世界資本主義システムにおける蓄積と混沌の体系的なサイクル：ミッシングリンク|社会経済レビュー|オックスフォードアカデミック
Systemic cycles of accumulation and chaos in the world capitalist system: a missing link ★
Abstract
We re-examine the systemic cycles of accumulation (SCA) of Arrighi (2010) and Arrighi and Silver (1999) which provide a framework for the analysis of the cyclical patterns of geographical expansion of trade and production and the related shifts of hegemonic power within the world capitalist system. Within the SCA framework, the last stage of a hegemonic cycle is characterized by what is called 'systemic chaos'. However, the drivers of these dynamics have not been explicitly analyzed. This article fills this gap by providing a link between the accumulation process and systemic chaos. Introducing the logistic map into the SCA analysis, our approach provides the missing detailed understanding of how systemic chaos is an outcome of the contradictory socioeconomic dynamics of capital accumulation itself while being based on the key insights of the SCA framework of hegemonic cycles.
1. Introduction
A rich literature within comparative and historical sociology has focused on hegemonic transitions as a theoretical lens to interpret geographical and socioeconomic reconfigurations (e.g. Gilpin, 1981; Cox, 1987; Frank et al 1996; Peet, 2002; Gunitsky, 2014). This has obtained new relevance in the context of the ongoing shifts in the global economic order. The influential work of Arrighi (2010) and Arrighi and Silver (1999) on the theory of systemic cycles of accumulation (SCA) provides an analytical framework where historical capitalist development is explained by hegemonic cycles that emerge from internal contradictions of capital accumulation which continuously evolve as capital overcomes socioeconomic barriers to accumulation. The accelerating disintegration of the global political and economic order amidst the rising tension between the USA and China and the confrontation between Russia and the West raises the question of the stability of the current world system with new urgency. In Arrighi and Silver's framework, the immanent instability of the present juncture can be characterized by what is known as chaos, a state of a complete lack of order. However, the concrete link between the drivers of this state of disorder and the general processes which define the SCA remains loose. In this article, we show that by expressing the SCA accumulation process as it occurs in the course of an SCA through a logistic map, we are able to consistently replicate the different phases in the accumulation cycle and establish the link between chaos and the rest of the SCA dynamics.
The notion of 'chaos' has been introduced to the study of world systems by Abu-Lughod (1989) who compared world systems with weather systems, while Rosenau (1990) applied the concept of chaos to changes in world politics. Arrighi (2010) and Arrighi and Silver (1999) build on these previous contributions and introduce the concept of 'systemic chaos' to capture systemic behavior during hegemonic transitions and the related spatial reorganization of trade and production within the world system. Both from a mathematical, and a political economy viewpoint, what is most interesting is not the observation that there are chaotic dynamics as such, but to develop an understanding of the specific forces and their interaction which drive the chaotic behavior of a system (which can be physical, social, political, economic etc.). Identifying the drivers of chaos has been a key focus in the research of Rosenau (1990), Arrighi (2010), as well as Arrighi and Silver (1999). They do so by studying hegemonic shifts in the past and highlight that their 'investigation has sought clues as to what [the] underlying patterns [of the chaotic world] might be in the present turbulence by uncovering the underlying patterns in comparable past instances of systemic change' (Arrighi and Silver, 1999, p. 22).
Arrighi and Silver's SCA analytical framework posits a repeated pattern in the dynamics of the accumulation of capital where an initial phase is characterized by stable accumulation concentrated around a specific geographic location which is followed by a transition characterized by a spatial reorganization where the system exhibits turbulent dynamics. The increasing geographical expansion and intensification is on the one hand able to overcome existing barriers to capital accumulation but at the same time further destabilizes the capitalist system as a whole. The end of an SCA overlaps with the end of a given hegemonic center and the birth of a new one starting with the stable expansion of accumulation in this new location. This cyclical behavior is shown in the graph from Arrighi (2010) reproduced below.
As Arrighi (2004, 2007) also argues, the SCA framework shares some of the key insights of Harvey's (1981, 2003), theory of 'spatio-temporal fixes' and 'switching crises' according to which spatial expansion and geographic reorganization can temporarily overcome crises which are the outcome of so-called barriers to accumulation. But this spatial expansion at the same time creates new crisis tendencies. The fact that the spatio-temporal fix does not provide a permanent solution provides a useful intuition regarding why according to the SCA approach, the process of accumulation is turbulent. However, even when we add Harvey's insights, it remains open to what the precise dynamic is, which forges the path from turbulence to chaos. This leads to the more general question of whether there is a theoretically consistent way to add this missing link between turbulence and chaos to the SCA framework.
By linking the SCA framework to the logistic map, we show that the foundational socioeconomic dynamics described by Silver and Arrighi in relation to the initial phases of global capital accumulation can indeed give rise to chaos in the strict mathematical sense of this term. Focusing on the specific (mathematical) definition of chaos with respect to the accumulation process, is part of the contribution of this work, as through this we are able to connect chaos with the rest of the SCA. More precisely, in the theory of SCA, each long cycle is composed of two phases: The first phase (A-phase) exhibits stability while the second one (B-phase) is characterized by turbulence and geographic shifts. The B-phase also corresponds to a period of expansion of financial activities across sectors and space where financial markets become the dominant source of profits. We show that during the B-phase, chaotic dynamics governing the accumulation process can emerge and this emergence is part of the financial (and commercial) expansion of the accumulation process to overcome its previous barriers.
The logistic map is not only an elegant mathematical choice for our purpose of establishing a link from turbulence to chaos due to its simplicity. The logistic map also resonates directly with Arrighi's (2010) own graphic depiction of the accumulation process as illustrated in the figure above. The logistic map represents the evolution of a variable over time, where the specific dynamics of the process depend on the value of what is called a bifurcation parameter. Arrighi and Silver (1999), too, refer to a bifurcation point at which the world system changes its behavior qualitatively. In our interpretation of the logistic map, the bifurcation parameter corresponds to barriers to capital accumulation. These barriers can be temporarily overcome through a spatial expansion of commercial and financial capital activities. Put differently, an expansion of commercial and financial capital activities leads to an increase in the value of the bifurcation parameter. As the value of the parameter grows, the dynamic behavior of the whole socioeconomic system changes. These changes occur in distinct phases in Arrighi and Silver's theory as well as in the logistic map. As a result, we can show that the barriers to accumulation and the related push to overcome these can be systematically interpreted using the logistic map and can be linked to the phases in the SCA. The last phase characterized by chaotic dynamics—as discussed in Arrighi (2010) and Arrighi and Silver (1999)—now arises directly from the preceding turbulent phase.
The structure of the rest of the article is as follows. The next section provides an overview of the different literatures to which our article is related and discusses the respective contributions. Section 3 presents the key points which define the SCA framework and its connection to the spatio-temporal fix. It also introduces the logistic map as a baseline model of the accumulation process in SCA, by explicitly linking the map's bifurcation parameter to the barriers of capital accumulation. In Section 4, we show how the increase in the value of the bifurcation parameter to overcome accumulation limits leads to a sequence of different accumulation dynamics which correspond to the different phases in SCA, including the chaotic one. The final section provides a concluding discussion.
2. Links to relevant literatures
In addition to working out the concrete link between chaos and the rest of the dynamics characterizing the SCA, our work makes a number of additional contributions within the broader field of socioeconomics. First and foremost, our reinterpretation of SCA provides a framework to integrate different layers of social change (e.g. territories, place, space, time, scale, social, economic (Jessop et al, 2008) and provides a language to interpret the non-linear behavior in socioeconomic change in the context of hegemonic shifts. Within this approach, we strengthen the systemic link between SCA, spatio-temporal fixes and switching crises. Arrighi (2007) points to the synergies between the SCA framework and Harvey's spatial analysis. This article aims to provide a step toward a systematic integration of these two foundational contributions through a careful analysis of their relationship in the different phases of cycles of accumulation.
Second, while our approach provides an analytical link between the historical patterns analyzed within the SCA framework, we do not claim that the outcome of the process that we analyze is predictable or predetermined. We show how the logistic map can be used as an interpretative tool, which can help us clarify the phases and transitions in the SCA theory on its own terms. The way in which the bifurcation parameter moves is exogenous to the logistic map and depends on political and socioeconomic processes that are historically contingent and shaped by human agency. If the barriers of accumulation are overcome as a result of these socioeconomic processes determined outside our formulation, the logistic map can provide us with a heuristic to interpret the dynamics that arise. As a result, our observation not only confirms the consistency between the rise of systemic chaos and the accumulation process in SCA but also reformulates the B-phase as being composed of two distinct sub-phases—turbulence and chaos—that prepare the hegemonic shift.
Third, our article is also linked to different works within the Social Sciences which have used logistic maps or their continuous time analogue, the logistic equation, to model a variety of social and economic processes which are characterized by complex dynamics. The logistic map was first introduced by May (1976) to study the evolution of a population of insects. Epstein and Axtel (1996) use a logistic growth function, which is related to the logistic map, to model population dynamics in an environment with finite resources. Di Guilmi and Galanis (2021) and Di Guilmi et al. (202) use the logistic equation to model the effects of the relative share of voters on inequality and capitalists' taxes respectively. Galanis et al. (2022) use a logistic equation to model the influence of countries' climate action on the reduction of greenhouse gas emissions. Works in economics such as Miśkiewicz and Ausloos (2004) and Tarasova and Tarasov (2017) use a logistic map to model business cycles. While logistic maps and logistic equations have been used in different setups to study the evolution of social and economic phenomena, to our knowledge, our article is the first to apply the logistic map to the study of long-run dynamics of the world capitalist system.
Fourth, our work is also broadly related to a variety of works within political economy which look at how various social and economic interactions lead to distinct phases of capitalist development which in some cases take a cyclical form. While these literatures are too extensive to be comprehensively discussed in this literature review, we highlight some of the most relevant contributions to our work. The role of accumulation dynamics in capitalist systems is a key focus of the (French) regulation approach, where the economic processes of accumulation generate a stabilizing social and institutional framework which in turn enhances the stability of the accumulation path (Aglietta, 1979; Lipietz, 1986; Boyer, 2000). From a similar viewpoint, the social structure of accumulation provides insights into variations (long waves) of social structures characterizing different phases of capitalist development. In the SSA, each newly emerging structure creates conditions which initially allow for accumulation to expand and then create contradictions leading to its own destruction (Gordon et al., 1982; Bowles et al., 1986, 1990; Kotz, 1987). Following the more traditional long-wave studies pioneered by Kondratieff (2004 [1922]) and Kondratieff and Stolper (1935) and Schumpeter (1927, 1939), Mandel (1975, 1980) locates the slow and steady dissolution of capitalist expansion in a falling rate of profit. Neo-Schumpeterian studies discuss the emergence of long waves where technological advancements driven by the search for profitable outlets for capital, followed by the diffusion of innovations, exhaust economic expansions, leading to a slowdown of accumulation (Mensch and Schnopp, 1980; Freeman, 1983; Perez, 2003). All of these theoretical approaches have in common that they link capital accumulation to larger processes of socioeconomic change. Arrighi's work builds on these previous contributions and links his cyclical vision of historical change to chaos theory. Our article now builds a bridge between Arrighi and chaos in a mathematical sense.
3. SCA
The first two phases that we observe in the logistic map perfectly fit the 'A' and 'B' phases of the SCA framework. We argue that this chaotic phase 'endogenously' evolves from the dynamics of turbulence: capital continues to further extend the various forms of expansion in the turbulent phase to overcome new barriers to accumulation. In this process, turbulence eventually gives way to chaos. Thus, turbulence and chaos should be seen as two sub-phases within the B-phase of capitalist expansion of various socioeconomic forms. In the phase of turbulence, the role of the spatio-temporal fix as one of the ways in which accumulation barriers are overcome becomes more prominent and a switching crisis is set in motion. Nonetheless, the hegemon remains initially dominant as the financial center of the capitalist system. In the chaos phase, these two processes—the financial dominance of the outgoing hegemon and the dominance of the emerging hegemon in production—come into conflict. This conflict breeds chaos and the accumulation process becomes erratic as the global socioeconomic order starts to disintegrate. This prepares the geographic shift in hegemony. As a result, our observation not only confirms the consistency between the rise of systemic chaos and the accumulation process in SCA but also reformulates the B-phase as being composed of two distinct sub-phases—turbulence and chaos—that prepare the hegemonic shift.
3.1 General framework
In the long 20th century, Arrighi (2010) presents an analysis of hegemonic cycles in the capitalist world system. For Arrighi, '[t]he concept of "world hegemony" … refers specifically to the power of a state to exercise functions of leadership and governance over a system of sovereign states' (Arrighi, 2010, p. 28). This power is derived at least in parts by the capacity of the hegemonic state to lead the world system in a way that is perceived by other states as being not only in the interest of the hegemon but also conducive to a more general interest (Arrighi, 2007, p. 149). SCA drives hegemonic cycles and rests on Braudel's (1984) notion of reoccurring financial expansions (Arrighi, 2001). In such reoccurring financial expansions, profits which are initially plowed back into the further expansion of trade and production but eventually cannot be invested without jeopardizing profit margins, lead capitalist agencies to hold larger portions of their incoming cash flows in liquid form.
Arrighi argues that over the last 700 years, the capitalist world system has experienced four different SCA each of which corresponds to a different world hegemon and a different geographic location of the core of the capitalist world system—the Italian city states, the Netherlands, Great Britain and most recently the USA. SCA start with an initial material expansion and endogenously leads to financial expansion where large sums of capital are transferred to the rising global center of accumulation, providing the economic foundation for the hegemonic transition. Importantly, each of the Dutch, British and US hegemonies has been the outcome of a competitive struggle for world leadership. This struggle creates the conditions for chaos and hegemonic crises, gives rise to new SCA and new hegemons, and also creates an ever-greater global concentration and consolidation of economic and political power. Each cycle exceeds the previous one in terms of the mass of accumulated capital and geographical size as well as the complexity of the organization and integration of previously externalized processes.
According to Harvey (1981), geographical expansions of financial and commercial capital provide a 'spatial-fix' allowing to temporarily overcome economic crises related to low profitability. Importantly, Harvey (1981, 2003) does suggest that the spatial fix is linked to the permanent process of capital accumulation and hence is not just a spontaneous solution to acute crises related to the accumulation process. The link between the spatial fix and finance is spelled out in The New Imperialism, where Harvey (2003) includes the temporal aspect of the spatial fix and coins the term 'spatio-temporal fix'. Harvey's contribution is to the tradition of theories of imperialism going back to Luxemburg (1951 [1913]), Lenin (1963 [1916]) and Hobson (1902) who have all developed the expansionary drive of capitalism as a key feature of the accumulation process. Harvey locates the drive for expansion in the sphere of realization (appropriation of surplus value), and identifies finance capital as the manager of this process. A switching crisis constitutes the acute form of the spatio-temporal fix where capital is devalued in one place and future income thus starts to flow from other geographic regions (Harvey, 2003, pp. 121–122). As Foley (2013) develops, this corresponds to a falling apart of value creation and value appropriation. To overcome barriers to accumulation, value creation is relocated to the periphery, but that value is still appropriated in significant parts by capital from the old hegemonic center. This means that spatio-temporal fixes lead to an increasing dissociation between those two moments (production and appropriation of value) in the accumulation process, actually exacerbating their contradiction, which in turn necessitates complex politico-institutional fixes.
There are clear overlaps between the SCA, spatio-temporal fixes and switching crises. In fact, Arrighi (2007) points to the link between Harvey's concept and SCA. However, he refrains from a systematic incorporation of his and Harvey's conceptualizations. We aim to do so here and show that by consolidating them, the transition from tranquillity to chaos can also be supported coherently within this expanded framework.
Harvey's concept of the 'spatio-temporal fix' ultimately presents an interpretation of Marx. Marx captures this idea when he writes: 'The tendency to create the world market is directly given in the concept of capital itself. Every limit appears as a barrier to be overcome. … [but] … it does not by any means follow that it has really overcome it, and, since every such barrier contradicts its character, its production moves in contradictions which are constantly overcome but just as constantly posited' (Marx, 1973, pp. 408–410). Capital finds a way out of overaccumulation, but the spatio-temporal fixes are no permanent solutions. Harvey (1982, p. 192) defines overaccumulation, in general, as 'a surplus of capital relative to opportunities to employ that capital'. More specifically, overaccumulation can take more particular manifestations, all arising from the contradiction between the evolution of the productive forces and barriers posed by social relations, such as 'a glut of material commodities on the markets expressed as an excess of inventories over and beyond that normally required to accomplish the smooth circulation of capital', 'idle capital within the production process', 'surplus money capital and idle cash balances over and beyond the normal monetary reserves required', 'surpluses of labour power—underemployment in production', or 'falling rates of return on capital advanced expressed as falling real rates of interest, rates of profit on industrial and merchants' capital, declining rents, etc' (Harvey, 1982, p. 195). However, when overaccumulation occurs, capital like water is finding new avenues when faced with a blockage, and will pursue new opportunities for accumulation. But eventually, these new opportunities, too, will be exhausted.
Arrighi (2007, p. 25) takes inspiration from Adam Smith's concept of the extent of the market as limiting the degree of the social division of labor and as he points out, rather than seeing the economic independence of the political, Smith had built his analysis on Hobbes' insight that wealth and power are inseparable. In fact, Weber (2019) shows the significance of this link for Smith's political economy in general, especially for his conceptualization of money. Arrighi (2005a, 2005b) also stresses similarities to Arendt (1958) who links the accumulation over and above what can be invested profitably to a spatial expansion of capitalism. There, 'superfluous men' and 'superfluous capital' search for employment abroad as a solution to the internal contradictions that created that surplus. The idea of such an 'overaccumulation crisis' has roots both in Smith and Marx and is fundamental in SCA. According to Smith, there is a general tendency for profits to fall when too much capital is competing as a result of general overaccumulation. This drives up wages and squeezes profits. Another reason for falling profits is overproduction: Marx suggests that when wages are too low, aggregate demand is falling short of supply pushing down profits. For a discussion on the tendency of the profit rate to fall see Foley (1986) and Fine and Saad-Filho (2016) among others. The fact that '[o]nly the unlimited accumulation of power could bring about the unlimited accumulation of capital' (Arendt, 1958, p. 137) highlights the significance of political organization for the expansion of capital.
Due to the key role of accumulation, each of the different phases of an SCA should be understood in relation to the dynamics of the circuit of capital; the process from a monetary investment via production and trade to a monetary revenue that exceeds the initial investment yielding a profit for the capitalist. In SCA, this general formula is reinterpreted as a general theory of the organization of society and the evolution of the world capitalist system as a whole. Thereby, the circuit of capital serves as a lens to analyze the historical development of the capitalist system while linking to Marx's theory of crisis and falling rate of profit. Importantly, each SCA corresponds to a specific political, geographic and economic configuration of the world capitalist system. In each cycle, the initial phase of material expansion eventually culminates in a conflict between a falling rate and a growing mass of profit as the accumulation barriers under a given political and economic configuration are approached (Arrighi, 2010, pp. 232–233). This generates a drive toward an intensified spatio-temporal fix as well as a switching crisis signaling a hegemonic transition. But rather than leading immediately to a collapse of global hegemony, a financial expansion creates a belle époque where the declining global economic center switches to financing an economic expansion in a different geographical location. Now, profitability is temporarily restored and the accumulation barriers of capital are pushed back further.
With the framework we establish in this work, we are able to explicitly show how the SCA framework effectively demonstrates that the spatial and institutional barriers of the world market are constantly overcome through geographical expansion and reorganization of the system as such, as a result of dynamics originating from the accumulation of capital itself.
3.2 The role of chaos
The phase of SCA in which a spatial relocation and intense financial expansion pushes the socioeconomic accumulation barriers, signals the beginning of the transition from one hegemon to the next. This transition is characterized by what Arrighi calls systemic chaos. More specifically '"[c]haos" and "systemic chaos," […] refer to a situation of total and apparently irremediable lack of organization' (Arrighi, 2010, p. 31). Furthermore, he provides a summary of possible channels through which systemic chaos can emerge:
'It is a situation that arises because conflict escalates beyond the threshold within which it calls forth powerful countervailing tendencies, or because a new set of rules and norms of behavior is imposed on, or grows from within, an older set of rules and norms without displacing it, or because of a combination of these two circumstances.' Simply put, it is a situation of escalating conflicts and a collapse of predominant rules and norms. Arrighi highlights the role of systemic chaos to hegemonic transition: 'As systemic chaos increases, the demand for 'order' – the old order, a new order, any order! – tends to become more and more general among rulers, or among subjects, or both'. (Arrighi, 2010, p. 31)
Note that the quote above provides both a definition of (systemic) chaos through its characteristic of 'total and irremediable lack of organization' and also describes the possible channels (conflict and lack of rules and norms) that can lead to chaos and through this to a hegemonic transition and a geographic reorganization of the world system. Even though the definition is not specific and the relationship between (systemic) chaos and the notion of chaos in mathematics and physics is not explicitly discussed by Arrighi (2010) or Arrighi and Silver (1999), the property of chaotic systems to appear as random or unpredictable can be related to what they refer to as a 'lack of organization'. More specifically the characteristic of apparent unpredictability is sufficient to prevent a system from being organized. Given the role of accumulation within the SCA framework, the lack of organization is necessarily linked to the accumulation process: a lack of order and organization undermines stable capital accumulation and leads to chaotic accumulation dynamics.
3.3 SCA through the logistic map
Arrighi (2010, 1996) and Arrighi and Silver (1999) see the SCA as a theoretical project that aims to show how the evolution of the world capitalist system through the succession of different hegemons is not random but can be explained through an analysis of world capitalism as a historical social system. Thereby, the ambition is for 'This reconstruction [to] proceed gradually through a comparative analysis of successive SCA and through heavy borrowing from whichever theoretical construct can provide the most plausible and parsimonious explanation of the observed patterns' (Arrighi, 1997, p. 159). Following this same approach, we assume the most plausible parsimonious functional form that can explain the observed patterns.
The parameter
The first important insight of this type of representation is that for relatively low values of
At this point, it is also important to note that while an increase in
Figure 1.
This is figure 3.10: 'Metamorphosis Model of Systemic Cycles of Accumulation' from Arrighi (2010, p. 242).
Figure 2.
This is figure 3.7 from Arrighi (2010, p. 235).
The slope
In sum, the crisis of accumulation that occurs toward the end of the A-phase triggers a systemic push to overcome the barriers to capital accumulation and leads to a bifurcation in the start of the B-phase, as shown in Figure 2. However, overcoming the fall of profitability does not last for long as the slope will change again becoming less vertical leading to a continuous need for
The second important insight from the logistic map representation of the SCA is that as
In order to show that the logistic map with the above interpretation of
4. Stages within SCA
4.1 Stable accumulation
The stable accumulation phase begins with initial investments that establish a 'particular bloc' of agencies and rules that form a new hegemony with a new geopolitical center. In this phase, capital shapes the new geographical space in its image and subordinates it to its laws and needs. In this initial part of the stable phase the profit rate is still low (this corresponds to the initial horizontal part of the S-curve shown in Figure 2). But once hegemony is established a virtuous cycle of an ever-increasing division of labor is kicked off (this is the first part of the S-curve where the slope is higher than one, i.e. more than 45 degrees). However, this virtuous cycle is not without limits and a continuous expansion will sooner or later lead to a situation where profit margins will be under threat.
Profitability, the very force of the initial expansion, eventually creates the conditions that set an end to the process: 'Decreasing returns set in; competitive pressures on the system's governmental and business agencies intensify; and the stage is set for the change of phase from material to financial expansion' (Arrighi 1996, p. 155). This corresponds to the B-phase of the curve where the gradient is less than one and the geographical expansion is intensified. In order to be able to show the correspondence with the logistic map, we present two cases with relatively low values of
Figure 3.
Initial material expansion phase of stable accumulation, ◆◆ = 1.2.
Figure 4.
Initial extended expansion phase, r = 2.
Both graphs show a logistic (S-shape) accumulation process as the one shown in Figure 2. While in Figure 3 of the initial material expansion phase, the maximum value of for
The material expansion and the financial expansion figures in Arrighi (2010) can be thought of as the two different parts of Figure 2, where the first corresponds to the M-C-M' part and the second to the M-C-C' part of the graph. Arrighi (1996, p. 157) notes that 'every phase of financial expansion is indeed characterized by the emergence of a newly successful MCM' circuit'. We can therefore think of MCC' in his graph as a new circuit of capital in relation to the initial MCM'. The two lines in the B-phase in Figure 2 correspond to two different values of
Note that the logistic shape of Figure 4 also demonstrates that the tendency for the rate of profit does not disappear as
4.2 Turbulent accumulation
The extended expansion is in fact 'a sign of "autumn" (Braudel, 1984, p. 246)' as Arrighi and Silver (1999, p. 31) argue drawing on Braudel, and is largely driven by what Harvey (1981, 2003) calls a 'switching crisis'. As more and more capital from the declining hegemon is channeled into liquid assets the world enters the B-phase of the cycle of accumulation. Finance is no longer grounded in production and the continued expansion gives way to what has come to be known as financialization: As money is exchanged for more money, profits are derived from speculation and accumulation becomes turbulent. At the same time, a new material expansion phase sets off in the ascending parts of the world. This material expansion is initially driven by the spatio-temporal fix and the resulting relocation of production from the declining hegemon but increasingly takes on a life of its own. The interstate and interenterprise competition for more and more mobile capital intensifies. Financialization and intensified international competition give rise to further turbulences. In the beginning, these turbulences are local, but as the dynamic unfolds, they eventually become global.
This type of destabilizing dynamics is depicted by Arrighi (2010) in two figures (reproduced below) to capture two types of turbulence: local turbulences, which initially increase but eventually fade out when the accumulation curve returns to a stable increasing trajectory; and systemic where the turbulence is increasing over time without returning to a stable path. The nature of finance contributes to the intensification and spread of turbulence; through financial expansion, the financial system allows for capital (re)allocation to geographies with high rates of profit (Arrighi, 1983, chapter 4; Luxemburg, 1951 [1913], chapter 30). Both Luxemburg (1951) and Arrighi (1983) emphasize the central role of finance in the export of capital, and the management of imperialism in general. Arrighi (2010) further discusses the importance of 'international networks' for the business agents of finance capital (Arrighi, 2010, pp. 169–174). Also Chesnais (2016) approaches finance capital from a global perspective, and demonstrates that finance regularly spearheades the dissolution of barriers to accumulation on a global scale. Perez (2003) locates the origin of financial crisis in the diffusion of innovations through finance, indicating the diffusive nature of finance capital. Thus, it is through capital exports that local disturbances that arise from overaccumulation can become global and that the export of capital potentially jeopardizes global stability based on world hegemony. Hence while the type of instability portrayed in the first graph of Figure 5 is temporary, the second one appears to be more long term or even permanent. In the case of systemic turbulence, there seem to be no endogenous forces that lead the world system back to a stable path.
Figure 5.
Figures 3.8 'Local Turbulence' and 3.9 'Systemic Turbulence' from Arrighi (2010, p. 242).
In order to show the correspondence between the behavior captured in Figure 5 and the dynamics generated by the logistic map as
Figure 6.
Local turbulence, r = 2.95.
As we can see, a further increase in
If the surpluses of capital and labour power exist within a given territory … and cannot be absorbed internally … then they must be sent elsewhere to find fresh terrain for their profitable realization if they are not devalued. … [But] … [t]he problem of overaccumulation is alleviated only in the short term. (Harvey, 2003, pp. 116–117)
As the geographical expansion progresses further, financialization deepens and capital becomes ever more mobile further intensifying interstate competition. A higher
Again, we observe an increase regarding the average value for the level of capital accumulation
These two examples of values for r demonstrate the correspondence between the accumulation dynamics derived through increasing values of the bifurcation parameter of the logistic map and the insights of the SCA process shown in Figure 5. This demonstrates the correspondence between the SCA dynamics and the logistic map.
4.3 Chaos
For Arrighi and Silver (1999, p. 21), hegemonic transition at the end of an SCA is through 'a process of radical reorganization of the modern world system that changes substantively the nature of the system's components, the way in which these components relate to one another, and the way in which the system operates and reproduces itself.' Based on Abu-Lughod (1989, p. 369) in such a situation 'the "same-cause-yields-same-effects" logic that underlies our thinking…is ill-equipped to apprehend this kind of change, and we should instead draw inspiration from "chaos theory"' (Abu-Lughod, 1989).
While the relationship between chaotic dynamics and hegemonic transition is mentioned in Arrighi (2010), the concrete link is not analyzed. Furthermore, it is not clear whether a possible link would fit with the SCA framework. Despite the systemic turbulences that arise when a continuous expansion reaches a certain threshold, the barriers to accumulation are pushed even further as capital encounters further barriers arising from the contradictions set in motion by its previous solution to the previous barriers. Considering that '[t]he entire credit system … rests on the necessity of expanding and leaping over the barriers to circulation and the sphere of exchange' (Marx, 1973, p. 416), credit facilitates the geographical expansion of capital, speculation is fueling more speculation and the barriers to accumulation are pushed once again. This corresponds to a further increase in
However, if
Figure 7.
Systemic turbulence, r = 3.3.
Figure 8.
This shows the link between extended expansion and chaos when the SCA is represented by a logistic map. Thus, the use of a logistic map to express the accumulation process underlying SCA along with the theoretical understanding of the fact that spatio-temporal fixes (and switching crises) are only a temporary solution hence there is a continuous need for pushing toward higher accumulation levels, hence a continuous push to overcome previous barriers. This also means a continuous increase of the value of the bifurcation parameter. As chaos appears after the bifurcation parameter crosses a threshold, it means that chaos is an endogenously created sub-phase following the preceding sequence of stable expansion, local and systemic turbulence.
Our analysis leads to a reformulation of the original SCA graph where the accumulation process is divided into two phases A and B. Using our insight, the B-phase includes two sub-phases. The first corresponds to the original insights of Arrighi (2010) where a stable extended expansion is followed by local and then systemic turbulence, while the second sub-phase corresponds to chaos and means that the hegemon has lost its power and the transition is under way.
The different parts of the B-phase can be presented through the bifurcation diagram of the logistic map below, which in this case shows the behavior of the accumulation process for different values of the bifurcation parameter.
The horizontal axis represents different values for the bifurcation parameter and the vertical axis is the values for
Figure 9.
Bifurcation diagram of the logistic map.
In the next part where
In the last stage, when
To sum up, Figure 9 corresponds to the accumulation process within a single SCA. An increase in
5. Conclusion
The aim of this article has been to show that by expressing the dynamics of the global accumulation process at the basis of the SCA through the use of a logistic map, we are able to explicitly place the endogenous emergence of chaos within the SCA phases. Our starting point has been the well-known fact that for low values of its bifurcation parameter, the logistic map corresponds to a logistic (sigmoid) graph. Hence, given that the accumulation process underlying the SCA is described by a sigmoid, as the logistic map, for certain parameter values is also a sigmoid, this is a suitable formal representation. Our analysis was based on three further key observations.
The first is related to two observations the bifurcation parameter. On the one hand, higher values of the bifurcation parameter allow for higher levels of accumulation, while on the other there is a constant need for increasing its value, as new accumulation barriers appear. This means that for a capitalist economy where the accumulation process is described by a logistic curve, there will be an endogenous push to overcome the barriers of accumulation and the value of the bifurcation parameter. This increase corresponds to geographic expansion and intensification of commercial and financial capital activities and hence shows that the parameter has not only a socioeconomic but also a spatial interpretation.
The second observation is related to the exact mapping of the different stages of the SCA with the various dynamics portrayed by the logistic map as the bifurcation parameter crosses certain threshold values. Not only as the parameter increases, we are able to replicate the key insights of the SCA but chaos also follows the turbulent last phase of the SCA.
Third, in order for the hegemon of the world capitalist system to be able to overcome accumulation barriers, a geographical expansion and organizational complexification takes place. This provides a fix to the slowdown of the accumulation process; however, this fix is only temporary which means that there is a continuous need for an increase in the bifurcation parameter. This highlights how the process that leads to different phases of the SCA framework is endogenous within the capitalist accumulation process.
Hence, our analysis shows that exactly because the logistic map can represent the SCA and the spatio-temporal fixes are only temporal, chaos is actually inherent in the accumulation process. Through this approach, we have 'extended' the (B-phase of the) SCA framework by explicitly including the chaotic dynamics which are related to hegemonic transition as a 'natural' next step in the accumulation process. The theoretical framework we established consists of a consolidation of Harvey's (1981, 2003) spatio-temporal fix and switching crisis concepts with Arrighi's (2010) and Arrighi and Silver's (1999) framework of SCA.
Adding the missing link in this article leads to new research questions. Possible extensions of the logistic map include for example the explicit incorporation of the different fixes to overaccumulation crises and/or allowing for the explicit role of hegemony and power in stabilizing the accumulation process. Combining the two would be particularly interesting, and would also allow us to systematically analyze the role of hegemony and power in stabilizing general expanded reproduction, not just the special case of an acute overaccumulation crisis.
Acknowledgements
We would like to thank Beverly Silver, Ali Khan, Sahan Karatasli and the participants at the General Seminar at the Arrighi Center for Global Studies at John Hopkins University for their valuable comments and the fruitful discussion and Karsten Köhler and Gregor Semieniuk for their generous comments, as well as all other participants at the LPEN workshop for their remarks. All remaining mistakes are our own.
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