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.

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.

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.

Markets, Morality and Mathematics

One of the key critics of Aquinas’ argument that a merchant could charge what heliked, providing the future was uncertain, was Pierre Jean Olivi, who was born near Béziers in Languedoc around 1248. Olivi entered the Franciscan order when he was twelve and was sent to Paris to study theology in 1267, and although he spent four years at the University he did not graduate with a masters degree. When he left Paris he appears to have started working on a theological work that took him over twenty years to complete and addressed a a range of questions, including the nature of free will. During this time he travelled widely in southern France and Italy and came into conflict with the Church hierarchy. 

Franciscans had an oath of poverty, and within a couple of generations of the founding of the order this oath began to be re-interpreted. Some Franciscans took the view that they kept to the oath if they did not own anything, others believed that this was a loop-hole, the oath required that a Franciscan should limit their use of goods. Olivi became a leader of this ‘rigorist’ or ‘spiritual’ wing of the Order. In 1282 he was accused of heresy and his writings destroyed, though he successfully defended himself in 1287 and was able to carry on teaching until his death in 1298. However, his tomb quickly attracted pilgrims and the Church, faced with a growing cult banned his writings in 1299, destroyed his tomb in 1312, and finally, when the Holy Roman Emperor, Louis the Bavarian, used some of Olivi’s arguments to attack the Papacy, he was condemned, again, as a heretic and all his works were obliterated. Umberto Eco’s book, The Name of the Rose, and the subsequent film, have these events in the background. 

Olivi’s fideism, the view that faith and reason are independent of each other and that you cannot rationalise faith, meant that he was sceptical towards Aristotelian empiricism and it was in this context that he made a revolutionary observation with regard to the selling of grain to the starving Rhodeans. He argued that the metaphysical probability of more grain arriving in Rhodes, giving the merchant excessive profits, had a certain reality, which Aquinas was ignoring by focusing on the ‘physical reality’ of the prices being offered in the market. Olivi said

 The judgement of the value of a thing in exchange seldom or never can be made except through conjecture or probable opinion, and not so precisely, or as if understood and measured by one invisible point, but rather as a fitting latitude within which the diverse judgements of men will differ in estimation.

This does not mean Olivi, despite his belief in absolute poverty, felt the merchant should charge a lower price for the grain. While Aquinas felt the market price was justifiable, but it was more moral for the merchant to lower the price, Olivi believed that the market mechanism was important. It was to the common good if prices did rise during a famine as it would encourage an increase in the supply of food.

Olivi applied this approach to the question of loans. As the historian Joel Kaye explains

if someone intends to invest his money in trade or profit, and instead, out of charity, lends the money to a friend in need, can he expect back from his friend not only the sum lent but in addition the profit he lost in not investing in trade? Olivi’s answer to this question was an unqualified yes: the borrower was responsible for indemnifying the lender for his loss of “probable profit”. and for restoring a “probable equivalence”.

 Olivi introduces the idea that market exchange is about equating expectations.

Olivi, despite his position in the Spiritual Franciscan movement, seems to have been a close observer of markets. As well as developing the ideas of Aquinas and Albert the Great, he commented that the market price depended not just on ‘need’ but on three factors; its scarcity, usefulness and desirability. Since desirability is subjective, different people will value the same good differently and based on these ideas, Olivi was able to explain the ‘value paradox’, why water, essential to life, was less valuable than gold, of no use, because gold is scarcer than water.

As a result of his condemnation for heresy, Olivi’s economic thought was retained only by a few Franciscans who secretly read his works, but, of course, could not acknowledge the influence he had on them. As a result has been only recently realised that the writings of another Franciscan, San Bernardino of Siena, were based on Olivi. Bernardino was born into a noble family in Tuscany in 1380 but was orphaned when he was six. Raised by an religious aunt he spent much of his spare time studying law and nursing the sick, remaining in Siena when it was hit by plague in 1400 and miraculously surviving. Bernardino became a strict Franciscan, abstaining from all pleasures, developed a reputation as an inspiring preacher, and now he is he regarded as the most important Italian missionary of the fifteenth century.

Just as it is surprising that Olivi observed markets, it is also surprising that such an ascetic as Bernardino wrote the first book on entrepreneurship, On Contracts and Usury between 1431 and 1433. Bernardino realised that to be successful a merchant had to be well informed; of prices, the qualities of goods and the market, be diligent in keeping accounts; be hard working; and, importantly, be willing to take on risk and he recognised that there were very few people who had all the these qualities. The book was written at a time when the Catholic Church had condensed morality into three ‘Christian’ virtues, Hope (Spes), Faith (Fides) and Charity (Caritas), and four ‘Pagan’ or ‘Cardinal’ virtues, Courage (Fortitudo), Justice (Iustitia), Temperance (Temperantia), and Prudence(Prudentia). An ethical life was one that exhibited all, not just some, of the virtues and within this context a merchant could, just as much as a knight, be seen as being ethical. 

Seven Virtues  c. 1460 Pesellino (Francesco di Stefano) workshop,  Birmingham Museum of Art, Birmingham, AL

The thirteenth century saw a flowering of European science, driven by a flood of classical texts being translated from Arabic. Aristotle became “the Philosopher” and his works came in for particular attention. In Nicomachean Ethics Aristotle considers the justice of economic exchange and argues that reciprocal, fair, exchange in the market as being fundamental to a well functioning society since it binds individuals together. Exchange is not performed in order to generate a profit, for gain, but to correct for inequalities and to establish a social equilibrium. So, for medieval scholars, like Aquinas and Olivi, the virtue of Justice should be central to the actions of a merchant.

Prudence is the ability to judge between different courses of action, it is at the root of reason and rationality and can be seen as the motivation for all science. This virtue is the one most closely associated, in the modern mind at least, with effective merchants. Temperance is the virtue least associated with modern bankers, its corresponding vice being gluttony. However, the modern understanding of temperance as denial is not only how a medieval friar would have understood the virtue. Temperance is at the root of humility, an acceptance that the human is not all-knowing. A good merchant would exhibit the virtue by allowing for the unforeseen, and consequently, diversifying, or at least not betting the house on a single venture. Prudence and Temperance complement each other.

Courage, the remaining Pagan Virtue, is demonstrated by the merchant in being able to commit to a risky venture. However, Courage untempered by the other virtues is rashness, and should be avoided.

Faith is the ability to believe without seeing, and was central to Olivi’s whole philosophy. The Latin root is fides, which gives federal, and captures the concept of trust, the very essence of finance. While Faith is backward looking, you build trust, Hope is its forward-looking complement. When Christian Huygens was translating his ‘On the Reckoning at Games of Chance’ from the Dutch into the more scholarly Latin he had a lot of trouble translating the word kans (‘chance’), which would normally be translated as sors. Eventually, he, or his editor van Schooten, chose expectatio , giving the English term ‘expectation’ (in the mathematical sense). While the English are left expecting, Huygens had also considered using the term spes, or ‘Hope’ and the French have taken this line, using the word espérance when referring to mathematical expectation. Statistics can be seen as the mathematical expression of Faith, while Probability captures Hope. Again, a merchant would need to express these virtues if they wished to be successful in business.

Charity, along with Temperance, is the virtue least likely to be associated with merchants. While we now think of charity in terms of giving to others, in the past it was associated with a love, or care, for others. When business people talk about being ‘customer focused’ they are talking about exhibiting the virtue of Charity. Shakespeare’s play The Merchant of Venice is not about the moneylender Shylock, but ‘Antonio, a merchant of Venice’ who characterises Christian love or agape demonstrated by his sacrifices for his young friend Bassanio. The view that Antonio and Bassanio were physical lovers is a modern misreading based on an ignorance that the medieval mind was much capable of distinguishing storge (famillial love), philia (friendship), eros (physical love) and agape (spitritual love).

In the U.S. the review of the financial crisis of 2007–2009 was not undertaken by the regulator, which was possibly not inclined to give a thorough and independent review of what crippled the economy, but passed to an independent commission, The National Commission on the Causes of the Financial and Economic Crisis in the United States. They concluded that

We conclude there was a systemic breakdown in accountability and ethics. The integrity of our financial markets and the public’s trust in those markets are essential to the economic well–being of our nation. The soundness and the sustained prosperity of the financial system and our economy rely on the notions of fair dealing, responsibility, and transparency. In our economy, we expect businesses and individuals to pursue profits, at the same time that they produce products and services of quality and conduct themselves well.

Unfortunately–as has been the case in past speculative booms and busts–we witnessed an erosion of standards of responsibility and ethics that exacerbated the financial crisis. This was not universal, but these breaches stretched from the ground level to the corporate suites. They resulted not only in significant financial consequences but also in damage to the trust of investors, businesses, and the public in the financial system.

Olivi and Bernardino would be spinning in their graves.

The status of morality and ethics in finance has changed significantly between the seventeenth century, when Huygens and Bernoulli constructed mathematical probability on the basis of commercial ethics, and today when ethics seems to have been expunged from the science of economics. The change point is often associated with the early Victorian period, associated with Romanticism. The ‘liberal’ philosopher John Stuart Mill argued that (political) economics

is concerned with [man] solely as a being who desires to possess wealth, and who is capable of judging the comparative efficacy of means for obtaining that end.

Around the same time, the future poet-laureate, Alfred, Lord Tennyson, wrote about nature “red in tooth and claw”. In 1859 Darwin published the On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life which explained evolution in terms of natural selection. In the popular perception, nature became seen as being driven by a bitter struggle for survival, un-regulated by a divine architect. Modern science was demoting man from being created in God’s image to the status of a higher ape, as Darwin wrote in his 1871 book, The Descent of Man

My object in this chapter is to shew that there is no fundamental difference between man and the higher mammals in their mental faculties.

The Descent of Man goes on to argue that “the civilised races of man will almost certainly exterminate, and replace, the savage races throughout the world”, and Adolf Hitler would be the champion of the Romantic triumph of will over reason in the twentieth century.

The reaction to Romantic Fascism was ‘positive science’, and consequence was the abandonment of six of the virtues from economics, and to focus on what Deirdre McCloskey has described as “Prudence Only”, blind rationality. Prof McCloskey is, perhaps, being too extreme, the widespread use of mathematics suggests residual Faith and Hope, but there has definitely been an associated lack of humility (Temperance) The irony is, ethics have been banished from finance, in the main, by academics teaching students to focus on ‘rational expectations’ (Prudent Hope) and ignore Temperance (the counterbalance to Gluttony) and Charity (the counterbalance to Greed), not because the markets are fundamentally unethical and immoral, but because this is seen to be “good science”.

Ian Hislop, the British commentator also discusses how banking changed around the time that Romanticism dominated culture in When Bankers Were Good.

Notes

${}^1$Kaye [1998, p 121]

${}^2$Kaye [1998, p 124]

${}^3$Kaye [1998, p 126]

${}^4$Kaye [1998, p 119], also Franklin [2001, pp 265–267]

${}^5$Rothbard [1996, pp 60–61], Kaye [1998, pp 123–124]

${}^6$Rothbard [1996, pp 81], Kaye [1998, p 118]

${}^7$Rothbard [1996, pp 81–82]

${}^8$Kaye [1998, p 51]

${}^9$Hacking [1984, p 95]

${}^{10}$FCIC [2011] p xxii

${}^{11}$Sylla [2006], Sylla [2003]

${}^{12}$Friedman [1953]

${}^{13}$Persky [1995, quoting Mill, p 223]

${}^{14}$MacCulloch [2009, pp 861–862]

${}^{15}$Darwin [1871, pp 36]

${}^{16}$Darwin [1871, pp 200–201]

${}^{17}$McCloskey [2007]

References

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