Turing’s Economics: A Birth Centennial Homage

Click to go to the Alan Turing Year website

This month marks the centennial of the birth of mathematician Alan Turing, the “father” of modern computing and artificial intelligence. To celebrate the occasion, we’ll be publishing a series of articles on modelling and economics. The series starts with a contribution from Professor K. Vela Velupillai of the Algorithmic Social Sciences Research Unit at Trento University’s Economics Department, and Elected Member of the Turing Centenary Advisory Committee.

The “Five Turing Classics” – On Computable Numbers, Systems of Logic, Computing Machinery and Intelligence, The Chemical Basis of Morphogenesis, and  Solvable and Unsolvable Problems– should be read together to understand why there can be something called Turing’s Economics. Herbert Simon, one of the founding fathers of computational cognitive science, was deeply indebted to Turing in the way he tried to fashion what I have called “computable economics”, acknowledging that “If we hurry, we can catch up to Turing on the path he pointed out to us so many years ago.”

Simon was on that path, for almost the whole of his research life. It has been my mission, first to learn to take this “path”, and then to teach others the excitement and fertility for economic research of taking it too.

A comparison of Turing’s classic formulation of Solvable and Unsolvable Problems in his last published paper in 1954 and Simon’s variation on that theme, as Human Problem Solving, would show that the human problem solver in the world of Simon needs to be defined – as Simon did – in the same way Turing’s approach was built on the foundations he had established in 1936-37. At a deeper epistemological level, I have come to characterize the distinction between orthodox economic theory and Turing’s Economics in terms of the last sentence of Turing’s paper (italics added): “These, and some other results of mathematical logic may be regarded as going some way towards a demonstration, within mathematics itself, of the inadequacy of ‘reason’ unsupported by common sense.”

We – at ASSRU – characterize every kind of orthodox economic theory, including orthodox behavioural economics, advocating the adequacy of “reason” unsupported by common sense; contrariwise, in Turing’s economics we take seriously what we now refer to as Turing’s Precept: ‘the inadequacy of reason unsupported by common sense’.

At another frontier of research in many of what are fashionably referred to as “the sciences of complexity”, some references to Turing’s The Chemical Basis of Morphogenesis is becoming routine, even in varieties of computational economics exercises, especially when concepts such as “emergence” are invoked. It is now increasingly realized that the notion of “emergence” originates in the works of the British Emergentists, from John Stuart Mill to C. Lloyd Morgan, in the half-century straddling the last quarter of the 19th and the first quarter of the 20th century.

A premature obituary of British Emergentism was proclaimed on the basis of a rare, rash, claim by Dirac (italics added): “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.”

Contrast this with Turing’s wonderfully laconic, yet eminently sensible precept in his 1954 paper (italics added): “No mathematical method can be useful for any problem if it involves much calculation.”

Turing’s remarkably original work on The Chemical Basis of Morphogenesis was neither inspired by, nor influenced any later allegiance to the British Emergentist’s tradition – such as the neurological and neurophilosophical work of Nobel Laureate, Roger Sperry.  On the other hand, the structure of the experimental framework Turing chose to construct was uncannily similar to the one devised by Fermi, Pasta and Ulam in 1955, although with different purposes in mind.

Turing’s aim was to devise a mechanism by which a spatially homogeneous distribution of chemicals – i.e., formless or patternless structure – could give rise to form or patterns via what has come to be called a Turing Bifurcation, the basic bifurcation that lies at the heart of almost all mathematical models for patterning in biology and chemistry, a reaction-diffusion mechanism formalised as a (linear) dynamical system and subject to what I refer to as the linear mouse theory of self-organisation, for reasons you can discover here.

Those interested in the nonlinear, endogenous, theory of the business cycle know that the Turing Bifurctions are at least as relevant as the Hopf Bifurcation in modeling the “emergence” and persistence of unstable dynamics in aggregative economic dynamics.

Turing’s Economics straddles the micro-macro divide in a way that makes the notion of microfoundations of macroeconomics thoroughly irrelevant; more importantly, it is also a way of circumventing the excessive claims of reductionists in economics, and their obverse! This paradox would have, I conjecture, provided much amusement to the mischievous child that Turing was, all his life.

Useful links

Pr Velupillai kindly provided this extended version of his article, including notes and comments

Computable Economics (Elgar, 2012) edited by Veupillai, Zambelli and Kinsella brings together the seminal papers of computable economics from the last sixty years and encompass the works of some of the most influential researchers in this area, including Turing

Applications of complexity science for public policy from the OECD Global Science Forum

Algorithmic Social Sciences Research Unit (ASSRU) at the Univesity of Trento

Alan Turing

Comparative advantage: Doing what you do best

Click to download the working paper

The mathematician Stanislaw Ulam did not have a high opinion of the social sciences. He once challenged Paul Samuelson, Nobel laureate in economics, to name one social science proposition that was both true and non-trivial. Samuelson nominated comparative advantage: “That this idea is logically true need not be argued before a mathematician; that it is not trivial is attested by the thousands of important and intelligent men who have never been able to grasp the doctrine for themselves or to believe it after it was explained to them.”

Samuelson was right. The absolute advantage Adam Smith talks about is simple and intuitive: it makes obvious sense for France to export wine to Scotland and import Scotch whisky. Comparative advantage is much more complicated. Ricardo introduced the notion in his 1817 book On the Principles of Political Economy and Taxation, using the example of England and Portugal and the production of cloth and wine. Portugal is more productive than England in both. Intuitively, you’d say that it makes sense for Portugal to export both, and that English industry would have little to gain from trade.

However, no country can develop a comparative advantage in everything because comparative advantage is a concept of the relative costs of doing things, so some things have to be comparatively more or less advantageous. Moreover all countries must have a comparative advantage in something. (You can find a good explanation of why this is the case here).

Ricardo demonstrated numerically that in fact if England specialised in one of the goods and Portugal in the other, total output of both goods would rise, allowing both countries to gain from trade.

Two centuries after Ricardo, can comparative advantage still provide useful guidance to policy makers? A new working paper from OECD’s Przemyslaw Kowalski argues that it can. Kowalski looks at what determines comparative advantage today, as part of the OECD project on The Effects of Globalisation: Openness and Changing patterns of Comparative Advantage. Kowalski analyses the bilateral trade of 55 OECD and selected emerging market economies and 44 manufacturing sectors covering the entirety of merchandise trade He examines physical capital, human capital, financial development, energy supply, business climate, and labour market institutions as well as import tariff policy.

 Comparative advantage is still an important determinant of trade, but the OECD countries’ economies are more similar than they used to be, so the possibilities of trade driven by comparative advantage differences within the OECD grouping aren’t as great as they once were. However there are still marked differences between OECD and non-OECD countries, while the differences among non-OECD countries don’t seem to be diminishing much. That means that comparative advantage is more important for North-South and South-South trade than for North-North trade.  

If you look at OECD and non-OECD countries as a whole, it’s interesting to see where differences have been decreasing and increasing. these differences decreased (although there are still big variations) as regards physical capital, average years of schooling, tertiary education, primary energy supply, and availability of credit. On the other hand, cross-country variation increases for regulatory quality, rule of law, control of corruption as well as import tariffs.

Most of these factors can be influenced significantly by policy. The trick is to make sure that trade and other policies don’t cancel each other out, but with so many factors interacting it’s not easy. Luckily for government policy makers, help is at hand from this year’s Nobel laureates in economics, Thomas J. Sargent and Christopher Sims. 

Working separately, but in a complementary fashion, they’ ve developed methods for analysing causal relationships between economic policy and what happens in the economy. Sargent has mainly studied the effects of systematic policy shifts – such as attempts to reduce fiscal deficits – while Sims looks at how shocks spread through the economy.

Even if you’re one of those important and intelligent men who can’t grasp comparative advantage, you can probably see why the Sveriges Riksbank gave Sargent and Sims the prize this year.

 Useful links

Globalisation, Comparative Advantage and the Changing Dynamics of Trade collects OECD work that builds on recent contributions to the theory and empirics of comparative advantage, emphasising the role of policy in shaping trade. Click on the image to find out more and browse the book.

OECD work on trade

International trade: Free, fair and open?

Soros and the next big idea

It isn’t just economies that have been in trouble over the past couple of years; the profession of economics has also been going through a rough patch. Critics argue that, in the wake of the financial crisis, some of the favourite ideas of mainstream economists in recent decades are now looking a little threadbare.

Few have had more to say on the subject than George Soros, the billionaire investor and philanthropist. But rather than just complaining, Soros is trying to do something about it. He’s spent $50 million to establish The Institute for New Economic Thinking, which aims “to confront the flawed mechanisms in our economic and financial infrastructure and develop new paradigms in economic understanding.”

The institute has assembled an impressive advisory board of 26 men (the absence of women has not gone unnoticed), including five Nobel laureates (Amartya Sen and Joseph Stiglitz are among them), leading academics such as Harvard’s Kenneth Rogoff, the former IMF chief economist and blogger Simon Johnson, and the former BIS economist William White, who now chairs a senior economics committee at the OECD.

The institute’s first conference starts today (Thursday, 8 April) at King’s College, Cambridge – John Maynard Keynes’ alma mater – under the title “The Economic Crisis and the Crisis in Economics”.

The economics commentator Anatole Kaletsky, another of the institute’s advisors, describes the event as an opportunity “to reopen many of the debates closed down by unrealistic theories”.

This is not the first time Soros has challenged economic orthodoxies. The author of a number of books, he’s long questioned approaches like the efficient markets and rational expectation hypotheses, which have provided the intellectual underpinning for market liberalisation in recent decades. Instead, Soros promotes his own theory – “reflexivity” – that he believes better describes the complex interaction between realities and perceptions in markets.

Soros introduces some of his ideas in this lecture series, and they’re summarised in this book review by John Cassidy.

Whether Soros’s theories will ever become mainstream economic thinking remains to be seen. But his commitment to fresh thinking – and deep pockets – may well ensure that The Institute for New Economic Thinking is a player in the search for economics’ next big idea.

Useful links

OECD Insights: From Crisis to Recovery