Tag Archives: complexity

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

Abstract

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 are 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 for 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 its 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 the 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,

The 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 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, the 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 to various stimuli. The core usually has much fewer 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 the 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 centre and periphery are a series of oppositions. […] In this centrifugal vs. centripetal motion, phenomena are driven from the centre to the periphery while, conversely, phenomena may push their way into the centre 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).

5. 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.

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.

Endnotes

[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 qualitative network analysis (Teige, 2013:141). However, this movement did not gain wide acceptance, but Teige also discusses the work that built on them.

Carrying Von Bertalanffy’s baton: Systems, complexity and network science, Part 2

Title: Carrying Von Bertalanffy’s baton: Systems, complexity and network science, Part 2

Author: Dr. Burgert Senekal, University of the Free State.

Ensovoort, volume 42 (2021), number 6: 1

Abstract

Ludwig von Bertalanffy wrote extensively on General Systems Theory (GST) and defined and discussed the properties of systems. In the current article, Von Bertalanffy’s views on aspects such as emergence, the methodological implications of emergence, and self-organisation, are discussed in the context of contemporary complexity theory and network science. It is shown how Von Bertalanffy viewed these key aspects of systems and their study in similar ways as contemporary network science.

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

1. Introduction

Part 1 of this series of articles situated network science and systems theory within the context of the Information- and Connected Age and recent technological advances. The present article focuses on network science as an approach to complex systems.

Network science is related to several theoretical frameworks. First, however, it is an approach to complex systems, together with nonlinear dynamics and statistical physics (Barabási, 2016:16, Duijn, 2016:15, Amaral and Ottino, 2004:1655). Although network science has developed its own theoretical concepts (see e.g. Barabási, 2016, Caldarelli, 2013 and Newman 2010), the current and following articles focus on general principles that network science shares with systems theory. Furthermore, a distinction can be made between simple and even complicated systems on the one hand, and complex systems on the other, and the distinction is also discussed in the current series of articles. The current article is not intended to provide a complete overview of all aspects of systems theory, but rather to lay the foundation for a better understanding of interdependence and network science.

More specifically, the current article discusses the following characteristics of systems and networks: the concept of emergence, methodological implications of emergence, causality, and self-organization.

2. The relationship between part and whole: emergence in complex systems

Laing (1990:204) quotes one of his patients, Julie, who was diagnosed with schizophrenia, “I’m an in divide you all.” This statement illustrates a number of concepts that are important for the study of systems. First, there is the relationship between words (entities) that accomplishes something greater when combined in a sentence: when this sentence is read quickly, one can hear her state that she is an individual. The whole therefore represents something more than what is present in the individual words. Second, on a semantic level, Julie illustrates what happens to her when that whole is broken down into its constituent parts: her existence literally perishes when the word individual is broken down into syllables – she is “divided.” These are core concepts of systems theory that are discussed in the current article.

A network or system consists of entities and their links or relationships, always with the emphasis on relationships (Nøkleberg, 2014:43, Wyseur, 2011:25). Stegbauer (2017:18) argues, “It is not the combinations of properties of individuals that are central, nor their attitudes or subjectivity; network research focuses on the structure of the relations.”[1] These relationships result in interdependence, where the existence of entities is dependent on their relationships with other entities (Page, 2011:17, Bar-Yam, 1997:12). Plsek (2001:309) also notes the importance of relationships when defining a system as, “the coming together of parts, interconnections, and purpose” (see also Kilcullen, 2010:193).

As with other system properties, this emphasis on relationships is clearly articulated by Von Bertalanffy (1968:55; 1972:417), who defines a system as, “a set of elements standing in interrelations.” More exact and comprehensive is however Strauss’s (1985:1-2) description of a system from the perspective of GST,

According to general systems theory, it must be considered that each system consists of interconnected parts which in their interrelations are mutually dependent on one another and which precisely – thanks to this reciprocal involvement – constitute the dynamic nature of each true totality.[2]

In aggregates, on the other hand, there is no significant interaction between entities. Viljoen (1986:4) provides the example of a heap of sand and a diamond to illustrate the difference between a system and an aggregate: while the molecules in a diamond are arranged in a specific pattern, the same is not the case with a heap of sand. Systems are about “order and coherence,” and “To be able to understand the system, one must not only know the elements, but also the relationships between them”[3] (Senekal, 1987:24, 25, see also Ehlers, 1989:188). Because the relationships within a system represent such an important facet of a system, the operation of a system can only be understood by investigating its structure (Nistor, Pickl and Zsifkovits, 2015:10).

Interdependence is a key concept that distinguishes a system from a collection, and therefore also an important concept in a complex versus a simple system. Although it is often stated that complex systems consist of a large number of components, the distinction between a simple and a complex system does not lie in the number of components from which it is composed (Amaral and Ottino, 2004:1654): since complexity is the result of interactions between entities within the system, it is insufficient to classify a system as complex merely on the basis of the number of components of which it is composed. Glattfelder (2010:175) mentions for example that a human being consists of about 25 000 genes and a grain of rice consists of 50 000 genes, but the former is obviously more complex than the latter. In other words, it is the interactions between elements that lead to the distinction between complex and simple systems.

There is no clear definition of a complex system (Duijn, 2016:15, Mobus and Kalton, 2015:169, Kwapień and Drożdż, 2012:119), and Amaral and Ottino (2004:1653) speculate that if one were to ask 10 scientists to formulate a definition, one would probably end up with 11 definitions. Several attempts have been made to define a complex system, and in the examples below it can be seen that interdependence is an important component of these efforts:

  • “A complex system is a system formed out of many components whose behaviour is emergent, that is, the behaviour of the system cannot be simply inferred from the behaviour of its components” (Bar-Yam, 1997:10).
  • “A complex system is a system with a large number of elements, building blocks or agents, capable of interacting with each other and with their environment. […] The common characteristic of all complex systems is that they display organization without any external organizing principle being applied. The whole is much more than the sum of its parts” (Amaral and Ottino, 2004:148).
  • “Complexity examines how components of a system, through their dynamic interactions, “spontaneously” develop collective properties or patterns that are not implicit in, or at least not in the same way implicit in, individual components”[4] (Urry, 2004:23).
  • “it is a system composed of many interacting parts, such that the collective behaviour of those parts together is more than the sum of their individual behaviours. The collective behaviours are sometimes also called ‘emergent’ behaviours, and a complex system can thus be said to be a system of interacting parts that displays emergent behaviour” (Newman, 2011:1).
  • “a complex system is a system built from a large number of nonlinearly interacting constituents, which exhibits collective behaviour and, due to an exchange of energy or information with the environment, can easily modify its internal structure and patterns of activity” (Kwapień and Drożdż, 2012:118).

An important term implied in these definitions (and included explicitly in the definitions of Bar-Yam and Newman), is emergence.[5] Emergence refers to Aristotle’s well-known statement that the whole is more than the sum of the parts (Glattfelder, 2013:2, Page, 2011:7, Von Bertalanffy, 1972:407, 1968:18). Ropohl (2005:27) describes emergence as when, “the properties of wholeness cannot be explained solely from the properties of individual parts, but only from the special way in which the parts interact”[6] (see also Kwapień and Drożdż, 2012:118, Wyseur, 2011:24, and DeLaurentis, 2007:364 for similar definitions).

Von Bertalanffy also considered emergence as a key feature of systems. He (1956:33) defines emergence as follows, “Each higher level presents new features that surpass those of the lower levels” (see also Von Bertalanffy, 1928:64).

Emergence is found in all systems. A written text, for example, is composed of letters, words and sentences, but can elicit feelings of happiness, sadness or anger from a reader. Language itself is a complex system (Kwapień and Drożdż, 2012) which on many levels consists of the interactions between entities. Senekal and Geldenhuys (2016) note that the letters ‘o’, ‘e’, ‘s’ and ‘p’ can be combined in such a way in Afrikaans that they express surprise (“oeps,” English “oops”), a medium of communication (“e-pos,” English “email”), a literary genre (“epos,” English “epic”), and vulgarity (“poes,” English “cunt”) – it is, among other things, the way in which the letters are combined and thus how the elements are connected that leads to meaning (for an overview of language as a complex system, see Kwapień and Drożdż, 2012, and Senekal and Geldenhuys, 2016).

Chemical compounds are frequently used to illustrate the concept of emergence. Christakis and Fowler (2010:26) state, for example, that the taste of a cake is quite different from the sum of the cake’s ingredients. Kilcullen (2010:195) also maintains that the taste of sugar (C12H22O11) originates at the molecular level and that a study of the atoms from which sugar is composed does not give an indication of the taste of their combination. Mobus and Kalton (2015:505) in turn note that Sodium (Na) and Chlorine (Cl) are on their own toxic, but the right combination, Sodium Chloride (NaCl) (table salt), is an essential part of the human diet.[7] It is the relationships that are crucial in systems; in the words of Wilden (1980:215), “entities do not create relationships so much as relationships create entities” (original emphasis).

One of the clearest expositions of emergence can be found in Page (2011:217), who frames the concept in the form of Equation (1).[8]

In other words, the function of x plus y is greater than the function of x plus the function of y – the whole is more than the sum total of the parts. Steyn (1984:8) illuminates further,

This organized whole is not traceable to the individual elements of which it is composed, and on the whole, there is a holistic perspective in this approach: The organization of components in systemic relationships gives the whole characteristics that do not only differ from the components taken in isolation, but are often also not present at all in the components alone; something that is a consequence of the organizational effect.[9]

The example of Sodium Chloride above illustrates, for example, Steyn’s argument: emergence means that the properties of the whole are not present in the elements themselves. Note, however, that emergence is present in any system, whether simple or complex, and is therefore not a distinctive feature of complex systems.

Given the importance of emergence in a complex system, any view of a complex network must include this characteristic of complex systems. Lawson, Ferris, Cropley and Cook (2006:9) define a network as follows,

A network is formed when a number (between two and infinity) of distinct entities that may be similar or dissimilar (nodes, elements, components, people, military formations, software instructions) are connected and interact such that new properties or behaviours emerge that are beyond the capabilities of any of the entities acting alone. These emergent properties cannot be predicted using reductionist consideration of the distinct entities. They are of interest because of the functions they perform and the purposes they serve, while the distinct and dissimilar entities included within a particular network boundary are those that are understood to be most significant in determining the emergent properties.

This definition of a complex network is the most comprehensive definition I have encountered to date and forms the backdrop of all conceptualisations of networks discussed in the current series of articles.

3. Reductionism versus holism: methodological implications for the study of systems

Since the properties of the whole are not present in the properties of the elements, emergence has important methodological implications for the study of systems. Mobus and Kalton (2015:11), Plsek (2001:311), De Beer (1997:81) and Von Bertalanffy (1950:134) contend that the paradigm of science over the past few centuries has been reductionism, in other words that a better understanding of the parts would lead to a better understanding of the world. This mechanistic Newtonian worldview suggested that the whole could be fully understood and predicted if science could comprehend the parts in totality. Wyseur (2011:24) refers to Julius Caesar’s saying, “Divide et impera” (divide and conquer). In other words: divide (analyse) and understand. He (2011:11) clarifies,

The mathematical laws led to a world view in which the universe was seen as a great mechanism. Mankind proved able, on the basis of mathematical language and empirically sound experiments, to derive absolute laws from nature in order to make predictions about the future. If one could derive all natural laws and know the positions of all particles present in the cosmos, it was possible to fully calculate and thus predict all movements and changes in time. This casts an absolutely deterministic view of the workings of the universe. The universe in its entirety was seen as one big clock. The ultimate goal of science was to unravel all natural laws in order to maximize the prediction possibilities.[10]

Planck’s quantum theory (as later refined by Heisenberg and Schrödinger) – together with Einstein’s theory of relativity – ushered in a new perspective within science, which called the Newtonian perspective into question (Wyseur, 2011:12, De Beer, 1997:78, Marais, 1992:20). Einstein’s theory of relativity showed that the position and time of the observer plays a role in observations (De Beer, 1997:82-83), while quantum physics, where Heisenberg identified the uncertainty principle (Mobus and Kalton, 2015:273, De Beer, 1997:85), also raised questions about the measurability of objects and further contributed to a questioning of science’s ability to undertake absolutely objective observations.

The most important scientific paradigm shift for the purposes of the current article, however, was the realization that the properties of the whole cannot be predicted by a better understanding of the parts, in other words that analysis will bring only limited knowledge of the world. Von Bertalanffy (1968:18-19) argues,

The system problem is essentially the problem of the limitations of analytical procedures in science. […] ‘Analytical procedure’ means that an entity investigated be resolved into, and hence can be constituted or reconstituted from, the parts put together, these procedures being understood both in their material and conceptual sense. […] Application of the analytical procedure depends on two conditions. The first is that interactions between ‘parts’ be nonexistent or weak enough to be neglected for certain research purposes. Only under this condition, can the parts be ‘worked out,’ actually, logically, and mathematically, and then be ‘put together.’ The second condition is that the relations describing the behaviour of parts be linear; only then is the condition of summativity given, i.e., an equation describing the behaviour of the total is of the same form as the equations describing the behaviour of the parts; partial processes can be superimposed to obtain the total process, etc. (see also Von Bertalanffy, 1968:36-37).

In line with Von Bertalanffy’s argument, Bar-Yam (1997:11) and others writing about complexity, e.g. Smaling (2013:91), Koithan, Bell, Niemeyer and Pincus (2012:10), Macklem (2008:1844), De Beer (1997:86), and Anderson (1972:393), argue that emerging properties cannot be studied by reductionist methods; entities must be studied within the complex web of relationships within which they exist. Anderson (1972:393) contends for example,

The behaviour of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each level of complexity entirely new properties appear, and the understanding of the new behaviours requires research which I think is as fundamental in its nature as any other.

It is therefore insufficient to try to achieve a better understanding of the human brain, for example, by simply studying individual neurons (Telesford, Simpson, Burdette, Hayasaka and Laurienti, 2011:295), or to try to understand why traffic jams occur by examining only the individual driver (Christakis and Fowler, 2010:25, Kumpula, 2008:2). One of the examples of a complex system that is most commonly mentioned in the literature on complex systems is a living organism, and Kresh (2006:24) maintains that emergence here also points out the shortcomings of reductionism, since the collective behaviour of living organisms cannot be reconstructed from the components of the system. Glückler (2017:23) also reasons in terms of human beings, “People act in dependence on situational and structural opportunities and not solely on the basis of ‘oversocialized’ internalization of given norms or ‘under-socialized’ compliance with logic such as rationality.”[11]

A more precise example. In the Afrikaans film industry from 1994-2014, as studied in Senekal (2015), there are 88 023 collaborative relationships between 1 866 actors, with an average path length of 2,35 between actors in this network. For the entire film industry, there are 805 103 collaborative relationships between 6 274 people (including all role players). There are therefore 814,65% more collaborative relationships for the whole industry (the whole) than for the actors (a component of the film industry), but the average path is not 814,65% longer for the whole industry, but rather shorter: 2,17. The average path length in the actor network thus provides no indication of what the average path length will be for the entire network, which illustrates that some facets of complex systems are not reducible to the study of components.

Because of emergence, systems theory then places the emphasis on studying the relationships that constitute the system. Ropohl (2005:28) summarises the systems-theoretical approach, “Systems thinking prefers systematization over elementalization, holistic models over atomistic models, multidimensionality over one-dimensionality, integration over differentiation, synthesis over analysis.”[12]

According to Cong and Liu (2014:599), network science is ideally suited to take emergence into account when studying complex systems; network science “makes it possible to probe into the complexity of real-world systems in their entirety and thus constitutes one, if not the only, solution to the challenge of reassembling complex systems and capturing their holistic properties.” Network science enables the scientist to consider each entity and each relationship in a system, as well as to study the individual entity within this complex web of relationships.

However, network science still suffers from an important limitation: all relationships that affect an entity cannot be practically included in a study. Part of the problem is data: finding all relevant data points, and getting them in a format where they can be included in the study, is currently not possible. In other words, network science seeks to consider as many connections as possible, but never includes all relationships that affect the component. The important issue here is however that systems theory and network science are not under the impression that parts can be understood in isolation, even though it is currently not yet feasible to take all relationships into account in every study.

4. Causality in complex systems

Emergence also affects our understanding of causality. In a simple system, if one understands the workings of the parts, predictions can be made with a great deal of certainty. For example, if one understands the parts of a motor vehicle and how they function together, it can be predicted whether a car will function as expected. Because linear causality applies to the simple or complicated system such as a motor vehicle, the mechanic’s job is relatively simple: find the part that is not functioning as it should, and replace it. When all parts are in working condition, the motor vehicle will also be in working condition. Von Bertalanffy (1968:45) explains,

The only goal of science appeared to be analytical, i.e., the splitting up of reality into ever smaller units and the isolation of individual causal trains. Thus, physical reality was split up into mass points or atoms, the living organism into cells, behaviour into reflexes, perception into punctual sensations, etc. Correspondingly, causality was essentially one-way: one sun attracts one planet in Newtonian mechanics, one gene in the fertilized ovum produces such and such inherited character, one sort of bacterium produces this or that disease, mental elements are lined up, like the beads in a string of pearls, by the law of association.

The same degree of predictability does not apply to complex systems. Prigogine (1997:4) – one of the key theorists of unpredictability and non-linear processes – writes, “Classical science emphasized order and stability; now, in contrast, we see fluctuations, instability, multiple choices, and limited predictability at all levels of observation.” In complex systems, causality is not a single or even an accumulation of causes (Byrne and Callaghan, 2014:190, Smaling, 2013:90, Weideman, 2009:67). In simple systems, a cause can be identified with certainty, for example that a pen has fallen due to gravity, or that ice has melted due to a temperature above 0°C and air pressure falling within a normal spectrum of surface air pressure (an accumulation of causes). In complex systems, however, in the words of Wilden[13] (1980:39), “causes cause causes to cause causes” (original emphasis). Nicolis (1995:1-2) explains,

A striking difference between linear and nonlinear laws is whether the property of superposition holds or breaks down. In a linear system the ultimate effect of the combined action of two different causes is merely the super-position of the effects of each cause taken individually. But in a nonlinear system adding two elementary actions to one another can induce dramatic new effects reflecting the onset of cooperativity between the constituent elements. This can give rise to unexpected structures and events whose properties can be quite different from those of underlying elementary laws, in the form of abrupt transitions, a multiplicity of states, pattern formation, or an irregularly markedly unpredictable evolution of space and time referred to as deterministic chaos.

A clear example of unpredictability in a complex system can be found in the fall of the Soviet Union. Papp, Alberts and Tuyahov (1997:30-31) explain that although reforms in the 1980s were aimed at decentralizing economic decision-making and leading to improved production, it rather created confusion and economic uncertainty in the Soviet Union and reduced Soviet production. Reforms were to encourage popular support for communism by involving more people in the political decision-making process, but rather led to more Soviet citizens questioning and eventually rejecting the system. There are many reasons why the Soviet Union collapsed, including their weak economy, technological disadvantage compared to the West, the war in Afghanistan and these reforms, but the important issue to keep in mind here is that it is the way in which various factors are combined that ultimately led to this unpredictable outcome. Interactions are the key to unpredictability in complex systems, as Eusgeld, Nan and Dietz (2011:681) contend, “a complex system can never be fully knowable not only due to rapid changes in the system state (high dynamic) and nonlinear behaviour, but also interconnections within the system (interdependencies).”

Because communities are also complex systems, unpredictability sometimes hinders efforts to improve communities’ conditions. One example of such an unexpected result is the well-meaning efforts of Western film stars to distribute mosquito nets in Africa, which undermine local netmakers’ businesses and thus increase people’s vulnerability to malaria in the long term (Kilcullen, 2013:243). In South Africa, the African National Congress (ANC) banned alcohol sales in March 2020 to combat alcohol-related crimes such as domestic violence during the Covid-19 epidemic (Harding, 2020), but less than two months later, President Ramaphosa had to admit that violence against women increased during the lockdown (Chothia, 2020).

Simple linear causality is deeply embedded in human thinking. One such example is the cause of shooting incidents at high schools in the US, which is a phenomenon that is frequently attributed to teenagers playing violent video games. This alleged causal link is criticised by Watts (2011:116-117), as it ignores the vast majority of adolescents who never harm anyone, even though they also play these video games. Similarly, the high availability of firearms in this country is also frequently blamed for these incidents. One could offer the same critique of this claim: if firearms are the cause, why are there so few incidents? There were 583 shooting incidents at American schools between 2013 and 2019 (Everytown, 2019) in a country with around 300 000 000 firearms (33-34% of adults own firearms, Agresti and Smith, 2010), which raises the question: what about the other firearms? And why are there no such incidents in South Africa, where there are also large quantities of firearms (between 3 700 000 and 7 200 000) (GunPolicy, 2020) that are privately owned? If the firearms are the cause, why does one American adolescent take his father’s firearm and shoot his fellow students, while the other one does not, and why does the South African teenager not take his father’s firearm and shoot his fellow students?

The problem with such alleged simple causal relationships is that a human being is a complex system where such simplistic causal relationships are not valid. People who advocate to ban video games or firearms in the US to prevent shooting incidents, try to replace the faulty part – like the mechanic – in the hope that the whole system will function flawlessly thereafter. But a human being (a complex system) is not a motor vehicle (a simple system). For one American adolescent, his decision to perpetrate a massacre can be helped by the fact that he can easily obtain a firearm, and he may have grown up with violent video games, but his neighbour may also easily obtain a firearm and play the same video games, but he does not harm anyone. The superficial similarities are not as important as the many differences: the two adolescents have different genetic compositions, are exposed to different influences, come from different parental homes, have different diets and many more. It is the combination of all factors in an individual’s social, biological and psychological spheres that leads to such incidents, not a single one.

Moreover, by identifying the wrong cause due to an outdated Newtonian, mechanistic worldview, the problem cannot be addressed because it cannot be correctly identified. What is needed is a complexity perspective. Prigogine (1984:203) contends, “We are trained to think in terms of linear causality, but we need new ‘tools of thought’.”

5. The web without a spider: self-organization in complex systems

Self-organization refers to the phenomenon where elements organize without any outside control (Duijn, 2016:15, Wyseur, 2011:35). Examples include the formation of patterns in a snowflake, as well as the formation of crystals, diamonds, dunes and chemical compounds. These examples represent simple systems, but the phenomenon is of course also found in complex systems. Koithan, Bell, Niemeyer and Pincus (2012:11) define self-organisation as follows,

A nonlinear distributed process throughout complex systems that is dependent on energy and information networks occurring in far-from-equilibrium states and yields order and emergent or arising behaviour befitting the environment or circumstance. Self-organization is complexification.

Von Bertalanffy (1968:98) proposed that organisms are capable of self-organisation, but extended his view to include all open systems,

Self-differentiating systems that evolve toward higher complexity (decreasing entropy) are, for thermodynamic reasons, possible only as open systems – e.g., systems importing matter containing free energy to an amount overcompensating the increase in entropy due to irreversible processes within the system […]. However, we cannot say that “this change comes from some outside agent, an input”; the differentiation within a developing embryo and organism is due to its internal laws of organization, and the input […] makes it only possible energetically.

To illustrate self-organisation, Cilliers (1998:88-90) provides the example of a school of fish, where the condition of the fish will depend on a large number of factors, including the availability of food, the temperature of the water, the amount of oxygen and light, the time of year, and so on. As these factors vary, the size of the school of fish will adapt itself optimally to the prevailing conditions, despite the fact that each individual fish can only look after its own interests. The system of the school of fish organizes itself as a whole to ensure the best relationship between the system and the environment. There is no agent who decides for the school, and also each individual fish does not understand the complexity of the situation.

A well-known human example of self-organization is the Mexican Wave at sports events, which is also mentioned by Christakis and Fowler (2010:25) and studied in detail by Farkas, Helbing and Vicsek (2002). A group of people stand up and throw their arms in the air, the group closest to them does the same, and the one closest to the next group does the same, and finally the ‘wave’ moves around the sports field with remarkable regularity. Again, there is no central control present; no single person coordinates the wave.

According to Christakis and Fowler (2010), self-organization is responsible for smoking cessation, spreading suicide over social networks, as well as happiness and depression, and also – their most famous finding – obesity (Christakis and Fowler, 2007). Kilcullen (2013:80-86) also discusses the tactics of Somali fighters as swarm tactics, where they appear coordinated in the absence of a central governing body. In his view, the American Task Force Ranger confronted such a “self-organizing swarm” (2013:73) in Mogadishu in October 1993 (this battle is familiar through Riddley Scott’s film, Black Hawk Down).

A related phenomenon is that of synchronization,[14] as discussed by Strogatz (2004), Boccaletti, Latora, Moreno, Chavez and Hwanga (2006:237-251), Barrat, Barthélémy and Vespignani (2008:136-159), and Csermely (2006:81). Synchronisation refers to “a process wherein many systems (either equivalent or non-equivalent) adjust a given property of their motion due to a suitable coupling configuration, or to an external forcing” (Boccaletti, Latora, Moreno, Chavez, and Hwanga (2006:237). Christian Huygens’s (1893[1665]) well-known 17th century discovery of synchronization between two pendulums is an example of synchronization between simple systems, but a variety of studies of synchronization between complex systems have already been undertaken. Through visual and acoustic interactions, fireflies flash in sync (Buck, 1938), crickets cricket in harmony (Walker, 1969), audiences clap their hands in sync (Néda, Ravasz, Vicsek, Brechet, and Barabási (2000), and women living together synchronize menstrual cycles (McClintock, 1971). On a much larger scale, the outbreak of syphilis was synchronized from Houston to New York between 1960 and 1993 (Grassly, Fraser and Garnett (2005).

Schmidt (1997:125) argues that cultural systems are also self-organising, “[M]odern literary systems are self-organising insofar as all decisions concerning literariness and literary values are made ‘inside’ the social system literature, i.e. in literary communications” (see also De Berg, 1997:145-147). There are gatekeepers, but the gatekeepers themselves are also part of the system. Roberts (1973:87) also writes that all identification of specific objects (books and writing traditions) as literature is carried out by the literary community itself. No central governing body coordinates the functioning of the literary system.

The same holds for works of art, where the intrinsic characteristics of the work of art do not determine the ultimate reputation of the work. Fraiberger, Sinatra, Resch, Riedl and Barabási (2018:825) explain,

Quality in art is elusive; art appeals to individual senses, pleasures, feelings, and emotions. Recognition depends on variables external to the work itself, like its attribution, the artist’s body of work, the display venue, and the work’s relationship to art history as a whole. Recognition and value are shaped by a network of experts, curators, collectors, and art historians whose judgments act as gatekeepers for museums, galleries, and auction houses.

Since self-organization is “the key concept in the science of complexity”(Plsek, 2001:313), any valid understanding of a complex network must also consider self-organization. This is how Barabási (2003:221) considers complex networks, “No central node sits in the middle of the spider web, controlling and monitoring every link and node. There is no single node whose removal could break the web. A scale-free network is a web without a spider.”

6. Conclusion

This article discussed some of the features of systems from a GST, complexity and network science perspective. Whether the issue is emergence or the methodological issues thereof, causality, or self-organisation, in each case, network science shares the views articulated by Von Bertalanffy. In terms of these features, then, it can be argued that network science continues many of Von Bertalanffy’s insights, albeit in a new guise.

The following article discusses further features associated with network science that correspond to Von Bertalanffy’s views.

Bibliography

Agresti, J. D. and Smith, R. K. 2010. Just Facts. http://www.justfacts.com/guncontrol.asp#f8 [Accessed 5 April 2016].

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

Amaral, L. and Ottino, J. 2004b. Complex systems and networks: challenges and opportunities for chemical and biological engineers. Chemical Engineering Science, 59:1653 – 1666.

Anderson, P.W. 1972. More is different. Science, 177(4047):393-396.

Bar-Yam, Y. 1997. Dynamics of complex systems. Colorado: Westview Press.

Barabási, A.-L. 2003. Linked. London: Plume.

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

Barrat, A., Barthélémy, M. and Vespignani, A. 2008. Dynamical processes on complex networks. Cambridge: Cambridge University Press.

Boccaletti, S. et al. 2006. Complex networks: Structure and dynamics. Physics Reports, 424:175–308.

Buck, J. 1938. Synchronous rhythmic flashing of fireflies. Quarterly Review of Biology, 13:301–314.

Byrne, D. and Callaghan, G. 2014. Complexity Theory and the Social Sciences. The state of the art. Oxon: Routledge.

Caldarelli, G. 2013. Scale free networks. Complex webs in nature and technology. Oxford: Oxford University Press.

Chothia, A. 2020. ‘Men in our country have declared war on women’ – Cyril Ramaphosa. https://www.thesouthafrican.com/news/gender-based-violence-gbv-increase-lockdown-cyril-ramaphosa/ [Accessed 19 May 2020].

Christakis, N. A. and Fowler, J. H. 2007. The spread of obesity in a large social network over 32 years. New England Journal of Medicine, 357(4):370-379.

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

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

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

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

De Beer, S. J. 1997. Holisme en ontwikkeling. Unpublished MA-dissertation: Randse Afrikaanse Universiteit.

De Berg, H. 1997. Communication as a challenge to systems theory. Canadian Review of Comparative Literature, March: 141-151.

Duijn, P. 2016. Detecting and Disrupting Criminal Networks. A Data Driven Approach. Unpublished PhD-thesis: University of Amsterdam.

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.

Everytown. 2019. Gunfire on School Grounds in the United States. https://everytownresearch.org/gunfire-in-school/2866/#2866 [Accessed 19 May 2020].

Farkas, I., Helbing, D. and Vicsek, T. 2002. Mexican waves in an excitable medium. Nature, 419:131–132.

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

Glattfelder, J. B. 2010. Ownership networks and corporate control: mapping economic power in a globalized world. Unpublished PhD-thesis: ETH Zurich.

Glattfelder, J. B. 2013. Decoding Complexity: Uncovering Patterns in Economic Networks. Heidelberg: Springer.

Glückler, J. 2017. Relationales Denken diesseits und jenseits der Netzwerkforschung. Soziologie, 46(1):22-27.

Grassly, N., Fraser, C. and Garnett, G. 2005. Host immunity and synchronized epidemics of syphilis across the United States. Nature, 433:417–421.

GunPolicy, 2020. South Africa — Gun Facts, Figures and the Law. https://www.gunpolicy.org/firearms/region/south-africa [Accessed 19 May 2020].

Harding, A. 2020. South Africa coronavirus lockdown: Is the alcohol ban working?. https://www.bbc.com/news/world-africa-52358268 [Accessed 19 May 2020].

Huygens, C. 1893[1665]. Letter to R. Moray (February 27, 1665). In: M. Nijhoff, ed. Euvres Completes de Christian Huygens. The Hague: Société Hollandaise des Sciences:246–249.

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

Kilcullen, D. 2013. Out of the mountains. The coming age of the urban guerrilla. London: C. Hurst and Co.

Koithan, M., Bell, I. R., Niemeyer, K. and Pincus, D. 2012. A complex systems science perspective for whole systems of complementary and alternative medicine research. Forschende Komplementärmedizin/Research in Complementary Medicine, 19(Supplement 1):7-14.

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.

Kumpula, J. 2008. Community structures in complex networks: detection and modeling. Unpublished PhD dissertation: Helsinki University of Technology.

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

Laing, R. 1990. The divided self. London: Penguin.

Lawson, E., Ferris, T., Cropley, D. and Cook, S. 2006. Development of a Foundation for Military Network Science. s.l.:Systems Engineering and Evaluation Centre (SEEC), University of South Australia.

Macklem, P.T. 2008. Emergent phenomena and the secrets of life. Journal of Applied Physiology, 104:1844–1846.

Marais, M. 1992. Die persoon in die sisteem: Kritiek op gesinsterapie. Unpublished MA-dissertation: Randse Afrikaanse Universiteit.

McClintock, M. 1971. Menstrual synchrony and suppression. Nature, 229:244–245.

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

Néda, Z. et al. 2000. The sound of many hands clapping. Nature, 403:849–850.

Newman, M. E. J. 2010. Networks. Oxford: Oxford University Press.

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

Nicolis, G. 1995. Introduction to Nonlinear Science. Cambridge: Cambridge University Press.

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.

Nøkleberg, M. 2014. Sammen for sikkerhet? En casestudie av sikkerhetsforvaltningen i Bergen. Unpublished MA-dissertation: Universiteit Bergen.

Page, S. E. 2011. Diversity and complexity. Princeton: Princeton University Press.

Papp, D. S., Alberts, D. S. and Tuyahov, A. 1997. Historical Impacts of Information Technologies: An Overview. In: D. S. Alberts and D. S. Papp, eds. The information age: an anthology on its impact and consequences. s.l.:CCRP Publication Series:13-35.

Plsek, P. 2001. Redesigning health care with insights from the science of complex adaptive systems. In: C. o. Q. o. H. C. i. America, ed. Crossing the quality chasm: A new health system for the 21st century. Washington: National Academy Press:309-322.

Prigogine, I. 1984. Order out of chaos: Man’s new dialogue with nature. New York: Bantam Books.

Prigogine, I. 1997. The end of certainty. Time, chaos, and the new laws of nature. New York: The Free Press.

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.

Schmidt, S. J. 1997. A systems-orientated approach to literary studies. Canadian Review of Comparative Literature, March: 119-136.

Senekal, B. A. and Geldenhuys, C. 2016. Afrikaans as ‘n komplekse netwerk: Die woord ko-voorkoms netwerke van woorde in André P. Brink se Donkermaan in Afrikaans, Nederlands en Engels. Suid-Afrikaanse Tydskrif vir Natuurwetenskappe en Tegnologie.

Senekal, B. A. 2015. ʼn Veelvlakkige netwerkontleding van die Afrikaanse filmbedryf (1994-2014). LitNet Akademies (Geesteswetenskappe), 12(2).

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

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

Stegbauer, C. 2017. Interdisziplinäre Netzwerkforschung. Soziologie, 36(1):17-22.

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.

Strogatz, S. 2004. Sync. The emerging science of spontaneous order. London: Penguin.

Telesford, Q. K. et al. 2011. The Brain as a Complex System: Using Network Science as a Tool for Understanding the Brain. Brain Connectivity, 1(4):295-308.

Urry, J. 2004. Globale complexiteit en het autosysteem. Tijdschrift voor sociologie, 25(1):21-35.

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

Von Bertalanffy, L. 1928. Kritische Theorie der Formbildung. Berlin: Borntraeger.

Von Bertalanffy, L. 1950. An Outline of General System Theory. The British Journal for the Philosophy of Science, 1(2):134-165.

Von Bertalanffy, L. 1956. A Biologist Looks at Human Nature. The Scientific Monthly, 82(1):33-41.

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

Von Bertalanffy, L. 1972. The History and Status of General Systems Theory. The Academy of Management Journal, 15(4):407-426.

Walker, T. 1969. Acoustic synchrony: Two mechanisms in the snowy tree cricket. Science, 166:891–894.

Watts, D. J. 2011. Everything is obvious. Once you know the answer. London: Atlantic.

Weideman, A. 2009. Uncharted territory: A complex systems approach as an emerging paradigm in applied linguistics. Per Linguam, 25(1):61-75.

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.

Endnotes

[1] Own translation from the original German, “Zentral sind dabei nicht die Kombinationen von Eigenschaften einzelner Personen und auch nicht deren Einstellungen oder deren Subjektivität; in den Mittelpunkt stellt die Netzwerkforschung die Struktur der Relationen.”

[2] Own translation from the original Afrikaans, “Wel moet volgens die algemene sisteemteorie verreken word dat elke sisteem uit onderling ineengeweefde onderdele bestaan wat in hul interrelasies wederkerig van mekaar afhanklik is en wat juis danksy hierdie wederkerige betrokkenheid die dinamiese aard van elke egte totaliteit konstitueer.”

[3] Own translation from the original Afrikaans, “Om die sisteem te kan verstaan, moet ʼn mens nie net die elemente ken nie, maar ook die relasies tussen hulle.”

[4] Own translation from the original Dutsch, “Complexiteit onderzoekt hoe componenten van een systeem doorheen hun dynamische interactie ‘spontaan’ collectieve eigenschappen of patronen ontwikkelen die niet impliciet zijn aan, of op zijn minst niet op dezelfde manier impliciet zijn aan, de individuele componenten.”

[5] Emergence is by no means a new concept in science. In addition to, for example, Aristotle, John Stuart Mill (1843:III(6)1) argued, “To whatever degree we might imagine our knowledge of the properties of the several ingredients of a living body to be extended and perfected, it is certain that no mere summing up of the separate actions of those elements will ever amount to the action of the living body itself.”

[6] Own translation from the original German, “die Eigenschaften der Ganzheit nicht allein aus den Eigenschaften einzelner Teile, sondern nur aus der besonderen Art des Zusammenwirkens der Teile erklärt werden können.”

[7] Strauss (1985:3) argues that it is problematic to claim that a system consists of parts, and uses the example of sodium chloride to illustrate his argument. He writes, “Wanneer soutkorrels verdeel word, word telkens kleiner stukkies sout gekry – met as ondergrens ʼn enkele NaCl molekuul. Sodra hierdie kleinste (sout-gewys gesproke ondeelbare) eenheid verdeel word, is die sout tot niet en sit ons bloot met ʼn Natrium atoom en ʼn Chloor atoom! Dit toon onmiskenbaar dat Natrium en Chloor nie gesien kan word as integrale (egte) dele van tafelsout nie, hoeseer tafelsout ookal daaruit opgebou is. [When salt grains are divided, smaller pieces of salt are obtained each time – with a single NaCl molecule as the lower limit. Once this smallest (salt-wise indivisible) unit is divided, the salt is destroyed and we are left with a Sodium atom and a Chlorine atom! This unmistakably shows that Sodium and Chlorine cannot be seen as integral (real) parts of table salt, no matter how much table salt consist of it.]” Strauss’s argument, however, is similar to that presented here: the relationships between elements lead to something quite different from what is present in the properties of the individual elements.

[8] Page uses the symbol ≥, but when he explains the concept, he calls the function “greater than.” Using ≥ is probably a printing error.

[9] Own translation from the original Afrikaans, “Hierdie georganiseerde geheel is nie tot die individuele elemente waaruit dit bestaan, herleibaar nie, en in geheel gesien, is daar ʼn holistiese perspektief in hierdie benadering: Die organisasie van komponente in sistemiese verhoudings gee aan die geheel kenmerke wat nie net verskil van die komponente in isolasie geneem nie, maar dikwels ook glad nie in die komponente alleen geneem, gevind word nie; iets wat ʼn uitvloeisel van die organisasie-effek is.” See also Von Bertalanffy (1952:148; 1950:148) and Bar-Yam (1997:10) for similar statements.

[10] Own translation from the original Dutch, “De mathematische wetmatigheden leidden tot een wereldbeeld waarbij het universum als een groot mechanisme werd gezien. Het menselijk wezen bleek in staat om, op basis van wiskundige taal en empirisch verantwoorde experimenten, absolute wetten af te leiden van de natuur teneinde voorspellingen te kunnen maken over de toekomst. Indien men alle natuurlijke wetmatigheden zou kunnen afleiden en men de posities van alle aanwezige deeltjes in de kosmos zou weten, bestond de mogelijkheid om alle bewegingen en veranderingen in tijd volledig te berekenen en dus te voorspellen. Dit werpt een absoluut deterministische visie op de werking van het heelal. Het heelal in zijn totaliteit werd gezien als één groot uurwerk. Het ultieme doel van de wetenschap bestond erin alle natuurlijke wetmatigheden te ontrafelen om zo de voorspellingsmogelijkheden te maximaliseren.”

[11] Own translation from the original German, “Menschen handeln in Abhängigkeit situativer und struktureller Gelegenheiten und nicht allein aufgrund ‘übersozialisierter’ Verinnerlichung vorgegebener Normen oder ‘untersozialisierter’ Befolgung von Logiken wie zum Beispiel der Rationalität.”

[12] Own translation from the original German, “Das Systemdenken präferiert die Systematisierung gegenüber der Elementarisierung, holistische Modelle gegenüber atomistischen Modellen, die Mehrdimensionalität gegenüber der Eindimensionalität, die Integration gegenüber der Differenzierung, die Synthese gegenüber der Analyse.”

[13] Wilden does not write within the framework of complexity theory, but within the theory of open systems, as does Von Bertalanffy (who proposes the same argument (1968:45)), but as in the case of the latter, his understanding of an open system is highly similar to a complex system. One also finds a comparable similarity between the theory of open systems and that of complex systems in Steyn (1984).

[14] Carl Jung referred to the comparable concept of synchronicity, but as Csermely (2006:84) writes, the majority of Jung’s examples are “difficult to accept […] in the current state of scientific knowledge.”