Thursday, 31 May 2018

Anti-Semitism is the socialism of fools

This post is my response to the warning from the former Chief Rabbi Lord Jonathan Sacks of the dangers of "doing nothing" to combat anti-Semitism. The concern raised by Lord Sacks is that anti-Semitism appears widespread in the far left, as well as in its normal home in the far right. I will write about what I think I understand, meaning I will not venture into the issues relating to actions of the state of Israel. None of my best friends (that I know of) are Jewish though I have yet to meet an Israeli Jew who whole-heartedly supports the actions of the Israeli government.  

The quote, ‘Anti-Semitism is the socialism of fools’ is often attributed to the nineteenth century German social democratic leader, August Bebel. Its switching, to ‘Socialism is the anti-Semitism of intellectuals’, seems to capture the essence of the problem the far left have. Those that support gender equality and oppose Islamophobia or racism based on skin colour seem not to perceive anti-Semitism as a form of racism. This is relevant to me, as someone who is interested in the relationship between ethics, finance and mathematics because Semitism appears to represent something other ethnicity or culture that is related to money.  

Marx, like many leading socialists between 1850 and 1950, came from a Jewish roots. Marx’s parents came from rabbinical families with his paternal ancestry providing the rabbi’s of Trier. Marx’s father converted to Protestantism probably to enhance his career as a lawyer in the aftermath of secularising Enlightenment. Despite being raised a Christian and becoming an atheist in maturity, Marx is sometimes presented as an archetypal Yeshiva scholar. Marx developed theories based on written materials – “I am a machine condemned to devour books”. His research involved searching through works to find episodes in history to support his ideas, he never sought to objectively asses them or formulate a hypothesis to be tested empirically. This approach mirrored Lurianic kabbalah, a form of Jewish mysticism that places messianism at its heart. The most famous (or notorious) Lurianic prophet was Nathan of Gaza, who promoted Sabbatai Zevi as the messiah. Nathan, who had been born around 1643, came across Zevi in Jerusalem and proclaimed him messiah in 1665. This was when western Europe was in the grip of millenarianism and Lurianic kabbalah had superseded more rational Jewish approaches and the existence of a new messiah in Jerusalem was widely accepted. Nathan, more intelligent than the unstable Zevi, was able to develop predictions and explanations of events that seemed plausible but were vague enough to explain inconvenient facts. Even when Zevi converted to Islam to receive a pension from the Ottoman emperor, Nathan was able to justify the unfortunate turn of events as coherent with Zevi being the Jewish messiah. As well as adopting the method of the rabbinical scholar, Marx, like his cousin Henrich Heine, developed the lifestyle of the Jewish theologian. Judaism had survived persecution for centuries as a stateless religion run by an oligarchy comprising of rich merchants who supported rabbis. Marx adopted the role of the rabbi, schnorring off wealthy relatives and acquaintances to ensure his intellectual endeavours could be free from being contaminated by practical experience 

Marx is widely regarded as being an anti-Semite. The basis is an essay Marx wrote in 1844, On the Jewish Question, which was developed while Marx was formulating historical materialism. Marx makes the following argument 
Let us consider the actual, worldly Jew – not the Sabbath Jew, as Bauer does, but the everyday Jew. 
Let us not look for the secret of the Jew in his religion, but let us look for the secret of his religion in the real Jew. 
What is the secular basis of Judaism? Practical need, self-interest. What is the worldly religion of the Jew? Huckstering. What is his worldly God? Money. 
... 
The Jew has emancipated himself in a Jewish manner, not only because he has acquired financial power, but also because, through him and also apart from him, money has become a world power and the practical Jewish spirit has become the practical spirit of the Christian nations. The Jews have emancipated themselves insofar as the Christians have become Jews. 
... 
In the final analysis, the emancipation of the Jews is the emancipation of mankind from Judaism 

Marx’s argument is not that Judaism creates ‘hucksters’ but that ‘hucksters’ creates Jews. The ‘material conditions’ of commerce creates the religion of the Jews. By turning Christians into pedallers, the Jew converts them. So long as ‘capitalism’ exists, the Jews will flourish. 

Marx did not confine his anti-Semitism to economic theory. He corresponded to Engles about a leading German socialist, Ferdinand Lassalle, who was Jewish. Marx called Lassalle a “Jewish Nigger”. In 1861 Marx wrote to Engles  
A propos Lassalle-Lazarus. Lepius in his great work on Egypt has proved that the exodus of the Jews from Egypt was nothing but … the expulsion of the “leprous people” from Egypt. At the head of these lepers was an Egyptian priest, Moses, Lazurus, the leper, is then the archetype of the Jew and Lassalle is the typical leper. 
A year later, referring to Lassalle 
It is now perfectly clear to me that, as the shape of his head and the growth of his hair indicates, he is descended from the Negroes who joined in Moses’ flight from Egypt (unless his mother or grandmother on his father’s side was crossed with a nigger). This union of Jew and German on a Negro base was bound to produce an extraordinary hybrid. 

The problem the far left has with Judaism is almost hard-wired in. The Jew is the archetype of the capitalist; destroy capitalism and Judaism disappears. Marx secularises anti-Semitism into anti-capitalism. Here-in lies the problem the far left has with anti-Semitism.

Lenin often used the phrase “Anti-Semitism is the socialism of fools” and based Imperialism: the highest stage of capitalism on a book, Imperialism, by the British socialist, John Hobson. Th genesis of Hobson’s ideas came when he went to report on the Boer War for the Manchester Guardian. In The War in South Africa: Its Causes and Effects, Hobson blames “a small group of international financiers, chiefly German in origin and Jewish by race” (p 189 ff.). On this Marxist basis, the roots of imperialism are identified in the Rothschilds.

To the poor anti-Semite, the Jew is the banker pulling the strings that control capitalism and the world. To the rich, the Jew is the poor beggar selling shoddy goods that undercut their own. Jews are caricatures, never people. Anti-Semitism, since the Jewish emancipation, has revolved around negative aspects to commerce and finance. This is why it affects me, since understanding finance requires that people do not approach it from a perspective blind with prejudice. More generally, anti-Semitism affects the Muslim and Afro-Caribbean because it is the prototype on which all (western) racism is formed.

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.