Parade's End

The BBC's transmission of Ford Maddox Ford's Parade's End (a co-production with HBO, and adapted by Tom Stoppard who has a good appreciation of mathematics - Rosencrantz and Guildenstern Are Dead) reminded me that the central character, Christopher Tietjens was an actuary, probably the most famous actuary in English literature.

I came to Ford through his collaborator Joseph Conrad, a teenage interest with Coppola's Apocalypse Now led me to Conrad and a love of sailing inspired me to read all his novels while an undergraduate. I read the first two books of Parade's End after graduating.

I always thought Ford made Tietjens an actuary to highlight his fidelity, his trustworthiness.  Statistics provides the foundation for our belief, our faith, in science, that is why Bertrand Russell (following Poincare) observed

It is important to realise the fundamental position of probability in science. ... As to what is meant by probability, opinions differ (p 301, An Outline of Philosophy)

around the same time Ford was writing Parade's End.  So, in making Tietjens an actuary, and the Second Wrangler of his year, Ford is emphasising Tietjen's  faithfulness, which is most obvious in his relations with his adulterous wife, Sylvia, and the more compatible Valentine Wannop.  Tietjen's character is magnified by placing him alongside the less virtuous, but more successful, MacMaster.

The trajectory of Tietjen's career, the trauma of serving at the front impacted his work as a mathematician,  echoes the real life experience of  Émile Borel.  Borel was the star of his generation of French mathematicians.  His 1894 thesis laid the foundations for modern probability theory and within 16 years he had been appointed Deputy-Director of the most prestigious of the French 'grandes  écoles' the École normale supérieure.  Borel served in the war, but more significanltly, his adopted son was killed at the front.  After the war, Borel pre-empted von Neumann's work in Game Theory and established the Institut de Statistiques de l'Université de Paris, but after 1924 abandoned mathematics for politics, serving as a minister and then, in his seventies was active in the Resistance.  In his lifetime ha had been awarded the Croix de Guerre, Médaille de la Résistance with rosette, and the Grand Croix Légion d'Honneur.

When thinking about this, I remembered that Tietjens, as a statistician, had a series of battles with government regarding the manipulation of figures.  This suggests that not much has changed, with the government still being accused of doctoring the numbers, and modern statisticians still worry about public faith in their figures.

However, in one respect the situation for mathematics now is worse than it was when Parade's End was written.  Would a contemporary author of Ford's prestige choose to make a character a mathematician to emphasise their virtue.  It suggests that the reputation of mathematics has been in decline since the 1920s when Russell and Ford were writing.  Could this be related to G. H. Hardy's 1940 statement

I have never done anything ‘useful’. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world. (p 49, A Mathematician's Apology)

Hardy's autobiography is significantly different from Borel's.  Since this time, British (pure) mathematics, which encompasses probability, has abandoned the world that Tietjens and Borel lived in, and isolated itself in academic cloisters, to everyone's detriment.

As a footnote, Hardy, who is credited with introducing continental 'rigour'  (rigour mortis?) , into British mathematics, opposed the Cambridge Mathematical Tripos, on which the Wranglers were selected, because he felt it had ossified British mathematics.  That might have been the case, but the Tripos produced more than just pure mathematicians, it delivered leaders in professions as diverse as the law, medicine, the church, politics, as well as actuaries.

Teaching kids to gamble

I do a workshop of couple of hours each summer with kids who have finished their Standard Grades (GCSEs in England, i.e they are 16) and are moving on to their Highers (A-level) labelled "Deal or no Deal".  My aim is to encourage students to think a bit differently about maths, in particular to appreciate the relevance tof maths to areas other than the physical / natural sciences.

The workshop is popular, I had thought it was because the TV show was popular but it turns out only a couple of kids watch the show regularly.  The students had been told

The world is uncertain and mathematics is exact, so how can maths help in making decisions about the future?

The workshop will look at a number of simple games that involve making decision when you don't know what will happen, and investigate how maths can help you make the winning choice.  The workshop will show how maths is as important in understanding economics, biology and psychology as in understanding physics or engineering.

I started the workshop by talking about the role of gambling in mythology/religion, referring to Hellenic, Hindu, Chinese and Biblical examples.  I then suggested that gambling (or casting lots) is something common to all cultures, like language, mathematics, music and art are, but physics and agriculture are not.  To explore this point further I split the group into groups of five and ask them to gamble for smarties.  One of the 5 is given more smarties than the rest and the idea is that by playing fair games this imbalance is corrected.  There is a simple java simulation (don't play it too long as one player usually wipes out the others) and I go on to talk about how anthropologists think that gambling prevents the establishment of hierarchies in neolithic societies (eg Mitchell or Altman).

The group was of 25 and so I got them to order themselves by date of birth - there were two pairs sharing the same birthday.  The purpose of this was to enable the group to split into pairs who did not know each other (well).  I then got the pairs to participate in the Ultimatum Game and then talk about how "fairness" is a learnt human concept (Murnighan and Saxon, Henrich et al., Jensen et al.).

I then talk about how Cardano undertook the first mathematical analysis of gambling in response to trying to address the issue of the ethics of gambling.  I give one of the key quotes and then explain how the idea of mathematical expectation comes out of this.  When the group were happy that this was all OK, I present the Petersburg game and ask for offers to play it.  The best offer is 2 I then calculate the game's expectation.

Some of the students identify the risk as the key issue, and after a brief discussion I offer some more games based on dice and ask which one each participant prefers.  Un-remarkably almost half prefer B, the lowest variance game, and I explain that variance is a measure of uncertainty and is associated with risk.

I then ask whether taking a risky decision is always a bad idea.  I present the case of a bird in winter who needs to find food to survive the night and outline this as a game.  The students work out there is a risky and safe strategy (based on variance) and I ask them to try and work out if there is a good strategy, playing safe or taking risks.  After the students play about and we discuss their suggestions I run through a java simulation. The simulation (after a few runs) enables me to demonstrate that the re are two regions in the time-berry state space were taking risks is better than playing safe.

I then discuss the Deal or No Deal game, and, with the results of 22 games, I discuss how a mathematician might analyse the game.  I finish off with Cardano's 350 year old advice, maths is of little practical value but does help in understanding, and the only way to be ethical in gambling is through science.

Is "Risk Intelligence" a dangerous concept?

At a time when there is an emphasis on inter disciplinary research, it is not that useful to divide science into separate categories.  However one distinction that, as a mathematician, I find useful is  between Romantic and Enlightenment science.  Enlightenment science is concerned with the universal, and is developed by collaborative analysis, and, to facilitate both the collaboration and analysis, mathematics plays an important role.  Romanticism emerged in the second half of the eighteenth century and dominated British and German culture in the following half-century.  Romantic science emerges out of senses trying to understand the whole, rather than the parts, sentiment over reason, and is often the result of an individual genius's struggle, frequently against dark forces.  

The archetypical romantic scientists are Alexander Humboldt, Lewis and Clark and Darwin, who developed science through exploration.  The archetypal romantic mathematician is Galois, whose career was hindered by his reliance on intuition rather than the clear proof favoured by the French Academy and a myth has grown up around him that he did his most significant work the night before he was killed in a duel over a love affair.

I have been thinking a lot about the transformation from Enlightenment to Romanticism, because there seems to have been a massive change in the relationship between science and finance in the first half of the nineteenth century, at the time that Romanticism dominated culture.  

I thought about this distinction after listening to Dylan Evans promoting his book Risk Intelligence on the radio. Evans defines Risk Intelligence as the "ability to estimate probabilities accurately" (0.24 on audio), such as the chance a horse wins a race (0.52).  Evans goes on to make the point that our educational system does not train people in making decisions under uncertainty (1.29), what he calls a "twilight zone" (1.40).  Further on he explains that because finance (2:57) became to rely on mathematical models and the "intuitive gambler types were edged out and as a result Wall Street haemorrhaged risk intelligence" (3:35), and this transformation was partly responsible for the failures of finance.

One point I would agree with Dr Evans on, that there needs to be an effort to get concepts around uncertainty onto school curricula.  In fact, at the "Credit Crisis Five Years On" meeting recently I asked Andy Haldane if he felt the Bank of England had a role to play in helping shape curricula in this way.  I think there are significant issues with Evans' view that the chance of a horse winning a race can be estimated accurately, Knightian uncertainty / Keynes' irreducible uncertainty' spring to mind.  However, my main concern is in the claim that it was the use of mathematics that was partially responsible for the failures of finance.

It struck me that in the interview,  Evans seems to be endorsing Romantic Science, there is an emphasis on "intuition" over mathematics in what he says and reference to "twilight", the darkness that is a feature of Romanticism.  But just because Risk Intelligence might be a Romantic idea, doesn't mean to say it is dangerous. The danger with a concept like Risk Intelligence is the emphasis on there are some people who are "good" at risk, there is a link to that other idea that emerged out of Romanticism, the idea of genius, and that mathematics is a hindrance, not a help, in finance.

Why is mathematics important in finance?  It goes back to why Fibonacci's Liber Abaci was a publishing phenomena at a time when books were hand copied - the mathematics it described enabled merchants to write down, disseminate, discuss and improve their financial models.  This is the point of mathematics, whether in physics or finance, and why mathematics is such an important part of Enlightenment science but missing from the Romantic: Enlightenment science is collaborative and needs a common language, and its arguments are written in that language, mathematics.

The problem with modern finance is not in the mathematical models, but in that the models were an end in themselves and not a means for developing a consensus, understanding, knowledge about finance. Banks employed geniuses to develop these models in house that they kept secret, or, they bought black boxes that had been created by geniuses elsewhere.  When mathematicians, such as Phillipe Artzner and Freddy Delbaen  or Michael Gordy, shone a light on the some of the leading industry models, their illumination was blocked by the towering geniuses, the "masters of the universe", working in banking.

When you read the book, rather than listen to the interview, the issue of mathematics in finance is not as significant.  In fact, the whole book rests on a mathematical model of RQ (compare with IQ or Samuelson's "Portfolio IQ", "PQ"), which is implemented on-line for you to test your own RQ.  

Evans claims the motivation behind RQ is a 1986 paper Ceci and Liker where RQ is identified as a type of intelligence uncorrelated with IQ.  Unfortunately, Ceci and Liker's science was not up to much, and within two years this key result was overturned by better analysis.  In fact "RQ" seems to be highly correlated to "IQ".  Evans argues that Banking regulation should involve measuring the RQ of bankers.  The problem is anyone can "game" RQ (when I did the test I got a very high score of 80 because I realised immediately what was going on). 

Having laid the basis of RQ Evans attempts to describe how you can improve your RQ, which boils down to understanding the limitations of what you know.  This does not strike me as particularly novel, and might be labelled as "science", which has been described as "organised scepticism".  

In fact, Evans' criticism of maths in finance turns out to be  more a criticism of calculation in finance, and this has been addressed more tangentially, but more eloquently, by the philosopher Richard Sennett in The Craftsman.  Sennett makes the point that we can all be craftsmen in the modern age, if we learn a craft.  Developing RQ seems no different from becoming skilled in understanding risk.  What is important in becoming a craftsman is hard work in a social context (crafts were traditionally regulated by a guild) and this is why I feel RQ is not simply a banal idea but a dangerous one.

The Romantic Evans seems to believe in an intuitive genius that can be developed outside  of the workshop, I think this is dangerous because I believe the solution to banking's problems lies in open discussion and debate about the risks and rewards of finance (i.e. science), and that good bankers are skilled craftsmen who have learnt their trade by spending hours developing their skill in the work place.  If something has happened in finance over the last 25 years it is that banks have not been recruiting schoolboy apprentices (I knew three people who left school to go into finance, one to a Bank of England apprenticeship) who they train up over five years, but have been recruiting staff "off the shelf" out of universities and assuming that these academically trained men and women have the right skills for banking.  Or they have recruited ready-made business experts such as Andy Hornby and Fred Goodwin.

Dylan Evans's central argument, that people who are gifted in making risky decisions can be identified and hired to run finance, relegating the need for good ethics, is dangerous.

A banker, a pharmacist and physicist walk into a pub .... and pay $3 billion

One of my favourite jokes:  "I make all the big decisions at home - what our policy on Iran, Chinese exchange rates and the Eurozone crisis should be.  I leave the mundane issues - like where we live, how we raise our children, where we go on holiday - to my wife".  Given the news coverage yesterday, dominated by Barclays, the Higgs-Boson and GSK there could be a version "Physical scientists investigate all the important questions - the origin of the universe, the existence of the Higgs Boson and why the dinosaurs became extinct.  We leave the mundane issues - like why banks fail or how to respond to the diabetes epidemic - to the Social Scientists".

A Higgs Boson like(?) particle has been found, modulo a "5-sigma" event - recall Goldman's heralded the Credit Crisis in August 2007 by going public with a much (much, much, much) more rare 25-sigma event.    Call me churlish, but having spent $3 billion plus (and the plus is augmented by much of the fitting, commissioning and operation of the machines is done by PhD students working at levels that would probably breach the European Working Time Directive and UK minimum wage legislation, luckily its in Switzerland) it was inevitable that they would find the Boson.  A bit like it was inevitable that Wayne Rooney, the "white Pele", apparently, would play a central role in England's Euro 2012 performance, because he costs Manchester United so much.

My point is, if the UK's contribution to the $3 billion LHC had been diverted into serious scientific study of markets, involving many disciples and not just the Platonic forms of neo-classical economics, things might (modulo a 5?-sigma event) be different in the sense that people might (modulo a 5?-sigma event) be better off.  The trouble is, the "scientific establishment" rarely take the social sciences that seriously, possibly because it is about "us" and not "things", and so rarely give it priority in funding.

In this respect, mathematics is a social science.  In 2010 the outgoing "President of the Board of Trade" for the UK, Lord Mandelson, who was responsible for signing off the science funding budget, allocated some £40 million to enhancing Blackpool Tower, about the same as he allocated to maths research that year.  Enhancing the imitation of the French Eiffel Tower rather than enhancing the imitation of French achievement in mathematics.  Mathematics enables experiment when there is no apparatus - the Higgs Boson was (is) a mathematical object that exists as a physical(?) object because $3 billion has been spent to build the lab for the physical experiments.  This is why mathematics is fundamental to understanding markets, because we cannot undertake experiments in markets, not because asset prices are Levy processes.

Bio-tech, is firmly in the camp of legitimate science since Tony Blair bet the UK's research pot on in 1997.  However,  bio-tech has not grown in the past 15 years in the same way that finance has grown, Blair's investment has not paid dividends.  Just as the ethics of big banking are in crisis, so are the ethics of big pharma.    GSK were fined, that magic number of, $3 billion, about 6 times the fine on Barclays.  Was GSK's crime 6 times worse than Barclays?  If so why haven't there been calls for judicial or parliamentary investigations into the behaviour of the UK's pharmaceutical industry? If Barclays' sin was equivalent to GSK's, why the small sanction?

Could it be that the government  spending money on bio-tech research puts the industry under public scrutiny, this puts pressure on the regulator to ratchet up the sanctions.  Bankers pour money into the coffers, rather than take money out, on condition that the government leaves the industry to its own, hidden, devices.

All these calls for a judicial enquiry into the behaviour of the UK banks are a bit lame, in my opinion.  There has recently been an excellent judicial review of practices in financial services, Lord Penrose's Review of the collapse of Equitable Life.  The Equitable was the world's oldest public (i.e. open to all) life insurers that collapsed around the time that LTCM collapsed, essentially the firm had been giving away long term swaptions (Guaranteed Annuity Rates), rather than providing them at a cost.  The "hole" that the Equitable left was estimated at the time as about the same size as the LTCM hole (around $3 billion), though as the Equitable was a life company the current loss suffered by policy holders is in the region of £4 -£5 billion (note the change in currency).  The government at the time asked the Scottish Judge, George Penrose, to conduct a review of the collapse in 2001 and he reported in 2004.  Some quotes:

One of the regulators involved with Equitable referred to the boundary between prudential and conduct of business regulation as more an awkwardness than a lacuna. While that may be a fair comment on how the two branches were intended to operate, in practice the lack of co-ordination of prudential and conduct of business regulation in relation to the Society was unacceptable. (ch 20, 64)

 Many readers of this report will be frustrated that it has not provided answers to two questions: who is at fault for the problems encountered by the Society, and who deserves redress as a consequence? It has been no part of this inquiry to attempt to answer either question. The first inevitably involves issues of the scope of duty and of breach of duty that I was not asked to consider and that I would have been unwilling to consider as part of an inquisitorial process. The current proceedings at the instance of the Society speak eloquently of the complexity of the questions that arise from allegations of breach of duty relating to a relatively short period compared to the period covered by the inquiry, and a selection of issues from the wider range that I have discussed. An open adversarial process such as would have been necessary to replicate the litigation process over the longer period and the wider range of issues would have been beyond contemplation. (ch 20, 77, my italics)

 Almost 10 years on, it seems, not much has changed, apart from in 2010 the government agreed to compensate the policyholders for the lax regulation.  A few weeks ago I received a cheque for £159, some 15 years after the firm collapsed.

It is interesting that in 1998, LTCM collapsing owing $3 billion spawns congressional hearings,  books and TV programmes, by 2012 $3 billion is a corporate fine.

Financial crises, ethics and academics: A bit more Mea Culpa would help

Joris Luyendijk, the anthropologist who interviews finance professionals for The Guardian has recently published an interview with an London based academic who  is a quant "of sorts".  Joris, as an anthropologist, has been trained to interview people and distinguish the wheat from the chaff, and appreciate when they are constructing myths to protect their psyche from unpalatable truths.

One unpalatable truth that (primarily Anglo-Saxon) academics have to face up to is their role in the current financial crises that have ravaged first the Atlantic nations and now the Mediterranean ones, but not much elsewhere.  The first myth in relation to the crisis is that it was all "evil bankers". This was created not by academics but governments whose hands were covered in the blood of Mortgage Backed Securities, sub-prime lending (and borrowing)  and Private Finance Initiative securitisation.

However, possibly more guilty, but less exposed, are academics in finance and economics.  If it wasn't so worrying it would be hilarious that in 2008 UK Economics was judged to be the jewel in the crown of British academia which lead the monarch to ask the obvious question, why did none of the brilliant economists (advising her government at least) see the crisis coming?

Eugene Fama has recently explained that (his) economics never failed.  The didactic joke is "A psychotic builds castles in the skies, a neurotic lives in them and a psychiatrist collects the rent", on this basis Fama seems to be both psychotic and neurotic, though I don't think he's paying any rent, suggesting his psyche is already shot and doesn't need any protection.

More rational economists look to the large slow moving targets, in this case mathematics.  One of the most influential making this case was the Adair Turner, trained in economics and history and the Financial Services Authority's Chairman.  Lord Turner put the blame on "a  mis-paced reliance in sophisticated mathematics"

The increasing scale and complexity of the securitised credit market was obvious to individual participants, to regulators and to academic observers. But the predominant assumption was that increased complexity had been matched by the evolution of mathematically sophisticated and effective techniques for measuring and managing the resulting risks. Central to many of the techniques was the concept of Value--at--Risk (VAR), enabling inferences about forward-looking risk to be drawn from the observation of past patterns of price movement. This technique, developed in the early 1990s, was not only accepted as standard across the industry, but adopted by regulators as the basis for calculating trading risk and required capital, (being incorporated for instance within the European Capital Adequacy Directive)

This is good rhetoric:  start with a statement that no one would quibble with, follow this with something that slips into conjecture and then conclude with something that is base opinion, but carries the weight of deduction.  I would suggest an over reliance on lax thinking, like this, has been more of a problem.  The Financial Times was not impressed.

The  lecturer seems to be following this line, it is the "mathmos" with vaguely Aspergers like qualities who could not communicate in banks that caused the problems.  Does he mean  Ed Thorp? James Simons? Antony Ledford?   In my experience, I worked in industry before taking my PhD, it is the students who have social skills that leave the cloistered world of universities and go into the more corporate, collegiate atmosphere of the work place.  Is the criticism of quants in the work place a case of projection?

Having identified the problem personalities we move on to the philosophical

I do research and I teach. When I see my students go off on careers in the City I do wonder: can't society make better use of all that talent?

What would be a better use of their talent?  Working for British Aerospace building weapons and bribing governments?  Maybe working for Novartis developing drugs and suing health boards for using cheaper alternatives. There is a tendency amongst academics to be unable to recognise that their students may not want to imitate their teachers, and don't want to ensconce themselves in academic ivory towers.  The exaggerated difference between the salary rates is the protective myth: I if it were not for filthy lucre, my students would follow in my footsteps.

Commenting on both these issues, of social skills and use of talents, go back and read about Newton at the Mint.  A grumpy academic but a personable financier, and in the opinion of Maynard Keynes, as important as a financier as a physicist.

The University of London is very difficult for students to get into, probably harder than Oxbridge for flagship degrees.  Investment Banks usually recruit BScs/MScs at £32k-£40k and have around 40% attrition after 3 years, English universities, charging £27k for a BSc or £20k+ for an MSc, don't like to highlight these unpalatable facts to students trying to get onto their courses.  Rather, they attract students with the promise of stellar salaries if you make the grade and get a place.  Academics are responsible for accepting students onto their degrees and are responsible for what they teach and how they teach it.  The "the recruitment circus that banks and financial firms roll out" is not that different from the hoops the elite universities make applicants jump through.

If you get AAB at A-level with an A in mathematics you can come and study Actuarial Science at Heriot-Watt.  If you get an average grade above around 65% in your degree you will graduate with a full set of exemptions from the basic actuarial exams, you graduate "part-qualified".  A part-qualified actuary earns between £25k-£32k.  Around 92% of our students go into graduate employment, the same rate as the LSE (according to the Sunday Times rankings), though only about 60% will be working as part-qualified actuaries.

When I talk to prospective students they ask about their "personal statement" , which, along with the interview is a big part of the UL application that they will make to us alongside Warwick.  At Heriot-Watt there is a tradition of taking anyone who meets the grade, we don't read personal statements ( a student from the local Currie High School is unlikely to have had the opportunities to pad out their statement that a student from Heriot's or Fettes would) and the "interview" is an opportunity for the students to learn about us, not for us to judge the student.

English students are the customers, they are paying the universities.  The government has no cap on universities taking students with AAB, that means an AAB student is "pure profit" for a university and the universities should be competing for them, not AAB students competing for the university (or this is what neo-classical economics would posit).

Our London academic argues

There is a generation gap between students and professors, clearly. Many of my colleagues conceive of a university education at least partly as Bildung, an opportunity for young people to discover, develop and realise themselves, and we believe society will benefit from that.

Most of our students could not care less about all this. They conceive of us as a hurdle; a selection station to get through. They aren't here to learn, they are here to pass

If this is really the case, the academic should make this clear to applicants, you are paying us lots of money "to discover, develop and realise" yourself, rather than you are paying us lots of money to buy a lottery ticket for a position at a bulge bracket bank.  At Heriot-Watt we are honest; come here and become an actuary.

The interview begins where I shall end: ethics.  Academics decide what to teach, and it is generally academics who have decided not to teach ethics.

There are two ways to look at money, as a 'convenient' commodity to facilitate exchange, or as a representation of a 'social relation'.  Money is gold or money is credit.  If money is nothing more than a commodity then its key feature is scarcity, if money is credit the critical variable is trust.  For centuries the 'City of London' has been associated with   the concept that "my word is my bond'', giving a clear indication as to where the City's financiers thought the emphasis should be.

The breakdown of this ethos did not begin, as many imagine, with Thatcherite policies or Reaganomics of the 1980s.  In 1950  a case was heard in the British courts,  Buttle v Saunders.  Saunders managed a trust for Buttle, and had agreed to sell a piece of land owned by the trust for £6,142 to a Mrs Simpson.  Before the transaction had become legally binding, another person offered the trust £6,400 for the land.  However, Saunders believed ``my word is my bond'' and declined the higher offer in favour of the original agreement with Mrs Simpson.  The beneficiary of the trust, Buttle,  took Saunders to court, and the court ruled in favour of Buttle

 The only consideration which was present to [the trustees] minds was that they had gone so far in the negotiations with Mrs Simpson that they could not properly, from the point of view of commercial morality, resile from those negotiations.

'Commercial morality' was not a valid consideration  and the sale to Mrs Simpson was declared null and English home-buyers could never again be certain that a purchase would be completed, 'gazumping' had arrived.

Three years after Buttle v Saunders Milton Friedman published  The Methodology of Positive Economics that begins with a reference to Neville Keynes's The scope and method of political economy.  The implication that Friedman offers the reader is  that ``Keynes called for'' the ``construction of a distinct positive science'' is somewhat mischievous.  Neville Keynes distinguished the `positive' economics from the `normative' economics ``an ethical, realistic, and inductive science'', principally advocated by the German Historical School

The school explicitly calls itself ethical; it regards political economy as having a high ethical task, and as concerned with the most important problems of human life. The science is not merely to classify the motives that prompt to economic activity; it must also weigh and compare their moral merit. It must determine a standard of the right production and distribution of wealth, such that the demands of justice and morality may be satisfied. It must set forth an ideal of economic development, having in view the intellectual and moral, as well as the merely material, life; and it must discuss the ways and means such as the strengthening of right motives, and the spread of sound customs and habits in industrial life, as well as the direct intervention of the State by which that ideal is to be sought after. ...

However, unlike Friedman, Neville Keynes sees the two approaches as, at least, complementary

The method of political economy cannot adequately be de-scribed by any single phrase; and accordingly no one method will be advocated to the entire exclusion of other methods. It will, on the contrary, be shewn that, according to the special department or aspect of the science under investigation, the appropriate method may be either abstract or realistic, deductive or inductive, mathematical or statistical, hypothetical or historical.

Positivism, the idea that science is an "impersonal way of arriving at the objective truth about natural phenomena'',with its associations with 'Baconian science', 'knowledge is power', and empiricism, became a doctrine attached to many branches of science by the mid-1960s.  This doctrine was taught in universities, particularly in the English speaking world}, and it is hardly surprising that if educators are removing ethics from university science, then there will be a breakdown of ethics in society.

Our academic argues its difficult to teach ethics to the Asperger's types that he has to deal with, because it involves complex issues and debates.  I disagree.  Virtue ethics, as promoted by Deidre McCloskey, with its blending of the seven virtues in an alchemical manner is easy for Asperger's types (like myself) to deal with. The problems come with consequentialism, which again is popular with academics because it allows them to blather for ages without coming to a definite answer. 

There is an alternative view of ethics and quants, and that was written by the mathematician with a background in the humanities, Steven Shreve.  Shreve, a leading financial mathematician who is behind Carnigie-Mellon's prestigious Masters in Financial Engineering writes

 we need people with integrity managing our financial systems. Teaching ethics is difficult, and guaranteeing that listeners will implement those teachings is impossible. It is not easy for a quant to sound the alarm that his models are being stretched beyond their limits, knowing that if he is taken seriously it will result in the loss of business to competing firms and may result in the loss of his job. We cannot instil in sixteen short months behaviour that properly requires years of nurturing and mentoring. We do what we can, leading by example, penalizing students for academic dishonesty, setting and enforcing rules for ethical conduct when interacting with potential employers, posing ethical dilemmas for classroom discussion, and encouraging our graduates to consult with fellow graduates when facing tough ethical decisions.

This is the response of a quant, the problem is difficult, but we do what we can, recognising the limitations.

On the Shoulders of Merchants: Gresham, Stevin and science

When the short lived Edward VI became king of England in 1547, the nation’s wealth was based on the export of one commodity, wool, out of London and into Antwerp [Stone, 1947, p 104]. Edward was succeeded by his Catholic sister Mary, who married Philip of Spain but died young and was followed by her Protestant sister, Elizabeth, in 1559. During the turbulent times of Elizabeth’s reign, security, and not prosperity, became the main object of Tudor economics.

Central to managing the economy was Thomas Gresham. Born in London around 1519 into a prominent merchant family, Gresham was appointed the ‘Royal Factor’ at Antwerp in 1551. The role of the Factor was to arrange for Antwerp speculators to lend money to the English crown, mainly to cover the costs of war. The loans were typically short term, lasting six or twelve months, and so the Factor had to continually re-negotiate the agreements. Gresham realised that key to the process was ensuring that the exchange rate was favourable, and to this end he managed the trade in English Bills of Exchange, making sure they were in short supply, and so more valuable, in Antwerp, when he wanted to borrow money. This was no mean feat and, despite falling out of favour with Mary, Gresham became an influential member of the Elizabeth’s court.[Burgon, 2004, [pp9-12], [Johnson, 1940, pp 594-600]

Gresham moved in the circle of Elizabeth’s Secretary of State, William Cecil, Lord Burghley, advising him to develop the English armaments industry in preparation for war [Burgon, 2004, [pp9-12]. Apart from the likes of the spy Francis Walsingham, and the writers Christopher Marlowe and Philip Sydney, others in the group were the mathematicians Robert Recorde and John Dee. Recorde, one time Controller of the Royal Mint, is famous for introducing the “=” sign into mathematics, in the book The Whetstone of Witte dedicated to the Governors of the Muscovy Trading Company that had created to develop English the wool trade with Russia. John Dee is notorious today for being a ‘magician’, but during his lifetime his fame was based principally on his mathematical knowledge, which included the ability to cast horoscopes, Dee had worked with Cardano when the Italian was in London. Dee was also an adviser to the Muscovy Company and worked with Gresham on commercial ‘projects’ to “make this kingdome flourishing triumphant, famous and blessed” [Hadden, 1994, p 109]. This system, where the economy was run to ensure a nation controlled its own armaments industry and accumulated gold or silver, became known as ‘mercantilism’ and would dominate Europe until the Enlightenment.

In 1565 Gresham established the Royal Exchange, modelled on Antwerp’s Bourse, to trade commodities and currencies. He returned to London in 1567, as the Dutch Revolt became inevitable, and in 1579 he died of a stroke. In his will, Gresham left all the revenues from the buildings that made up the Royal Exchange along with his mansion on Bishopsgate to the Company of Mercers and the City of London. In return, these two bodies were to support seven academics, in Law, Rhetoric, Divinity, Music, Physics, Geometry and Astronomy, to be housed in his mansion. The properties were held by Gresham’s widow until she died in 1596, and Gresham’s College opened in 1598. According to the historian, Francis Johnson

The opening of Gresham College was the culmination of a long effort in Elizabethan England to bring about the establishment of a permanent, endowed foundation which would offer instruction and further research in the mathematical sciences and provide a convenient rallying point for all who were concerned with promoting progress in the practical application of these sciences to useful works. [Johnson, 1940, p 424]

Remarkably, the mathematical chairs at Gresham College preceded those at Oxford, where the Savilian chair was established in 1619, and Cambridge would wait until 1663 to create the Lucasian chair in mathematics. [Johnson, 1940, pp 423–424]

Across the Channel, one of the most significant characters emerging out of the turmoil of the Dutch Revolt was Simon Stevin. Born in 1548 in Bruges, like Gresham, Stevin had originally trained in the abbaco tradition and worked as a merchant’s clerk in Antwerp then as a tax official back in Bruges, where he wrote his first book Tafelen van Interest (‘Tables of interest’) which he published in 1582, before moving to the University of Leiden in 1583. He taught mathematics at the University, one of his students being Prince Mauritz of Nassau, who had succeeded his assassinated father William the Silent as leader of the Dutch Revolt. Stevin was involved in the the Dutch Republic’s government, becoming Inspector of Dyke’s, an important post in the low countries, in 1592, and Quartermaster-General in 1604, advising Mauritz on tactics including how to breach dikes in order to flood the land and hinder the Spanish. [Sarton, 1934]

One of Stevin’s most influential posts was as the director of the Dutch Mathematical School, established in 1600 by Mauritz to train military engineers. In 1605 Stevin published a textbook for the School, the ‘Mathematical Tradition’, which was a comprehensive overview of mathematics and included a whole section on ‘Accounting for Princes in the Italian manner’. In a very short period, the Dutch Mathematical School became the centre for merchant’s training in north western Europe. This in turn forced the authorities at the University of Leiden, which provided the School with its facilities, to take practical sciences, in particular mathematics, a bit more seriously [Poitras, 2000, pp131–132].

The significance of the School was that, up to this point, universities had maintained the Aristotelian view of mathematics as being only concerned with the quadrivium, abstract arithmetic and geometry or astronomy applied to calculating dates, and music [Dear, 2001, p 17]. These were not very prestigious in the scholastic world and mathematicians were generally poorly paid [Dear, 2001, p 104]. The incorporation of the practical mathematics curriculum into the University of Leiden can be seen as a conclusion of the integration of the abbaco and scholastic traditions that had begun with Pacioli a century earlier.

Stevin was particularly remarkable in that he wrote almost exclusively in Dutch or French, but rarely in Latin. This meant that his books were read widely and a consequence of the popularity of his writing has had a lasting effect on the Dutch language; it is one of the few European languages that has its own, rather than using Latin or Greek, words for many mathematical terms. For example the Dutch for mathematics is wiskunde, which literally means ‘the art of certain knowledge’. In writing in the vernacular Stevin was disassociating himself with both the scholastic and humanist traditions, which were so enamoured with Greek and Roman ideas, and emphasising the practical usefulness of science in everyday life.

As well as being active in government and administration, Stevin was also a prolific scientist, addressing both theoretical and practical problems and the economic historian Philip Mirowski has suggested that Stevin’s bookkeeping inspired his physics [Mirowski, 1989, p 121]. Practically he designed a new, more efficient, windmill, based on mathematics, to drain the land and power Dutch industry, creating a wind powered industrial revolution. Theoretically, he showed that Aristotle’s science was fundamentally flawed. 

One revolutionary step Stevin took was in regard to the fundamental nature of numbers. The Hellenistic mathematicians had taken the number ‘1’, unity, to be the generator of numbers; ‘3’ is made up of three unities, and so on which related to Aristotle’s theory of measuring using the minimum unit of the thing being measured. Stevin explicitly states that ‘1’ is a number like any other number, because mathematical operations can be performed on it, just as on other numbers. He then makes a startling observation for the time, numbers are continuous, there are no gaps in them as there are gaps between 1 and 2 of a half and a quarter, or a quarter and an eighth, and so on [Katz, 1993, p 347].

Another example, is concerned with the nature of motion.  In his Physics Aristotle starts by discussing the concept of motion and then, having pinned down the idea through reasoning, or logic, goes on to deduce the properties of moving bodies, including the belief that heavier objects fall faster than lighter objects [Hall, 1962, p 161]. In an experiment that is usually attributed to Galileo dropping things from the Tower at Pisa some years later [Hall, 1962, p 78], Stevin disproved this core belief of Aristotle. The Dutch bookeeper was less interested in what ought to happen, but rather what actually happened.

Another result usually associated with Galileo was concerning the tides. Galileo’s original title for the the ‘Two World Systems’, the book that got him into trouble with the Catholic Church, was Dialogue on the Ebb and Flow of the Sea, because, as a consequence of the Copernican theory and mathematics, Galileo argued that there would be one tide a day. When he sent the book to the Church for approval, he was told to change the title because every European sailor knew that there were two tides a day. For the Church of the time, built on Aristotle, Galileo’s use of mathematics to describe reality was not just philosophically wrong, it also resulted in absurd conclusions. The historian, Harold Brown puts a modern slant on the issue

Galileo’s attempt to account for the tides as a result of the combined daily and annual motion of the earth, and his belief that this argument provided a physical proof that the earth moves, stands as something of an embarrassment.Brown [1976]

Galileo was often preceded by Stevin, and it is ironic that Stevin had more successfully addressed the theory of tides in 1608 based on the Moon’s influence [Sarton, 1934, p 280]. Galileo’s error was in ignoring the Moon and attempting to explain the tides by the Earth’s movement around the Sun – a little too Heliocentric.

References

   H. I. Brown. Galileo, The Elements and the Tides. Studies in History and Philosophy of Science, 7(4), 1976.

   J. W. Burgon. The Life and Times of Sir Thomas Gresham: Volume 2. Adamant Media Corporation, 2004.

   P. Dear. Revolutionizing the Sciences. Palgrave, 2001.

   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.

   A. R. Hall. The Scientific Revolution 1500-1800. Longmans, 1962.

   F. R. Johnson. Gresham College: Precursor of the Royal Society. Journal of the History of Ideas, 1(4):413–438, 1940.

   V. J. Katz. A History of Mathematics: an Introduction. Haper Collins, 1993.

   P. Mirowski. More Heat than Light: Economics as Social Physics, Physics as Nature’s Economics. Cambridge University Press, 1989.

   G. Poitras. The Early History of Financial Economics, 1478–1776. Edward Elgar, 2000.

   G. Sarton. Simon Stevin of Bruges (1548-1620). Isis, 21(2):241–303, 1934.

   L. Stone. State control in sixteenth-century England. The Economic History Review, 17 (2):103–120, 1947.

The IMA Conference on Mathematics in Finance

Since John Maynard Keynes rescued a collection of Newton's private papers and declared that "Newton was not the first of the age of reason. He was the last of the magicians" the popular imagination has looked at the influence of esoteric arts on the emergence of Western' science. What is often forgotten is that in almost the same breath, Keynes declared Newton as "one of the greatest and most efficient of our civil servants", in recognition of his work as Master and Warden of the Mint, positions that he held longer than his Chair at Cambridge.

The significance of the relationship between mathematics and finance is often overlooked when considering the development of science. Probability is, to both Poincare and Russell, the foundation of all science, emerged out of the analysis of financial contracts and Bernoulli first identified the number e in the context of interest payments. On a more profound level, historians such as Richard Hadden, Joel Kaye and Alfred Crosby have provided compelling arguments that the uniquely European 'mathematisation' of science came out of a synthesis of commercial practice, following Fibonacci, and scholastic analysis. Copernicus wrote on money before he wrote on planets.

While equity options trading dominated the 1980s, today, the Black-Scholes-Merton pricing formula is used more as a gauge of market volatility than to price traded contracts and the problems of finance have moved on to managing the complex interactions of many agents in the economy. It is in recognition of this evolution that the financial world has changed, not just in the last four years but over the past 25 years, that the Institute of Mathematics and its Applications (the British equivalent of SIAM) is sponsoring its first conference on mathematics in finance, to take place in Edinburgh in  2013.

Algorithmic trading is currently the focus of financial innovation. Investors, such as pension funds, will use algorithms implemented on electronic trading systems to , hopefully, optimise their market transactions. Market makers, and speculators, will use algorithms to search the markets for profit opportunities, often executing transactions in milliseconds in high frequency trading. Algorithmic trading is typically light on mathematics, using simple trend following or mean reverting criteria, and relies more on computational developments.

Since the recent Financial Crises society has realised that financial innovation, like any technological development, is not always a good thing. The Quant and Mammon report of 1998 called for academics to support banks in innovation, today the emphasis has shifted and the consensus is that academics should be trying to understand the financial system and support society's eyes and ears, the Regulators, as much as the Banks. In response to this, the IMA have invited the Bank of England to help organise the conference and provide guidance on what the Regulators' key concerns are.

The Bank of England believes that recent developments in financial mathematics have focused on microeconomic issues, such as pricing derivatives. Their concern is whether there is the mathematics to support macroeconomic risk analysis, how the whole system works. While probability theory has an important role to play in addressing these questions, other mathematical disciplines, not usually associated with finance, could prove useful. For example, the Bank's interest in complexity in networks and dynamical systems has been well documented.

The initial outline of the conference is that it will have three parallel sessions, covering developments in algorithmic trading, the concerns of the Bank of England and contemporary issues in mainstream financial mathematics. For example, in the algorithmic trading stream topics could include data mining, pre-trade analysis, risk management and agent based modelling. As well as the Bank of England’s interest in models of market failure and systemic risk, more esoteric topics such as non-ergodic dynamical systems and models of learning in markets would be interesting. Topics associated with mainstream financial mathematics could include control in the presence of liquidity constraints, Knightian uncertainty and behavioural issues and credit modelling. 


In addition to the main mathematics Conference organised by the IMA, the Scottish Financial Risk Academy is planning to organise an "Industry Day" at the end of the Conference. 

Applied mathematics is developed as a consequence of solving problems. While it is easy to criticise the world's bankers, it is harder to come up with solutions to the complex issues they face. It is always worth remembering that the laws of physics (almost surely) do not change, but finance is constantly transforming itself. Ever since the time that Newton left Cambridge for the City, the UK has built its prosperity on financial innovation, funding the wars with France and the Industrial and Agricultural Revolutions. today financial services account for some 10% of the UK's GDP and it is only fitting that applied mathematicians consider whether they can provide solutions to the difficult problems the sector faces.

The IMA Conference on Mathematics in Finance, scheduled for early April 2013, aims to provide a forum for mathematicians to become more involved in the industry and for industry to become more involved in mathematics, and we would invite any mathematician, academic or practitioner, to attend.


If you would like to register your interest in attending the conference, please contact the IMA.

Creation myths

There is currently a debate being carried out on the internet between Steve Keen  and Paul Krugman on the nature of money. For those (like myself) who do not have a formal training in the discipline, economists will consider money to be either endogenous or exogenous to the economy. Endogenous theories posit that money is created by the economy, exogenous theories place money as a ‘tool’ outside of the ‘real’ economy.

Mainstream, ‘neo-classical’ economics is based on exogenous theories and  describes money emerging as a tool to facilitate exchange. First there was barter,  but then the problem of a “double coincidence of wants” lead the rational caveman to introduce money. This description has no basis in fact. Just as astrophysicists use telescopes to look back in time, anthropologists visit isolated communities to see how society evolved, and the evidence of this research is summarised by Caroline Humphrey

Barter is at once a cornerstone of modern economic theory and
an ancient subject of debate about political justice, from Plato
and Aristotle onwards. In both discourses, which are distinct
though related, barter provides the imagined preconditions for the
emergence of money …[however] No example of a barter economy,
pure and simple, has ever been described, let alone the emergence
from it of money; all available ethnography suggests that there
never has been such a thing.

The barter $\Rightarrow$ money story originates in Plato and Aristotle and, unlike much of Aristotle’s physics, became integrated into modern science.

An earlier Greek writer, Herodotus, the first Greek historian writing some 150 years before Aristotle, recorded that the Lydians, from modern Turkey, invented games and money, implying that they were the first gamblers. The earliest tokens used as ‘money’ were not specific weights of a certain metal but roughly cut pieces of metal with an official stamp on them.

 Coins, tokens with a specific weight of a precious metal, emerged in the  Mediterranean and Near East at around the same time as states started employing mercenary armies. States paid soldiers in gold to conquer some community, the soldiers then spent the gold in the colonised lands and the state  recovered the gold by taxing the colonised merchants and innkeepers that the soldiers had paid for food and lodgings. Greek and Roman citizens never paid tax, only the conquered paid for the privilege and were bound to the conqueror by having to exchange their resources for the Imperial currency. The model would survive, known as the the State Theory of Money, and drive colonialism in the modern age. For example, in the 1920s the British taxed Kenya at a rate of about 75% of wages and forcing the colonised to grow cash-crops to be consumed by the colonisers. The Belgians did not tax the Congo – they relied on forced, rather than ‘free’ wage labour.   These observations are sometimes used to support the theory that markets are created by governments, they are a consequence, not a pre-cursor, of civilisation.

As well as Herodotus’ historical account of the introduction of money, the  Greeks had a mythological account. Athena was the goddess of wisdom, just war, the domestic crafts and agriculture. In summary, the Greeks associated Athena with the skills and characteristics of civilisation, and the image associated with this blog is from a mosaic of Athena (as Minerva) in the Library of Congress. She was born out of the union between the Titans Zeus and Metis, the goddess of prudence and cunning. However, Zeus had been warned that Metis would give birth to children who would challenge him, and so immediately after they had slept together, Zeus swallowed Metis whole, but too late to prevent Athena’s conception, and Metis’s pregnancy took place in Zeus’s belly. Sometime later, Zeus was struck down by a terrible headache and asked Hephaestus, the god of fire, metal working, and technology, if he could do anything about it. Hephaestus split open Zeus’s head and Athena emerged, fully formed and wearing armour.

Athens was named in her honour after she and Poseidon competed to become the city’s patron god by offering gifts to the citizens. Poseidon gave the city a brackish spring, which was the basis of the city’s sea power and prosperity through trade. Athena won the competition by giving the city the olive tree, which gave the city wood, oil and food. She is sometimes known as Athena Parthenos, indicating her virginity, and the Parthenon is her temple on the Acropolis, Athens’ citadel.

Hephaestus, who was the most loyal of the gods, had an arranged marriage with Aphrodite, but the goddess of love and beauty resented being married to the lame and ugly blacksmith and so spent her time with Ares. When Athena visited Hephaestus to have some weapons made, the frustrated blacksmith attempted to rape the virgin. She resisted and was able to escape, but not before Hephaestus ejaculated on her thigh. She wiped the semen of her leg  and onto the ground where it fertilised Gaia, the goddess of the earth. The result of the union was the mortal, Erichthonius, who was raised by Athena in the Parthenon and became King of Athens. The Greek tradition is that this king gave the citizens of Athens, the plough, the four-horse  chariot, he had inherited his father’s lameness and needed transport, and money.

This is a more absorbing story than the standard economic narrative that out of barter emerged money, the medium of exchange. As well as being more interesting it is possibly more meaningful, suggesting money is a consequence of a synthesis of civilisation, technology and agriculture with the influence of the war in the background. Money is central to society.

Athena and Hephaestus play another role in the development of economic theory, as characters in what is considered the first Greek text that addresses economics, written by the poet Hesiodwho probably lived around 750 BCE, an approximate contemporary of Homer.  Archaeologists identify the period around 800 BCE as the transition between the Bronze Age and the Iron Age, and while traditionally this was seen as a time of positive technological progress, the archaeological record paints a more disturbing picture. The transition from the Bronze to Iron Age in North Western Europe took place during a mini-ice-age between 850 and 760 BCE and is now associated with a switch from interconnected communities active in regional trade to isolated communities centred on Iron Age forts. The impact of the change was food shortages, conflict replaced trade and communities moved into the hilltop forts that are still features of the British landscape. The archaeological record for the Aegean at the time also suggests that climate change led to a long running famine and there was migration from the main city-states into new areas for farming. Hesiod’s father had been a farmer and merchant in north-western Anatolia, but the recession had forced him to move to Boeotia, a barren region about 100 kilometres north-west of Athens. When he died he left his estate to his two sons, Hesiod and Perses. The oldest of Hesiod’s poems, that still exists, Works and Days, is essentially the story of how Perses, a lazy good-for-nothing, bribed the local judges and obtained most of the father’s legacy, which he then squandered. Hesiod overcame the loss of his inheritance through hard work and ended up happier and richer than his brother.

Works and Days is split into two parts; the first explains how evil, the source of strife, first came about through the Myth of Pandora’s Box. The story of Pandora starts with the theft from Zeus of the secret of fire and from Hephaestus and Athena the crafts, by the Titan, Prometheus (‘forethought’). Prometheus had created mankind and passed these secrets on to humans. Zeus, not satisfied with punishing Prometheus for the theft by chaining him to a rock and having his liver eaten each day, decided to punish the mortals as well. He asked  Hephaestus to create a the first woman, Pandora, ‘all gifts’ who was given such characteristics as beauty by Aphrodite, cunning by Hermes and the skill to spin thread by Athena. Zeus ensured she was also lazy and
foolish.

Pandora was sent to Earth to seduce Prometheus’s dim-witted brother, Epimetheus (‘afterthought’), with a single possession a jar which had been given to her under the strict instruction never to open it. However, Pandora had been given the gift of curiosity, by Zeus’s long-suffering wife Hera, and so one day she opened the jar, which contained all the evils that afflict mankind; disease, strife, war and the need to work, and these all escaped into the world. Realising her mistake, Pandora put the lid on the jar, trapping the last thing left in there – hope. Hesiod is saying that work is necessary as a consequence of Zeus’s punishment of mankind, and the story bears a remarkable resemblance to that in Genesis.

The second part of the poem then goes on to say that people can free themselves from poverty and misfortune through hard work

Both gods and men are angry with a man who lives idle; but let it
be your care to order your work properly, that in the right season
your barns may be full of victual. Through work, men grow rich
in flocks and substance, and working they are much better loved
by the gods.

The final part of the poem is a practical advice on how to run a household, the word  ‘economics’ comes from the Greek for ‘household management’, and farming. The reason why this poem is considered an early economic work, rather than a straightforward myth, is that it identifies the role that scarcity has in determining  human behaviour. The gods make life a struggle for mankind, and so we have to work hard.

The Greeks recognised the significance of the relationship between Pandora  and Athena and the story of Pandora’s birth was featured on the base of Athena’s statue in the Acropolis. Just as with the myth of the origin of money, the Pandora myth might lack literal truth but it is rich in meaning. It highlights a causal relationship between understanding technology and a greater complexity in life that results in strife.

Today, many scientists, in particular social scientists, regard knowledge as  ‘shared belief’, not necessarily ‘justified belief’, science is less about ‘truth’ and more about ‘consensus’. Deirdre McCloskey, who is simultaneously a professor of economics, history and English at the University of Chicago, recommends an Italian definition of science

the speculative, agreed–upon inquiry which recognizes and distinguishes,
defines and interprets reality and its various aspects and parts, on
the basis of theoretical principles, models and methods rigorously
cohering

Science is speculative, not certain, and agreed–upon, not secret. It is on this basis  that society can begin to understand the value of science.

This definition of science allows economics to base itself on an unjustified myth  that barter evolves into money. However, it could alternatively allow economics to build itself on the Pandora myth, a myth that is remarkably similar to the story of the Fall in the Bible. It might be argued that the barter-money myth is un-scientific, since it is not supported by evidence, just as the Biblical myth is not supported by evidence. However, the barter-money myth endures because it conforms to two key characteristics of mainstream contemporary science. The myth is progressive, it describes a linear process where by the system evolves from a primitive beginning to the complex end we experience, and it is material, its explanations, involving people, goods and metal tokens, do not rely on metaphysical concepts such as society, trust or
belief.

Physicists will argue that, while social sciences can be built on such shaky foundations, the certainty of physics is not. This overlooks the fact that physicists are constantly disregarding old theories and building new ones. Physics is the  ultimate science because it is so eager to evolve. This makes it difficult to contradict, because it will embrace its contradictions, indubitable but not
immutable.

Notes

${}^1$Humphrey [1985, p 48]

${}^2$Ingham [2004, p 98]

${}^3$Ingham [2004, p 76]

${}^4$Gordon [2005]

${}^5$McCloskey [1995, p 6]

References

   B. Gordon. Aristotle and Hesiod: The economic problem in Greek
thought. Review of Social Economy, 63(3), 2005.

   C. Humphrey. Barter and economic disintegration. Man, 20(1), 1985.

   G. Ingham. The Nature of Money. Polity Press, 2004.

   D. McCloskey. The limits of scientific knowledge. In R.F. Goodman
and W. R. Fisher, editors, Rethinking Knowledge, Reflections Across
Disciplines. State University of New York Press, 1995.