10
arguably over half of the 45 definitions listed by Lloyd constituting one or another of its
varieties. Many of these definitions are derived from the already-mentioned information
theory of Shannon and Weaver (1948), e.g. Solomonoff (1964) and Kolmogorov (1965),
which eventually boil down to descriptions of the minimum length of a computer
program that will describe the information or system (Chaitin, 1987) or some variation of
this (Rissanen, 1989).9 A harder line view is that a system is only truly computationally
complex if it is not computable at all (Blum, Cucker, Shub, and Smale, 1998).10
Advocates of this approach (Albin with Foley, 1998; Velupillai, 2000, 2005,
2009; Markose, 2005) argue that its greater precision makes it a superior vehicle for
scientific research in economics. It must be admitted that there is some truth to this.
Nevertheless, the vast majority of research in economics that identifies itself with
complexity tends to be more of the dynamic variety described above. Furthermore, this
definition is certainly less useful when we consider the question of the economics
profession itself as a complex evolving system. Here we consider that the first two
definitions provide a more useful construct for analysis than this admittedly challenging
and substantial view of complexity, which we expect has the potential for important
future research in the area of economic complexity. Not only is the economics profession
a set of hierarchies, but it also evolves through a set of local interactions among dispersed
networks of influence.
4. What Do We Mean by Cutting Edge Complexity Work?
9 Velupillai (2000, 2005, 2009) discusses the relationships between these different definitions.
10 In such cases the program is of infinite length, that is, it does not halt. A fundamental source of this may
involve problems associated with the incompleteness concept of Godel (Lewis, 1985). An application to
general equilibrium is due to Richter and Wong (1999).