Carrying Von Bertalanffy’s baton: Systems, complexity and network science, Part 3

Title: Carrying Von Bertalanffy’s baton: Systems, complexity and network science, Part 3
Author: Dr. Burgert Senekal, University of the Free State.
Ensovoort, volume 42 (2021), number 6: 2



The first two articles in this three-part article series showed how network science realised the vision of Von Bertalanffy. In the current article, concepts such as the hierarchical organisation of systems (systems-of-systems), the importance of adaptability, and the core/periphery structure of systems and networks is discussed. Von Bertalanffy’s views in terms of these features are again compared with views from within network science. As such, the article concludes the three-part article series on the relevance of Von Bertalanffy within a contemporary, data-driven complexity paradigm.


Keywords: Von Bertalanffy, General Systems Theory, systems science, complexity, network science

1.      Introduction

The previous article discussed system characteristics such as emergence and self-organisation, as seen by Von Bertalanffy, and how these relate to current views within network science. The current article discusses further properties of systems and their relation to network science, including the distinction between complex and complicated systems, systems-of-systems, and the core / peripheral structure of systems and networks. As in the previous article, Von Bertalanffy’s views are presented in the context of current network science.

2.      The distinction between a complicated and complex system

The previous article discussed self-organisation and emergence with reference to General Systems Theory (GST) and network science. Since self-organization and emergence are found in simple as well as complex systems, what defines a complex system and distinguishes a complex from a complicated system? As Cilliers (1998:5) phrases the issue, “A snowflake, although wondrously complex in appearance, is only complicated.”

Von Bertalanffy viewed adaptation as part of the functioning of open systems. He (1968:131) writes about biological systems,

If, after cessation of the “stimulus,” the constant of catabolism returns to its normal value, the system will return to its original state. If, however, the disturbance and hence the change of rate of catabolism persists, a new steady state will be established. Thus the system develops forces directed against the disturbance, tending to compensate increased catabolism by increased intake. It therefore shows “adaptation” to the new situation. These, too, are “self-regulative” characteristics of the system.

The difference between a complicated and a complex system lies in adaptability, which refers to, “the ability of the social system to adapt to its environment with its particular structuredness”[1] (Conradie, 1980:77). The complex system may be composed of millions of parts, but it is only considered a complex system if the system is adaptable; adaptability[2] is a “central characteristic” (Amaral and Ottino, 2004:159) of complex systems (Nistor, Pickl and Zsifkovits, 2015:11).

Ottino (2005:1842) cites the example of a Boeing 747-400, which consists of around 3×106 parts:

In complicated systems parts work in unison to accomplish a function; pieces are connected to each other according to a blueprint and the blueprint does not change. One key defect (in one of the many critical parts) brings the entire system to a halt. Not so in complex systems; the system may still function if pieces are removed.

For example, plane crashes have occurred when a bolt was not manufactured to standard, as happened with the crash of Partnair Flight 394 near Denmark in 1989. Three bolts came loose, the plane’s tail fin came off and the plane crashed into the sea.

In contrast, Holland (1992:18) names the immune system as an example of a complex system. The immune system consists of a large number of antibodies that are constantly fighting to destroy a continually changing set of invaders. Because the invaders can manifest in an almost infinite variety of forms, the immune system cannot simply compile a list of all possible invaders. Even if the time exists to be able to undertake such a task, there is simply not enough space to store all the information, and in addition, new pathogens (such as multidrug-resistant tuberculosis or Covid-19) develop daily. Instead, the immune system must change or adapt its antibodies when new invaders appear.

The economy is usually regarded as a complex system (Newman, 2011:3). The economic crisis that is probably most referred to in the network literature is the 1997 Aisin crisis at the Toyota complex (Borgatti and Li, 2009:9, Csermely, 2006:204, Watts, 2004:254-260). Toyota distributes the manufacture of spare parts through a network of hundreds of companies, including the manufacture of a key component of vehicle brakes, the P-valve, which is manufactured at the Kariya plant of the company Aisin Seiki. On February 1, 1997, the plant burned down, disrupting Toyota’s entire production line. Toyota used their network of companies to create an alternative, Aisin provided staff and building plans, and within a few days, 62 companies converted their production facilities. Nine days after the fire, the production of P-valves was back on schedule (Borgatti and Li, 2009:9). The network of companies that handle Toyota’s production was therefore able to adapt when one of its subdivisions no longer functioned, similar to how a living organism would adapt to the loss of a limb.

In cultural systems, the adaptation of the Afrikaans publishing industry after 1994 can serve as an example of adaptability in a complex system. In 1998 the budget for school book purchases was cut by 85%, libraries’ purchases of Afrikaans books were drastically reduced, the bookseller CNA was liquidated in 2003, and publishers such as Daan Retief and Benedic / Makro had to close. But the industry adapted: in 2001, Naspers grouped its separate publishers (Human and Rousseau, Tafelberg, Kwêla and Van Schaik) together under NB Publishers in an attempt to combine resources and recover from financial losses (Kleyn, 2013:45-46). It is also important to note that these adjustments – as in the above case of Toyota – were undertaken from within the system and are therefore also an example of self-organization.

3.      Systems-of-systems

Complex systems consist of smaller subsystems (microsystems) and at the same time belong to larger supersystems (macrosystems), as Kwapień and Drożdż (2012:123) contend, “The majority of complex systems display multilevel structure organization, in which individual elements from higher structural levels are on their own complex systems at lower structural levels” (see also Cong and Liu, 2014:603, Eusgeld, Nan, and Dietz, 2011:681, Kresh, 2006:6-8, Ropohl, 2005:27, Wilden, 1980:402, Boshoff, 1977:2, and Simon, 1962:468). Von Bertalanffy (1968:160) also conceived of systems as hierarchical in nature,

The living organism is a hierarchical order of open systems. What imposes as an enduring structure at a certain level, in fact, is maintained by continuous exchange of components of the next lower level. Thus, the multicellular organism maintains itself in and by the exchange of cells, the cell in the exchange of cell structures, these in the exchange of composing chemical compounds, etc.

In addition, Von Bertalanffy (1968:87) argues that this property of systems is not limited to living organisms but indicates how the world is organized,

Reality, in the modern conception, appears as a tremendous hierarchical order of organized entities, leading, in a superposition of many levels, from physical and chemical to biological and sociological systems. Unity of Science is granted, not by a utopian reduction of all sciences to physics and chemistry, but by the structural uniformities of the different levels of reality.

Complex systems can be described as systems-of-systems, which is a term that refers to, “multiple, heterogeneous, distributed, occasionally independently operating systems embedded in networks at multiple levels” (DeLaurentis, 2007:363). A human being is an example of a system of systems, which belongs to an institution or company, a community, a population, and humanity as a whole (supersystems), but at the same time consists of, among other things, an immune, nervous, digestive and circulatory system, which is made up of organs, cells, molecules and atoms (Wyseur, 2011:28).

In a similar way, a conflict system consists of subsystems. Kilcullen (2010:197) writes that an insurgency can include logistics, intelligence, propaganda, recruitment, planning and operational subsystems. These are ‘systems within systems’ and the thousands of nested interactions of subsystems within the supersystem are, according to Kilcullen, key elements in its power.

It is further important that such systems-of-systems are also interconnected (DeLaurentis, 2007:366) – interdependence between systems is just as important as the interdependence between components, as Schoeman (1981:3) also recognises, “A system forms a whole or unit that consists of different parts or subsystems that are related to each other and interact with each other.”[3] When it comes to investigating complex systems, Smaling (2013:93) argues that interdependence between different levels of the system must also be taken into account,

The bottom line is that a complex system is a hierarchical system, none of which can be reduced to another layer, not down and not up, without significant loss. This insight has implications for the research of a complex system: to come to a proper understanding of a complex system, multiple levels or layers will have to be studied. And especially in their mutual relationships and their part-whole relationships[4] (See also Hattingh, 2002:87).

A variety of systems can be represented in such a hierarchical structure. Hattingh (2002:89) suggests that the community can be considered as such,[5] as can be seen in Figure 1 left. Mobus en Kalton (2015:184) in turn suggest the biological hierarchy adapted in Figure 1 on the right.

Figure 1 A social and biological system

The individual (here the mother or child), is thus itself a complex system, but is embedded in the supersystem of the family. In turn, the family is embedded in an organization (here the school), which is embedded in society, and ultimately in a global system (here the United Nations or UN). It is also important to note that horizontal as well as vertical interactions take place: the mother, father and child interact just as the families belonging to the school also interact. Ehlers (1989:188) writes,

By analogy with the system model, each family is a subsystem in a larger system (neighbourhood, city and society). At the same time, each family is also a supersystem that consists of a number of subsystems (breadwinner, housewife, parent and child). The family as a subsystem is influenced in its structure and functioning by the environment in which it occurs. As a supersystem, the family is again influenced by the family members and the roles they play.[6]

The hierarchy represented on the right flows from the hierarchy on the left. The individual (for example the child) consists of, among other things, the organ system, which is made up of cells. In a cell, a functional unit level can be distinguished, which consists of, among others, mitochondria and chromosomes. These components are in turn made up of, among others, proteins, fats and deoxyribonucleic acid (DNA), which in turn are made up of, among others, chemical molecules such as amino acids, fatty acids, and carbohydrates. The latter is again composed on an atomic level of carbon (C2), hydrogen (H2), nitrogen (N2), oxygen (O2), phosphorus (P) and sulphur (S2).

Even-Zohar (1990:91) claims that culture can also be seen as, “to behave as a polysystem, that is a heterogeneous, multi-stratified, and functionally structur(at)ed system-of-systems,” and earlier (1979:290) describes a polysystem as, “a multiple system, a system of various systems which intersect with each other and partly overlap, using concurrently different options, yet functioning as one structured whole, whose members are interdependent.” The systems could represent literary works, for example, and the supersystems, youth and children’s literature, leisure literature, and serious literature (what Senekal 1987 calls E-literature). Note that texts can function simultaneously within more than one supersystem (Senekal, 1987:186). In addition, texts can also move between supersystems, for example Deon Meyer who gained renown as a leisure literature writer, but later became a canonized writer. Furthermore, the entire cultural system is embedded in larger supersystems, as Van Rees and Dorleijn (2006:16-17) contend,

The cultural field is embedded in society, conceived as the whole of interdependent spheres: besides the cultural, in particular the political, economic and social sphere. Embedding means that political decisions and socio-economic factors influence what happens in the cultural field. At the same time, however, culture itself […] also influences society.[7]

Simon (1962:469-470) already noted that symbolic systems such as books display a hierarchical structure, with words organized in phrases, phrases in sentences, sentences in paragraphs, paragraphs in sections and sections in chapters, which are eventually organized in the form of the whole book. Simon’s (1962:469-470) hierarchical division can be seen in Figure 2 on the left, while the figure on the right represents a cultural system.

Figure 2 Cultural systems

The same phenomenon of systems-of-systems is also recognized within network science (Porter, Onnela, and Mucha, 2009:1084, Meunier, Lambiotte, Fornito, Ersche, and Bullmore, 2009:1), where the phenomenon of a ‘network of networks’ dates back at least as far as 1973 (Kivelä, Arenas, Barthelemy, Gleeson, Moreno and Porter, 2014:204). Csermely (2006:32) writes that a network is like a matryoshka, with what he calls a top network consisting of networks, which in turn also consists of networks. A network of neurons, for example, consists of cells, which include protein interaction networks, just as the world economy consists of countries, which in turn are made up of companies. These examples have been simplified; one could move from the world economy to the individual atom and each time the lower networks are the upper networks for the networks below, just as each system is made up of subsystems, which in turn is made up of even smaller subsystems, and so on. Lindelauf (2009:92) writes that living systems can be represented as such hierarchical networks at different levels within network science:

… genetic networks in which proteins and genes are the nodes and the chemical interactions the edges; the nervous system where nerve cells are nodes and axons are the edges; and finally social systems with individuals or organizations as nodes and social interactions as edges.[8]

In network science, this facet of complex networks is studied using modularity (Q) (Meunier, Lambiotte, Fornito, Ersche, and Bullmore, 2009:1).  

4. The core, the periphery and the boundary

Every complex system is in fact an open system that exists through its interactions with other systems; as Wilden (1980:36) writes, all systems that involve life or thinking are open systems that are in constant communication (interaction) with their environment. Von Bertalanffy (1940:521) distinguishes between open and closed systems as follows,

The organism is not a closed, but an open system. We call a system “closed” when no material “from outside” enters it and none emerges to the same “outside”. An open system is called one in which materials are imported and exported[9] (see also Senekal, 1987:173, Viljoen, 1986:8, Strauss, 1985:1, Wilden, 1980:xxxi, and Von Bertalanffy, 1968:39).

A living organism, for example, needs imports from its environment (O2, H2O and nutrients), and must also export outputs (CO2, faeces, and urine) in order to live. If this interaction with the organism’s environment is stopped, death is the end result.

Steyn (1984:9) writes that a social system’s interaction with its environment is equally crucial:

In the case of the open system, […] of which the social system is a good example, the system is not only in a certain interaction with the environment, but this interaction with the environment is of essential importance in the organization of the system, its viability and continuity and its ability to change.[10]

The same applies to literature, which is an open system that cannot be isolated from its environment (Senekal, 1987:147). Kleyn (2013:43) for instance states, “The literary system is an open system that is not independent of or unaffected by other systems, and that interacts with the immediate environment (and subsystems).”[11]

Businesses are also in an open relationship with their environment. Of course, economic conditions affect the operation of a business, for example the exchange rate that will affect a company’s imports and exports. Political circumstances also affect the business: during apartheid, sanctions had a real impact on a company’s ability to trade with overseas firms, and Senekal (2017) indicated the clear impact that sanctions had on South Africa’s position in the world trade network.

The boundary of the system is where this interaction takes place with other systems. For systems, the boundary can be concrete or a demarcation point, for example where the study object is demarcated, and at the same time a peripheral area that functions away from the core.

First, any scientific study needs a demarcation point, because as Viljoen (1986:9) points out, the total environment within which a system functions is of course unmanageable. Wilden (1980:219) asserts that boundaries are methodological rather than real, and Steyn (1984:10) claims that where the boundaries of a system are drawn depends on the investigation when she refers to,

… the fact that the boundaries between the system and its environment become increasingly arbitrary in nature and that the components of a system can be seen in one context as parts of a particular system, but in a different context, depending on the perspective of the observer, the one component can be seen as the environment for another component.[12]

For example, the boundaries of the literary system can be drawn in such a way that writers, works, literary figures, critics and all role players are included in the literary system, but the people in that system are also citizens of a country, and members of organizations and communities. People function in various systems, and in this respect Eugene Terre’Blanche is a clear example: As the author of two stage dramas (Two Oxen: a single-act drama for the South African Police 1968 and Sybrand: a single-act drama 1969), Terre’Blanche is part of the Afrikaans literary system of the 1960s, but by the time these dramas were published, he was already part of the political system as a member of the police and the Herstigde Nasionale Party (Restored National Party) (the system where he later gained notoriety). If the literary system is investigated, the network will be drawn in such a way that people involved in the production and distribution of literary works are included, but if another investigation is undertaken, for example the social interactions between people in the country, the boundaries will otherwise be drawn to not only include these role players. Entities therefore function simultaneously across different systems, and therefore the boundary of the system is first and foremost a methodological construction.

Mobus and Kalton (2015:74) write, however, that the boundaries of a system are otherwise physical, for example in the case of a cell, where the membrane represents the boundary. For a man it is his skin, for a book its cover, for a country its national borders and for a business its premises. It is therefore interesting to note that a system is often described on the basis of the properties of its boundary (Mobus and Kalton, 2015:96). For example, a red apple describes a fruit with a specific shape that reflects light at a certain frequency, a white rhino is so named based on the shape of its mouth, and of course people are also classified based on their skin colour and appearance.

Each system or network has a core and periphery, and Csermely et al. (2013:96) note that the core / peripheral structure of networks has been studied since the seventies, especially with reference to social networks, citation networks in scientific fields and economic networks. They (2013:95) write that a core / peripheral structure has been identified in a variety of networks, including protein interaction networks, metabolic networks, neural networks, ecosystems, in the social networks of humans and animals, the World Wide Web, Wikipedia, the Internet, power supply networks, transport networks and economic networks.

Network science’s view of the core and periphery of a network shows a great deal of agreement with its view from systems theory. From the perspective of network science, the periphery is characterized by a higher degree of variation, dynamics and change, there are fewer constraints, and the boundary is more plastic than the core (Csermely et al., 2013:94). Hoppe and Reinelt (2010:607) add that the periphery brings new ideas and resources to the core and is also a place where expatriates from the core are found. In contrast, the core is more rigid and is characterized by less variation and dynamics than the periphery, and also the core is generally more stable (Csermely, et al., 2013:94).

Biological systems clearly illustrate the importance of the core. For example, human temperature is more stable in the core than on the periphery (nose, ears, toes, and fingers), and temperature changes on the periphery do not destabilize the system. However, if the temperature in the core fluctuates, the whole system is in danger, and usually the temperature in the core falls between 36,5 °C and 37,5 °C. Hyperthermia occurs when the core temperature exceeds 37,5 or 38,3 °C, and hypothermia occurs when the core temperature drops to below 35,0 °C, and both can be fatal. In other words: instability in the core jeopardizes the existence of the whole system, which is not the case with instability on the periphery. The stability of the core is essential for the functioning of a complex network:

The development of network core increases network robustness and stability in a large variety of real-world networks. This is mainly due to the rich connection structure of the core allowing a high number of degenerate processes, ensuring cooperation and providing multiple options of network flow re-channelling, when it is needed. Importantly, core processes enable a coordinated response of various stimuli. The core usually has much less fluctuations than the periphery, and has much more constraints, therefore changes (evolves) slowly (Csermely, et al., 2013:108).

A core / peripheral structure can be found, for example, in the communication patterns of neurons in the human brain. According to Csermely et al. (2013:110) this structure is of special importance for brain functioning, and note the important role that the core plays in stabilizing the system,

… the learning process of human brain can be described by the presence of a relatively stiff core of primary sensorimotor and visual regions, whose connectivity changes little in time, and by a flexible periphery of multimodal association regions, whose connectivity changes frequently. The separation between core and periphery is changing with the duration of task practice and, importantly, is a good predictor of individual differences in learning success. Moreover, the geometric core of strongly connected regions tends to coincide with the stiff temporal core. Thus, the core/periphery organization of the human brain (both in its structure and dynamics) plays a major role in our complex, goal oriented behaviour.

A similar core / peripheral structure is found in social networks, where high status people or the elite are concentrated in the core, while low status people are found on the periphery (Csermely, et al., 2013:111, Easley and Kleinberg, 2010:553, Christakis and Fowler, 2010:117). In Senekal, Stemmet and Stemmet (2014:124) it was indicated that the US functioned within the core of the global arms trade network during the Cold War, while the ANC functioned on the periphery (the ANC obviously did not have its own arms industry at the time).

However, when newcomers form ties with individuals in the core, they are drawn closer to the core (Csermely, et al., 2013:111). Fraiberger, Sinatra, Resch, Riedl and Barabási (2018:827) indicate that artists who initially exhibited at high prestige institutions pursue a noticeably more successful career. Artists who started exhibiting at high-prestige institutions at the core of the art network showed a lower dropout rate in their research and tended to maintain their status. In contrast, those who started at the edge of the network showed a high dropout rate, but if they persisted, their access to top settings gradually improved.

At the same time, the core also marginalizes those who do not comply with the norms of the core: “The development of cooperation may also lead to the segregation of a cooperating core of social networks, pushing out defectors to the network periphery” (Csermely, et al., 2013:107).

This view of the core from network science is also shared by the polysystem theory in literature. The periphery of the literary system then contains elements that are new to the system (in other words, renewal enters the literary system from the periphery), as well as elements that are worn out and moved from the core to the periphery (Codde, 2003:106). Even-Zohar (1990:88, 14) writes,

The polysystem, i.e., the ‘system of systems,’ is viewed in polysystem theory as a multiply stratified whole where the relations between center and periphery are a series of oppositions. […] In this centrifugal vs. centripetal motion, phenomena are driven from the center to the periphery while, conversely, phenomena may push their way into the center and occupy it (see also Even-Zohar, 1979:293).

The core also dominates the literary system, according to Roberts (1973:85), “It is the nucleus of the literary megacommunity (the literary community proper) that does all of the identifying of literature.” In cultural systems, therefore, renewal enters the system from the periphery, while the periphery also houses elements that have been displaced from the core. The core itself dominates the whole system and is more stable; one thinks, for example, of NP van Wyk Louw or DJ Opperman’s position in the core of the Afrikaans literary canon which can be seen in the fact that their works are prescribed at universities year after year and they always occupy an important position in Afrikaans literary histories.

One way to clearly visualize the core and periphery is through the use of force-directed layout algorithms, as undertaken in Senekal (2014).

4.      Conclusion

As can be seen in the foregoing article, there is a significant conceptual overlap between network science and systems theory. In many key aspects, such as the core/periphery structure, the hierarchical system-of-systems structure, and the ability of the system to adapt, network science shares Von Bertalanffy’s views.

One of the important differences between network science and systems theory is network science’s stronger emphasis on quantitative methods: although Von Bertalanffy’s GST is formulated mathematically, the application of systems theory is often rather the application of the idea of a system without a mathematical basis, e.g. Boshoff (1977), Conradie (1980), Schoeman (1981) and Steyn (1984), as also found in Even-Zohar’s (1979; 1990) polysystem theory and applications thereof (e.g. Lötter, 2012, and Kleyn 2013). Cong and Liu (2014:599) argue that the systems theory perspective on language usually amounts to a metaphorical use and is not taken much further. This is a statement that cannot be made against network science:[13] network science is always concerned with mathematical models, calculations and algorithms, and is pre-eminently a quantitative approach. Barabási (2016:22) writes, “To contribute to the development of network science and to properly use its tools, it is essential to master the mathematical formalism behind it.”

Network science may be a “new” (Barabási, 2016:18) science, but as this article series has shown, some of the seeds of network science were sown by Von Bertalanffy as much as 70 years ago. Network science has however achieved what Von Bertalanffy’s GST could not, namely to achieve wide acceptance in the scientific community and among the general public.

5.      Bibliography

Amaral, L. and Ottino, J. 2004. Complex networks. Augmenting the framework for the study of complex systems. European Physical Journal, 38:147–162.

Barabási, A.-L. 2016. Network science. Cambridge: Cambridge University Pres.

Borgatti, S. P. and Li, X. 2009. On Social Network Analysis in a Supply Chain Context. Journal of Supply Chain Management, 45(2):5-22.

Boshoff, M. C. 1977. Die algemene sisteemteorie as uitgangspunt by die beplanning van ‘n basiese biblioteek- en inligtingkundige opleidingsprogram. Pretoria: Publikasiereeks van die Universiteit van Pretoria.

Christakis, N. and Fowler, J. 2010. Connected. London: Harper.

Cilliers, P. 1998. Complexity and Postmodernism: Understanding Complex Systems. London: Routledge.

Codde, P. 2003. Polysystem Theory Revisited: A New Comparative Introduction. Poetics Today, Issue 1:91-126.

Cong, J. and Liu, H. 2014. Approaching human language with complex networks. Physics of Life Reviews, 11:598–618.

Conradie, H. 1980. Die Uitgebreide Sosiale Sisteemteorie. Suid-Afrikaanse Tydskrif vir Sosiologie, 11(2):73-83.

Csermely, P. 2006. Weak links: Stabilizers of complex systems from proteins to social networks. Heidelberg: Springer.

Csermely, P., London, A., Wu, L.-Y. and Uzzi, B. 2013. Structure and dynamics of core/periphery networks. Journal of Complex Networks, 1:93-123.

DeLaurentis, D. 2007. Role of humans in complexity of a system-of-systems. In: V. Duffy, ed. Digital Human Modeling. Proceedings of the First International Conference on Digital Human Modeling, ICDHM 2007, Held as Part of HCI International 2007, Beijing, China, July 22-27, 2007. Berlin: Springer:363–371.

Easley, D. and Kleinberg, J. 2010. Networks, crowds and markets. Reasoning about a highly connected world. New York: Cambridge University Press.

Ehlers, C. 1989. Die burgermag en die gesin. Suid-Afrikaanse Tydskrif vir Sosiologie, 20(3):187-194.

Eusgeld, I., Nan, C. and Dietz, S. 2011. “System-of-systems” approach for interdependent critical infrastructures. Reliability Engineering and System Safety, 96(6):679-686.

Even-Zohar, I. 1979. Polysystem Theory. Poetics Today, Autumn, 1(1/2):287-310.

Even-Zohar, I. 1990. Polysystem Studies. Poetics Today, 11(1):1-94.

Fraiberger, S. P. et al. 2018. Quantifying reputation and success in art. Science, 362:825–829.

Hattingh, J. G. 2002. Die gebruik van fantasie om kreatiwiteit by kleuters te bevorder : ‘n Begeleidingsprogram vir moeders. Unpublished PhD-thesis: University of the Free State.

Holland, J. H. 1992. Complex Adaptive Systems. Daedalus:17-30.

Hoppe, B. and Reinelt, C. 2010. Social network analysis and the evaluation of leadership networks. The Leadership Quarterly, 21(4):600-619.

Kilcullen, D. 2010. Counterinsurgency. London: C. Hurst and Co.

Kivelä, M. et al. 2014. Multilayer networks. Journal of Complex Networks, 2:203–271.

Kleyn, L. 2013. ’n Sisteemteoretiese kartering van die Afrikaanse literatuur vir die tydperk 2000-2009: Kanonisering in die Afrikaanse literatuur. Unpublished PhD-thesis: University of Pretoria.

Kresh, J. Y. 2006. Integrative systems view of life: Perspectives from general systems thinking. In: T. S. Deisboeck and J. Y. Kresh, eds. Complex Systems Science in Biomedicine. Heidelberg: Springer:3-29.

Kwapień, J. and Drożdż, S. 2012. Physical approach to complex systems. Physics Reports, 515(3):115-226.

Lindelauf, R. 2009. De relevantie van sociale en complexe netwerktheorie in counter-terrorism en counter-insurgency. Militaire Spectator, 178(2):92-101.

Lötter, J. C. 2012. Die retoriese rol van literêre feeste, met toespitsing op die US woordfees en die Amsterdamse Weerwoordfestival. Unpublished MA-dissertation: University of Stellenbosch.

Meunier, D. et al. 2009. Hierarchical modularity in human brain functional networks. Frontiers in neuroinformatics, 3:1-12.

Mobus, G. E. and Kalton, M. C. 2015. Principles of systems science. Heidelberg: Springer.

Newman, M. E. J. 2011. Complex systems: A survey. arXiv preprint:1-10.

Nistor, M. S., Pickl, S. W. and Zsifkovits, M. 2015. Visual Analytics of Complex Networks: A Review from the Computational Perspective. International Conference on Modeling, Simulation and Visualization Methods:10-15.

Ottino, J. M. 2005. New Tools, New Outlooks, New Opportunities. AIChE Journal, 51(7):1840-1845.

Porter, M. A., Onnela, J.-P. and Mucha:J. 2009. Communities in networks. Notices of the AMS, 56(9):1082-1097.

Roberts, T. J. 1973. The Network of Literary Identification: A Sociological Preface. New Literary History, 5(1):67-90.

Ropohl, G. 2005. Allgemeine Systemtheorie als transdisziplinäre Integrationsmethode. Technikfolgenabschätzung – Theorie und Praxis, 2(14):24-31.

Schoeman, W. 1981. Sisteemontwikkeling: ‘n Uitdaging aan die sielkunde. Johannesburg: Randse Afrikaanse Universiteit.

Senekal, B. A. 2014. Olga Kirsch se posisie in die Afrikaanse literêre sisteem (1900-1978). Werkwinkel, 9(2):9-36.

Senekal, B. A. 2017. ’n Verkenning van Suid-Afrika se veranderende posisie in die wêreldhandelnetwerk 1948–1994. Journal for Transdisciplinary Research in Southern Africa, 13(1):a430.

Senekal, J. H. 1987. Literatuuropvattings: ‘wese’ en ‘waarhede’ van ‘n nuwe literêre teorie. Bloemfontein: University of the Free State.

Simon, H. A. 1962. The Architecture of Complexity. Proceedings of the American Philosophical Society, 106(6):467-482.

Smaling, A. 2013. Complexiteitsdenken en kwalitatief onderzoek. Kwalon, 18(2):89-98.

Steyn, A. F. 1984. Buckley: die moderne oop-sisteembenadering. Suid-Afrikaanse Tydskrif vir Sosiologie, 15(1):5-16.

Strauss, D. 1985. Sisteemteorie en die sosiologie. Suid-Afrikaanse Tydskrif vir Sosiologie, 16(1):1-8.

Van Rees, K. and Dorleijn, G. J. 2006. Het Nederlandse literaire veld 1800-2000. In: G. J. Dorleijn and K. Van Rees, eds. De produktie van literatuur. Het literaire veld in Nederland 1800-2000. Nijmegen: Vantilt:15-38.

Viljoen, H. 1986. Die Suid-Afrikaanse romansisteem. ‘n Vergelykende studie. Unpublished PhD-thesis: University of the Northwest.

Von Bertalanffy, L. 1940. Der Organismus als physikalisches System betrachtet. Die Naturwissenschaften, 28:521-531.

Von Bertalanffy, L. 1968. General systems theory: Foundations, development, applications. New York: George Braziller.

Watts, D. J. 2004. Six Degrees. The Science of a Connected Age. London: Vintage.

Wilden, A. 1980. System and structure: essays in communication and exchange. New York: Tavistock.

Wyseur, S. 2011. De evolutie naar non-lineaire complexiteit in digitale mediacultuur; een exploratieve literatuurstudie. Unpublished MA-dissertation: University of Gent.

[1] Own translation from the original Afrikaans, “die vermoë van die sosiale sisteem om by sy omgewing aan en in te pas met sy besondere gestruktureerdheid.”

[2] Newman (2011:7) calls adaptability “A common property of many though not all complex systems,” but it must be borne in mind that he distinguishes between complex and complex adaptable systems.

[3] Own translation from the original Afrikaans, “‘n Sisteem vorm ‘n geheel of eenheid wat uit verskillende dele of subsisteme bestaan wat verwant is aan mekaar en in interaksie met mekaar verkeer.”

[4] Own translation from the original Dutch, “Het komt erop neer dat een complex systeem een hiërarchisch systeem is waarvan geen van de lagen tot een andere laag gereduceerd kan worden, niet omlaag en niet omhoog, zonder belangrijk verlies. Dit inzicht heeft gevolgen voor het onderzoek van een complex systeem: om tot een behoorlijk begrip van een complex systeem te komen zullen meerdere niveaus of lagen bestudeerd moeten worden. En dan vooral in hun onderlinge relaties en hun deel-geheelrelaties.”

[5] Hattingh (2002:89) suggests two more systems, namely the organ system (for example the digestive system) and the cell system (for example individual cell of the body). For the sake of uniformity, only five levels are indicated in the current figure.

[6] Own translation from the original Afrikaans, “Na analogie van die sisteemmodel is elke gesin ‘n subsisteem in ‘n groter sisteem (buurt, stad en samelewing). Tegelykertyd is elke gesin ook ‘n suprasisteem wat uit ‘n aantal subsisteme (broodwinner, huisvrou, ouer en kind) bestaan. Die gesin as subsisteem word in sy struktuur en funksionering beïnvloed deur die omgewing waarin dit voorkom. As suprasisteem word die gesin weer deur die gesinslede en die rolle wat hulle vervul, beïnvloed.” See also Marais (1992:30).

[7] Own translation from the original Dutch, “Het culturele veld ligt ingebed in de samenleving, opgevat als het geheel van onderling afhanklijke sferen: naast de culturele, met name de politieke, de economische en de sociale sfeer. Inbedding betekent dat de politieke beslissingen en sosiaal-economische faktoren van invloed zijn op wat er in het culturele veld gebeurt. Tegelijkerijd echter oefent ook cultuur zelf […] invloed uit op de samenleving.”

[8] Own translation from the original Dutch, “genetische netwerken waarbij proteïnen en genen de knooppunten zijn en de chemische interacties de verbindingen; het zenuwstelsel waarbij zenuwcellen knooppunten zijn en axons de verbindingen; en ten slotte sociale systemen met individuen of organisaties als knooppunten en sociale interacties als verbindingen.”

[9] Own translation from the original German, “Beim Organismus handelt es sich nicht um ein geschlossenes, sondern um ein offenes System. Wir nennen ein System ‘geschlossen’, wenn kein Material ‘von aussen’ in dasselbe ein-, und keines aus demselben ‘nach aussen’ austritt. Ein offenes System heisse ein solches, in welchem Ein- und Ausfuhr von Materialien stattfindet.”

[10] Own translation from the original Afrikaans, “By die oop sisteem, […] waarvan die sosiale sisteem by uitstek ‘n goeie voorbeeld is, staan die sisteem nie net in ‘n bepaalde wisselwerking met die omgewing nie, maar is hierdie wisselwerking met die omgewing van essensiële belang in die organisasie van die sisteem, die lewensvatbaarheid en kontinuïteit daarvan en die vermoë daarvan om te verander.”

[11] Own translation from the original Afrikaans, “Die literêre sisteem is ‘n oop sisteem wat nie onafhanklik van of onbeïnvloed deur ander sisteme staan nie, en wat met die direkte omgewing (en subsisteme) in interaksie is.”

[12] Own translation from the original Afrikaans, “die feit dat die grense tussen die sisteem en sy omgewing toenemend arbitrêr van aard word en dat die komponente van ‘n sisteem in een konteks as dele van ‘n bepaalde sisteem gesien kan word, maar in ‘n ander konteks, afhangende van die perspektief van die waarnemer, kan die een komponent as die omgewing vir ‘n ander komponent gesien word.”

[13] An exception in this case is the so-called Uppsala circle in the 1990s, which consisted of Leos Müller, Niklas Stenlås and Ylva Hasselberg. They strove for a qualitative network analysis (Teige, 2013:141). However, this movement did not gain wide acceptance, but Teige also discusses the work that built on them.

Leave a Reply

Your email address will not be published. Required fields are marked *