IS A TRANSDISCIPLINARY PERSPECTIVE ON ECONOMIC …



IS A TRANSDISCIPLINARY PERSPECTIVE ON ECONOMIC COMPLEXIY POSSIBLE?

J. Barkley Rosser, Jr.

James Madison University

Email: rosserjb@jmu.edu

Website:

October, 2009

Codes: A12, B40, C00

Abstract: Marshall’s problem regarding the relationship between economics and physics and biology is considered within the context of the possibility of a transdisciplinary approach that would truly combine the various disciplines. While a combined econophysics is very much an ongoing enterprise, and a possible econobiology may be emerging along several different lines, a full combination of all three is not in sight except possibly in the area of global climate-economy modeling. It is argued that heterogeneous interacting agent forms of complexity are likely to provide the best methods for achieving such transdisciplinary models.

Acknowledgements: The author acknowledges useful input from Richard H. Day.

“When demand and supply are in stable equilibrium, if any accident should move the scale of production from its equilibrium position, there will be instantly brought into play forces tending to push it back to that position; just as if a stone hanging by a string is displaced from its equilibrium position…

But in real life such oscillations are seldom as rhythmical as those of a stone hanging freely from a string; the comparison would be more exact if the string were supposed to hang in the troubled waters of a mill-race, whose stream was at one time allowed to flow freely and at another partially cut off. Nor are these complexities sufficient to illustrate all the disturbances with which the economist and the merchant alike are forced to concern themselves.

If the person holding the string swings his hand with movements partly rhythmical and partly arbitrary, the illustration will not outrun the difficulties of some very real and practical problems of value.” ---Alfred Marshall, 1920, p. 346.

I. Introduction: A Meditation on Marshall’s Problem

Alfred Marshall is rightly recognized as a supreme formulator of the truly neoclassical economics that we find still lurking in most economics textbooks, along with Walras, with this approach arguably culminating later in the work of Paul Samuelson and then the general equilibrium existence theorem of Arrow and Debreu.[1] However, even as he stands in this position of grand expositor of orthodoxy, the quotation above shows that Marshall knew better, that he understood that the vision he promulgated had severe limits when it came to being applied in the real world. While this recognition would be usually shoved into the background, it provided an essential tension that permeates Marshall’s work, something that one can find in the work of most of the recognized icons of neoclassical orthodoxy if one looks closely enough.[2] Thus, Marshall can be seen as a precursor of modern complexity economics, even if only in dark corners of his work.[3]

Marshall is also an appropriate starting point for this paper in that he also attempted to draw into economics influences from other disciplines, most notably physics and biology. It can be argued that he completely failed at integrating these two into economics, especially in some combination of the two. The major parts of his standard theory, reproduced in textbooks, reflects a watered-down version of mid-19th century physics, as Mirowski (1989) has argued, while in his Preface he declared biology to be the “Mecca” of economics, even as he arguably failed to follow through on this declaration with a meaningful effort. This failure would be the touchstone for the critical coiner of the term “neoclassical,” Thorstein Veblen, who denounced Marshall’s use of physics as a static and stultifying method when compared with the possible adoption of Darwinian evolutionary theory that he championed (Veblen, 1898).[4]

So, we can pose the question of this paper as being “Marshall’s problem.” Is it possible to integrate other disciplines, especially physics and biology simultaneously, into economics in a way that both contains its orthodox core as well as providing a way to understand the limits of that core in a complex world? Such a successful integration would be transdisciplinary rather than merely multidisciplinary or interdisciplinary.[5] Is or can econophysics be transdisciplinary (Rosser, 2006)? What about the much less developed econobiology? And can these be integrated into a higher level transdiscipline that can provide a meaningful perspective on economic complexity?[6] This is the modern version of Marshall’s problem.

II. A Collection of Complexities

In order to be able to approach this question we must confront the knotty problem of the meaning of complexity. Many have despaired of finding a clear or useful definition of this widely used (and abused) term. We shall adopt a hierarchical view of this, following Rosser (2009a), seeing three levels of this problem. The lowest level is what Rosser (1999) labeled “small tent complexity,” which emphasizes the assumption that agents are heterogeneous in many ways with respect to each other and that they interact primarily in a local way with their neighbors in some sort of space. This is the sort of complexity described by Arthur et al. (1997), and has been strongly associated with the Santa Fe Institute and computer simulations of such heterogeneous agent-based models.[7] Economic models adopting this sort of complexity rarely exhibit global equilibria or global rationality, often exhibiting evolutionary processes of ongoing change and innovation. Certainly within economics this has been what most people think of when they think of complexity economics, and it emphasizes that in order to understand aggregate phenomena, it is advisable to model from the micro level up explicitly with heterogeneous agents in order to see the emergence of the aggregates, which cannot simply be imputed directly from the behavior of the individuals. This follows Kirman (1992) in his critique of representative agent modeling, and is exemplified for macroeconomic modeling by Delli Gatti et al. (2008).

The second level up is what Rosser (1999) labeled “big tent” complexity, or dynamic complexity, which embeds the “small tent” complexity within it. This can be defined, following Day (1994) as referring to systems that do not endogenously converge on a point, a limit cycle, or a continuous expansion or contraction (although there is some discussion about whether limit cycles should be included or if all periodic cycles should be excluded). This broader definition contains what Horgan (1997) dismissively labeled the “four C’s”: cybernetics, catastrophe theory, chaos theory, and [small tent, or heterogeneous agent] complexity theory, with him coining the term “chaoplexology” to combine the last two. He argued that there was such confusion in all this that observers were ultimately facing “complexity turning into perplexity,” and that each of these four C’s had been intellectual fads, not worthy of serious longer term consideration.

Rosser (1999) responded by agreeing that indeed all of these suffered going through fad phases as “intellectual bubbles,” but that this did not mean that each did not in fact contain a core of useful and reasonable ideas. The overshooting up of prestige for each was followed by a crash that then tended to overshoot in the opposite direction sometimes (although this seems to have happened to a lesser degree with the still speading small tent complexity of agent-based modeling).[8] Furthermore, Horgan indeed picked up on something genuine that has been going on, that these four C’s represent a cumulative intellectual development that has proceeded over a several decade period, drawing on certain underlying themes, most notably nonlinear dynamics. Rather than a faded dead end, this development has in fact reached a critical mass or intellectual bifurcation point, where such ideas are now entering the mainstream, at least in economics to some extent, if not all the way into the intellectual core of economic orthodoxy a la Marshall’s standard story as augmented by Walras, Samuelson, and Arrow-Debreu.[9] Whereas in the past economists would (like Marshall) hide in footnotes oddities such as multiple equilibria that might appear in their models, now they are more likely to trumpet such discoveries and findings as being of central interest.

Finally, the third level of defining complexity is the level that Rosser (2009a) labels meta-complexity, where it is indeed recognized that there is a plethora of definitions of complexity. Horgan (1997, p. 303) provides a list of 45 such categories as gathered up to that time by Seth Lloyd, although many of these appear to be minor variations of each other. Even with its great length it would appear not to be complete, as it does not clearly include either the small tent or broad tent dynamic definitions just discussed, although the last few are connected and associated with those who have worked on agent-based modeling at the Santa Fe Institute (self-organization, complex adaptive systems, edge of chaos). Indeed, there are other meanings that have been used by economists that do not fit into any of the 45 listed by Horgan or into the big tent dynamic definition provided above.[10]

Now it might seem that this sprawling collection of conceptualizations of complexity justifies the jibe of Horgan (drawn originally from Francisco Doria) that complexity became perplexity. However, as noted, many of the definitions are indeed minor variations on a few themes, with information being perhaps the most widespread. As argued by Velupillai (2000), Shannon’s (1948) entropic definition of information provides the original foundation for a series of related definitions of algorithmic and computational complexity due to Kolmogorov, Solomonoff, Chaitin, and Rissanen.[11] These do not fit into the broad tent dynamic definition of Rosser and have been put forward with enthusiasm recently by various observers (Markose, 2005; Velupillai, 2005) on the grounds that they are more rigorous in their definition and measure than other alternatives, and much recent discussion has focused on these and related definitions. Rosser (2009b) provides a defense of the dynamic definition as being more useful in most applications and situations than these definitions for economics, while recognizing their potential ability to provide more exact measures of degrees of complexity.

In any case, for the remainder of this paper we shall mostly focus on the dynamic definitions of complexity, with the greatest part of this on the small tent version that emphasizes heterogeneous interacting agent models, even while keeping these broader views in mind.

III. Econophysics as a Transdisciplinary Perspective?

Probably the most developed potentially transdisciplinary perspective on economic complexity is econophysics. This was only neologized in the mid-1990s by H. Eugene Stanley, with Mantegna and Stanley (2000, viii-ix) defining it as the “multidisciplinary field…that denotes the activities of physicists who are working on economic problems to test a variety of new conceptual approaches deriving from the physical sciences.” While this definition has a peculiarly sociological nature to it (based on who is doing econophysics almost more than what they are doing), the essential idea of applying physics theories to economics is clearly the key, with the recently developing econophysics emphasizing approaches somewhat at variance with the most orthodox economic theoretical approaches. A particular aspect of physicists predominating in this new field is the emphasis on starting with data and trying to find models or theories that might explain the data, while economists tend to assume that their standard theories are correct and then seek to find them working in data. At their most forceful, some argue that economic theory is so useless that econophysics models will completely replace it to the point that students will no longer take Principles of Economics, and will take statistics and physics courses instead (McCauley, 2004).

Since this appearance in the mid-1990s, arguably inspired at least partly by the interactions between economists and physicists at the Santa Fe Institute, the most intensive area of application has been in financial economics (Bouchaud and Cont, 2002; Farmer and Joshi, 2002; Sornette, 2003), with applications to the distributions of income and wealth probably the next most common (Levy and Solomon, 1997; Drăgulescu and Yakovenko, 2001; Chatterjee et al. 2005). Other prominent applications have included the size distribution of cities (Gabaix, 1999) and the size distribution of firms (Axtell, 2001),[12] along with a variety of others (Rosser, 2006), although curiously many of the studies on urban and firm size distributions have been done by economists (e.g. Gabaix and Axtell).

While other arguments and theories have entered into these efforts, a major theme and focus has been upon finding and modeling power-law distributions in these data, which tend to be linear in log-log plots and exhibit kurtosis or “fat tails,” usually ignored in most standard economics models. Roughly, the apparent stylized facts are that financial asset returns clearly exhibit such kurtosis, wealth distributions and the upper ends of income distributions may do so, city sizes almost certainly do so, while there is some evidence of firm sizes doing so, although this is more controversial. The alternative for most of these is either the Gaussian distribution or a transformation of it such as the lognormal or Boltzmann-Gibbs.

While these efforts have moved forward, controversy has broken out over some of the methods used by some econophysicists, with Gallegati et al. (2006) arguing that many econophysics studies claim greater degrees of originality than deserved, that many use insufficiently rigorous statistical techniques, that exaggerated claims of the universality of empirical findings sometimes made, and that many of the theoretical models put forward have difficulties or face unacknowledged limits. Rosser (2008) has argued that while many of these arguments have substance for many econophysics papers in the past, many of these problems are being corrected, especially as physicists are increasingly working with economists, although Lux (2009) has documented how econophysicists can get misled into making embarrassing mistakes if they fall into using overly simplistic economic theoretical models. Rosser suggests that a model of entropic equilibrium by Foley (1994) might provide an interesting physics-based alternative theoretical foundation for the analysis of markets.

However, the question of the relationship between economics and physics is a deep and complicated one, with mutual influences and feedbacks going back a good two centuries, with the fact that much of the standard Marshallian framework was influenced by an earlier and simpler model of physics, as noted by Mirowski (1989). Among the ironies is that the original discoverer of power-law distributions, now being promulgated by physicists to explain economic data, was an economist, Vilfredo Pareto (1897). This would later be reintroduced into dynamic economics by the mathematician Mandelbrot (1963), although one who was initially influenced by him, Eugene Fama (1963), would later turn away from his approach and become among the most prominent developers of the market efficiency hypothesis and conventional financial economics (Fama, 1970). However, among geographers and urban economists, power-law distributions were used over a long time (Zipf, 1941). Another curiosity is that prior to its application to Brownian motion by Einstein (1905), the random walk was applied to the stock market by Bachelier (1900), with this being forgotten, and that this now-very-conventional approach to financial economics was reintroduced into economics by a physicist (Osborne, 1959). Furthermore, the first to apply statistical mechanics models to economics was an economist (Föllmer, 1974), well before the solid state physicists got into the act two decades later (most econophysicists are solid state physicists). So, the question of who influenced whom when is a very tangled one.[13]

IV. Econobiology as a Transdisciplinary Perspective?

It must be stated at the outset that while ecological economics may constitute a self-conscious transdisciplinary enterprise, the same cannot be said for any nascent “econobiology,” with nearly as many of the references to this term being negative and made by econophysicists denying that there can even be a truly scientific econobiology because of its presumed lack of invariance principles (McCauley, 2004, chap. 9). Nevertheless, besides ecological economics, there have long been various forms of evolutionary economics, some more oriented to the biological roots than others, and some implying or emphasizing complex dynamics or potential complex dynamics.[14] Likewise, there has been a well-established mathematical bioeconomics, due originally to Clark (1990), which has been more readily open to models of complex dynamics. This latter in particular looks to be the most serious foundation for a potential econobiology that would be equivalent to and able to interact with econophysics in some form or other (Rosser, 2001, 2009c).

Following the realization that open access fisheries may exhibit backward-bending supply curves (Copes, 1970), a long line of development has followed along the lines of Clark and used various dynamic complexity ideas to study the serious problems of fishery dynamics, including of fishery collapse (Jones and Walters, 1976) and irregular dynamic patterns of fish populations (Conklin and Kolberg, 1994). Such backward-bending situations arise when a fishery gets overfished beyond its maximum sustained yield level, so that increased fishing effort leads to fewer fish being caught, and price hikes lead to such increases in fishing effort. More recently, Hommes and Rosser (2001) have studied complex fishery dynamics within the consistent expectations equilibria framework due to Grandmont (1998) and Hommes and Sorger (1998), with Foroni et al. (2003) studying how these fishery dynamics within backward-bending supply curve situations can generate multiple basins of attraction with fractal basin boundaries.[15]

Another area of study in complex econobiology has involved forestry (Rosser, 2005). While forestry dynamics tend to be much more slowly moving than fishery dynamics, the existence of complicated time patterns of benefits from forests, with animals grazing when they are young through various forms of recreation during middle and sometimes very late periods, along with various externality factors such as carbon sequestration and prevention of soil erosion and flooding, to timber harvesting, can serve as a basis for complex dynamics in optimizing frameworks (Swallow et al. 1990). Furthermore, complex dynamics can arise because of the predator-prey dynamics between insects, birds, and trees in forests (Ludwig et al., 1978), with such dynamics setting up forests for large-scale changes and even collapses in response to apparently insignificant events far away from them, rather reminiscent of the “butterfly effect” of chaos theory, although not specifically a matter of chaotic dynamics (Holling, 1988). This can happen as for example when the draining of a wetland at a crucial location on the migratory route of birds who eat insects on trees causes them to shift to a different forest for their post-migration location, thus triggering an insect outbreak in the old location, decimating the forest.

Just as small changes in migratory patterns of birds can lead to catastrophic collapses of forests, so too can small changes in land management practices lead to sudden, large changes in the character of lakes, as they go from a more normal oligotrophic state to an undesirable eutrophic state as a critical level of phosphorous loading is passed (Carpenter et al., 1999). A detailed study of the nature of the bifurcations points and related mathematics of these systems has been carried out by Wagener (2003).[16]

Yet another example is the possibility of chaotic climatic-economic interactions, which is arguably not econobiology, per se, although impacts on agriculture are part of the feedback loops in these models, with complex oscillations as economic changes affect climatic changes, which in turn lead to economic changes (Chen, 1997; Matsumoto and Inaba, 2000). But these are certainly complex ecologic-economic systems of the highest order and significance, with all the difficult policy issues thereby ensuing (Rosser, 2001; Weitzman, 2007). Arguably of the models we have discussed so far, these may be the ones with the greatest potential for a genuinely transdisciplinary integration of physics, biology, and economics, if not precisely a combination of econophysics as it has developed with some version of econobiology.

The policy issues here involve groups attempting to cooperate in situations regarding common property resources, which traditionally has been studied using game theoretic models based on the prisoner’s dilemma (Sethi and Somanathan, 1996). The search for institutional frameworks that can achieve cooperation in such cases is one of the largest subjects in all of social science, much less economics or econobiology (Ostrom, 1990; Bromley, 1991; Rosser and Rosser, 2006). However, considering the problem from an evolutionary and evolutionary game theoretic stance raises problems of the evolution of cooperation, and the difficult problem of multi-level evolution (Crow, 1953; Hamilton, 1972; Henrich, 2004), which remains a difficult and controversial topic. We note at this point that under certain frameworks of heterogeneous interacting and learning agents, the evolution does not settle down and presents a pattern of evolution with endlessly changing patterns as agents switch from one strategy to another (Lindgren, 1997).

Which brings us to what is arguably the most controversial element of complex dynamics in econobiology, the concept of emergence in evolution, which the preceding discussion of emergence of cooperation among higher level groups can be viewed as a part of. This is an idea that has been vigorously touted, especially by some at the Santa Fe Institute as virtually a central key to evolutionary processes (Langton, 1990; Kaufmann, 1993; Crutchfield, 1994), while being ridiculed as vague and poorly formulated by many critics, ranging from Horgan (1997, chap. 8) to computable economists such as Markose (2005) to econophysicists such as McCauley (2004, chap. 9).[17] Emergence is an old idea in evolution (Lloyd Morgan, 1923), with roots inspiration going back to John Stuart Mill (1843) and his “heteropathic laws,” although reductionist evolutionists such as Dawkins (1989) have long rejected such ideas as retrograde and fanciful “holism” or “organicism,” supposedly disproven by Williams (1966). However, the idea has flourished in many forms and contexts, from general systems theory (von Bertalanffy, 1962) to hierarchical theories of agent-based modeling (Wolfram, 1984) to mathematical models of flocking and herding (Cucker and Smale, 2007). While many do not like this idea, it lies at the heart of the idea of algorithmic market forms (markomata) evolving to higher levels of Chomskyian (1959) hierarchies that has been proposed by Mirowski (2007) as a new form of integration of biology and economics with computation, if not necessarily with physics or econophysics.

V. Does Complexity Really Help Explain Anything about Markets?

So, the Mirowski markomata involves a world in which higher level markets emerge that embed lower level markets, as futures markets embed spot markets, and options markets embed futures markets, and various derivatives markets embed options markets, and so on and on and upward and upward, with substantial increases in these higher-order markets in recent years, The question arises as to whether or not this evolution toward increasing complexity is a good thing or not, with some officials (Geithner, 2006) expressing concern even before the difficulties in real estate markets became clearer in August, 2007 regarding their ability to engage in stabilization policy in the face of financial crisis for the simple reason that they are unable to discern properly what is going on in the markets, and which have played out even more dramatically with the widespread crashes of such markets beginning in September 2008. Of course, a long literature of conventional wisdom has supported the idea that more assets and more markets spread risk, thereby reducing volatility, and increasing efficiency and welfare (Shiller, 2003).

While this view is deeply entrenched, doubts have been raised for some time on both fronts at the purely theoretical level for cases in which markets are incomplete, with Hart (1975) and Elul (1995) showing that welfare may decrease with an increase in the number of assets as long as the system is sufficiently far below being complete (in completeness welfare is maximized in general equilibrium in this standard framework). Citanna and Schmedders (2005) show that price volatility may increase under the same circumstances. Branch (2004) finds considerable heterogeneity of expectations empirically among market traders, and Gerlach et al. (2006) find empirically an increase in market volatility since the 1970s, a period of increasing numbers of assets and market depth. Nevertheless, the conventional theoretical literature has been unequivocal that an ultimate move to complete markets will be welfare improving and stabilizing.

However, this general result of convergence on greater stability and efficiency as markets approach completeness becomes overturned once agents with heterogeneous expectations and strategies are allowed to enter the models, as they are certainly present in the real world (Shiller, 2000).[18] Brock, Hommes, and Wagener (2009) present a model of heterogeneous traders dealing in Arrow securities who vary in their expectations formation and in their strategies, with some being rational, some exhibiting systematic bias, and some extrapolating trends. They examine a variety of cases, and find a variety of outcomes. However, a fairly robust result is that if there are a sufficient number of traders who extrapolate trends, then increasing the number of hedging instruments may well increase the volatility of the markets and lower the welfare generated by the market, despite the best efforts of rational traders in the market. This result harks back to an old literature that has blamed “trend chasers” and “technical traders” for destabilizing markets (Baumol, 1957; Zeeman, 1974).

While this is certainly an interesting result, it does not entirely capture the sense that one gets from the discussions by people such as Geithner. This result involves an unequivocal increase in volatility as measured by variance with an increase in Arrow securities, assuming that there are enough trend extrapolaters in the market. However, much discussion by policymakers seems to suggest that there is a conflict in what is going on, that indeed much of the time the increase in the number of securities actually does stabilize the market, reducing volatility and perhaps increasing welfare, while at the same time the danger of financial fragility has increased, with fears of a “Minsky moment,” a very large collapse (Minsky, 1972). Such fears heightened after August, 2007, culiminating in the crisis of September 2008. In effect, it would seem that rather than an unambiguous increase in variance, what may be happening is a reduction of variance coinciding with an increase in kurtosis, a fattening of the “fat tails.” Such an outcome would resemble the “stability-resilience tradeoff” observed in ecology by Holling (1973). Such an outcome might well be derivable from the Brock-Hommes-Wagener model if there is a sufficiently nonlinear responsiveness of the movement in and out of being trend extrapolaters, which would be consistent with more general results found in Brock and Hommes (1997), where increases in the willingness to change strategies tends to destabilize and complexify dynamics.

We shall note one further model in which a real world financial market phenomenon is explainable within the context of a model with heterogeneous agents. This is Gallegati, Palestrini, and Rosser (forthcoming) which shows how with heterogeneous agents who learn and face transactions costs and Minskyian financial constraints, market dynamics can occur that exhibit pattern of a bubble going up, peaking, declining slowly for a period (the “period of financial distress”), and then crashing suddenly sometime later. No theoretical model has clearly generated such patterns,[19] even as Kindleberger (2000) has documented that the overwhelming majority of famous historical bubbles going back to the early 1600s have followed such a pattern rather than the accelerating up and then crashing from the peak pattern that most theoretical models generate (or the also rare but not well-modeled, slow move up followed by a slow move down, which may not be a bubble anyway). Such patterns were long observed in such famous historical bubbles as the Mississippi Bubble and the South Sea Bubble, with much discussion about the differences between the traders who got out at the peak versus the less well-informed, experienced, and so forth traders who were left “holding the hot potato” as the market slid from the peak before crashing (Rosser, 2000, chap. 5). These discussions were ruled out in a world where agents were assumed to homogeneously possess rational expectations, but are allowed in a world of heterogeneous expectations.

So, allowing for heterogeneous interacting agents, the sine qua non of the “small tent” complexity, proves to be very helpful in understanding real phenomena observed in financial markets both historically and currently.

VI. Conclusion

Regarding Marshall’s problem, we have probably failed to solve it, except for the occasional example such as analyzing global warming where physical, biological, and economic issues all come into play, or perhaps in situations where an econophysics model might encounter an ecological principle such as Holling’s stability-resilience tradeoff. More generally the old conflict between the greater precision and quantitative rigor of the physics-based models as compared with most biological or evolutionary models appears to come into play.

However, we have seen that at the lower level of transdisciplinary approaches such as econophysics or econobiology, these may well be very useful when combined with various sorts of complexity methods to analyze economic dynamics. A grand synthetic transdisciplinary perspective on economic complexity is probably beyond our reach, except in occasional cases, but the transdisciplinary perspective at a more modest level is alive and well, and promises an interesting research program.

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[1] Colander (1995) has argued that while his contemporary Walras developed explicitly the concept of general equilibrium, Marshall was well aware of the idea, but avoided developing it openly precisely because of his awareness of the potential complications and complexities involved. Both he and Walras were aware of the possibility of multiple equilibria, and in his early years Walras was more aware of these vicissitudes as well, becoming more “orthodox” after 1900 (Walker, 2006). For a discussion of how “orthodox economics” is not necessarily identical to “mainstream economics” see Colander et al. (2004), with the essential idea being that “orthodox” refers to an intellectual framework, whereas “mainstream” refers to a sociological category, those who are in the leading and dominant positions in the profession.

[2] So, Arrow would be one of the founders and principal supporters of the Santa Fe Institute and Debreu would contribute to the weakening of general equilibrium theory by the Sonnenschein-Mantel-Debreu theorem (Debreu, 1974).

[3] Marshall’s invention of the concept of quasi-rent also provides the base for an alternative approach to dynamics as developed by Day (1963, 2004).

[4] See Hodgson (1993) for further discussion.

[5] The term “transdisciplinary” is used by ecological economists to describe their discipline. Richard Norgaard in Colander et al (2004, p. 248) argues that “multidisciplinary” refers to separate disciplines conversing with each other while maintaining fully their mutual distance. “Interdisciplinary,” which came into fashionable use after multidisciplinary, refers to the establishment of narrowly specialized niche disciplines that take a few ideas from one discipline and a few ideas from another to create this specialized niche discipline, such as “water economist,” who would draw on parts of hydrology and parts of economics. Transdisciplinary implies a broader linking and integration across the disciplines at a deeper level.

[6] We shall focus on these two combinations of natural sciences with economics, while recognizing that other such combinations exist or may exist that we shall not discuss further here, with sociophysics (Chakrabarti et al., 2006), although this arguably revives an earlier effort that went under different names (Weidlich and Haag, 1983). We also shall not discuss such well-established transdisciplines within the social sciences such as political economy, economic psychology, and socio-economics. There is a barely nascent econochemistry that is barely developed at all (Hartmann and Rössler, 1998; Rosser, 2006).

[7] Although he used a chessboard rather than a computer to study his models, it is generally accepted that the first such efforts were made by Schelling (1971).

[8] Probably the hardest crash of these was experienced by catastrophe theory, and Horgan used its crash to denigrate the other three. However, Rosser (2007) provides a defense of the use of catastrophe theory in economics, and points out that among mathematicians it never experienced either the initial fad/bubble (or not to the degree it did in other disciplines) and thus did not experience the crash as severely, always retaining respectability as a branch of broader bifurcation theory (Arnol’d, 1992). See also Puu (2003).

[9] That this may be the case has been argued by Blume and Durlauf (2005).

[10] One of these is “structural,” as used by Pryor (1995) and Stodder (1995). Rosser (2009b) argues that these really “complicatedness” rather than “complexity,” noting that these two words come from different roots in Latin (Israel, 2005). They simply refer to their being many interconnections between different sectors of the economy, some of them obscure, as in an input-output matrix with many entries. For an alternative list of ideas of economic complexity, see Warsh (1984).

[11] Albin (1982) was the first to apply the computational problems arising from the Gödel incompleteness and inconsistency theorems of logic to economics. See also Albin with Foley (1998).

[12] Axtell’s study supported a much earlier one that had been much ignored by economists by Ijiri and Simon (1977).

[13] It has been argued that an early conscious advocate of the idea that natural and social sciences should rely upon common statistical theories was first put forward coherently the physicist Majorana (1942), just prior to his mysterious disappearance, making him arguably the first true econophysicist.

[14] Hodgson (200^) has argued that Darwinian evolution is the supreme complex system.

[15] See also Bischi and Kopel (2002).

[16] A broader study of critical ecological thresholds of many sorts has been done by Muradian (2001).

[17]

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