On Metaphors and Mechanisms

We have explored in the previous posting how, in order to understand innovation, evolutionary economics loosely adopts, adapts and extends concepts of evolutionary biology to apply these in an economic context.  To avoid confounding a cardinal assumption of free will of the innovator and the entrepreneur, it is often emphasised that evolution here serves as a metaphor rather than a mechanism.  One should not directly transpose biological mechanisms into the social domain.  They are considered signposts to guide an enquiry, not rigid conduits to channel thinking.

Whilst biological metaphors have a natural resonance with innovation, it is the physical sciences that have had a more enduring and intimate contact with economic thought.  Back in the second half of the 18th century the two subjects found themselves in particularly close proximity.  Around this time, Adam Smith met Voltaire, friend and collaborator of Émilie du Châtelet who was instrumental in elucidating of the nature of kinetic energy[1] and later died from complications of childbirth in the same year as she had completed the first French translation of Newton’s Principia Mathematica.  In this pre-revolutionary epoch, in Paris the Lumières were fermenting ideas mixing early economic concepts of the Physiocrats lead by François Quesnay, with the science of Jean d’Alembert who with Diderot had recently created a new and novel Encyclopédie.  Smith among many others was present and could not have remained uninfluenced by such a prestigious gathering when ten years later he produced his seminal work on An Inquiry into the Nature and Causes of the Wealth of Nations.

 Quesnay_Tableau  MONIAC Prototype at Leeds
The Tableau économique from 1758 in which François Quesnay and the Physiocrats considered agricultural surpluses as the source of wealth, which then flowed back and forth to the landowners and to the industrialists in the cities[2]. A prototype  MONIAC (Monetary National Income Analogue Computer) from 1949 that uses fluidic logic to model the workings of the UK economy[3].(Exhibited at the University of Leeds)

The further development of Political Economics proceeded though the 19th century, involving such notable figures as David Ricado, John Stuart Mill and Karl Marx.  Then around 1870 there was the “Marginal Revolution” initiated through independent publications of Léon Walras, Joseph Stanley Jevons and Carl Menger.  Again these later developments can link their origins to the principles of mechanics, as is particularly evident in the words and equations of Walras.  This is no more clearly demonstrated than in his 1909 final summary publication Économique et mécanique, which concludes with the following translated remarks:-

In examining as carefully as one might wish the four theories given above namely, the theory of maximum satisfaction with the exchange [of commodities] and the maximum energy of a balanced beam, and also the theory of general [economic] equilibrium of the market and that of the universal equilibrium of celestial bodies, one will find between these two mechanical theories a single unique difference: the exteriority of the two mechanical phenomena and intimacy of the two economic phenomena, and thus, the ability to make everyone aware of the conditions of equilibrium of the beam and conditions of universal equilibrium of the sky, due to the existence of common measures for these physical phenomena, and the inability to demonstrate to anyone the conditions of equilibrium of the exchange and the conditions for a general equilibrium of the market, because of a lack of common measures for these psychological phenomena.  We have metres and centimetres to note the length of the lever arm of the beam and grams and kilogrammes to note the supported weights.  We also have instruments to determine the relative movement of stars.  We are not able to measure the intensity of need between those who exchange goods. But this should be of no consequence because with each exchange, consciously or unconsciously, a person will know deep down whether his needs are satisfied or not in proportion to the value of the goods exchanged.  Whether the measure be externally made or be internal, depending on whether the measurements are physical or psychological, this does not prevent the measurement itself and a comparison of quantities and quantitative relationships, and therefore as a consequence the science should be mathematical.


Walras goes on further to ask whether actually the masses and forces of mechanics and the equivalent utilities and scarcity of commodities in economics are not all abstract factors to make the mathematical equations work in their respective domains.

Following the classical mechanics of the balanced beam and the movement of stars used by Walras, later came an association with the newer science of thermodynamics, which describes the steam engine and all other systems through which mechanical work can be drawn from the flow of heat from a hotter to a cooler temperature.  While classical mechanics is time-invariant, the mechanisms of thermodynamics only work in one direction, heat flows only from high to low temperatures and the arrow of time has a single and specific direction.  Such properties make thermodynamics a natural metaphorical associate for economic phenomena.

Around 1875 the renowned physicist and mathematician Willard Gibbs in his publication On the Equilibrium of Heterogeneous Substances applied thermodynamic principles to chemical systems and their equilibria.  The complex mathematics delayed a broad adoption of this work, which later became recognised as one of the greatest achievements of 19th century science.

In his 1947 treatise Foundations of Economic Analysis, the American economist Paul Samuelson, who interestingly had a direct intellectual lineage back to Willard Gibbs himself, recast the mathematics of thermodynamics to apply to equilibrium phenomena in the marginal supply and demand of neoclassical economics. This opened up a rich seam of mathematical formalism that greatly enhanced the reach and power of neoclassical economic theory over subsequent decades.  Samuelson and several other economists became Nobel laureates as a result of these endeavours.

Mathematically the thermodynamic and economic equilibrium are both systems of constrained optimisation (on energy and utility) with a similar set of equations of state.  However, there has been little enthusiasm to link the parallel mechanical and economic worlds.  Samuelson[4] in 1960 asked:

Why should there be laws like the first or second laws of thermodynamics holding in the economic realm? Why should “utility” be literally identified with entropy, energy, or anything else? Why should a failure to make such a successful identification lead anyone to overlook or deny the mathematical isomorphism that does exist between minimum systems that arise in different disciplines?


Over time this view must have changed as in 1947 Samuelson begins his Foundations of Economic Analysis with the words:

The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features.   This fundamental principle of generalization by abstraction was enunciated by the eminent American mathematician E. H. Moore more than thirty years ago.


It is a matter of debate, therefore, whether we are dealing with metaphors or with mechanisms.

But where does innovation sit in this macroeconomic analysis?  In the mathematical development of neoclassical economic theory it is assumed that rational economic consumers maximise their utility and firms maximise their profit, to attain a stable equilibrium.  Innovation then appears as an external (exogenous) factor which accounts for increased growth through increased productivity with time.  It was not until the 1980s that technological change through innovation was brought inside the neoclassical economic analysis, with an Endogenous Growth Theory in which the mathematics is adjusted to accommodate the effect of technological innovation by adjusting for the otherwise conventional diminishing returns of deployed capital.

The weakness of mainstream neoclassical economics to deal with innovation is explored by Nathan Rosenberg in his Exploring the Black Box.  This book from 1994 includes an exploration of the “path-dependent aspects of technological change”, in which it is clear that there is a close interweaving of science and technology development that cannot be understood except from a historical and time dependent perspective.  As considered within evolutionary economics, technologies such as the transistor, laser and information theory have extended the impact of innovation well beyond their original domain of application and justification.  These uncertainties weaken the hold that neoclassical economics can take on innovation, as acquisition of knowledge is not costless but costly, and the outputs of R&D cannot be rationally selected at the point of investment.

Quite different forms of microeconomic analysis have been developed, aided by the availability of computational numerical models, in which concepts of statistical mechanics and the explanation of such physical phenomena as the phase changes of solids to liquids and gases have seen analogous mechanisms applied in economics.  In these numerical simulations of the behaviour of large numbers of independent entities, molecules or economic agents, unexpected patterns emerge from a soup of complex interactions and which resemble real world phenomena.  This emergent behaviour of complex systems can at least explain some of the unpredictability of economic phenomena even though the insights they provide are essentially qualitative.  These interesting ideas are brought together in Critical Mass: How One Thing Leads to Another by Philip Ball

Notwithstanding the merits of the above economic ideas based on classical mechanics, thermodynamics and statistical mechanics, they do not say very much at all about technological innovation.  Each theoretical approach is naturally dependent on the acuity of its underlying assumptions, such as the rational behaviour and economic equilibrium that leads to an optimum market exchange.

It is clear that an innovation theory should not be founded on an a priori assumption of economic equilibrium as novel ideas can be inherently disruptive to this.  It should recognise the relevance of the biological metaphor.  The strength of the relationship with mechanics, which has been deployed for two centuries, must therefore be adapted.

So we will propose a hybrid metaphor combining the biological with the mechanical, and linking these to the social and economics domain to create an integrated science of innovation.

Whether we end with a metaphor or a mechanism, it is not necessary to establish a bloodline between the mechanical, biological and innovation disciplines.  Rather, we leave the last words on this point to the Nobel Prize winning economist Paul Krugman[5]:-

In economics we often use the term “neoclassical” either as a way to praise or to damn our opponents. Personally, I consider myself a proud neoclassicist. By this I clearly don’t mean that I believe in perfect competition all the way. What I mean is that I prefer, when I can, to make sense of the world using models in which individuals maximize and the interaction of these individuals can be summarized by some concept of equilibrium. The reason I like that kind of model is not that I believe it to be literally true, but that I am intensely aware of the power of maximization-and-equilibrium to organize one’s thinking – and I have seen the propensity of those who try to do economics without those organizing devices to produce sheer nonsense when they imagine they are freeing themselves from some confining orthodoxy.



[1] Establishing that kinetic energy is ½mv2 where m is the mass and v the velocity of a moving body

[2] http://en.wikipedia.org/wiki/Tableau_économique

[3] http://en.wikipedia.org/wiki/MONIAC_Computer

[4] As quoted by Eric Smith and Duncan K Foley in Classical thermodynamics and economic general equilibrium theory.  Journal of Economic Dynamics & Control 32 (2008) 7–65.  This paper gives an interesting analysis of some important fundamental differences between the thermodynamic and economic analyses.

[5] For his 1996 talk to the European Association for Evolutionary Political Economy: http://web.mit.edu/krugman/www/evolute.html

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