How ergodicity reimagines economics for the benefit of us all

The principles of economics form the intellectual atmosphere in which most political discussion takes place. Its prevailing ideas are often invoked to justify the organisation of modern society, and the positions enjoyed by the most wealthy and powerful. Any threat to these ideas could also be an implicit threat to that power – and to the people who possess it. Their response might be brutal.

And so it was, after rumours recently spread that a widely known economist had redeveloped much of economic theory, and reached conclusions suggesting that the economic world could be greatly improved if it was radically reorganised. The ideas leaked out before their official publication, and drew intense interest from economists, politicians and social activists who sensed a potential moment of world-changing importance. Just hours before he could present his results to a global audience, however, the economist was killed in a mysterious car accident in Berlin. His manuscript went missing. But the accident was no accident – the economist was murdered by a conspiracy of political and financial interests determined to suppress thinking that could erode their power.

The story above is fiction – but plausible fiction taking place in the murky nexus of power, ideology and economics. It’s the focus of the German-language novel Gier (2019), by the Austrian author Marc Elsberg, who was inspired by research articulated in the paper ‘Evaluating Gambles Using Dynamics’ (2016) by Ole B Peters of the London Mathematical Laboratory (LML) and the late Nobel laureate Murray Gell-Mann of the Santa Fe Institute (SFI) in New Mexico. In the novel, Elsberg tries to imagine how a new way of thinking about economics could provoke a violent backlash by those benefiting from current illusions about the field. The thriller follows a dramatic scavenger hunt across Berlin, as authorities try to piece together who was behind the murder – and more importantly, what were the incendiary ideas that the economist was about to present.

In the real world, through the pages of scientific journals, in blog posts and in spirited Twitter exchanges, the set of ideas now called ‘Ergodicity Economics’ is overturning a fundamental concept at the heart of economics, with radical implications for the way we approach uncertainty and cooperation. The economics group at LML is attempting to redevelop economic theory from scratch, starting with the axiom that individuals optimise what happens to them over time, not what happens to them on average in a collection of parallel worlds.

The new concept is a key theme of research initiated by Peters about a decade ago, and developed with the collaboration of Gell-Mann and the late Ken Arrow at SFI, and of Alex Adamou, Yonatan Berman and many others at the LML. Much of this view rests on a careful critique of a model of human decisionmaking known as expected utility theory. Everyone faces uncertainties all the time, in choosing to take one job rather than another, or deciding how to invest money – in education, travel or a house. The view of expected utility theory is that people should handle it by calculating the expected benefit to come from any possible choice, and choosing the largest. Mathematically, the expected ‘return’ from some choices can be calculated by summing up the possible outcomes, and weighting the benefits they give by the probability of their occurrence.

But there is one odd feature in this framework of expectations – it essentially eliminates time. Yet anyone who faces risky situations over time needs to handle those risks well, on average, over time, with one thing happening after the next. The seductive genius of the concept of probability is that it removes this historical aspect by imagining the world splitting with specific probabilities into parallel universes, one thing happening in each. The expected value doesn’t come from an average calculated over time, but from one calculated over the different possible outcomes considered outside of time. In doing so, it simplifies the problem – but actually solves a problem that is fundamentally different from the real problem of acting wisely through time in an uncertain world.

Expected utility theory has become so familiar to experts in economics, finance and risk-management in general that most see it as the obvious method of reasoning. Many see no alternatives. But that’s a mistake. This inspired LML efforts to rewrite the foundations of economic theory, avoiding the lure of averaging over possible outcomes, and instead averaging over outcomes in time, with one thing happening after another, as in the real world. Many people – including most economists – naively believe that these two ways of thinking should give identical results, but they don’t. And the differences have big consequences, not only for people trying to do their best when facing uncertainty, but for the basic orientation of all of economic theory, and its prescriptions for how economic life might best be organised.

The upshot is that a subtle and mostly forgotten centuries-old choice in mathematical thinking has sent economics hurtling down a strange path. Only now are we beginning to learn how it might have been otherwise – and how a more realistic approach could help re-align economic orthodoxy with reality, to the benefit of all.

Of particular importance, the approach brings a new perspective to our understanding of cooperation and competition, and the conditions under which beneficial cooperative activity is possible. Standard thinking in economics finds limited scope for cooperation, as individual people or businesses seeking their own self-interest should cooperate only if, by working together, they can do better than by working alone. This is the case, for example, if the different parties have complementary skills or resources. In the absence of possibilities for beneficial exchange, it would make no sense for an agent with more resources to share or pool them together with an agent who has less. The standard economic approach, by nature, tends to come down in favour of splintering society into individuals who see only their own interests, and it suggests that they do better by this approach.

Things change dramatically, however, if one considers how parties do when facing uncertainty and repeatedly undertaking risky activities through time. As Elsberg illustrates in his novel, such conditions greatly expand the scope for pooling and sharing resources to be beneficial to all parties. From a basic point of view, pooling resources provides all parties with a kind of insurance policy protecting them against occasional poor outcomes of the risks they face. If a number of parties face independent risks, it is highly unlikely that all will experience bad outcomes at the same time. By pooling resources, those who do can be aided by others who don’t. Mathematically, it turns out that such pooling increases the grow rate of resources or wealth for all parties. Even those with more resources do better by cooperating with those who have less. This insight needs further development, but suggests that the scope for beneficial cooperation is much greater than previously believed.

The developing ideas of Ergodicity Economics are described in a set of lecture notes, in the aforementioned 2016 paper, and in a number of blog posts that describe some of the ideas and their implications. The ideas offer a completely new perspective on matters ranging from optimal portfolio management to the dynamics of wealth inequality, and the circumstances under which sharing and pooling resources can be beneficial to all. If spread widely, these ideas could exert influence over the economics profession and encourage governments to take a fundamentally different approach to policy.

As such, one might expect these ideas to generate considerable controversy, perhaps even forcible resistance – as explored in the novel Gier.

Mark Buchanan

This article was originally published at Aeon and has been republished under Creative Commons.

Muhammad: an anticlerical hero of the European Enlightenment

Publishing the Quran and making it available in translation was a dangerous enterprise in the 16th century, apt to confuse or seduce the faithful Christian. This, at least, was the opinion of the Protestant city councillors of Basel in 1542, when they briefly jailed a local printer for planning to publish a Latin translation of the Muslim holy book. The Protestant reformer Martin Luther intervened to salvage the project: there was no better way to combat the Turk, he wrote, than to expose the ‘lies of Muhammad’ for all to see.

The resulting publication in 1543 made the Quran available to European intellectuals, most of whom studied it in order to better understand and combat Islam. There were others, however, who used their reading of the Quran to question Christian doctrine. The Catalonian polymath and theologian Michael Servetus found numerous Quranic arguments to employ in his anti-Trinitarian tract, Christianismi Restitutio (1553), in which he called Muhammad a true reformer who preached a return to the pure monotheism that Christian theologians had corrupted by inventing the perverse and irrational doctrine of the Trinity. After publishing these heretical ideas, Servetus was condemned by the Catholic Inquisition in Vienne, and finally burned with his own books in Calvin’s Geneva.

During the European Enlightenment, a number of authors presented Muhammad in a similar vein, as an anticlerical hero; some saw Islam as a pure form of monotheism close to philosophic Deism and the Quran as a rational paean to the Creator. In 1734, George Sale published a new English translation. In his introduction, he traced the early history of Islam and idealised the Prophet as an iconoclastic, anticlerical reformer who had banished the ‘superstitious’ beliefs and practices of early Christians – the cult of the saints, holy relics – and quashed the power of a corrupt and avaricious clergy.

Sale’s translation of the Quran was widely read and appreciated in England: for many of his readers, Muhammad had become a symbol of anticlerical republicanism. It was influential outside England too. The US founding father Thomas Jefferson bought a copy from a bookseller in Williamsburg, Virginia, in 1765, which helped him conceive of a philosophical deism that surpassed confessional boundaries. (Jefferson’s copy, now in the Library of Congress, has been used for the swearing in of Muslim representatives to Congress, starting with Keith Ellison in 2007.) And in Germany, the Romantic Johann Wolfgang von Goethe read a translation of Sale’s version, which helped to colour his evolving notion of Muhammad as an inspired poet and archetypal prophet.

In France, Voltaire also cited Sale’s translation with admiration: in his world history Essai sur les mœurs et l’esprit des nations (1756), he portrayed Muhammad as an inspired reformer who abolished superstitious practices and eradicated the power of corrupt clergy. By the end of the century, the English Whig Edward Gibbon (an avid reader of both Sale and Voltaire) presented the Prophet in glowing terms in The History of the Decline and Fall of the Roman Empire (1776-89):

The creed of Mahomet is free from suspicion or ambiguity; and the Koran is a glorious testimony to the unity of God. The prophet of Mecca rejected the worship of idols and men, of stars and planets, on the rational principle that whatever rises must set, that whatever is born must die, that whatever is corruptible must decay and perish. In the author of the universe, his rational enthusiasm confessed and adored an infinite and eternal being, without form or place, without issue or similitude, present to our most secret thoughts, existing by the necessity of his own nature, and deriving from himself all moral and intellectual perfection … A philosophic theist might subscribe the popular creed of the Mahometans: a creed too sublime, perhaps, for our present faculties.

But it was Napoleon Bonaparte who took the Prophet most keenly to heart, styling himself a ‘new Muhammad’ after reading the French translation of the Quran that Claude-Étienne Savary produced in 1783. Savary wrote his translation in Egypt: there, surrounded by the music of the Arabic language, he sought to render into French the beauty of the Arabic text. Like Sale, Savary wrote a long introduction presenting Muhammad as a ‘great’ and ‘extraordinary’ man, a ‘genius’ on the battlefield, a man who knew how to inspire loyalty among his followers. Napoleon read this translation on the ship that took him to Egypt in 1798. Inspired by Savary’s portrait of the Prophet as a brilliant general and sage lawgiver, Napoleon sought to become a new Muhammad, and hoped that Cairo’s ulama (scholars) would accept him and his French soldiers as friends of Islam, come to liberate Egyptians from Ottoman tyranny. He even claimed that his own arrival in Egypt had been announced in the Quran.

Napoleon had an idealised, bookish, Enlightenment vision of Islam as pure monotheism: indeed, the failure of his Egyptian expedition owed partly to his idea of Islam being quite different from the religion of Cairo’s ulama. Yet Napoleon was not alone in seeing himself as a new Muhammad: Goethe enthusiastically proclaimed that the emperor was the ‘Mahomet der Welt’ (Muhammad of the world), and the French author Victor Hugo portrayed him as a ‘Mahomet d’occident’ (Muhammad of the West). Napoleon himself, at the end of his life, exiled on Saint Helena and ruminating on his defeat, wrote about Muhammad and defended his legacy as a ‘great man who changed the course of history’. Napoleon’s Muhammad, conqueror and lawgiver, persuasive and charismatic, resembles Napoleon himself – but a Napoleon who was more successful, and certainly never exiled to a cold windswept island in the South Atlantic.

The idea of Muhammad as one of the world’s great legislators persisted into the 20th century. Adolph A Weinman, a German-born American sculptor, depicted Muhammad in his 1935 frieze in the main chamber of the US Supreme Court, where the Prophet takes his place among 18 lawgivers. Various European Christians called on their churches to recognise Muhammad’s special role as prophet of the Muslims. For Catholics scholars of Islam such as Louis Massignon or Hans Küng, or for the Scottish Protestant scholar of Islam William Montgomery Watt, such recognition was the best way to promote peaceful, constructive dialogue between Christians and Muslims.

This kind of dialogue continues today, but it has been largely drowned out by the din of conflict, as extreme-Right politicians in Europe and elsewhere diabolise Muhammad to justify anti-Muslim policies. The Dutch politician Geert Wilders calls him a terrorist, paedophile and psychopath. The negative image of the Prophet is paradoxically promoted by fundamentalist Muslims who adulate him and reject all historical contextualisation of his life and teachings; meanwhile, violent extremists claim to defend Islam and its prophet from ‘insults’ through murder and terror. All the more reason, then, to step back and examine the diverse and often surprising Western portraits of the myriad faces of Muhammad.

Faces of Muhammad: Western Perceptions of the Prophet of Islam from the Middle Ages to Today by John Tolan is published via Princeton University Press.

John Tolan

This article was originally published at Aeon and has been republished under Creative Commons.