Adam Smith's Demon

Re-reading The Wealth of Nations with René Thom

What is Adam Smith actually doing in Book IV of The Wealth of Nations?

I ask this question because there is a widespread belief that general equilibrium theory begins with Smith, roughly a hundred years before anyone thought to put the words ‘general’ and ‘equilibrium’ together in the same sentence. Consider the following example from Arrow and Hahn’s classic General Competitive Analysis (1971) which is broadly representative. In the opening chapter the authors claim that The Wealth of Nations gives the first account of how a system of self-interested actors can be consistent with a coherent state of equilibrium:

Smith also perceived the most important implication of general equilibrium theory, the ability of a competitive system to achieve an allocation of resources that is efficient in some sense… Thus it can be maintained that Smith was a creator of general equilibrium theory, though the coherence and consistency of his work may be questioned.’

This version of the history of economic theory underpins the notion, sometimes found in textbooks, that Gerard Debreu and Kenneth Arrow solved Smith’s problem when they proved the two fundamental welfare theorems in the 1950s. Thus, in the laudatio issued by the Royal Swedish Academy of Science on the occasion of Debreu’s being awarded the Nobel prize for economics, we are told that he demonstrated the ‘internal logical consistency’ of Adam Smith’s ‘model of the market economy’.

Associating Smith with the major achievements of modern mathematical economics, whether justified or not, has led to an equally widespread belief that economics became a science with the publication of The Wealth of Nations. No less a historian than Mark Blaug has said that, compared with Smith, the works of his predecessors feel like ‘dress rehearsals for a science, rather than the real thing’. We may find much in the way of common sense and interesting ideas in Turgot, Cantillon and Quesnay, but they lack a ‘solid core’ of theory on which to build a system. By contrast, what makes Smith the genuine article is the central proposition, summarised in the passage on the invisible hand, that orderly behaviour can arise from the pursuit of individual self-interest. With this established we can finally get on with the scientific work of discovering causal relationships between economic data.

Given how I have set up the story so far, you might expect me to now condemn it as nonsense. But, in a certain mood, the idea that it was Smith who elevated economics to a science, and that this had something to do with a theory of equilibrium, is quite plausible¹. Blaug certainly has a point when he says that there is an abrupt change in economic theory after Smith. Within a few generations of his death we move from the vagaries of pre-Adamite economics to the increasingly sophisticated mathematical theories of Walras, Edgeworth, Pareto and Bachelier, which are still with us today, in one form or another.

And yet this argument creates a sort of paradox, one of those tame but nonetheless curious paradoxes which litter the history of ideas, and which I want to discuss in the remainder of this post. Put simply - it is not obvious that Smith was doing anything that is recognisable as science when he came up with his invisible hand theory:

As every individual, therefore, endeavours as much as he can, both to employ his capital in the support of domestic industry, and so to direct that industry that its produce may be of the greatest value; every individual necessarily labours to render the annual revenue of the society as great as he can. He generally, indeed, neither intends to promote the public interest, nor knows how much he is promoting it. By preferring the support of domestic to that of foreign industry, he intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain; and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention.

This is not a strict deductive argument involving a body of logically connected propositions. Nor is it a case of induction from a well-ordered set of experimental data. It is not even a ‘model’, to use the language of the Royal Swedish Academy of Science, if we mean by that a set of specifiable variables related in a simple mathematical argument. But at the same time it is not mere metaphor-making. To again quote Blaug, there is a sort of compressed ‘verbal mathematics in prose’ to this passage. Which leaves us with the question - what is its validity as a theoretical proposition?

What I want to suggest here is that Smith is doing exactly as the French mathematician René Thom recommends we do when faced with a particularly complicated ‘black box’. I am referring to a paper with the rather mysterious title ‘At the Boundaries of Man’s Power’, which Thom wrote in the 1970s when systems theory was all the rage. In it Thom proposes that science is a process of explicating ‘black boxes’ and that nature should be pictured as a string of such boxes. Since the time of Galileo the preferred method has been the analytical-reductionist one of breaking the box down into pieces. This only works when the resulting elements are stable, reproducible and also sufficiently simple that they can be formalised with ‘close approximation’ and without an ‘overly complicated graph of interaction’. Where none of these conditions hold, as is the case with an economic system which also has ‘memory’ in its mechanism, a different approach is required:

This approach, which we shall call ‘hermeneutic’ consists, grosso modo, in reversing Auguste Comte’s famous law of three stages: if the behaviour of a system cannot be described by a simple explicitly formulated law, let us first try to describe this behaviour qualitatively with respect to tendencies, properties of an abstract character, which control it. And if we are not able to explain the facts by these tendencies, then, as a last resort, let us imagine that a “spirit,” a psychic entity (the ghost in the machine) at least partially controls the system, and let us try to put ourselves in its place’

Thom calls this mode of analysis a ‘subjective simulation’ and its purpose is to bring to light the ‘strategy of the system’s internal demon’. I have enjoyed re-reading The Wealth of Nations in the light of this interpretation, as that really does seem to be Smith’s approach. And it is because of Smith’s wide and generous intelligence, his eclecticism, common sense, as well as his careful criticism of the basic facts of economic life, that this imaginative synthesis is so penetrating. Thom had enough sense to concede that such a process may seem irrational, but it does constitute a long and venerable tradition - we might think of Maxwell’s demon, the vast mathematical ‘intelligence’ in Laplace, and, in economics, Walras’ ‘calculateur’ who orchestrates the adjustment process across markets, turned into an ‘auctioneer’ in the work of Morishima. If you have read or watched any of the many interviews with Richard Feynman he appears to have spent half of his life imaging what it would be like to be a particle or an electromagnetic field.

All of which reinforces my conviction that, with respect to scientific methodology, Paul Feyerabend was right in preferring anarchy to regimentation.

1. Of course, in a different mood I find myself in agreement with that other fine historian of economics, Terence W Hutchison, who writes the following, in a footnote to his essay ‘Subjectivism, Methods and Aims’:

‘That a profound misconception regarding Adam Smith and ‘rigour’ may have spread to what might be called the ‘Nobelity’ of the profession is indicated in James Tobin’s paper ‘The Hidden Hand in Modern Macroeconomics’. Tobin states indisputably that [...] ‘Smith’s conjecture was eventually rigorously proved by Arrow and Debreu’. It was not, of course, Smith’s conjecture which was ‘eventually rigorously proved by Arrow and Debreu’. What was ‘eventually rigorously proved’ was a vacuous mathematical theorem of very jejune relevance for anyone seriously interested in real-world policymaking, which has almost no bearing on the case for or against either a free-market, or a government-regulated economy, because of the fantastically unrealistic assumptions on which the theorem depends [...] the prospect is hardly attractive of having the writings of the great economists of the past bowdlerised or eviscerated in the interests of what - from a practical point of view - are, quite frankly, pretty boring and irrelevant mathematics’