, but they become applied to individuals, or in the case of Mandeville, how a skilled politician should be able to harness the passions of the people to the benefit of the state.  In particular, Mandeville identifies how personal avarice can be used to temper the other passions.

In Hirschman's account 'Interests' become the main tamers of passions and by the nineteenth century they are equated with wealth, due mainly to Adam Smith  and from this point individual profit maximisation emerges as a virtue that results in public good. Interests guide the hidden hand.

Hirschman notes that the noun 'interest' is difficult, and this is covered in the current edition of the Oxford English dictionary:

There is much that is obscure in the history of this word, first as to the adoption of Latin interest as a noun, and secondly as to the history of the Old French sense ‘damage, loss’. No other sense is recorded in French until the 16th cent. As this was not the 15th cent. sense of English interess(e), it is curious that the form of the French word should have affected the English. The relations between the sense-development in French and English in 16–17th cent. are also far from clear.

The main meaning of the word 'interest' is

 1. The relation of being objectively concerned in something, by having a right or title to, a claim upon, or a share in.

  a. The fact or relation of being legally concerned; legal concern in a thing; esp. right or title to property, or to some of the uses or benefits pertaining to property;  

with the earliest example coming from 1450 "Noon of youre Liege peple hafuyng interest, right or title, of or in ony of the premisses." and in 1478 we have "He neuer knywe..þat I hadde any clayme or entrest in the maner off Heylesdon.".

Relevant to our discussion is the second definition

 2.a. The relation of being concerned or affected in respect of advantage or detriment; esp. an advantageous relation of this kind.

with a 1533 use "Without interest we commit sinne, seeyng peyne commyng withall."  This is significant as it highlights the role of interests in repressing sin.

 b. That which is to or for the advantage of any one; good, benefit, profit, advantage.

with a 1579 example "Caried with ambicious respectes touching their interests and desires particular."

The OED places the financial meaning as secondary, but older:

II. Senses related to medieval Latin interesse, as used by Matthew Paris a1259, and frequently from 13th c. (see Du Cange), in the phrase damna et interesse, in French legal phraseology dommages et intérêts, the indemnity due to any one for the damage and prejudice done to him. Cf. Old French interest (1290 in Godef.) in sense ‘damage’, also recompense for damage done or caused, ‘damages’. In sense 10   French interest (now intérêt) occurs in Rabelais, 1535.

9.a. Injury, detriment. 

 9.b. Compensation for injury, ‘damages’. (French dommages et intérêts medieval Latin damna et interesse.) Obs. rare.

and the examples are two hundred years older than the common meaning:  1259 Propter usuras, pœnas,et Interesse, or 1274   Tam super principali, quam super custibus, dampnis, et interesse refundendis

and the penultimate meaning is the technical, financial, meaning

10. a. Money paid for the use of money lent (the principal), or for forbearance of a debt, according to a fixed ratio (rate per cent.).

In medieval Latin interesse (Interest) differed from usura (Usury) in that the latter was avowedly a charge for the use of money, which was forbidden by the Canon Law; whereas originally ‘interesse refers to the compensation which under the Roman Law, was due by the debtor who had made default. The measure of compensation was id quod interest, the difference between the creditor's position in consequence of the debtor's laches and the position which might reasonably have been anticipated as the direct consequence of the debtor's fulfilment of his obligation’. This compensation was always permissible when it could be shown that such loss had really arisen (damnum emergens). At a later period, lucrum cessans—loss of profit through inability to reinvest—was also recognized as giving a claim to interesse; both cases appear to be included in the formula damna et interesse. The interesse was originally a fixed sum specified in the contract; but a percentage reckoned periodically, so as to correspond to the creditor's loss, was afterwards substituted (as sometimes in England in the first half of the 13th cent.). Interest in the modern sense was first sanctioned by law (though apparently under cover of the mediæval theory) by 37 Hen. VIII, c. 9 (see quot. 1545); this statute was repealed in 1552, but re-enacted in 1571.

1529   King Henry VIII Instr. Orator Rome,   Which money..shalbe truely repayde with interesse.

1545   Act 37 Hen. VIII c. 9 §3   Be it also enacted..that no person or persons..by way or meane of any corrupte bargayne, loone, eschaunge, chevisaunce, shifte, interest of any wares..accepte or take, in lucre or gaynes, for the forbearinge or givinge daye of payment of one hole yere of and for his or their money..above the sume of tenne poundes in the hundred.

Originally interest was the charge a debtor had to pay a creditor for non-repayment, it was a compensation payment.  In the Middle Ages, this damnum emergens became lucrum cessans, a payment from the borrower to the lender in compensation for the loss of investment opportunities available to the lender.  Over time interest came to indicate "a right or title to, a claim upon, or a share in" something.

It is here that I see the crux, interests imply a stake suggesting that the hidden hand will only work if an individual has a stake in society.

One aspect of Hirschman's account that had me thinking is that the implication was there is an internal dialogue taking place within individuals, there was no reference to the external, cultural pressures, on an individual.

The reason I thought about this is that when faced with a moral decision, I am not concious of sublimating one passion with another, rather I am concious of peer-pressure, what my friends and family might think of me.  I guess in the framework that Hirschman presents this would be covered by 'honour', and maybe  explicitly highlighting the fear of shame, a feature of Calvinism, might not be well received by an 'Enlightened' audience.  Another explanation could be that the likes of Montesquieu, Hume and Smith took it as given that an individual is a part of the society that they will improve by pursuing their personal interests.  None the less, it struck me that if the individual is set adrift from their society and culture, their morals are likely to be compromised (anyone who has experienced working as an ex patriate might be familiar with this phenomenon; I witnessed it working in Abu Dhabi in the 1990s, where adultery was the norm amongst westerners, not the exception).  This to me is a the heart of The Pirate Fairy, and a central risk of Seasteading.

One character whom one might expect to appear in Hirschman's account, but does not, is Hugo Grotius.  Grotius is widely regarded as setting the foundations of international relations in the modern era and Hedley Bull describes a contemporary interpretation of Grotius' theory of 'international society' as

A society of states (or international society) exists when a group of states, conscious of certain common interests and common values, form a society in the sense that they conceive themselves to be bound by a common set of rules in their relations with one another, and share in the working of common institutions. If states today form an international society . . . this is because, recognising certain common interests and perhaps some common values, they regard themselves as bound by certain rules in their dealings with one another, such as that they should respect one another's claims to independence, that they should honour agreements into which they enter, and that they should be subject to certain limitations in exercising force against one another. 

On the basis of Hirschman's claim that during the seventeenth and eighteenth centuries, philosophers adapted state-craft to individual behaviour, I think we can gain insight into the role of interests in guiding the hidden hand by replacing 'state' with 'individual' in the above quotation.

My intuition is that if people become alienated from society then we can't rely on their self-interest promoting the well-being of society, as proposed by Smith and others.  When Zarina becomes alienated from the other fairies she loses here good judgement.  Whether Seasteaders can construct a 'new Jerusalem', as the puritan immigrants to north America set out to do in the seventeenth century, remains to be seen.  But I am doubtful: the 'founding fathers' had a definite moral compass that bound them together, not an infantile desire to do as they see best justified by their personal wealth.

Mark Carney's recent Mansion House speech touches on some of these issues.  For example, when Carney argues that

The Bank of England’s general approach was consistent with the attitude of FICC markets, which historically relied heavily on informal codes and understandings. That informality was well suited to an earlier age. But as markets innovated and grew, it proved wanting. 

can the "informality was well suited to an earlier age" be interpreted as that when the City was less 'global', and market participants closer to each other, they shared 'common interests' which become diluted as traders become separated and potentially alienated (as in the case of Zarina).

Carney goes on to argue that "Real markets are resilient, fair and effective. They maintain their social licence." and "Real markets don’t just happen; they depend on the quality of market infrastructure."  Developing these themes, he highlights the final report the Fair and Effective Markets Review, noting that

Firms’ systems of internal governance and control that were incapable of asserting the interests of firms – let alone the wider market – over those of close-knit trading staff;

highlighting how market participants must share common interests that transcend the local interests of trading cliques.   Carney goes on to observe that the result was

All these factors contributed to an ethical drift. Unethical behaviour went unchecked, proliferated and eventually became the norm. Too many participants neither felt responsible for the system nor recognised the full impact of their actions. For too many, the City stopped at its gates, though its influence extended far beyond. 

I am fairly sure that these comments are relevant as much to those advocating Seasteading as Fixed Income, Currencies and Commodity traders cast adrift from broader society.

Finance and Mathematics: where is the ethical malaise?

This is a draft of an article that has been accepted by The Mathematical Intelligencer and offers an argument very similar to Romer's 'mathiness' argument as discussed in my previous post.

Discussions of the role of mathematics in finance appearing in The Mathematical Intelligencer can be split into two classes. Marc Rogalski [26] and Jonathan Korman [18] capture a widespread fury at a collapse in commercial ethics while Ivar Ekeland [6] and Peter Haggstrom [13] offer economic facts. The conclusions of Rogalski and Korman can be summarised as that mathematicians should spurn the financial world; Haggstrom and Ekeland point to technocratic solutions, characterised by better regulation. I do not buy into the argument that the problems of finance can be solved by regulations, it is, as both the U.K. and U.S. governments have identified¹, an ethical problem. But I also do not think it is virtuous for mathematicians to spurn finance, so I am not completely aligned with Rogalski or Korman. My position is that mathematicians should be forthright in presenting financial mathematics as a discipline centred on the concept of justice, making it explicit that successful finance must be moral finance.

During the Financial Crisis of 2007-2009 I was the U.K. Research Council's ‘Academic Fellow' in Financial Mathematics, meaning my background is, like Ekeland and Haggestrom, that of a financial mathematics ‘insider'. In this role I was expected to explain the discipline I represented to U.K. policy makers, both in government and in the media. As I attempted to meet these expectations I took an unconventional step for a mathematician and started looking into the origins of mathematical probability, both technically and the cultural context. I noticed that in solving the Problem of Points, in 1654, Pascal and Fermat were pricing a derivative contract on a binomial tree, and their solution would today be recognised as the Cox-Ross-Rubinstein option pricing model, published in 1978. There was a difference between the 1654 and 1978 models, CRR give a methodology for identifying the branch probabilities on the tree, Pascal and Fermat assume they are a half. This raised the question: how did Pascal and Fermat conceive the probabilities they used?

The answer came, initially, in some work the historian Edith Dudley Sylla did in the process of translating the Ars Conjectandi. Sylla observes that

equity among associates or partners rather than probabilities in the sense of relative frequencies provided the foundation for the earliest mathematical probability theory.[28, p 13]

and that

the foundations (...) [were] not chance (frequentist probability), but rather sors (expectation) in so far as it was involved in implicit contracts and the just treatment of partners.[28, p 28]

Intrigued by this point, I followed the path of mathematical probability from the origins of western mathematics in Fibonacci's text on financial mathematics, the Liber Abaci, to contemporary mathematics' Fundamental Theorem of Asset Pricing. The Fundamental Theorem is a consequence of Black and Scholes' paper on pricing options [2] that is based on the arbitrage argument, which originates in Aristotle's discussion of justice in commercial exchange in Nicomachean Ethics and features in the Liber Abaci. The novelty of contemporary financial mathematics is not in the techniques used, or the products traded², but in the fact that, today, mathematicians approach the problem of one of ‘positive' science, not ‘normative' ethics. For example, Black and Scholes opens with the observation that “it should not be possible to make sure profits”³, appealing to a consequentialist argument that if you get your price wrong⁴ someone will bankrupt you, where as medieval merchants were conscious of the Catholic Church's injunction that a riskless profit was turpe lucrum (filthy money).

Back in 2009, at the start of this journey, I took a position similar to Ekeland: there are economic laws that “outweigh the puny might of mathematicians” and the solution is in the hands of regulators. Today I have a darker view of the role of mathematics in the markets.

European science is often distinguished from other cultures' science by the fact that it is mathematicised and there is an argument, first offered in 1934⁵ but developed more recently [12, 17], that this came out of Aristotle's examination of ethics in commerce. Justice in exchange is distinguished from distributive and restorative justice by Aristotle as being characterised by equality, “there is no giving in exchange”, it is a reciprocal arrangement essential in binding society together and for social cohesion [17, p 51; 3, 1133a15-30]. It is notable that Aristotle approached this ethical problem mathematically, since he rarely applied mathematics to the physical world elsewhere [12, p 75; 4, p 13; 3, 1094b15-28]. On this basis, the medieval Scholastic scholars realised that money was a universal measure, up until then Hellenic thought (including Islamic scholarship of the time) had considered different physical properties, such as time and space, to be ‘incommensurable' - it was impossible to represent momentum, mass x length/time, mathematically - and it was this property of money as a universal measure that enabled the development of modern physics based on mathematics [4, 17]. To appreciate the point, Copernicus wrote on money before he wrote on the planets; Stevin, founder of the influential Dutch Mathematical School, was a financier; the financier Gresham endowed the first chair of mathematics in England and laid the foundations for the Royal Society. Recently, Bernard Bru has explained the significance of Bachelier's experience of stock-markets in the development of Kolmogorov's ideas on probability [30, pp 20-21]. The close relationship between mathematics and finance is born out of the fact that finance is concerned with relations, measured as prices, between objects. Finance informs mathematics on measurement and uncertainty while mathematics is critical to finance because we cannot perform experiments in the economy. It might not be possible to divorce the two disciplines, even if we wanted to.

The classicist Richard Seaford offers some insight into this account when he goes into the roots of western thought and argues that Greek philosophy, including democracy and mathematics, are a consequence of Archaic Greece's use of money [27]. He notes that other ancient civilisations were based on centralised re-distribution, where as pre-Socratic Greek society was based on exchange, reliant on a conception of equality and reciprocity. He suggests that when the Pythagoreans assigned a number to every object, they were, in fact, pricing the object.

The view that finance is socially corrosive is more novel than the practices of finance. One way of approaching Shakespeare's The Merchant of Venice is as a study of the four natures of love - erotic, familial, friendship and the highest form of love - charity/caritas/agapi - and Shakespeare personifies charity in the form of Antonio, the merchant of Venice. Throughout the seventeenth and eighteenth century, commerce was considered a civilising influence, in The Rights of Man (1792) Thomas Paine writes “commerce is a pacific system, operating to cordialise mankind” following a path laid by Montesquieu, Hume, Condorcet and Adam Smith [15, 8].

After the Industrial Revolution, these attitudes all but disappeared and today it would be inconceivable to personify Christian love in the form of a merchant. An explanation for this cultural shift can be found in Dialectic of Enlightenment [1] where it is argued that the Enlightenment led to the objectification of nature and its mathematisation, which in turn leads to ‘instrumental mindsets' that look to optimally achieve predetermined ends in the context of an underlying need to control external events. Where as during the seventeenth and eighteenth centuries public spaces emerged, the public sphere, which facilitated rational discussion that sought the truth in support of the public good, through the nineteenth century, mass circulation mechanisms came to dominate the public sphere and these were controlled by private interests. As a consequence, the public became consumers of information rather than creators of a consensus through engagement with information [11].

One aspect of this process of alienation for the public is the attitude that mathematics is an almost mystical pursuit that can reveal hidden truths, but only for the initiated, a recurring theme in the presentation of mathematics in popular culture. This is nicely captured in a documentary film on the development of the Black-Scholes-Merton equation where the economist Paul Samulelson describes how he ‘discovered' Bachelier's thesis, much as Indiana Jones might discover a magical artefact,

In the early 1950s I was able to locate by chance this unknown book by a French graduate student in 1900 rotting in the library of the University of Paris and when I opened it up it was as if a whole new world was laid out before me.⁶

This trope might seem benign in the context of popularising mathematics, but when combined with the idea that mathematics is immutable and indubitable, themes of traditional histories and philosophies of mathematics, we are given the impression, to paraphrase William Tait, that

A mathematical proposition is about a certain structure, such as financial markets. It refers to prices and relations among them. If it is true, it is so in virtue of a certain fact about markets. And this fact may obtain even if we do not or cannot know that it does. [29, p 341]

While mathematicians themselves might not make this claim explicitly, mathematics has been used by many to obscure and legitimise financial activity, passing over any consideration of the ethical implications of those activities. Ekeland might see mathematics as ‘puny', but others value its authority and there are too many examples of how mathematics has been employed to prevent democratic oversight of the markets. In their submission to the Parliamentary Commission on Banking Standards in 2013 the Bank of England was highly critical of how some firms have used advanced mathematical techniques to ‘pull the wool' over the eyes of the regulator [22, v. II, para. 89] while U.S. authorities identified that this type of mathematical sleight of hand played a part in the ‘London whale' episode [23, p 14]. The existence of the Gaussian copula as a ‘'truth-teller' of the value of complex debt portfolios played a central role in the Crisis of 2007-2009, justifying the actions of banks, despite its short-comings being known to mathematicians [31, 21, 9]. In the early 1970s, the Black-Scholes-Merton framework played an important part in legitimising the re-emergence of financial derivatives markets [20, p 158]. As long ago as 1877 a large, corporate, insurer defended their actions in undermining fraternal/mutual insurers to legislators with the argument that

There are certain fundamental rules †which can only be understood by actuaries, and it is impossible for me to go into here [19, p 198]

An antidote to the causes and consequences of ‘instrumental mindsets' identified above is to turn away from the philosophical paradigm of Foundationalism, which sees language as being made up of statements that are either true or false and complex statements are valid if they can be deduced from true primitive statements. This approach is exemplified in the standard mathematical technique of axiom-theorem-proof. An alternative approach is to shift the focus from what language says (true or false) to what it does. Specifically, the function of language is to enable different people to come to a shared understanding and achieve a consensus, this is defined as discourse⁷ [10]. Because discourse is based on making a claim, the claim being challenged and then justified, to be successful discourse needs to be governed by rules, or norms. The most basic rules are logical and semantic, on top of these are norms governing procedure, such as sincerity, and finally there are norms to ensure that discourse is not subject to coercion or skewed by inequality. This is why reciprocity is central to financial mathematics, it is a norm of market discourse, embedded in the language of mathematics.

Mathematics has not been passive in recent financial crises and I would argue that if mathematicians are not part of the solution, they are part of the problem. For me, the correct response of mathematicians to the financial crises is to work in support of those who wish to redirect finance from regarding markets as competitive arenas to seeing them as centres of cooperative, democratic, discourse⁸. In this vein I have developed the argument [16] that reciprocity is the central message of financial mathematics and it is one of three norms of market discourse, the others being sincerity and charity. For this case to be coherent I have followed Putnam [25] and abandoned the idea of mathematics being a value-neutral truth-teller, rather it is a means of discourse. This is a significant step if you perceive mathematics as being monogamous with the natural and physical sciences, or even celibate. I believe certain twentieth century mathematicians, such as Poincaré⁹ [14], Ramsey [5] and Putnam, would have sympathy with the approach I take, particularly in the cases where mathematics is employed in the social and human sciences.

Notes

¹In the U.S. Financial Crisis Inquiry Commission’s report of 2011 and the U.K. ‘Changing Banking for Good’ report of 2013.

²Most of these products existed in medieval times, the ‘Triple Contract’ shares the features of ‘structured products’ prominent in the crisis. ‘Mortgage Backed Securities’ were introduced in the U.S. in the late nineteenth century — see [19, Ch 5] for an enlightening account. It is not in the interests of well dressed bankers to tell their clients that what they are charging fat fees for existed before Columbus.

³This is the basis of Ekeland’s argument.

⁴Ramsey’s ‘Dutch book’ argument, which has been described as a modern version of the ‘Golden Rule’, “Do unto others as you would have them do unto you”, Luke 6:31.

⁵By the Marxist theoretician Borkenau in The Transition from the Feudal to the Bourgeois World View.

⁶The programme is ‘The Midas Formula’ also known as ‘The Trillion Dollar Bet’ and is available on YouTube. The relevant section is around 12:20/48:53 minutes. A transcript is available at http://www.bbc.co.uk/science/horizon/1999/midas_script.shtml.

⁷According to a recent translator of Fibonacci, a key feature of the techniques given in the Liber Abaci was that they enabled ideas to be transmitted and improved upon [7, Introduction].

⁸An I.M.F. paper on the crisis, Resolution of Banking Crises: The Good the Bad and the Ugly (WP/10/146) reveals that countries with a significant proportion of ‘not for profit’ mutual banks (e.g. Germany, France, Italy) did not require the public bailouts needed in the U.K. and U.S. — finance is not necessarily capitalist.

⁹Poincaré’s approach is captured in his observation “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” [24, p 91].

References

[1]    T.W. Adorno and M. Horkheimer. Dialectic of Enlightenment. Stanford University Press, 1944 (2002).

[2]    F. Black and M. Scholes. The pricing of options and corporate liabilities. Journal of Political Economy, 81(3):637-654, 1973.

[3]    S. Broadie and C. Rowe. Aristotle: Nicomachean Ethics: Translation, Introduction, Commentary. Oxford University Press, 2011.

[4]    A. W. Crosby. The Measure of Reality. Cambridge University Press, 1997.

[5]    D. Edgington. Ramsey and Pragmatism: Probability, conditionals and truth. Cambridge Workshop on Pragmatism, May 2012.

[6]    I. Ekeland. Response to Rogalski. The Mathematical Intelligencer, 32(2):9-10, 2010.

[7]    L. Fibonacci and L. Sigler. Fibonacci's Liber Abaci: A Translation Into Modern English of Leonardo Pisano's Book of Calculation. Springer, 2003.

[8]    M. Fourcade and K. Healy. Moral views of market society. Annual Review of Sociology, 33:285-311, 2007.

[9]    M. B. Gordy. A risk-factor model foundation for ratings-based bank capital rules. Journal of Financial Intermediation, 12(3):199-232, 2003.

[10]    J. Habermas. The Theory of Communicative Action: Reason and the rationalization of society. Beacon Press, 1985.

[11]    J. Habermas. The Structural Transformation of the Public Sphere: An Inquiry Into a Category of Bourgeois Society. MIT Press, 1991.

[12]    R. W. Hadden. On the Shoulders of Merchants: Exchange and the Mathematical Conception of Nature in Early Modern Europe. State University of New York Press, 1994.

[13]    P. Haggstrom. Mathematicians in the world of finance. The Mathematical Intelligencer, 34(1):6-7, 2012.

[14]    G. Heinzmann. Henri Poincaré and his thoughts on the philosophy of science. In E. Charpentier, E. Ghys, and A. Lesne, editors, The Scientific Legacy of Poincaré. American Mathematical Society / London Mathematical Society, 2010.

[15]    A. O. Hirschman. Rival interpretations of market society: Civilizing, destructive, or feeble? Journal of Economic Literature, 20(4):1463-1484, 1982.

[16]    T. C. Johnson. Reciprocity as a foundation of Financial Economics. The Journal of Business Ethics, Forthcoming, doi: 10.1007/s10551-014-2257-x.

[17]    J. Kaye. Economy and Nature in the Fourteenth Century. Cambridge University Press, 1998.

[18]    J. Korman. Finance and mathematics: A lack of debate. The Mathematical Intelligencer, 33(2):4-6, 2011.

[19]    J. Levy. Freaks of Fortune: The Emerging World of Capitalism and Risk in America. Harvard University Press, 2012.

[20]    D. MacKenzie. An Engine, Not a Camera: How Financial Models Shape Markets. The MIT Press, 2008.

[21]    D. MacKenzie. The credit crisis as a problem in the sociology of knowledge. American Journal of Sociology, 116(6):1778-1841, 2011.

[22]    PCBS. Changing Banking for Good. Technical report, The Parliamentary Commission on Banking Standards, 2013.

[23]    Permanent Subcommittee on Investigations. JPMorgan Chase Whale Trades: A Case History of Derivatives Risks and Abuses. Technical report, Committee on Homeland Security and Governmental Affairs, 2013.

[24]    H. Poincaré. Science and Hypothesis. In S. J. Gould, editor, The Value of Science: Essential Writings of Henri Poincaré. Modern Library, 1902 (2001).

[25]    H. Putnam. The Collapse of the Fact/Value Dichotomy and Other Essays. Harvard University Press, 2002.

[26]    M. Rogalski. Mathematics and finance: An ethical malaise. The Mathematical Intelligencer, 32(2):6-8, 2010.

[27]    R. Seaford. Money and the Early Greek Mind: Homer, Philosophy, Tragedy. Cambridge University Press, 2004.

[28]    E. D. Sylla. Commercial arithmetic, theology and the intellectual foundations of Jacob Bernoulli's Art of Conjecturing. In G. Poitras, editor, Pioneers of Financial Economics: contributions prior to Irving Fisher, pages 11-45. Edward Elgar, 2006.

[29]    W. W. Tait. Truth and proof: The Platonism of mathematics. Synthese, 69(3):341-370, 1986.

[30]    M. S. Taqqu. Bachelier and his times: A conversation with Bernard Bru. Finance and Stochastics, 5(1):3-32, 2001.

[31]    G. Tett. Fools' Gold. Little Brown, 2009.

Mathiness: not just a problem of macro-economics

I was aware of the "mathiness" discussion initiated by the macro-economist Paul Romer, but have only recently read the articles because while the discussion was taking place I was finishing of an article for The Mathematical Intelligencer that presents a remarkably similar argument (noting that mathematicians consider a coffee cup and doughnut to be the same).

Romer's concern is in the field of economic growth - an area I am unfamiliar with -  but two related statements caught my attention

For the last two decades, growth theory has made no scientific progress  toward a consensus. ... The question posed here is why the methods of science have failed to resolve the disagreement between these two groups.

and, postulating on why science has failed to come to a consensus, Romer offers an explanation as "mathiness"

Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in natural versus formal language and between statements with theoretical as opposed to empirical content.

My article for the Intelligencer is titled "Finance and Mathematics: where is the ethical malaise" and was written in response to a series of articles  about the role of mathematics in financial crises.  I begin my piece

Discussions of the role of mathematics in finance appearing in The Mathematical Intelligencer can be split into two classes. Marc Rogalski and Jonathan Korman capture a widespread fury at a collapse in commercial ethics while Ivar Ekeland  and Peter Haggstrom off er economic facts. The conclusions of Rogalski and Korman can be summarised as that mathematicians should spurn the financial world; Haggstrom and Ekeland point to technocratic solutions, characterised by better regulation. I do not buy into the argument that the problems of finance can be solved by regulations, it is, as both the U.K. and U.S. governments have identified, an ethical problem.

I go onto to explain that mathematics has not been neutral in recent financial crises

In their submission to the Parliamentary Commission on Banking Standards in 2013 the Bank of England was highly critical of how some fi rms have used advanced mathematical techniques to 'pull the wool' over the eyes of the regulator [para. 89] while U.S. authorities identified that this type of mathematical sleight of hand played a part in the 'London whale' episode [p 14]. The existence of the Gaussian copula as a 'truth-teller' of the value of complex debt portfolios played a central role in the Crisis of 2007-2009, justifying the actions of banks, despite its short-comings being known to mathematicians. In the early 1970s, the Black-Scholes-Merton framework played an important part in legitimising the re-emergence of financial derivatives markets. As long ago as 1877 a large, corporate, insurer defended their actions in undermining fraternal/mutual insurers to legislators with the argument that

 "There are certain fundamental rules . . . which can only be understood by actuaries, and it is impossible for me to go into here [p 198]"

 In my piece, for the mathematics community, I note that while mathematicians might see these abuses, which I am fairly certain could be ascribed to 'mathiness' as coined by Romer, as being abuses of mathematics, we do bear some responsibility.

Many mathematicians, but probably only a minority, argue that there is an issue with mathematics in that it is often used to obscure rather than enlighten.  Part of this trope is the presentation of mathematics as a mystical key that can unlock hidden truths:
In economics, my favourite example is Samuelson's account of how he 'discovered' Bachelier's thesis, much as Indiana Jones might uncover a magical artefact

(From the BBC programme "The Midas Formula/The Trillion dollar Bet")

This all might seem benign in to context of encouraging people to engage with mathematics, but when combined with he dominant philosophical paradigm of Foundationalism and finance, problems emerge.

Foundationalism sees language as being made up of statements that are either true or false and complex statements are valid if they can be deduced from true primitive statements. This approach is exemplified in the standard mathematical technique of axiom-theorem-proof and so arguments presented mathematically are automatically imbued with the quality of 'truth' and so hold authority.

I then give a Habermasian explanation of what happens when mathematics and finance come together.

the Enlightenment led to the objectification of nature and its mathematisation, which in turn leads to 'instrumental mindsets' that look to optimally achieve predetermined ends in the context of an underlying need to control external events. Where as during the seventeenth and eighteenth centuries public spaces emerged, the public sphere, which facilitated rational discussion that sought the truth in support of the public good, through the nineteenth century, mass circulation mechanisms came to dominate the public sphere and these were controlled by private interests. As a consequence, the public became consumers of information rather than creators of a consensus through engagement with information.

Habermas, and Pragmatic philosophy more generally, offer an antidote by switching the emphasis of what language says (whether it is true or false) to what it does

Specifically, the function of language is to enable different people to come to a shared understanding and achieve a consensus, this is de fined as discourse. Because discourse is based on making a claim, the claim being challenged and then justified, to be successful discourse needs to be governed by rules, or norms. The most basic rules are logical and semantic, on top of these are norms governing procedure, such as sincerity, and finally there are norms to ensure that discourse is not subject to coercion or skewed by inequality.

This is the basis of my claim that Reciprocity is a Foundation of Financial Economics.

With regard to the 'mathiness' discussion it is interesting to see that Romer argues the issues are in the collapse of 'economic norms', so are diagnosis and treatment appear aligned.  My criticism of Romer is mild, and it is that he has not presented his case in the context of Pragmatism, which would provide him with a firmer foundation for his case (I recommend Haack and Misak  as bedrocks).

However, I do not see my contribution as calming the criticism there has been for Romer, because my suggestion is the issue is not with one, or another, local mis-understanding but a fundamental issue with the dominant pardigm supporting science.  Economists might disagree on their growth models but they are likely to agree that science is based on Foundationalism.  This said, the problems Romer, and I, identify are pervasive, with science being unable to resolve many problems ranging from finance to climate change.