Tuesday, 20 March 2018

The Golden Rule

There are two versions of the Golden Rule. The standard is “ Do to others what you want them to do to you” and appears in most developed religions. Colloquially it is “Those that have the gold, make the rules”.

Someone raised this distinction on my work in financial ethics by asking “Are you saying participants in financial markets should be benevolent in how they price instruments?” They answer rhetorically with the observation that the reality is that the markets are motivated by greed and fear with leading market participants acting in a ‘brutish’ manner that motivates the rest to conform. On this basis, ethics needs to be ‘realistic’ in referencing the ‘facts on the ground’ and accommodate human nature. Faced with this reality, you can try to ensure the regulator is of good character (‘superiorly prudent’ to use Adam Smith’s language) and might be able to improve the functioning of markets.

My correspondent referred me to the Menian Dialogue in Thucydides History of the Peloponnesian War as an example of ‘realism’.

This was interesting to me. While I don’t know the full context and Thucydides’ intent, I am confident that there is a widely held view that the behaviour of the Athenian negotiators was an example of hubris; the Menian negotiator even notes that the gods would be on their side. The subsequent defeat of Athens was therefore nemesis. My justification was that hubris/nemesis was a central theme of Greek classical culture along with the idea that a human can never be so sure as to be certain. The Athenian’s were confident that they could sack Menos without fear of reprisal; they were wrong, and I understand the Athenians surrendered to Sparta because they were concerned about the precedent they had set at Menos. Note that there is an important financial connection: the term Romans used for interest was poine the spirit that accompanies Nemesis.

A related topic is this Stoic problem:

A grain merchant from Alexandria arrives at Rhodes, which is gripped by famine.  The merchant knows that other merchants are following him with plentiful supplies of grain, though the town’s inhabitants do not know this.  How should the merchant price the grain he has? 

Cicero, in De Officiis, had argued that the merchant should charge a lower price based on the knowledge of the coming relief. Thomas Aquinas disagreed; the merchant may think that there are more grain shipments on the way, but they do not know. Hence the ‘reality’ of the market prices in Rhodes could be employed. The Franciscans took a different approach, Pierre Jean Olivi, argued that the metaphysical probability of more grain arriving in Rhodes, had a certain reality, which Aquinas was ignoring by focusing on the ‘physical’ reality of the prices being offered in the market. Olivi observed that

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.

Olivi realised that market exchange was about equating expectations, not accepting concrete valuations agreed by property owners.  This was a major development over the Pythagorean approach of fixing the relationship between an object and a number.  Olivi regarded uncertain events ‒ such as more grain deliveries, lost ships, or defaults on debts ‒ as influencing prices and so fair exchange had to be based on the sharing and interpretation of information.  This meant that chance could be quantified, and there is a consensus that this observation is the genesis of the idea of mathematical probability.

Changing tack a bit to the issue of ‘power’. I have recently been looking at Beowulf. Beowulf is a rare example of pre-Christian northern European myth and raises the question, why did it survive? One explanation is that it highlighted the transitory nature of human power and so was useful story that Christian missionaries could use in emphasising the transcendent nature of divine power. The Norse myth of Ragnarok has similarly survived and similarly describes the temporality of power (the ‘Muspille’ interpretation). There is a similar structure in the relationship between the Illiad and Odyssey. Anger, honour and power motivate the Illiad whereas Odysseus personifies intelligence (cunning) and a desire to return to domesticity. To me, all these myths emphasise that society has to evolve away from one based the ‘reality of power’ to one based on the application of intelligence. The pragmatic explanation is that a society based on rational reflection and discourse is better able to respond to uncertainty; this is why democratic societies thrive.

These thoughts develop something I touch upon in my book is that there is a train of thought linking Thucydides, Hobbes, Descartes, Spinoza and through to Nietzsche and Schmidt that focuses on the reality of power that I reject. The problem, as I see it, is finance is fundamentally concerned with uncertainty. This means that one day you might clearly perceive what is in your best interests (Athens' subjugation of Melos) but you misunderstood, resulting in catastrophe. This is the pragmatic line, which emerged with Pierce's rejection of Cartesian certainties that he saw at the root of the US Civil War. Cheryl Misak's Truth, Politics and Morality informs me that the antidote is deliberative and I give a series of examples in my book about how (well functioning) markets undermine power. On this basis, I take a pragmatic position on ethics, i.e. culture is an environment in which practices that “work” evolve and these become habituated (the approximate origin of the Greek root of ‘ethics’, the Latin root of ‘morals’). For example, if a society wants to grow its population, contraception and abortion become immoral; if a society wants to limit population growth, they become legitimate.

On the specific issue of benevolence, I introduce the idea of charity in commerce through Shakespeare's The Merchant of Venice, which I present as an argument against "iron laws" and in favour of "merciful judgement"; that is don't trust the model but use judgement. I describe how British finance was built on Quaker institutions that had charity/benevolence as a keystone and there are numerous accounts of how they were able to prosper in a very uncertain environment because they put great store in charity, reciprocity and sincerity. Finally I describe the collapse of LTCM as being a consequence of a lack of charity. LTCM believed it was impregnable (like Athens) and so did not feel the need to act charitably. The account of their failure I use is they got the structuring of a fax wrong ("We need more money because the markets are in turmoil and there are lots of opportunities" instead of "There are lots of opportunities because the market is in turmoil, do you want to invest?") and in the resulting run they had no reliable friends.

Financial crises, I believe, can be characterised as representing a paradigm change, where an old ‘reality’ is replaced by a new reality. In order to inhibit the development of crises, people need to be doubtful of their circumstances and there need to be ways to allow opinions to change slowly without a (mathematical) catastrophe. There is the example of how the powers who created the Bretton Woods system could not conceive of the eclipsing of British and French power by German and Japanese economic might in the 1960s. J. P. Morgan doubted the profitability of CDO of MBS and so investigated the apparent reality and survived the crisis of 2007-2009; I think J.P. Morgan was like Odysseus where as Lehmans was more Achilles.

In my book, I try and bring these themes together by addressing the issue of voluntary slavery. Consequentialst/utilitarian ethics cannot reject voluntary slavery coherently, and so cannot reject slavery. The ‘reality of power’ cannot reject slavery. Deontological ethics, like Kant’s, can reject slavery. Pragmatic ethics rejects slavery on the basis that any rational opinion might be valid in solving a problem/prompting a gradual change in opinion. Since slaves are silenced from giving opinions, therefore slavery cannot be tolerated.

I believe my approach is coherent with Adam Smith, mainly because Smith worked within the Aristotelean framework. In the Theory of Moral Sentiments I note that Smith compares ‘prudence’ with ‘superior prudence’ as

Prudence, in short, when directed merely to the care of the health, of the fortune, and of the rank and reputation of the individual, though it is regarded as a most respectable and even, in some degree, as an amiable and agreeable quality, yet it never is considered as one, either of the most endearing, or of the most ennobling of the virtues. It commands a certain cold esteem, but seems not entitled to any very ardent love or admiration.

Wise and judicious conduct, when directed to greater and nobler purposes than the care of the health, the fortune, the rank and reputation of the individual, is frequently and very properly called prudence. We talk of the prudence of the great general, of the great statesman, of the great legislator. Prudence is, in all these cases, combined with many greater and more splendid virtues, with valour, with extensive and strong benevolence, with a sacred regard to the rules of justice, and all these supported by a proper degree of self-command. This superior prudence, when carried to the highest degree of perfection, necessarily supposes the art, the talent, and the habit or disposition of acting with the most perfect propriety in every possible circumstance and situation. It necessarily supposes the utmost perfection of all the intellectual and of all the moral virtues. It is the best head joined to the best heart. It is the most perfect wisdom combined with the most perfect virtue. It constitutes very nearly the character of the Academical or Peripatetic sage, as the inferior prudence does that of the Epicurean.

For Aristotle, reciprocity was a component of justice. Justice, itself, was, according to Plato, the virtue that ensures a functionally differentiated system, such as a society, works well. Therefore, my treating markets as centres of communicative action, governed by reciprocity, sincerity and charity, fits within Smith’s framework of ‘superior prudence’ as well as classical conceptions of the relationship between the polis and the individual, since the ideas are rooted in classical theory.

Friday, 2 March 2018

Mathematical Finance

I wrote this piece for the National Institute for Economic and Social Research's Rebuilding Macroeconomics project.
There are three types of mathematicians: those that can count and those that can’t. This aphorism challenges the public perception of mathematics as being concerned with calculation and is liked by mathematicians because it enables them to highlight what mathematics is concerned with, which is identifying and describing relationships between objects.

A more sophisticated misunderstanding relates to the way mathematics is conducted. The error originates in how mathematicians present their work, as starting with definitions and assumptions from which ever more complex theorems are deduced. This is the convention that Euclid established in his Elements of Geometry and led Kant to believe that synthetic a priori knowledge was possible. Euclid actually started with Pythagoras’ Theorem, and all the other geometric ‘rules’ that had emerged out of practice, and broke them into their constituent parts until he identified the elements of geometry. It was only having completed this analysis did he then reconstruct geometry in a systematic way in The Elements. Today the consensus within mathematics is that the discipline is analytic, from observations, not synthetic, outside of mathematics there persists a belief in the power of pure deductive, synthetic a priori reasoning.

Physical sciences are in tune with what mathematicians do. This is exemplified by Newton who gathered observations on the planets and invented calculus to interpret the data. On this basis he concluded that momentum was being conserved and deduced the gravitational law. The key idea originating with Newton is that momentum is an invariant in a dynamic system. This is understood most clearly when presented using calculus, the mathematics Newton invented. Since Newton, all significant advances in physics have been associated with the identification of an invariant (momentum, energy, increase in entropy, speed of light) and inventing clear and succinct ways of describing objects (mathematics) that re-presents nature based on an invariant.

Finance has developed a mathematical theory in the Fundamental Theorem of Asset Pricing that has the same status in mathematical finance as Newton’s Laws have in classical physics. The central principle, analogous to the conservation of momentum, is that of ‘no-arbitrage’. The Fundamental Theorem of Asset Pricing states that if an asset is priced on the principle of no-arbitrage then there is a reciprocal relationship in the exchange. There are at least two ways of understanding this principle. It is a version of Euclid’s ‘First Common Notion’: if A=B and C=B, then A=C. Money takes the role of “B” and arbitrates the value of A relative to C. Alternatively, it is a version of the scholastic argument that a riskless profit is a shameful gain (turpe lucrum).

The no-arbitrage principle is justified through Ramsey’s ‘Dutch Book Argument’ that requires markets are mediated by jobbers (market-makers or dealers in the US) rather than brokers. When a jobber quotes a price, they do not know whether the counter-party is looking to buy or sell at the price. The jobber will quote a price at which they will buy and a higher price at which they will sell. They signify confidence in their quote by having a narrow difference between the prices. If a jobber quotes a price that another trader believes is wrong, the trader will take the quote, immediately moving the market. These jobber-mediated markets are, therefore, essentially discursive. Jobbers are engaged in making assertions as to prices, which are challenged when others take the quote; this is ‘market making’. If the market agrees that a jobber has correctly priced the asset, no trading will take place - silence is consent - and the market dissolves.

Jobbers do not hold assets and prefer trading in financial contracts rather than hold physical assets, they have no commitment to the assets they trade and identify themselves as taking long and short positions rather than buying or selling. While they lack commitment to assets, jobbers must be sincere in their statements, they must believe the quote is right. This means, that in the face of radical uncertainty, a jobber’s price quote is reliable, it can be trusted.

The significance of reciprocity in markets rests on the no-arbitrage principle that can only be justified if exchange is being conducted by jobbers, who will buy and sell at the quoted prices. Markets in economics tend to be based on brokers who bring property owners, one a buyer, one a seller, together. The focus on broker-mediated markets rather than jobber-mediated markets means that the importance of reciprocity in exchange is obscured. The different emphasis is rooted in financial markets being concerned with uncertain futures whereas economic markets are concerned with immediate scarcities.

In modern business, if a manufacturer can sell a product at an enormous profit, creating an arbitrage, they are succeeding. Economic theory argues that in the presence of these excess profits, competitors can come in and the price of the product will fall. This appears to be no different to the situation in a jobber-mediated market: jobbers will bid (buy) at the cost of production and offer (sell) at that cost plus a risk premium, just as manufacturers will do in a competitive broker-mediated market. However, while the ultimate point might be the same for jobber and broker mediated markets, the routes to the point are different. For jobbers, no-arbitrage, and hence reciprocity, are iron laws that must not be breached, ever. In broker-mediated markets, arbitrages are transitory and the ideal is to capture them before they disappear; it is a virtue to break the principle of reciprocity. Prices at which exchange takes place in jobber-mediated markets are always disputed prices, but sincere; in broker-mediated markets, prices are always accepted, if not fair.

Consider some thought experiments. If a manufacturer, making arbitrage profits, was obliged to buy identical goods, manufactured by others, at the prices they themselves quoted, would they quote the same price? If a slum-landlord had to live in the accommodation they rented, would they rent inferior quality accommodation? Public services are often expensive because they are of a quality that the providers would like to receive. These examples highlight the ethical nature of dual-quoting, it imposes the categorical imperative: do unto others as you would have them do unto you.

Financial instability has long been blamed on jobbers, who trade ‘paper’ and lack commitment to material assets, they are 'disinterested'. However, bubbles are a consequence of property owners ‘ramping’ assets and selling them above their intrinsic value. The failure of Long Term Capital Management in 1997 was precipitated by an apparent arbitrage, in the ‘asset swap’ strategy involving rock-solid US government debt, being an illusion. The Credit Crisis was a result of investment banks believing they could construct mortgage backed securities (MBS), out of ‘real’ assets, for less than their worth, not realising the inherent risks because they believed in arbitrages. Investment banks have been fined for selling MBS above their internally recognised value; they were being profit maximisers but insincere. There is evidence that the ‘Bitcoin’ bubble of December 2017 was a consequence of it being easy to buy Bitcoin, but difficult to sell; something not possible in a jobber-mediated market. These are all situations where financial instability originates in a belief that the no-arbitrage principle could be ignored or that prices could be insincere, and so it was possible to earn risk-less profits.

Recognising that the no-arbitrage principle is analogous to Euclid’s First Common Notion means that arbitrageurs should be regarded in the same way as promoters’ perpetual-motion-machines are: mis-guided cranks. It also emphasises that exchange should be reciprocal, it should not involve profiting at another’s expense. Mathematics only works on the basis of Euclid’s First Common Notion; markets only work well on the basis of reciprocity.

Monday, 7 August 2017

Antifragility and justice

Towards the end of last week I noticed a flotsam on my Twitter feed coming from a storm involving NN Taleb and the prominent British classisist Prof Beard. The origins were in a BBC schools animation that depicted a Roman soldier as dark skinned. This elicited a response on Infowars that the BBC was re-writing history. I was interested in this because that week my family had driven down to the Vindolanda and Roman Army Museums on Hadrian’s Wall and I had been struck that a significant portion of the garrison at Vindolanda came from Hama in Syria, a region familiar today as being a source of refugees into Europe. Taleb was attacking Beard for being part of the conspiracy. Since the evidence for Syrians at Vindolanda comes from written records discovered in the 1970s, I cannot believe the ‘left’ are that competent at formulating such a clever consipiracy.

[PS there are links between Financial Mathematics and the mathematics of population genetics: Alison Etheridge is prominent in both fields.   My gut instinct was the apparent lack of non-Caucasian genes in the current British population was not evidence of their having been non-Caucasian Romans in Britain.  @mpigliucci explains this and highlights how Taleb is a victim of his own biases.]

I was also interested because Taleb was involved. Along with many academic mathematicians working on finance I do not have a strong affinity with Black Swan or Fooled by Randomness. The reason why is as follows. Taleb, along with other ‘public’ financial mathematicians like Elie Ayache and Doyne Farmer, were part of a cohort of applied mathematicians, engineers and physicists who entered finance in the 1970s and 1980s, were successful, became rich and have used that wealth to direct public perceptions of financial mathematics. At the time, option pricing was accomplished by solving partial differential equations and these ‘quants’ had expertise rooted in dynamical – deterministic – systems (note that Taleb’s mathematical PhD in Management Science was awarded in 1998, not before he went into Finance with an MBA). There is a sense amongst most actuaries and financial mathematicians, trained in probability theory, that Taleb’s books resonate with this audience because the books highlight the significance of randomness, something these people were not really educated in. As one senior British actuary said to me: “What does Taleb think actuarial science has been concerned with for 300 years if not Black Swans and not being Fooled by Randomness”. This frustration reflects decades of ‘quants’ in banks regarding actuaries as being ponderous dinosaurs.
A profile of Taleb by Malcolm Gladwell (who shares Taleb’s skill for simplification) suggested that Taleb’s ideas are founded on his experiences of the Lebanese civil war and surviving cancer. While Taleb dismisses this I wonder if there is some truth in the theory. Taleb is concerned with how people face up to uncertainty and how they respond, discussed most recently in Antifragile. I share this concern but have been dissatisfied with Taleb's arguments, in particular I feel that Taleb believes, like many of his colleagues, that there are individuals peculiarly able to make judgements under uncertainty. This was part of the motivation for writing Ethics in Quantitative Finance.
My reasoning is based in mathematics, which is subtly different to Taleb's which just uses mathematical symbolism. Consider a closed system of 100 agents, each initially endowed with $45. Now, at each time step each agent randomly gives another agent $1. What do you think the distribution of money should be? The immediate thought might be the distribution would remain uniform, with a little noise. However, this not the case, as presented in a nice simulation. Some people will end up with lots of money, others will be bankrupted. The rich can become rich simply through luck, not skill. This should not perturb the likes of NN Taleb or Robert Mercer, since the model does not consider how genius might skew the distribution, extending the right tail at the expense of the middle. It is more challenging to the 'left' who might seek to implement policies that make the wealth distribution more uniform, since such policies might be considered to be equivalent to pushing water up hill.
Moving on, there are some points that were made with respect to my last post about maths in economics that are important in understanding my approach. One comment was that
The more fatal weakness of this line of argument seems to me the starting assumptions: mathematics involves "identifying how we see relations between objects." That seems right, but left undefined here is the term "objects." What exactly is an object?

In mathematics, an object is something we can quantify. Now comes the problem: in economics, what we need to identify is the relation between emotions (greed, fear of loss, investor euphoria, etc.) and behavior (buying, selling, tolerance for risk, and so forth).

Alas, this requires that we mathematize emotions. To my knowledge, no one has succeeded in doing this in some 8,000 years of recorded history.
I take a less pessimistic view. Plato split the soul into three parts. The epithymetikon (‘from the heart’) was the part of the soul concerned with carnal desires, sometimes represented as a black horse. Alongside this was the thymoeides (‘spirit’) and represented energy and the motivation to act, this was sometimes represented as a white horse. The third component was the logistikon (‘reason’, from logos the Greek for ‘what is said’) or nous (‘mind’) that distinguishes right from wrong, which Plato associated with the Athenian temperament. The logistikon was sometimes represented as a charioteer controlling the other parts of the soul, making sure that the spirit would not become dominated by carnal desires, which would be wrong. Through the medieval period these ideas became refined into one of balancing passions and interests. This did not involve quantification, which is only a small part of mathematics, but by identifying a balance point, which involves measurement. Adam Smith's great contribution, according to Albert Hirschman, was in enabling the quantification of passions and interests through money, precipitating capitalism tied up with utility maximisation. My argument in EQF is that part of the long story of financial mathematics is concerned with this balancing of passions and interests and this was considered to be a question of Justice. This predates Smith's quantification of passions and interests,. When mathematics was dominated by geometry, this was considered in terms of proportions, but with monetisation came arithmetic.
Justice, according to Socrates and taken up by Plato and Aristotle and their heirs, is the quality that a complex, functionally differentiated system (a society) needs to enable it to work well. On this basis a society is Just when it enables individuals, who all have different capacities and capabilities, in the society to do their best by allowing them to do what they are best at. This relates to comments relating to the use of mathematics in economics raises, that people are different and so cannot be reduced to a mathematical representation (e.g. "The rigidity of mathematics makes it difficult to fully capture the richness and complexity of human behaviour "). This is true, however I highlight how financial mathematics is founded on reciprocity which is a component of Justice, and this is the fundamental invariant not just in finance, social systems in general but across any functionally differentiated system. The mathematics of the Fundamental Theorem of Asset Pricing is not involved in quantification but is concerned with ensuring Justice.
On the basis of this definition of Justice the universe is Just, since it works well as a complex, functionally differentiated system. It is concerned with different things being in the correct balance and is different from the idea that justice is based on everything being the same, which might be characterised as a 'left-wing' approach.
Now we can return to Taleb's account of "Antifragility" that starts with
Antifragility is ... behind everything that has changed with time: evolution, culture, ideas, revolutions, political systems, technological innovation, cultural and economic success, corporate survival, good recipes (say, chicken soup or steak tartare with a drop of cognac), the rise of cities, cultures, legal systems, equatorial forests, bacterial resistance … even our own existence as a species on this planet. And antifragility determines the boundary between what is living and organic (or complex), say, the human body, and what is inert, say, a physical object like the stapler on your desk.
This excerpt immediately raises the question: what is the difference between antifragility and Socrates' conception of Justice. Critically I have removed part of the text, which actually begins
Antifragility is beyond resilience or robustness. The resilient resists shocks and stays the same; the antifragile gets better.
Suggesting the antifragile is about improvement, but I don't think this establishes any clear water with the ancient philosophers. Furthermore the argument that the best antidote to fragility is "skin in the game" is not so different from the Enlightenment attitude, espoused from Locke to Kant, that only property owners could participate in democratic politics. The issue here, and dominated British politics for much of the nineteenth century, was that this excluded the majority from participating in democracy. Taleb's conclusion refers to the Golden Rule "Do to others what you want them to do to you".
These observations suggest that Taleb's argument in Antifragile is close to mine in EQF. The difference is I focus on how the idea of Justice is embedded in financial mathematics, why this is so and what it implies. My conclusion is that in oredr to be able to manage radically (Knightian/non-ergodic, etc.) uncertainty a broad range of opinions need to be solicited and considered and so markets are discursive arenas and must address truth, truthfulness and rightness. Taleb suggests the essence of his book is "Everything gains or loses from volatility. Fragility is what loses from volatility and uncertainty." This seems a little trite to me, echoing the actuary: "What has civilisation been worried about for 4,000 years?" The problem, as I see it , in Taleb's book is that he leaves himself open criticisms captured in a paper by Andrea Terzi (in what I would class as a 'left-wing' journal). The point Terzi makes is
Taleb admits that the system cannot be made foolproof to BSE [Black Swan events] but believes it can be made more resistant through some form of economic and social Darwinism. His prescriptions include consenting that what is fragile breaks early and never gets too big to endanger the system should a BSE appear; letting economic players who make errors be punished for their failures; not precluding recessions from mopping up the system from the unfit to survival; and not indulging in debt.
Taleb seems to have slipped into pseudo-Nietzschean philosophy that distinguishes man and superman. He seems to identify with the supermen and denigrates most scholars as 'imbeciles'. This view has been supported in the evidence of responses supporting Taleb's attack on Beard from, what look to me like, neo-Nazis. My concern is that I feel the problems of finance, that Taleb purports to solve, are about an obsession with identifying 'geniuses' at the expense of deliberation and doubt. 
 I am not allowing comments on this article as I anticipate they will be dominated alt-right abuse.

Thursday, 27 July 2017

Why mathematics has not been effective in economics

There are three types of mathematician: those who can count and those who can't.

It takes a few seconds to get this joke the first time you hear it, and every once and a while when I tell it to a class one student will raise a hand and asked for the 'third type'. Its a good joke because it challenges assumptions, here the assumption is that mathematics is concerned with arithmetic, which is just a minor branch of number theory.

At the end of June, before I went on holiday, I had been thinking about the role of mathematics in democracy. This was prompted by an invitation from a Norwegian mathematician to do some work in the topic. I contacted @BrendanLarvor asking who were the main scholars in the area. He pointed me to a recent paper that discusses a key issue. Many people see the role of mathematics in democracy as educating the public so that they can do their own calculations. Citizens are able to calculate the cost/benefit of Brexit, for example. But calculation is not what mathematics is concerned with. The paper is not an easy read but highlights the awareness amongst (some) mathematicians that mathematics is not straightforward. In particular the phrase "the role of mathematics in formatting the world as we experience it" resonated with me as being a key issue.

This led me to think about the role of mathematics in defining how the disciplines of finance and economics are arranged. A consequence of this was I invited people to answer a short survey on "Does a mathematical proof enhance a financial theory?". The survey was widely distributed (via @MarkThoma amongst others) but only elicited seven responses. The results are here (the survey is still open, btw). I was disappointed that only seven people seemed to share my interest to the degree that they would spend a little time answering the question. I concluded that either people were disinterested (possibly because they thought the question was trivial, like "Does water flow downhill") or that they did not understand the question (they do not feel confident about what is meant by a 'mathematical theory').

On returning from holiday, I noticed that @freakonometrics had retweeted an article from aeon about how "By fetishising mathematical models, economists turned economics into a highly paid pseudoscience" 

and then @rethinkecon sent out this

I have the opinion that almost all of the criticism of the use of mathematics in economics stems from a lack of understanding of what mathematics is, reflecting a general ignorance in economics that has led to the failure of mathematics in economics. To get an idea of my frustration consider the following argument about journalism. One might observe that there are many more photographs in newspapers today than there were 100 or so years ago. Using the argument that the problems of economics are in its use of mathematics is rather like saying the problems of contemporary journalism is down to photography.

The starting point of understanding the role of mathematics in finance and economics is to appreciate what mathematics is concerned with. Mathematics is concerned with identifying relations between objects: bigger smaller, to the left/right, symmetry, before/after and so forth. Top class mathematical research is concerned with discovering new ways of representing how things are related. More every-day research shows that A=B or how you go from A to B. Once the mathematicians have done their work, of "formatting the world as we experience it" by identifying how we see relations between objects, others then get on and do things. Mercator figured out how to make maps - a mathematical operation - sailors then used the maps and in the process forgot that what they were doing was using mathematics.

Mathematicians rely on other disciplines providing problems, mathematics, whatever the caricature of a mathematician dealing with abstract ideals will say. Mathematics then figures out a way of looking at the problem - the relations between its components - so that a solution can be found. The caricature of the mathematician is explained by how mathematics is presented. Rather than starting with the problem and then breaking it down into its components, mathematics is presented back to front. It starts with the components and then shows how these combine to deliver the observed phenomena. This 'back-to-front' approach originates in Euclid. The theorems at the end of Euclid's Elements were all well known hundreds, if not thousands, of years before he wrote The Elements around 300 BCE.

Euclid's approach is useful in that it identifies the essential elements of a theorem, these elements can be the used to construct novel theorems by combining them in innovative ways; think of a mathematical assumption as a chemical element and a theorem as a useful molecule. However there are a number of problems resulting from the way mathematics is presented. One effect is encapsulated in Kant's argument that synthetic a priori knowledge was possible. Kant used the example of Euclid to argue that it was because he had assumed Euclid had deduced the theorems from first principles. This is significant in that this fallacious argument was a foundation of Kant's rejection of Hume's claim that a necessary cause of an effect could never be identified. Another effect is it provides a model for a powerful rhetorical form that is persuasive, it was used in particular by Hobbes and Spinoza while Aquinas' writing has been compared to mathematics. Today 'mathematical' proofs that 1=2 are commonplace. More significantly this 'mathematical' approach was used by Hobbes to argue that if a highwayman offered you the choice of 'your money or your life' and you handed over your money, you were giving consent. It is not easy to discern flaws in these 'mathematical' arguments, and this is the day to day job of research mathematicians (a social scientists once Tweeted they had had a productive day, reviewing three papers: as a mathematician it will take me a week of hard graft to review a 10 page paper).

The effect in economics is most clearly seen in Friedman's argument, in the Methodology of Positive Economics, that the validity of an economic theorem should not rest on the realism of its assumptions. I will not dismiss Friedman as the arch-priest of neo-liberalism as I think the argument he makes has some merits (he focuses on the empirical outcome and would normally be regarded as 'anti mathematiciastion'). The attitude he shares with most economists, along with Kant, Hobbes and Spinoza, is that a 'mathematical' argument flows from assumptions to conclusions. A mathematician approach would be to try and tease out the correct assumptions from the observed behaviour. I would prefer the problem to be re-cast as "By fetishising synthetic a priori knowledge, economists turned economics into a highly paid pseudoscience".

The next question is why do economists do this. The answer is rooted in the observation that the 'mathematical' approach is powerful rhetorically: you can use it to convince everyone of almost anything, providing you can make the chain of arguments tricky enough to follow. From a philosophical perspective, Kant distinguished the ‘lower faculties’, such as mathematics, that would consider matters of pure reason independently of the concerns of the state from the ‘higher faculties’, engineering, jurisprudence, medicine and theology, were concerned with matters of authority and would be regulated and monitored by the state. If economics is mathematical it should inform the state, not be directed by the state, if it is not then it will have the same status (and funding) as theology (and, one would suppose, other modern social and human sciences).

More practical motivations were characterised by Frank Knight, who, around 1920, felt that economics had split into two strands. There was a mathematical science, which studied closed systems based on distorting assumptions, and a descriptive science, which could deduce nothing. Economics needed to take a middle path that was both realistic and informative. However, before the Second World War, most economists doubted the usefulness of mathematics in addressing problems involving radical uncertainty and human volition, such as the economy. These attitudes changed when it was seen that mathematics had transformed how the war, a similarly uncertain and human activity, had been fought; operations research, cryptography, supporting the physics of radar and weapons. Based on this experience and government faith in mathematics, economics began presenting itself as a mathematical science after the war. Two publications of 1944 led this transformation: The Probability Approach in Econometrics by Trygve Håvelmo and The Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern.

Håvelmo argued also that if economics wanted to be taken as seriously as physics, chemistry and biology, it needed to employ probability because that was the way that opinions were expressed in science. He believed that if this was done, economics would make new insights, just as physicists and biologists had. He also observed that the natural sciences had found a perspective on nature that made it appear to follow stable laws. The goal of The Probability Approach in Econometrics was to present how this could be realised. Morgenstern began The Theory of Games, like Håvelmo, with an argument for the use of mathematics in economics and explained that what was required was the careful definition of terms, a pre-requisite of mathematics but lacking in economics. To this end, von Neumann started with the axioms of utility that had been at the core of Carl Menger’s, unmathematical, economics.

When Håvelmo was awarded the Nobel Prize for Economics in 1989 he reflected that his aspirations for introducing mathematics to economics had not been met. He identified the primary issue as being that the economic models that ‘econometricians’ had been trying to apply to the data were probably wrong. More fundamentally, economics never generated new mathematics ‒ ways of seeing relationships ‒ in the way that the physical sciences had stimulated developments in mathematics. Economists had simply adapted concepts from other fields to their own devices.

To my mind, Håvelmo captures why mathematics is not unreasonable effective in economics. It is because economists use mathematics as 'part of the plumbing', a rhetorical tool to convince an audience of an argument. The  Unreasonable  Effectiveness of Mathematics in the Natural Sciences is founded on the fact that the natural science use mathematics to figure out relationships. The one exception to this rule (that I am aware of) in modern economics is the Fundamental Theorem of Asset Pricing, formulated by Harrison, Kreps and Pliska around 1980 (I dismiss game theory as this was originated in the early 1700s). The FTAP is analogous to the Mercator projection, it describes the basis on which models (maps) are made that guide probationers (navigators). “A market admits no arbitrage, if and only if, the market has a martingale measure” establishes a relationship.

Once mathematics has delivered ways of identifying relations in physics, 'invariants' can be identified, such as momentum, energy or the speed of light (Noether's Theorem is critical here). Physical theories are then tested on the basis of whether or not they adhere to a particular conservation law. Because economics is disinterested in using mathematics to identify relationships it has been unable to accomplish the next step of discovering invariants. It has tried, notably by sometimes hoping 'money' is an economic invariant.

In writing Ethics in Quantitative Finance (the points made here are expanded upon in the book) one of my aims was to think of finance as a mathematician. That is to consider the fundamental relationship, as expressed in the FTAP, and then think about what this implies as to the fundamental invariant. My conclusion was that reciprocity - and equality between what is given and received - is the invariant and I explore why this might be so. The hope is that finance and economics can actually achieve something useful for the wider community.

Friday, 23 June 2017

Political and Financial Crises: some connections between the Credit Crisis and the current crisis in UK politics

My book, Ethics in Quantitative Finance, was motivated by the wish to understand the relationship between mathematics and financial ethics in the aftermath of the Credit Crisis (GFC).  While the GFC occured a decade ago, the topics discussed in Ethics in Quantitative Finance are still relevant today as the UK endures a "Great Political Crisis", a year after voting to leave the European Union.  Had someone drawn a connection between mathematics, ethics and politics for me in 2006 I would have ignored them, suggesting that the scholarship underpinning the book is transformative.

A fundamental insight made in the book is that when market-makers (jobbers or dealers) give a  bid-ask quote, they are offering an opinion and so money is behaving as a language that carries that opinion in prices.  On this basis, I employ Habermas' theory of communicative action and in this context the book describes how mathematics ensures the objective validity of a price by ensuring reciprocity, the dual quoting ensures sincerity and the truthfulness of the price while the social rightness is delivered by charity.  I argue that these norms, truth, truthfulness and rightness, are developed in commercial practice and provide the basis for democratic discourse.  That is, sound politics are a consequence of sound commerce and I provide examples in pre-Socratic Greece, the emergence of bourgeois communes in high medieval  Europe and seventeenth century Britain and the Netherlands.  I also highlight that there is a symbiotic relationship between finance and politics: sound finance delivers sound politics, sound politics deliver sound finance.  Pre-Socratic Greeks understood that if there emerge wealth inequalities the political stability collapses but mathematics, by ensuring reciprocity, inhibits the emergence of inequality, and this is a theme returned to throughout the book.

The idea that reciprocity is deeply embedded in financial economics was fully formed by around 2011 - the RCUK, the UK government's research administrators, identified the idea a sa "Big Idea for the Future" seven years ago.  Explaining the significance of reciprocity took longer and was undertaken as I experienced the Scottish Independence Referendum campaign that lasterd from September 2013 until the vote in September 2014, the general election of 2015, the EU referendum campaign of 2016.  The general election campaign of 2017 highlighted the connections between the GFC and the current political crisis.

The Scottish Independence Referendum campaign was widely lauded (by English commentators) as a good example of public engagement in politics.  As someone voting in the referendum I regarded it as a complete failure of politics.  On one hand, the nationalists promised the electorate milk and honey in an independent Scotland, what became labelled a manifesto of hope.  The unionists prophesied doom and destruction.  In terms of parenting, one approach was to offer a child a toy to behave, the other was to threaten to take a way a toy if the child misbehaved.  There was no actual discussion of what was the best  policy, in terms of the metaphor t, the parents did not explain why they wanted the child to behave in a particular way.

This was encapsulated in the debate about the currency of an independent currency, and was the point on which I judged the validity of the arguments.  Alex Salmond asserted that Scotland would use the UK pound, as the obvious alternative of adopting the Euro was unpopular.  Unionists pointed out that Scotland would never be independent of England if it retained the UK pound.  What annoyed me was the referendum campaign did not discuss the relationship between money and sovereignty they, and the unionists, simply made assertions as to an unknowable future in an attempt to accumulate votes.

I understood the campaign in terms of a simple mathematical model of decision making under uncertainty that I often describe.  During a British winter, some birds need to eat up to 40% of their body weight to survive the night,  and so their very existence depends on making the right decisions about looking for food.  Let's say a bird has 6 hours to find 9 berries and it has two choices:

  • [Play it Safe] The bird stays where it is, where it knows there are berries in the hope of finding a few.  The chance of finding one or two berries in the hour is 50:50.
  • [Take a Risk] The bird flies off, in the hope of finding berry-bonanza but with a high chance of only finding enough to replace the energy lost in flying.  The energy cost of flying is one berry and the chance of only finding the one berry in the new field is 5 in 6, but there  is a 1 in 6 chance of finding 10 worms (and getting an excess of 9).
Notice that the expectation of both strategies is the same, one-and-a-half berries in an hour and so the bird can expect to get the nine berries in the six hours.  However the second approach is riskier (for any concave utility function the expected utility of the second strategy is always going to be less than the first).    However, if the bird has only found five berries after five hours, it is certain to die if it does not switch to the risky strategy, where it has a small chance of finding the 10 berries that will ensure survival.  A similar argument applies if the bird has found more than 8 berries after 5 hours - it can afford to take a risk.

The financial interpretation is that only the middle class should be risk averse the rich can afford to gamble, the poor have nothing (substantially) to lose by gambling but there is the small chance they become rich.  This is an explanation as to why the poor defy economic 'rationality' in buying lottery tickets, it is actually practically reasonable. In Ethics in Quantitative Finance I suggest that the adoption of utility in the nineteenth century was motivated by the rich de-legitimising speculation by the poor, since the poor can become rich through speculation.  Today, economists like to obscure this simple mathematical model under the veil of "prospect theory" or the S-shaped utility functions of Friedman & Savage.

On this basis I understood the nationalists inviting the Scottish voters to take the risk while the unionists were conforming to neoclassical economic theory and arguing the risks were too great.  Neither side was actually that interested in undertaking the political task of converging on a settled view of how Scotland should be governed.  Three years on, nothing much has changed here.

Three weeks ago, at the beginning of June, I had dinner with an old friend from my undergraduate studies who happens to be an external examiner for some of our MSc programmes.  We had had a similar dinner last year in the run up to the EU referendum and this year's dinner took place a week before the 2017 general election.  My friend's parents were immigrants from Cyprus and he dismissed the EU referendum as being indicative of the UK's xenophobia.  I disagreed, and went further to argue that it was just such attitudes by the British 'professional' class that led to the Leave vote.  I pointed out that, according the authoritative National Centre for Social Research, around 30% of Black and Asian voters voted to leave the EU while only 20% of the electorate as a whole regarded immigration as the main issue in the vote.  If you look at data the Leave voters were predominantly those poor in property, income and education.  The Leave campaign was identical to the Scottish nationalist campaign in promising milk and honey to the marginalised in a Brexit Britain: vote Leave, you have nothing to lose but might gain.

The prime example was "An extra £350 million a week to the National Health Service", which  appealed directly to the poor.  In the aftermath of the EU referendum the professional classes, those who are going to be risk averse, began discussing living in a "post-truth" world were facts no longer play a role in peoples' decision making.  The fact that these arguments ignore is that at there were no "matters of fact" pertaining to a post referendum Britain.  The Remain campaign mimicked the unionist campaign by calculating, to the nearest hundred pounds, how much worse off the average British family would be if it voted Leave.  This "fact" was as implausible as the "fact" that more money could go to the NHS, and I think the electorate recognised this and so the vote came down to taking the risk, or not.  Bres-xit won, when Yes (to Scottish independendce) lost because Brexit unified those above and below the "risk averse" region, wheras Yes isolated those below the "risk averse" region and did not appeal to those above it.

At the heart of  Ethics in Quantitative Finance is the idea that decisions about an uncertain future cannot rely on "matters of fact" relating to how nature is, what Locke described as physica, but on "judgement of the will", or practica.  Contemporary mathematics is closely associated with physica, but as I explain in the text, before the mid-nineteenth century mathematics concerned itself with both physica and practica.  A key episode in the diminution of practica in maths was the abandonment of moral expectation to solve the Petersburg game in favour of idealised utility functions.

My submission of the manuscript to Palgrave in early April was closely followed by the calling of the 2017 general election.  At the time my reaction was that the Prime Minister had reflected on the forthcoming Brexit process, decided it was going to be impossible and so called an election in the expectation that the Conservative government would lose.  This was regarded as absurd at the time given the lead the government had in the polls in April, a perspective confirmed by the local and Scottish government election results from the beginning of May.

However, the Conservatives proceeded to run an unbelievably inept campaign that centred on the ad nauseum repetition of a "strong an stable" mantra while its poll leave evaporated.  The Labour party focused on an anti-austerity campaign but was ambiguous about specific details.  I still don't understand what a Labour government would do in regard to EU relations or government finances.  The only thing I was sure of was they would subsidise the children of the rich and professional classes who attend university more than they would provide additional funding to the NHS.  Neither party offered the public an "honest set of choices".

The aim of the British Prime Minister in calling the election seems to have been to secure a mandate that would enable her to direct the Brexit negotiations as she wished.  In essence it was to accumulate as many votes as possible while the objective of th eLabour party was to prevent her doing so.  There was no substantial discussion of policy choices or the implications of those choices.

This reminded me of the environment in finance in the run up to the Credit Crisis.  Financial institutions were focused on reaping profits from investing in MBS of sub-prime mortgages, confident in the concrete number of market prices without reflecting on what those numbers implied.  It seems that in the sprinf of 2017 the Conservative government was focused on winning votes, confident in the concrete number of opinion polls without reflecting on what those numbers implied.  They saw a substantial lead and a "majority" in favour of Brexit without understanding where that majority originated.

The political turmoil the UK is experiencing is, like the Credit Crisis, as consequence of politicians (market participants) not being objectively true, subjectively truthfull and socially right.  The problem originate in the GFC.  In its aftermath, government policy has quietly supported the wealthy, through bank bailouts and price support delivered by QE, while loudly calling on the less well off to "tighten their belts".  The crisis will continue so long as the public do not trust finance or their politicians.

Monday, 12 June 2017

Egyptian and Mesopotamian approaches in economics

My previous post was born out of my frustration that some feel that there is a 'clash of cultures' that will inevitably lead to conflict between east and west/Islam and Christianity.  My view is that within Europe, the Middle East or China there are tensions between liberalism and authoritarianism with any society being susceptible to becoming dominated by either strand.  Every individual needs to decide whether to place there faith in authoritarianism or liberalism, a decision which will be dominated by their experience.

I believe a person's attitude to uncertainty will be fundamental in determining their view towards liberalism or authoritarianism. Cheryl Misak  explains the argument: if the future is unpredictable one must be liberal and open to any point of view, since a minority view might actually be the best.  If the future is predictable then one should place faith in those most competent at predicting the future.

Some ancient historians highlight how Mesopotamian society was founded on unpredictability while the opposite was true for Egypt, and this had profound effects on their cultures and religions.

Mesopotamia is a flat flood plain surrounded on three sides by mountains and to the south by desert. 
By Goran tek-en - Own workBased on;Karte von MesopotamienMesopotamia Syria, CC BY-SA 3.0, Link
The region, as an alluvial flood plain, was extremely fertile.  However it was susceptible to devastating floods, which tended to come at the end of the crop growing season, that could destroy communities.  The Mesopotamian civilisations were also vulnerable to invasions from mountain tribes, such as the Hittites from Anatolia to the north or Medes from the Zagros to the east.  As a result Mesopotamian religion sought to understand capricious gods and learn to predict their behaviour.   This motivated the development of astronomy supported by mathematics.

Ancient Egypt also survived because of a river, the Nile. The civilisation developed a few miles either side of the river and its delta, surrounded by desert that isolated the Egyptians from other civilisations.  Unlike the Tigris and Euphrates, the Nile followed a predictable cycle, flooding annually in a controlled manner.  Rather than bringing destruction, these annual floods rejuvenated the region just as it seemed to become gripped by drought.  A consequence was Egyptian civilisation was relatively static with a religion that focussed on cosmic equilibrium and

The difference between Egyptian and Mesopotamian approaches are highlighted in their different conceptions of the afterlife.   Egyptians believed that if individuals had lead a moral life such that they could pass the judgement of the gods, then their soul would enter paradise on death.  Because the natural world followed stable, predictable patterns, there were regular laws of nature and it followed that there were clearly defined laws of morality, which must be observed.  The Mesopotamian afterlife was a dark, desert-like underworld devoid of water or food; the dead ate dust.  Everyone ended up in this heel, whether they had been good or bad, reflecting the capriciousness of life.

Essentially, the Egyptian conception was based on justice: if a person leads a moral life they will be rewarded.  The Mesopotamians, on the other hand, did not assume an individual gets their just deserts.

I feel that much of the discussion around 'economic justice' presupposes that the world is governed by stable laws that represent an ideal (traditionally, the divine) and this means that choices can be judged as either good or bad.  I am not convinced such stable laws exist in societies and so clear cut judgements are difficult to arrive at.

I started thinking about these ideas after I spoke at the Edinburgh Science Festival and an audience member was angered by my lack of attention to the problem of wealth inequality.  They asserted that money should be distributed "democratically" and seemed to be under the impression that, as a mathematician, I claimed to have deduced a way of "fairly" distributing wealth.  As someone who is extremely sceptical that economics follows any identifiable patterns, just as the Mesopotamians seem to have rejected the idea that there are stable laws of nature, this has never been my objective.  What I am interested in is what is the role of mathematics in finance.  My conclusion is that financial markets are arenas in which parties work towards coming to agreement. This means that to work well they must be governed by discursive rules, rather than traditional norms about what is "good" or "evil".  I adopt Habermas and argue that statements in finance, prices quoted, must be true, truthful and right.  They must conform to  objective, subjective and social truth criteria.  To this end I argue that reciprocity determines the objective truth of a price and is linked to mathematics, while sincerity addresses the subjective truth and charity delivers social rightness.  Together these norms lay the foundations for trust in finance.

Monday, 22 May 2017

A Financial Approach to the 'Clash of Cultures'

Noah Smith has posed a question that resulted in a tweet thread

He later highlighted a book on the question of the ‘east-west divide’.  Noah’s question seems to have been prompted by discussion of the activities of Stephens Bannon and Miller in attacking Islam.

I can’t point Noah towards a book that explains the clash but for the past year I have been working on Ethics in Quantitative Finance which sheds some light on the topic, but from a different perspective.  The aim of the book is to investigate the relationship between mathematics, finance and ethics.  The initial findings were unexpected for a mathematician.  They revealed that there was a recurring theme that finance drove the development of science and democratic politics.  The book was written in the context of an emergence of intolerant populism that I experienced during Scottish Independence Referendum of 2014, the UK EU Referendum of 2016 and the US Presidential Election.

I became interested in Islam on the evening of 9 November 1989.  I was living in London as a recent graduate working for an oil company and, watching the collapse of the Berlin Wall with my two flat-mates we came to the conclusion that, following the collapse of Communism, tensions would emerge between Islam and the West, bearing in mind the two cultures had been allied against the Soviet Union for a decade.   The following weekend I bought Lapidus’ A History of Islamic Societies and spent the following decade forming a positive opinion of the culture, not least because in the early 1990s I spent about 6 months in the UAE.

A point struck me while reading a biography of Sir Richard Francis Bacon.  For most of Bacon’s lifetime, married women in Britain could not own property, it was all owned by their husbands.  This was not the case in Islam, with the famous example of Muhammed wife Khadija.  Rather than this custom being seen as progressive by Victorian Britain, it was regarded as another manifestation of the effeminacy of Islam and part of the justification for Europe’s dominance of Islamic states, from North Africa to East Asia.  Islam’s toleration of sexual diversity was another manifestation of this effeminacy.  Burton’s career in the East India Company was curtailed by his exploration of homosexual brothels and he coined the term ‘Sotadic zone’, which broadly coincided with the predominantly Muslim lands he was familiar with.  In Wilfred Thesinger’s 1920s books on Arabia there is discussion of mukhannath and mustergil, people who are transgender and long accepted in Arabic society.
These portrayals of Islam are diametrically opposite to contemporary attitudes.  Today it is the west that tolerates sexual diversity and gender equality while Islam is presented as repressive.  My conclusion was, and is, that Islam provides a convenient embodiment of “the other” where by specific examples of how Islam is opposite to the West come to dominate how the west sees Islam, while the similarities are ignored.  Many Muslims regard Friday 13th as the holiest day (the Arabic letter ‘M’ for Muhammed is the 13th in the alphabet); in the west it is regarded as unlucky. 

Both Islam and Christianity are built, substantially, on foundations laid by Greek philosophy.  One account (I think it is Unveiling Islam) of the difference is that Islam is rooted in the intellect ‒ it is logical to be a Muslim – where as Christianity is distinguished by its foundation on ‘charity’ (love).  This suggests that there is more in common between Islam and Christianity as there are differences this does not imply that there is not a ‘clash of cultures’, just that the clash is more complex than Christian v. Muslim or ‘East’ v. ‘West’. 

Greek culture that emerged around 600 BCE became known for being distinctive in its attitudes to politics and science.  Greek science developed a non-mythical cosmology.  The central idea emerged in Miletus, in Anatolia, and was apeiron (‘without limit’), something boundless, homogenous, eternal and abstract yet it held and motivated all things.  Simultaneously, across the Aegean in Athens, Greek ideas of democracy were codified.  The standard explanations used to argue that the non-mythical cosmology originated in the polis where citizens were equal and ruled by an impersonal law: democracy generates science.  This account did not acknowledge the temporal simultaneity of the origins of the ideas but there geographical separation.  There needed to be something that preceded democracy and science common to both Athens and Miletus.

A more empirical explanation for origin of the distinctive nature of Greek politics and science lies in the Greek adoption of money in everyday use. 

Money can be seen as a prototype for the apeiron.  Money is ‘fungible’, meaning one money-token is indistinguishable from any other, it is an empty signifier, like a word used in everyday language.  The impersonality of money means that it is universal and makes no distinctions; it is used by rich and poor uniting opposites.  There is a discrepancy between the value of money and its commodity value because money an abstract concept signified by a concrete token.  Because it is abstracted, unlike any substance, money is unlimited.  It has the power to transform objects, being able to turn wheat into wine in the market.  Together, these properties enable money to perform multiple functions simultaneously.  It is used to meet social obligations, such as tribute, legal compensation, and is the dominant means of conducting exchange; it stores value and is the unit of account.  Money’s myriad uses means that it becomes a universal aim of all members of the community using it. 

Money centralised social power in a single, abstract and impersonal entity.  In monetised, Greek, economies personal power arose from the possession of impersonal and non-substantial money.  The impersonality of Greek money nurtured the concept of equality, which is the foundation of democracy.  The Greek word nomos, associated with ‘law’, is the root of the Greek word for money, nomisma.  When combined with ‘auto’ – self – it gives autonomy, the idea that people can govern themselves and out of it, the concept of the individual emerges. 

The foundations of Athenian democracy where laid by Solon (c. 638‒558) when he instituted several legal reforms.  These sought to address instability created by conflicts in society caused by growing inequality created by the financialisation of society.  Solon’s reforms solved the problems by substituting judicial violence with fines, something that was only possible because money was widely used.  In the process, justice was depersonalised so that hostility between people was replaced by an impersonal quantification between an injury and its compensation.  While money was disruptive of society it was also integral to Solon’s reforms that created a political system in which all citizens were equal.

Greek’s highlighted how their culture was distinctive from that of their neighbours, notably those in the civilised East.  The Greeks contrasted Solon’s democratic laws to those of the Median tyrant Deioces .  The Greeks assumed that the Medes had originally lived in autonomous towns but Deioces determined to unite them under his rule.  He achieved this by gaining a reputation as an honest judge and then stopped giving judgements.  The Medes were so desperate for his decisions that they offered him the crown.  On achieving his objective Deioces ordered his subjects to build him the palace of Ecbatana, surrounded by seven concentric circular walls of different colours with the inner most being silver then golden.  Deioces hid himself from his subjects in the palace and ruled through messengers using a network of spies to monitor the kingdom.  The Greeks compared Solon’s position as impartial arbiter in an open court to Deioces’ despotism, where the judge was hidden.

The essential difference was that Greek society was monetised and operated through inter-personal exchange where as that of the neighbouring societies were re-distributive.  In re-distributive societies, power originated in the gods.  Priests (or a king, the distinction was often blurred) were the direct servants of the gods who mediated between the population and the divine.  All that the community produced was owned, exclusively, by the gods and managed by a hierarchy of priests/kings.  Produce was delivered to the temple (or palace) and the priests, from behind closed doors, would re-distribute the aggregate production per their own rules, taking a cut for their own use.  In return, the priest/kings were expected to provide material and social security: food stores, walls, law and order.  These societies maintained themselves so long as the priest/kings prevented famine and ensured peace and justice.  It was passed through the priests/kings into the community through a clear hierarchy.  The transference of power was often done through seals (amulets, talisman) that magically carried the power of the god.

Greek religious practice diverged from this standard model.  The Greek gods lived on ambrosia and nectar, not on mortal food.  When Homeric Greeks, in around 800 BCE, performed an animal sacrifice the smoke ‘honoured’ the gods, who were not located in their icons but ‘somewhere else’, alienated from the people.  The sacrificial meat was then shared out amongst the community.  The fairness of this sharing was fundamental to Greek culture, with both the Iliad and the Odyssey resting on problems resulting from unfair distribution.  Consequently, the wealth of the Greek temples was owned and managed, inclusively, by the community in an egalitarian manner, in contrast to the wealth of temples in re-distributive societies.  There is a relationship between these Greek religious practices and the emergence of money in Greek society.  The lowest value Greek coin was the obolos that took its name from the cooking spits (obelos) that were used to distribute sacrificial food and it is almost certain that the word drachma comes from obeliskon drachmai ‒ handfuls of spits.

The Odyssey focuses on the Greeks’ sense of identity and emphasises the humanity and individuality of Greek society.  It describes the transformation of Odysseus from an aristocratic warrior to a democratic leader and represents a metaphor for the transformation of Greek society from a hierarchy to a democracy.  It begins with Odysseus and his followers leaving the defeat of Troy and brutally attacking the Cicones.  This indicates that they have been traumatised by their experience of war and need to be tempered before returning to the ideal of Ithaca.  After attacking Cicones, the company arrive on the island of the Lotus-eaters.  Here the traumatised fighters can eat the lotus and fall into oblivion.  However, Odysseus chooses not to succumb to the intoxication, rather he introduces the key theme of Greek philosophy of reflecting on life and acting rationally.  This is essential in establishing an individual’s identity. 

The next episode is the story of the Cyclops and is an example of a rebirth myth, where the hero enters a tomb/womb and is reborn.  Odysseus’ inquisitiveness leads him to enter the cave of the cyclops, Polyphemus.  The cave is full of food (cheese-symbolic of animal husbandry).  Odysseus intends to exchange the cheese for wine but the cyclops does not understand the tradition of exchange and starts eating Odysseus’ while trapping Odysseus and the rest in the cave.  Odysseus realises he cannot defeat the cyclops using brute force, but must employ intelligence, in particular dolus (trickery, cunning) which is bestowed on Odysseus by Athena.  Odysseus’ plan is to offer Polyphemus wine as a gift (as distinct from in exchange), get him into a drunken stupor that will enable the crew to blind the cyclops and escape.  The meaning is that Odysseus is reborn as a thinker not a fighter and as a thinker he can defeat the myopic cyclops.

The encounter with the cyclops introduces the political theme of the Odyssey: should people be ruled by petulant autocrats supported by an aristocracy of warriors or by thinking individuals who can rationally solve problems.  The fact that Odysseus is still short of the ideal is demonstrated in the next encounter.  The crew stay with King Aeolus who gives to Odysseus a bag containing the winds that will prevent their ship returning to Ithaca.  However, Odysseus does not explain the gift to his crew.  They think the bag contains gold that Odysseus is keeping for himself.  While Odysseus sleeps the crew open the bag to share out the gold, releasing the winds that blow them away from their destination.  Odysseus and his crew are punished for not trusting each other.

Odysseus has further experiences that temper him.  The most profound being his trip to the underworld where he encounters the dead warriors from Troy, Achilles, Ajax and Agamemnon.  Achilles tells Odysseus that he would prefer to be a living servant than a dead hero.  This enlightens Odysseus who, having returned from Hades, is able to resist the temptations of the Sirens’ offer of fame and glory and ends up on the island of Ogygia, captured by the beautiful nymph Calypso.  Calypso offers Odysseus immortality and a life of pleasure, but she also represents death, in the same way that the oblivion of the lotus eaters is vacuous.  After seven or so years, Athena persuades Zeus to order Odysseus’s release and the hero escapes on a raft.  After all these trials, Odysseus has been transformed into a judicious individual and is able to return to Ithaca disguised as a beggar, the polar opposite of the aristocratic hero.

The difference between the Greek (democratic, individualistic) and Persian (hierarchical, re-distributive) cultures is exemplified in Herodotus’ description of the first contact between Athens and Persia in 507 BCE.  The Athenians were seeking Persian protection from the Spartans and initiated negotiations based on their experience gained in the agora, the main meeting place of the polis that also severed as the market (agora, forum in Latin), as that of equals.  This was inconceivable to the Persians who maintained a hierarchical state that ruled from the Indus valley to Anatolia.  The Persians promised to support the Athenians in exchange for them ritually offering earth and water.  After some discussion, the Greeks agreed.  They had not realised that they were symbolically submitting Athens to Persia and would be punished if they did not comply with Persian demands in the future.  Following this misunderstanding, it was inevitable that the Persians invaded Greece in 490 BCE.  Despite the material odds stacked against them, the Greeks, in the Delian League led by Athens, first defeated two invasions and then pushed the Persians out of much of the eastern Mediterranean by 449 BCE.

While the clash of cultures is not geographical (western v. eastern) or religious (Islam v. Christianity) but societal, relating to a difference in ideology between monetised societies based on reciprocal exchange resting on individual judgement in a democracy and those based on hierarchical distribution of resources based on autocratic, often hidden, decision making.  Within Europe this conflict repeats itself itself.  It is central to the Reformation, caricatured as between Calvinist merchants and Catholic aristocrats.  In England, there is the Civil War, that ends with the Commonwealth, the Anglicisation of the Latin res publica, followed by the political divide between Whigs and Tories.  The United States is the exemplar of Whig political philosophy, rooted in Locke’s empirical political theories.

The perennial question is why should an unstable monetised society (capitalist) be preferable to a re-distributive one (communist).  The answer depends on whether you believe the future is predictable or not.  If you believe that science can tame uncertainty the implication is that the optimal allocation of resources can be determined by a central authority, such as Deicoes.  If, on the other hand, you believe the future is not knowable, you cannot rely on the calculations of the auto/techno-cracy.  Instead it is best to allow anyone to participate in decision making in order to enable the best solution to be identified. 

This point was made by Moses ben Maimon, the twelfth century rabbi from the Almoravid Islamic Empire.  The Bible explains suffering on the basis that people were expelled from the Garden of Eden.  This is usually interpreted as going from plenty to scarcity into a world of scarcity but ben Maimon argued that God’s punishment was not so much about scarcity as uncertainty.  In the Garden of Eden, humans had perfect knowledge, which was lost with the Fall, and it is the loss of this knowledge which is at the root of suffering: if people know what will happen they can manage scarcity.  Up until the nineteenth century, it was widely accepted that the world was fundamentally uncertain.  This was expressed in Aristotle’s acceptance that there was a class of phenomena not amenable to science, the Scholastic’s acceptance that God could defy the laws of nature and Locke’s belief that knowledge would always be doubtful. 

Spinoza, a Jewish marrano living in Amsterdam in the mid-seventeenth century understood Greek philosophy through Judaic and Islamic interpretations had argued that the Olympian perspective of the scientist made the world deterministic.  He argued that people believed themselves to have free-will and had autonomy because they did not see the complete picture, being only finite.  Spinoza believed that the purpose of the individual was to lift themselves out of a mundane perspective so that they could understand the totality of creation, coming to understand the true nature of God’s will: the laws of nature.  The ethical nature of the Ethics was in describing how different actions helped, or hindered, the individual in approaching God, which would give the correct perspective on everyday phenomena.  Spinoza believed that at the most basic level people had direct knowledge of nature through their senses.  This could be improved into a scientific knowledge of the world that showed connections between phenomena and so could make generalisations.  The goal was to have direct knowledge of the generalisations, not mediated by ‘finite’ ideas or concepts and this knowledge delivered true freedom.  
Spinoza’s contribution to western philosophy was in suggesting that humans can reach a complete picture of the universe that delivered certain knowledge.  This was novel to Europeans rooted in the Scholastic tradition that synthesised Aristotle and Catholicism.  However, it was reminiscent of Jewish and Islamic mysticism.  Jewish mysticism ‒ Kabbalah ‒ had become prominent in the thirteenth century through Moshe ben Naiman Girondi, from Catalonia, while Sufi thought was legitimised in the eleventh century by the Islamic scholar al Ghazali.  Both these scholars challenged Hellenistic philosophy, with al-Ghazali’s repudiation of Aristotle in The Incoherence of the Philosophers being pivotal in the development of Islamic thought.  Associated with al-Ghazali was the doctrine of ‘occasionalism’, that effect follows cause not because of a physical law but only because God’s will.  Spinoza echoed this attitude when he argued that a law of nature was simply a consequence of God’s ‒ or nature’s ‒ consistency.  In Sufi metaphysics, there is the concept of ‘Unity of Essence’ (wahdat al-wujud, وحدة الوجود) and the idea that people seek ‘annihilation in God’ (fanaa, فناء‎‎) just as for Spinoza people sought a God-like perspective.  While Islam and Spinoza both denied contingency, they did not deny the ability of the individual to assert their own will, it was just that asserting one’s will against God ‒ or nature ‒ would be detrimental to the individual.   This idea of determinism was unusual in European thinking.  The Greeks (especially in the Oedipus myth) and Calvinists believed in predestination, that the fate of a person’s soul was destined , but an individual had will throughout their life.  Spinoza’s argument was that individuals do not have a choice in correct action; knowledge guides them to the correct course.  If someone makes an immoral choice, it is through ignorance. 

As a mathematician ‒ that is someone who sees an equivalence between a donut and a coffee cup ‒ there is no real clash of cultures between Donald Trump and Salman bin Abdulaziz, they are equivalent in representing non-democratic rulers.  While it seems incongruous that the President of the US is accompanied on state occasions by his daughter and son-in-law and that he is above the rule of law, this would be normal for an absolute monarch.  Modern populism involves an economic shift to the left accompanied by a cultural shift to the right.  It does not really matter if this is in Russia, India, Saudi Arabia, Britain or France.  The opposite of this populism is pluralistic debate rather than simple panaceas, which are destined to fail.