View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Unitn-eprints Research UNIVERSITA' DEGLI STUDI DI TRENTO - DIPARTIMENTO DI ECONOMIA _____________________________________________________________________________ ECONOMICS AND THE COMPLEXITY VISION: CHIMERICAL PARTNERS OR ELYSIAN ADVENTURERS? Kumaraswamy Velupillai _________________________________________________________ Discussion Paper No. 7, 2003 The Discussion Paper series provides a means for circulating preliminary research results by staff of or visitors to the Department. Its purpose is to stimulate discussion prior to the publication of papers. Requests for copies of Discussion Papers and address changes should be sent to: Prof. Andrea Leonardi Dipartimento di Economia Università degli Studi Via Inama 5 38100 TRENTO ITALY Economics and the Complexity Vision: Chimerical Partners or Elysian Adventurers? Part I1 K.Vela.Velupillai2 Department of Economics National University of Ireland, Galway Galway Ireland and Department of Economics University of Trento Via Inama 5 38100 Trento Italy October 6, 2003 1This work began as a review article of:Complexity and the History of Economic Thought, edited by David Colander, Routledge, London,UK, 2000; & The Complexity Vision and the Teaching of Economics, edited by David Colander, Edward Elgar, Cheltenham, UK, 2000. It has, in the writing, developed into my own vision of complexity economics. I am deeply indebted to my friend, colleague and fellow Salta- Zambaist, Nico Garrido, for invaluable help in preparing this paper. Alas, he is not responsible for the inevitable infelicities that remain. 2e-mail:[email protected] or [email protected] Contents I Visions and Traditions 2 1 Introduction 2 2 A Cautionary Tale - or Two 7 2.1 Mondrian and Klee - Pitfalls of Super¯cial Analogies . 7 2.2 Screwed up - and down - Chaos . 10 3 Evolution and Varieties of the Complexity Vision I 15 3.1 The von Neumann Tradition . 18 3.2 The Turing Tradition - Mark I . 24 4 Economic Theory, the `Teaching of Economics' and the Com- plexity Vision 28 1 Part I Visions and Traditions 1 Introduction `If, then, it is true that the axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented, can we ever hope to ¯nd the right way? . I answer without hesi- tation that there is, in my opinion, a right way, and that we are ca- pable of ¯nding it. Our experience hitherto justi¯es us in believing that nature is the realisation of the simplest conceivable mathemat- ical ideas. I am convinced that we can discover by means of purely mathematical constructions the concepts and the laws connecting them with each other, which furnish the key to the understanding of natural phenomena.' Einstein in his Herbert Spencer Lecture: On the Methods of Theo- retical Physics, given at the University of Oxford on 10 June 1933, quoted in: [69], pp.136-7; italics added. I begin with this apparently paradoxical statement by arguably the greatest natural scientist of the 20th century for two reasons. I interpret it, ¯rstly, as a salutation to Ockham's Razor; and secondly as a paradox that has to be confronted by complexity theorists of any variety. A principle that unites every kind of complexity theorist,and they are a richly varied class (see x3 and x5, below), is that observable `reality' pertaining to any ¯eld, physics, biology, chemistry, applied mathematics, economics, etc., is complex but this complex- ity emanates from simple building blocks - of concepts, methods and rules of interaction. Why, then, should this supreme scientist, of powerful intuitions, claim that nature is the realisation of the simplest conceivable mathematical ideas? Is it because even the `simplest conceivable mathematical ideas', when realised in natural phenomena, become enveloped in complex manifestations and it is the task of the theorist to disentangle the apparent complexities and bare the hidden simplicities underpinned by, and in, simple laws and concepts? Such an interpretation would be welcomed by the complexity theorist who is in the habit of showing how even unbelievably simple mechanisms are su±cient to demonstrate and encapsulate the complexity of phenomena in the natural, physical, biological, social and other phenomenological worlds. 2 But, for me at least, a paradox remains: why should simple mathematical ideas be manifested as complex natural phenomena? Why is it not the case that the simplicity is not carried over, uniformly, to nature's manifestations, too? And if it does not, as the complexity theorists are wont to point out and, indeed, use as their starting point and as a justi¯cation for their vari- ous disciplines, at what point does the transformation from simplicity of the mathematical ideas to the complexity of natural phenomena take place and can it be determined? I will have my own answer to this question when I dis- cuss computational complexity theory, a variety of complexity theory hardly touched in any of the papers of the two volumes being reviewed here. So much is being written about complex systems that one tends to forget that one of the guiding principles of generating complex dynamics has been to use simple building blocks. In a sense the paradox of complex systems and complex dynamics is that they emerge, endogenously, from simple interactions between simple entities - and the simplicity in the last two senses are, usually, intuitively obvious, requiring almost no de¯nitions of any sort. However, the more usual tenet of simplicity is, of course, some version of Ockham's Razor. It is well to bear in mind this tenet, or some equivalent version of it, at least tacitly, when reading this essay. When the Review Editor, through the good o±ces of one of the Editors, approached me almost one year ago about writing a Review Article of these two books, I agreed almost with alacrity. I expected that my evaluation of the contents and structure of the books would be largely positive, given my own intellectual background and my current research agenda, and that I would, in the process of writing it, learn something about the frontiers of the subject. I did not expect the contents to present new breakthroughs in conceptual un- derstanding of any aspect of complexity theory; nor did I expect the books to contain new techniques for analysing complex systems or new theories of complexity. I did expect, however, new perspectives on teaching some as- pects of complex systems or complexity theory to economists and, perhaps, also new ways of incorporating complexity themes in standard or orthodox economic theories. I thought also that there may well be new perspectives and evaluations of past theories and theorists, especially when viewed from a complexity theoretic point of view (whatever that may turn out to be, which I also expected the books to clarify or, at least, classify in some useful way). But now, almost one di±cult year later, the ¯nal product of my painful and sad struggle through these two books might appear in a largely negative form. It is not that I am, in principle, opposed to or sceptical about a complexity vision for economic theory; nor am I against a complexity vision to reinterpret 3 aspects of the history of economic thought and theory. For example Duncan Foley's recent book, [27], is an excellent example of what I ¯nd encouraging and interesting from this latter genre of work. It is simply that the contents of the books under review here are less than careful in their doctrine-historical re- search, their mathematical underpinnings and conceptual clari¯cations. Even when they venture out of these narrow domains and explore or invoke images and metaphors from, for example, the worlds of art, mathematical logic and applied mathematics, the claims are so preposterous that my initial enthusi- asms and natural empathy were gradually eroded and I felt that these works do a disservice to those of us who would like to promote a complexity vision for, and of, economic theory, applied economics and the history of economic thought. Emergence, order, self-organisation, turbulence, induction, evolution, crit- icality, adaptive, non-linear, non-equilibrium are some of the words that char- acterise the conceptual underpinnings of the `new' sciences of complexity that seem to pervade some of the frontiers in the natural, social and even the human sciences. Not since the heyday of Cybernetics and the more recent brief-lived ebullience of chaos applied to a theory of everything and by all and sundry, has a concept become so prevalent and pervasive in almost all ¯elds, from Physics to Economics, from Biology to Sociology, from Computer Science to Philosophy as Complexity seems to have become. An entire Institution, with high-powered scientists in many of the above ¯elds, including several Nobel Laureates from across the disciplinary boundaries as key permanent or visiting members, has come into existence with the speci¯c purpose of promoting the Sciences of Complexity1 I have found Duncan Foley's excellent characterisation of the objects of study by the `sciences of complexity' in [27], p.2, extremely helpful in provid- ing a base from which to approach the study of a subject that is technically 1I am referring, of course, to the Santa Fe Institute, which, refreshingly, has thought it prudent to have a permanent Economics division from the outset. In some senses the books being reviewed can almost claim to be manifestos of the Santa Fe approach to the study of complexity and its application to economic theory and applied economics. But, on a sceptical note, the almost untrammelled enthusiasm for a uni¯ed vision for all of the disciplines has the danger, in my opinion, of making essentially moral, human and social sciences like economics handmaidens to the concepts and methods of physics and, in this sense, we seem to be travelling along well trodden paths of the past.