Title: Carrying Von Bertalanffy’s baton: Systems, complexity and network science, Part 1
Author: Dr. Burgert Senekal, University of the Free State.
Ensovoort, volume 42 (2021), number 5: 3
Ludwig von Bertalanffy formulated his General Systems Theory (GST) shortly after World War II. He envisaged an umbrella science that would unite the scientific endeavour by identifying universal laws that could facilitate interdisciplinary research. In addition, he argued that computers allowed scientists to conduct research in a new way, and he advocated that the connections between entities are key to understanding how the universe functions. Although his GST only gained limited acceptance in the scientific community at the time, in recent years, GST has become an important component of complexity theory. In addition, Von Bertalanffy included network and graph theory under GST, and these theoretical avenues have developed into what is today known as network science, which is one of the most important components of complexity theory. This article shows how network science realised Von Bertalanffy’s vision in three important ways: by foregrounding connections, by facilitating interdisciplinary research and by using computers to study phenomena in news ways. Parts 2 and 3 of this three-part series of articles discuss key theoretical insights shared between Von Bertalanffy and network science.
Keywords: Von Bertalanffy, General Systems Theory, systems science, complexity, network science
Ludwig von Bertalanffy (1901-1972) proposed General Systems Theory (GST) through a series of publications (e.g. 1940, 1950a, 1950b, 1952, 1956, 1968 and 1972). His views have had a noticeable influence on science, across continents and disciplinary boundaries (Hammond, 2019). Among other insights, he recognized the potential of computer-driven research, argued that the workings of entities could not be understood in isolation, and suggested that systems theory could provide an approach to integrating science through interdisciplinary research. Although his GST did not succeed in these goals at the time, network science has realized this vision in the 21st century.
Network science has become one of the most important approaches within systems theory, and Barabási (2011:15) claims, for example, that network science has hijacked the theory of complexity. Von Bertalanffy (1972:416, 1968:21,90) also included graph theory (one of the components of network science) under the umbrella of GST (see also Geurts, 1974:215), although in Von Bertalanffy’s time, graph theory was still in a developmental stage. Barabási (2016:7) argues that network science has its roots in earlier approaches but has emerged as a distinct science in the early 21st century, and it is with this 21st century approach that the current study is concerned.
The current three-part series of articles examines network science as a continuation of Von Bertalanffy’s GST. In Part 1, network science is contextualized within the information revolution and the Connected Age (Watts, 2004), with specific reference to Von Bertalanffy’s insights in this regard. Parts 2 and 3 examine specific theoretical aspects of network science that are consistent with Von Bertalanffy’s insights. The aim is to show how network science realised Von Bertalanffy’s vision against the backdrop of the information revolution since the 1990s.
2. A note on the relationship between General Systems Theory and network science
Goldstein (2008:20) shows that complexity theory can be traced back to cybernetics, information theory, graph theory, GST, complex adaptive systems (CAS), game theory and far-from-equilibrium thermodynamics. Complexity theory is neither a unified theory nor a theory with singular roots – various authors have published in this domain, citing different influences. Von Bertalanffy’s GST has however become an important component of complexity theory.
As stated earlier, Von Bertalanffy (1972:416, 1968:21,90) included graph theory under the umbrella of GST. He (1972:416) writes,
System-theoretical approaches include general system theory (in the narrower sense), cybernetics, the theory of automata, control theory, information theory, set, graph and network theory, relational mathematics, game and decision theory, and computerization and simulation.
Network theory is sometimes considered to be the social branch of network science, whose history is e.g. documented in Freeman (2004). Graph theory is usually considered to be a branch of mathematics, and its history is described in Amaral and Ottino (2004). Note that Von Bertalanffy (1972:416) includes both network and graph theory as part of GST. As these branches developed, they were merged and combined with concepts from other branches, resulting in an entangled family tree. Watts and Strogatz (1998) is a case in point: they combine the theory of random graphs (mathematical graph theory) with social networks, in particular Milgram (1967). The result is a science of systems and networks that is difficult to demarcate and whose roots are difficult to separate.
Von Bertalanffy is seldom cited as a source in publications that use network theory, but this does not mean that his insights had no bearing on the discipline. Harary and Batell (1981) for instance use Von Bertalanffy as a source in one of the most influential journals in network theory, Social Networks. Note also that Freeman (2004:129) identifies Harary as one of the most influential authors in the social branch of network theory.
Like Von Bertalanffy, Harary and Batell (1981:30) see graph theory as an approach to studying systems,
… all conceptions of ‘system’ involve a set of units and their interrelationships. Since any binary relation has a natural representation as a graph or digraph, the points being the units (people, groups, or larger aggregations) and the lines the relations between them, a graph-theoretic approach immediately suggests itself.
Harari and Batell’s view of graph theory as a way of studying systems is found in numerous other publications as well. Glattfelder (2010:2) writes that any complex system “finds its natural formal representation in a graph,” and Kuhnert (2011:9) argues, “Complex networks can be represented formally by graphs and graph theory offers a mathematical framework for an exact treatment of such systems”1 (see also Mobus and Kalton, 2015:23, and Kuchaiev, Stevanović, Hayes and Pržulj, 2011:1).
In other words, while Von Bertalanffy conceived of network and graph theory as some of the theories incorporated under GST, GST itself has morphed and combined with other theories into what can broadly be termed systems science, of which network and graph theory remain part, although these theories have also evolved into what Barabási (2016) terms network science. A full discussion of the complex history of these disciplines will not be attempted here, but it should be noted that network science and GST form part of the complexity paradigm.
3. Three aspects of Von Bertalanffy’s vision
3.1 Interdependence and the Connected Age
The modern world is more interdependent than it has ever been, mainly due to the rapid advances in technology over the past few decades. The telegraph, telephone and radio all played a major role in making the world more interdependent, but technological advances since World War II, such as the introduction of television and satellites, had an even greater impact (Papp, Alberts and Tuyahov, 1997). Already before the advent of the World Wide Web, Senekal (1987:169) argued with reference to Afrikaans literature,
Even Afrikaans literary acts do not exist in isolation, but are closely intertwined with the international world and its thinking – to which it is indeed even electronically connected. This is much clearer today than in previous decades and even then, from the beginning of Afrikaans literature, there was a very strong import of other literatures into Afrikaans, from both Western and African traditions.2
Since the 1990s, however, technology has advanced even faster. The World Wide Web was founded in 1989, blogs in 1997, Google in 1998, Wikipedia in 2001, Myspace in 2003, Facebook in 2004, YouTube in 2005, Twitter in 2006 and Instagram in 2010 (Senekal and Brokensha, 2014). Along with these platforms, cell phones came into general use around the turn of the millennium and the iPhone was launched in 2007. Today, there are few households in the West that do not have access to the World Wide Web, it is estimated that there are more than 4 billion mobile phones worldwide, and Facebook has more than 2 billion users.
Due to information technology, information now spreads worldwide within seconds, bringing people into contact who would otherwise have been unconnected. Urry (2004:22) writes, “New technologies produce ‘global time’ by shortening or even ‘dematerializing’ distances between places and people.”3 South Africans became aware of the September 11 2001 terrorist attacks at the same time as Americans, while such information would have taken weeks to reach the Southern Hemisphere a hundred years ago. Through email, Skype, Facebook, Twitter, Instagram, WhatsApp and other online platforms, it is now possible to share in other people’s lives, no matter where they are.
Technology not only connects the world in terms of information: transport networks have evolved through the twentieth century that make different continents much more connected than before. Jan van Riebeeck’s journey to the Cape in 1652 took just over four months, while Magellan’s journey around the world (1519-1522) took three years, but such a journey can now be completed within hours. Luo, Yin, Di, Hardisty, MacEachren and Alan (2014) write that the world has recently become more interconnected, additionally with connections between different types of networks. For example, the World Wide Web (an information network) connects to transportation networks (technological networks) when a book is purchased online but delivered locally, or information networks maintain and expand social networks, or information networks allow terrorist networks to operate – groups such as the Islamic State of Iraq and Syria (ISIS) regularly use social media such as Twitter (Helmus and Bodine-Baron, 2017, Klausen, 2015), while Al-Qaeda’s affiliate, Al-Shabaab, also used this platform (Omand, Bartlett, and Miller, 2012:803). Heidtmann (2013:440) states, “our society [is] interconnected in many ways.”4
These links between entities and between networks have had a significant impact on culture, politics and the economy, including the use of information networks to resist governments (as seen during the recent Arab uprisings and the rise of the Islamic State in Iraq and Syria or ISIS), the global spread of epidemics such Covid-19, the increasing interdependence of economies, and on culture itself. Kaluza, Kӧlzsch, Gastner and Blasius (2010:1093) argue, “The ability to travel, trade commodities and share information around the world with unprecedented efficiency is a defining feature of the modern globalized economy.” In Watt’s (2004) view, we now live in an age that can be described as the Connected Age.
It is not only with regard to the present that interconnectedness is important: South Africa, for example, was established to function as an important node in the dominant transport network of the 17th century, namely the shipping network. Some historical networks have already been studied, of which Padgett and Ansell’s (1993) study of the Medici family in the 16th century and Pitts’s (1965) study of water transport networks in Russia during the Middle Ages are the most well-known. Interconnectedness has always been an important facet of the human environment and an emphasis on current technologies should not be seen as a denial that humanity was also interdependent in the past. What has changed, however, is that the level of interconnectedness has placed connectedness at the forefront to a greater extent than ever before.
This increasingly connected environment has meant that the term network has become a common term in the contemporary world (Barabási, 2016:22). Most people belong to some or other social networking platform, such as Facebook, Instagram or Twitter, connect to computers that are connected to the company or institution’s intranet or the global Internet, make cell phone calls through cell phone networks and so on. Schnelle (2018:49) writes that some people consider social network analysis (SNA) to mean analysing social media – a misconception I have found also. Social networking platforms are part of the network phenomenon, and so is the World Wide Web, but these are only part of this connectedness. As Easley and Kleinberg (2010:1) write, one can observe an increasing popular interest in interconnectedness during the first decade of the 21st century, and at the heart of this interconnectedness lies the concept of networks. By the turn of the millennium, Esterhuise (1999:19) remarked,
The consequence of this [the information revolution] is that the world has lost its density and hierarchical order. It’s turning into a web – with interdependent networks that are not only complex, but also fluid and turbulent.5
A number of popular science books were published on networks in the last two decades, including those of Barabási (2003; 2011), Buchanan (2003), Christakis and Fowler (2010) and Watts (2004; 2011). The growing popularity of network theory for scientific research is closely intertwined with this popular interest in networks; as Strogatz (2004:230) observes, “science itself reflects the network zeitgeist.” One could also argue that the increasing popularity of complexity theory – which is moreover related to network science – is also related to this zeitgeist.
This increasing interest in connectedness demands a re-evaluation of Von Bertalanffy’s contribution to science, as for instance done in Hammond (2019). As discussed in Part 2 of this article series, Von Bertalanffy emphasised that it is insufficient to study phenomena in isolation: an element’s connections are key to coming to a better understanding of the world. This emphasis on studying the ties between elements rather than the attributes of elements themselves lies at the heart of network science, as it does with GST. Von Bertalanffy, like network science, foregrounded connectedness.
3.2 Interdisciplinary science
Systems that are commonly seen as complex include governments, families, cultures, politics, traffic, the human body (from a physiological perspective), a person (from a psychosocial perspective), the brain, the immune system, ecosystems, the weather, swarms (birds or insects), economies, trade, language, socio-cultural systems and armed conflicts (Brownlee, 2007:2, Bar-Yam, 1997:2-4, Steyn, 1984:9). Complexity theory seeks to arrive at a better understanding of the functioning of these systems, and is “the ultimate of interdisciplinary fields” (Bar-Yam, 1997:1) or an “umbrella science” (Johnson, 2009:18) that “bridges” (Mobus and Kalton, 2015:6-7) various disciplines. Von Bertalanffy (1972:416) also suggested that GST is “by nature” interdisciplinary, as Senghaas (1968:51) explains,
The father of General Systems Theory assumed that if different sciences deal with systems, i.e. with relatively stable patterns of variables, it should be possible to develop a whole series of basic, common analytical concepts that can then be exchanged between any discipline. So the thesis of isomorphism was born anew, which is based on the assumption that there are indeed a whole series of structures and processes that could be worked out in all disciplines and applied to systems of all kinds.6
The same applies to network science, which has been applied in almost every discipline of science – from microbiology to archaeology, from epidemiology to education, from neurology to sociology (Barabási, 2016). Both network science and complexity theory bridge the gaps between disciplines and also transfer discoveries made in one field to another. As such, these theoretical perspectives not only study interactions, but also provide interactions between various disciplines; Barabási (2016:10) refers to “a cross-disciplinary fertilization of tools and ideas.” Stegbauer (2017:21) also argues,
Network research offers the opportunity for such an exchange; in this way, different specialist areas can learn from each other if the right contact surfaces can be constructed. In this case, you can transfer theories and methods between subjects and thereby advance your own discipline.7
Similarly, Heidtmann (2013:440) writes about the importance of network science in the mediation of interdisciplinary research,
As a result, the interdisciplinary research area of network science emerged with the aim of developing theoretical and practical ideas and methods to improve our understanding of networks of natural and human origin, amongst others through the use of ideas and results from mathematics, physics, computer science, operations research and from many other areas of natural, social and engineering sciences.8
This exchange of insights linked to different disciplines was Von Bertalanffy’s ideal for GST, and as such network science continues his vision in this regard. Von Bertalanffy (1950:142, 1968:80-81) writes,
… general system theory should be, methodologically, an important means of controlling and instigating the transfer of principles from one field to another, and it will no longer be necessary to duplicate or triplicate the discovery of the same principles in different fields isolated from each other. At the same time, by formulating exact criteria, general system theory will guard against superficial analogies which are useless in science and harmful in their practical consequences.
For this transfer of principles to occur between disciplines, GST had to identify and describe, “general system laws which apply to any system of a certain type, irrespective of the particular properties of the system or the elements involved” (Von Bertalanffy, 1950:138). This is precisely what authors such as Barabási (2011:15) found when applying network science,
By simultaneously looking at the World Wide Web and genetic networks, Internet and social systems, [network science] led to the discovery that despite the many differences in the nature of the nodes and the interactions between them, the networks behind most complex systems are governed by a series of fundamental laws that determine and limit their behaviour.
3.3 Network science and data science
Von Bertalanffy (1968:vii) suggests that the development of GST is closely linked to the development of digital computers by noting that it is “centred in computer technology, cybernetics, automation and systems engineering.” Elsewhere (1968:20) he argues that,
… computers have opened a new approach in systems research; not only by way of facilitation of calculations which otherwise would exceed available time and energy and by replacement of mathematical ingenuity by routine procedures, but also by opening up fields where no mathematical theory or ways of solution exist.
Barabási (2016:8) offers a similar perspective by arguing that the development of network science in the 21st century is due to two factors in particular: the development of large datasets as part of the information revolution, and the identification of universal characteristics shared by various networks. Improvements in information technology, in terms of software, hardware and data sets, mediated scientific investigations by the early 21st century that were not previously possible (Nistor, Pickl, and Zsifkovits, 2015:11, Heidtmann, 2013:441, Cohen and Havlin, 2010:16, Barabási, 2009:413, Kumpula, 2008:4).
Firstly, network science relies heavily on computer software, as for instance noted by Barabási (2016:11), Scott (2012:6), Freeman (2004:139), and Boissevain (1979:392). Although software played a role in network theory from at least as far back as the 1970s, software developments since the 1990s have led to significantly larger datasets being studied as a whole. Since the whole is always more than the sum of the parts – as discussed in the next article – the analysis of larger data sets as a whole could lead to new insights within network science. Software has also become more user-friendly and cheaper, which means more researchers have access to these technologies than was the case decades ago (Barabási, 2016:11).
Secondly, hardware has become exponentially faster over the past few decades. For example, the processing power of an Apple iPhone 6 surpasses the processing power of Cray-1, the world’s first supercomputer (Reed and Dongarra, 2015:59). Improving processor speed has played a crucial role in the development of network science (Van der Hofstad, 2014:1, Glattfelder, 2013:3), since astronomical data sets could now be studied with millions and even billions of data points. Together with the software that relies on this hardware and network science, researchers were able to observe similarities between different systems that were not previously possible.
Thirdly, the availability of large digital data sets has had a significant impact on the development of network science. The widespread use of computers since the 1990s has led to a data explosion, with data sets consisting of billions of data points but which can also be analysed in the finest detail. Authors such as Park and Leydesdorff (2013:757), Abreu and Acker (2013:549), Hitzler and Janowicz (2013:233) and Kitchin (2014:3) argue that we are currently on the brink of the fourth paradigm of science: the first was empirical science, the second the theoretical, the third – as Von Bertalanffy’s (1968:20) earlier quote indicates – computer-driven, and the fourth data science (Chen and Zhang, 2014:315). Data science enables us not only to study large, comprehensive datasets, but also to study those datasets as a whole. Barabási (2011:14-15) writes that the data explosion has created several opportunities for scientific investigations:
… something has changed in the past few years. The driving force behind this change can be condensed into a single word: data. Fuelled by cheap sensors and high-throughput technologies, the data explosion that we witness today, from social media to cell biology, is offering unparalleled opportunities to document the inner workings of many complex systems.
Similarly, Watts (2011:266) claims,
…just as the invention of the telescope revolutionized the study of the heavens, so too by rendering the unmeasurable measurable, the technological revolution in mobile, Web, and Internet communications has the potential to revolutionize our understanding of ourselves and how we interact. Merton was right: Social science has still not found its Kepler. But three hundred years after Alexander Pope argued that the proper study of mankind should lie not in the heavens but in ourselves, we have finally found our telescope. Let the revolution begin ….
Information technology is therefore linked to a general realization that the world has become more interdependent, but has also provided the data and tools (both hardware and software) to undertake large-scale investigations. Data is important for the development of a theory that seeks to gain a better understanding of complex systems, as Byrne and Callaghan (2014:40) for example criticize models of complexity that are not based on empirical research.
The importance of grounding theories and models in data cannot be overstated. As Von Bertalanffy (1968:23) already noted, there is often a gap between a scientific model and reality. In order to gain a better understanding of reality, models and theories must be calibrated with reality, as Watts and Strogatz (1998) and Barabási and Albert (1999) did with their small-world- and scale-free network models respectively.9 Freeman (2004:3) argues that social network analysis (SNA) is characterized by being based on “systematic, empirical data,” while Newman (2010:17) emphasizes that data is the starting point of almost any development within network science. Barabási (2011:15) argues,
These ideas have not been gleaned from toy models or mathematical anomalies. They are based on data and meticulous observations. The theory of evolving networks was motivated by extensive empirical evidence documenting the scale-free nature of the degree distribution, from the cell to the World Wide Web; the formalism behind degree correlations was preceded by data documenting correlations on the Internet and on cellular maps; the extensive theoretical work on spreading processes was preceded by decades of meticulous data collection on the spread of viruses and fads, gaining a proper theoretical footing in the network context. This data- inspired methodology is an important shift compared with earlier takes on complex systems. Indeed, in a survey of the ten most influential papers in complexity, it will be difficult to find one that builds directly on experimental data. In contrast, among the ten most cited papers in network theory, you will be hard pressed to find one that does not directly rely on empirical evidence.
In this respect, network science is also in line with data science and the shift in emphasis in the fourth paradigm from the deductive to the inductive method, as Csermely (2006:97) argues.
There is a lot of excitement in the scientific community about the promise of network science. Together with Amaral and Ottino (2004:147) and Maslov, Sneppen and Zaliznyak (2004:529), Barabási (2011:15) argues that network science has become an indispensable approach to the study of complex systems. This optimism often comes from physics, as evidenced by some statements made by some of the most influential network scientists:
- “if we are ever to have a theory of complexity, it will sit on the shoulders of network theory” (Barabási, 2011:15).
- “The network approach to the phenomenon of complexity has turned so beneficial that some researchers think of it to be the key to understand the principles of the complex systems structure and behaviour” (Kwapień and Drożdż, 2012:206).
- “If the day should ever come that we understand how life emerges from a dance of lifeless chemicals, or how consciousness arises from billions of unconscious neurons, that understanding will surely rest on a deep theory of complex networks” (Strogatz, 2004:232).
While network science is still in its infancy, this article has shown that network science continues Von Bertalanffy’s vision for GST in three important ways:
- By building bridges between disparate fields,
- By foregrounding the connections between entities, and
- By using computers to study phenomena in new ways.
These basic tenets that network science shares with GST will be elaborated on in the second and third articles in this article series.
- Own translation from the original German, “Komplexe Netzwerke können formal durch Graphen dargestellt werden und die Graphentheorie bietet einen mathematischen Rahmen für eine exakte Behandlung solcher Systeme.”
- Own translation from the original Afrikaans, “Selfs Afrikaanse literêre handelinge bestaan nie in isolasie nie, maar is ten nouste verweef met die internasionale wêreld en sy denke – waarmee dit inderdaad selfs elektronies verbind is. Dit is vandag baie duideliker só as in vorige dekades en toe reeds, van die begin van die Afrikaanse literatuur af, was daar baie sterk import van ander literature na Afrikaans, uit sowel Westerse as uit Afrikatradisies.” It is also noteworthy that this statement was made at a time when South Africa was at its most isolated by sanctions, boycotts and the arms embargo. The opening of South Africa to international influences since De Klerk announced in 1990 that South Africa’s path to a majority government had begun is not the focus here, but the reader must keep in mind that international efforts to isolate South Africa were terminated at the same time that the Internet became widely used.
- Own translation from the original Dutch, “Nieuwe technologieën produceren ‘globale tijd’ doordat afstanden tussen plaatsen en mensen verkorten of zelfs ‘dematerialiseren’.”
- Own translation from the original German, “unsere Gesellschaft [is] in vieler Hinsicht vernetzt.”
- Own translation from the original Afrikaans, “Die gevolg hiervan [die inligtingrevolusie] is dat die wêreld sy digtheid en hiërargiese ordening verloor het. Dis in ŉ web verander – met interafhanklike netwerke wat nie alleen kompleks is nie, maar ook vloeibaar en onstuimig.”
- Own translation from the original German, “Die Väter der allgemeinen Systemtheorie gingen davon aus, daß, wenn verschiedene Wissenschaften sich mit Systemen, also mit relativ stabilen Mustern von Variablen, beschäftigen, es möglich sein müsse, eine ganze Reihe von grundlegenden gemeinsamen analytischen Konzeptionen zu erarbeiten, die dann zwischen beliebigen Disziplinen austauschbar wären. So wurde die These des Isomorphismus neu geboren, welcher eben die Annahme zugrunde liegt, daß es in der Tat eine ganze Reihe von Strukturen und Prozessen gibt, die in allen Disziplinen erarbeitet und auf Systeme aller Art angewandt werden könnten.”
- Own translation from the original German, “Die Netzwerkforschung bietet die Möglichkeit für einen solchen Austausch; so können unterschiedliche Fachgebiete voneinander lernen, wenn es gelingt, die richtigen Kontaktflächen zu konstruieren. In diesem Fall kann man Theorien und Methoden zwischen den Fächern übertragen und dadurch die jeweils eigene Disziplin voranbringen.” See also Heidtmann (2013:440), Kwapień and Drożdż (2012:205) for similar perspectives.
- Own translation from the original German, “Folglich entstand das interdisziplinäre Forschungsgebiet der Netzwissenschaft (Network Science) mit dem Ziel, theoretische und praktische Vorstellungen und Methoden zur Verbesserung unseres Verständnisses von Netzen natürlichen und menschlichen Ursprungs zu entwickeln, u. a. durch die Nutzung von Ideen und Ergebnissen aus der Mathematik, der Physik, der Informatik, dem Operations Research und aus vielen anderen Bereichen der Natur-, Sozial und Ingenieurwissenschaften.”
- For a discussion of these models, see Newman (2010:552-564, 500-502) and Cohen and Havlin (2010:31-49, 51-62).
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