# Turing’s Economics: A Birth Centennial Homage

*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 19^{th} and the first quarter of the 20^{th} 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

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