ABSTRACT
The most interesting questions tend to be also the most difficult ones to answer. In any discipline, such questions might be those that pertain not only to the subject matter of the discipline but have wider implications for other disciplines. This also means that to answer such questions often requires some knowledge of other fields of study. After all, each discipline is a study of only a limited aspect of our very complex reality. In trying to gain this knowledge of reality, we all hope that, while we may never gain the full knowledge of reality, we may at least be a little bit ‘wiser’ about what we don’t know and perhaps more importantly, something about ourselves. The body of knowledge that is the lifetime work of K. Vela Velupillai takes us on a journey of discovery of such kind.1 Where do we begin? My own impression of the ultimate value of Vela’s work is in its contributions to the broadening of our understanding of the discourse in economics by placing it within a wider universe of knowledge. Most of us would like to think of economics as a well-defined discipline – one amenable to mathematical theorizing, empirical verification and policy recommendations. This is done, most of the time, with the rigorous tools of trade that we accumulate over time and often use with complete ignorance of where they came from. The consequence of such lack of exposure and appreciation of the history of economic theory with regards to our use of such tools condemns the discipline to paths that eventually leads to intellectual dead ends. Over the years, Vela has carefully and eloquently written about the manner in which economic theory was mathematized and its consequence.2 This history is that of the axiomatization of economic theory in the Hilbert tradition. It is a history about how economics adopted tools from a certain mathematical tradition (classical real analysis) while ignoring others and, worse, remained ignorant of subsequent developments that shattered the ‘completeness’ of the former (read Gödel). The dire consequence of the path taken in mathematizing economics is the demonstration, using an alternative mathematical tradition such as recursion theory, that most of the solutions or equilibrium (including their existence) derived using classical real analysis cannot be obtained in reality from a computational point of view. This has important implications for economics as almost all
(if not all) economic problems are posed as optimization problems which would imply the use of some algorithms or procedures to obtain the attendant solutions. What then would be a more appropriate way to mathematize economic theory? The choice of an appropriate ‘mathematical language’ to theorize about reality may require a deeper understanding of the nature of reality, i.e. impermanence, nature as a process. This is a view that finds resonance not only in the physical and natural sciences (evolution, thermodynamics) but also in ancient philosophy and religion (Parmenides, Buddha). This, I believe, is very much a view embraced by Vela (2005b) in his unpublished little essay. In this essay, we find a glimpse of the holistic and integrative nature of Vela’s thinking where there is no boundary between views on economics and on life. Moving forward with this line of thinking, we can then argue that the issue at hand is about the nature of the different types of mathematics and whether they lead to structures or systems that can or cannot capture reality. This is not an easy question to answer because ‘reality as process’ also implies that there is no ‘closure’ in reality, i.e. the universe does not stand still for us to capture (even here, we are trapped by a non-Einsteinian notion of time!). Perhaps, this is also related to the ineffectiveness of reductionist methods in making sense of emergence phenomena, where a computable perspective may yield deeper insights into reality – namely, an emergent system is ‘open’ in the sense of being universally computational and that finiteness in itself is an essential element of emergence. These insights are reminiscent of holistic views in older metaphysical traditions (e.g. Tao?) where one’s limitation(s) (e.g. bounded rationality) is an inextricable ingredient of our complex existence. Where do we go from here then? If we use a more ‘appropriate’ mathematical language, one that has process/computation as part of its nature (e.g. recursion theory), and show that we cannot obtain such and such a solution – does it mean that the chosen language has once again failed us or, more intriguingly, has it has captured the essence of reality, namely its impermanence (masquerading perhaps as incompleteness at a point in time) or that the future cannot indeed be known by any finite means and beings? These are deep questions and much of Vela’s writings inspire and prompt us to think beyond the narrow confines of our normal economic mind. Morning dew, Leaving no traces On a leaf . . .
