Information—Consciousness—Reality pp 181214  Cite as
Volume II: The Simplicity of Complexity
Abstract
Whereas most of the cosmos is comprised of rather simple largescale structures, on Earth, we find breathtaking complexity, down to microscopic scales. Indeed, it appears as though the universe is driven by a propensity to assemble ever more complex structures around us, guided by selforganized and emergent behavior. Naively one would expect complexity to be complicated to comprehend. Luckily, in the universe we inhabit, complex systems are encoded by simple rules of interaction. Like Volume I of the Book of Nature being written in the language of mathematics, Volume II, addressing complexity, is composed of simple algorithms decoding reality. Complex systems theory has a long history and raises philosophical questions. One of its most successful formal tools are networks. In fact, complex networks are ubiquitous in the domains of living and nonliving complexity. One particular organizational property in complex systems is akin to a “law of nature,” giving rise to universal behavior. These patterns, known as scaling laws, are to be found everywhere.
Level of mathematical formality: medium to low.
We inhabit a very particular place in the universe. The planet we find ourselves residing on is unlike any other patch of cosmic space containing matter. Every day we witness the interaction of a myriad of structures creating a vast richness of intricate behavior. We are surrounded by, and embedded in, a microcosm seething with complexity. Specifically, we are exposed to chemical, biological, and, foremost, technological and socioeconomical complexity.
Until very recently in the history of human thought, the adjective “complex” was thought to be synonymous with “complicated”—in other words, intractable. While the universe unveiled its fundamental mysteries through the Book of Nature—the ageold metaphor for the circumstance that the regularities in the physical world are explained mathematically by the human mind—the complexity surrounding us seemed incomprehensible. However, one specific cosmic coincidence allowed the human mind to also tackle and decode the behavior of complex systems. Before disentangling complexity itself, the next section will briefly review the notions introduced throughout the narrative of Part I: the two volumes of the Book of Nature.
Some general references on complexity are Holland (1995), Gladwell (2000), Johnson (2001, 2009), Strogatz (2004), Fisher (2009), Green (2014), Hidalgo (2015).
6.1 Reviewing the Book of Nature
Chapter 2 opened with the search for the Book of Nature. The belief that the human mind can read the universe like a book and extract knowledge has echoed throughout the ages. Over 300 years ago this belief materialized by the development of Newtonian mechanics. After this initial spark, mathematics reigned supreme as the most resourceful and efficient human knowledge generation system. In Chap. 3 a stunning tale of this success is told. Namely, how the notion of symmetry underlies most of theoretical physics. This then allows for very separate phenomena to be described by overarching and unified theories, as discussed in Chap. 4.
Analyzing this “unreasonable effectiveness of mathematics in the natural sciences” (Wigner 1960) leads to the following observation. The reality domain that is decoded by mathematics (or more generally speaking, formal thought systems) excludes the complexity surrounding us and contained within us. Consequentially, exclusively fundamental aspects of nature—ranging from the quantum foam comprising reality to the incomprehensible vastness of the cosmic fabric—are understood by analytical mathematical representations. This defines a paradigm of knowledge generation, called the fundamentalanalytical classification here (Sect. 5.1).
By the turn of the millennium, a new paradigm was born: the complexalgorithmic classification of knowledge generation (Sect. 5.2). The simple rules of interaction driving complex systems allow for a computational approach to understanding them. In other words, the mathematical tools are exchanged for algorithms and simulations running on computers.And I realized, that I had seen a sign of a quite remarkable and unexpected phenomenon: that even from very simple programs behavior of great complexity could emerge.
\([\dots ]\)
It took me more than a decade to come to terms with this result, and to realize just how fundamental and farreaching its consequences are.
An assertion that is remarkable in the face of Hawking’s previous stance, where he predicted the end of theoretical physics in the 1980s and 1990s (see Sects. 4.3.2 and 9.2.2). He then believed that a unified theory of quantum gravityc would soon be found, explaining everything. Even after all the excitement of string/Mtheory, we today appear no closer to this goal (see Sect. 10.2.2).I think the next century [the 21st Century] will be the century of complexity.
6.2 A Brief History of Complexity Thinking
For an illustration visualizing the rich and intertwined history of complexity thinking, see The Map of Complexity Sciences and the links within, first published in Castellani and Hafferty (2009) and updated since.^{2}
6.2.1 Complex Systems Theory
In the remainder of this chapter, the focus lies on complex systems theory (Haken 1977, 1983; Simon 1977; Prigogine 1980; BarYam 1997; Eigen 2013; Ladyman et al. 2013), a field emerging from cybernetics and systems theory at the beginning of the 1970s. The theory of complex systems can be understood as an interdisciplinary field of research utilizing a formal framework for studying interconnected dynamical systems (BarYam 1997). Two central themes are selforganization (Prigogine and Nicolis 1977; Prigogine et al. 1984; Kauffman 1993) and emergence (Darley 1994; Holland 1998). The former notion is related to the question of how order emerges spontaneously from chaos in systems which are not in a thermodynamic equilibrium. The latter concept is concerned with the question of how the macro behavior of a system emerges from the interactions of the elements at a micro level. The notion of emergence has a long and muddied history in the philosophy of science (Goldstein 1999). Other themes relating to complex systems theory include the study of complex adaptive systems (Holland 2006) and swarming behavior, i.e., swarm intelligence (Bonabeau et al. 1999). The domains complex systems originate from are mostly socioeconomical, biological, or physiochemical. Some examples of successfully decoding complex systems include earthquake correlations (Sornette and Sornette 1989), crowd dynamics (Helbing et al. 2000), traffic dynamics (Treiber et al. 2000), pedestrian dynamics (Moussaïd et al. 2010), population dynamics (Turchin 2003), urban dynamics (Bettencourt et al. 2008), social cooperation (Helbing and Yu 2009), molecule formation (Simon 1977), and weather formation (Cilliers and Spurrett 1999).
Complex systems are characterized by feedback loops (BarYam 1997; Cilliers and Spurrett 1999; Ladyman et al. 2013), where both damping and amplifying feedback is found. Moreover, linear and nonlinear behavior can be observed in complex systems. The term “at the edge of chaos” denotes the transition zone between the regimes of order and disorder (Langton 1990). This is a region of bounded instability that enables a constant dynamic interplay between order and disorder. The edge of chaos is where complexity resides. Furthermore, complex systems can also be characterized by the way they process or exchange information (Haken 2006; Quax et al. 2013; Ladyman et al. 2013). Information is the core theme of Chap. 13.
The study of complex systems represents a new way of approaching nature. Put in the simplest terms, a major focus of science lay on things in isolation—on the tangible, the tractable, the malleable. Through the lens of complexity this focus has shifted to a subtler dimension of reality, where the isolation is overcome. Seemingly single and independent entities are always components of larger units of organization and hence influence each other. Indeed, our modern world, while still being comprised of many of the same “things” as in the past, has become highly networked and interdependent—and, therefore, much more complex. From the interaction of independent entities, the notion of a system emerges. The choice of which components are seen as fundamental in a system is arbitrary and depends on the chosen level of abstraction.
A tentative definition of a complex system is the following:
A complex system is composed of an ensemble of many interacting (or interconnected) elements.

a set of objects (representing the agents);

a set of functions between the objects (representing the interactions among agents).
A natural formal representation of this abstraction is a network (Sect. 5.2.1). Now, the agents are characterized by featureless nodes and the interactions are given by the links connecting the nodes. The mathematical structure describing networks is a graph (Sect. 5.3.2). In essence, complex networks (being the main theme of Sect. 6.3) mirror the organizational properties of realworld complex systems.
In the same vein, a quote taken from an early and muchnoticed publication by the physics Nobel laureate Philip Warren Anderson (Anderson 1972, see also Sect. 5.2.1):But the more we are dealing with complex systems, the more we realize that reductionism has its own limitations. For example, knowing chemistry does not mean that we understand life.
Driven by the desire to comprehend complexity, reductionist methods are replaced or augmented by an embracing of a systemsbased and holistic outlook (Kauffman 2008). A revolution in understanding is ignited and a “new science of networks” born (Sect. 5.2.3). In other words, Volume II of the Book of Nature is unearthed.At each stage [of complexity] entirely new laws, concepts, and generalizations are necessary [. . . ]. Psychology is not applied biology, nor is biology applied chemistry.
6.2.2 The Philosophy of Complexity: From Structural Realism to Poststructuralism
One specific form of scientific realism is structural realism, a commitment to the mathematical or structural content of scientific theories. It is the “belief in the existence of structures in the world to which the laws of mathematical physics may approximately correspond” (Falkenburg 2007, p. 2). In a general sense, structural realism only admits a reality to the way things are related to one another, invoking the metaphor of a network (Wittgenstein 1922, 6.35):Scientific realism is the view that we ought to believe in the unobservable entities posited by our most successful scientific theories. It is widely held that the most powerful argument in favor of scientific realism is the nomiracles argument, according to which the success of science would be miraculous if scientific theories were not at least approximately true descriptions of the world.
In a similar vein, “the universe is made of processes, not things” (Smolin 2001, Chap. 4). See also Sect. 2.2 for more details.Laws [...] are about the net and not about what the net describes.
Alternatively, “ontic structural realism has become the most fashionable ontological framework for modern physics” (Kuhlmann 2015). See also Kuhlmann (2010) and Sects. 2.2.1 and 10.4.1.Clearly, then, the standard picture of elementary particles and mediating force fields is not a satisfactory ontology of the physical world. It is not at all clear what a particle or a field even is.
This outlook implies the following (Woermann 2016, p. 3):The most obvious conclusion drawn from this [poststructural/postmodern] perspective is that there is no overarching theory of complexity that allows us to ignore the contingent aspects of complex systems. If something is really complex, it cannot be adequately described by means of a simple theory.
While Volume I of the Book of Nature is rooted in structural realism, Volume II invites a philosophy that transcends the borders of clearcut and orderly interpretations and opens up to inquisitive exploration (Woermann 2016, p. 1):Along with Edgar Morin, Cilliers argues that complexity cannot be resolved through means of a reductive strategy, which is the preferred methodology of those who understand complexity merely as a theory of causation.
A philosophy grappling with complex systems needs to address the following (Cilliers 1998):To my mind, the hallmark of a successful philosophy is thus related to the degree to which it resonates with our views on, and experiences in, the world.

complex systems consist of a large number of elements;

a large number of elements is necessary, but not sufficient;

interactions are rich, nonlinear, and shortranged;

there exist loops in the interactions;

complex systems tend to be open systems and operate under conditions far from equilibrium;

complex systems have a rich history in that the past is coresponsible for the present behavior;

each element in the system is ignorant of the behavior of the system as a whole.
Finally, in Chap. 2, the notion of Platonism^{3} was introduced. Platonic realism posits the existence of mathematical objects that are independent of the mind and language and it is a philosophical stance adopted by many notable mathematicians. Although there also exists a structuralist interpretation of mathematics (Colyvan 2012), other scholars have argued that postmodern thought should be seen as the continuation of debates on the foundations of mathematics (Tasić 2001).Complexity is the result of a rich interaction of simple elements that only respond to the limited information each of the elements are presented with. When we look at the behavior of a complex system as a whole, our focus shifts from the individual element in the system to the complex structure of the system. The complexity emerges as a result of the patterns of interaction between the elements.
6.3 Complex Network Theory
The key to the success of complex network theory lies in the courage to ignore the complexity of the components of a system while only quantifying their structure of interactions. In other words, the individual components fade out of focus while their network of interdependence comes into the spotlight. Technically speaking, the analysis focuses on the structure, function, dynamics, and topology of the network. Hence the neurons in a brain, the chemicals interacting in metabolic systems, the ants foraging, the animals in swarms, the humans in a market, etc., can all be understood as being represented by featureless nodes in a network of interactions. Only their relational aspects are decoded for information content.
6.3.1 The Ubiquity of Complex Networks
 the physical world, e.g.,

computerrelated systems (Albert et al. 1999; Barabási et al. 2000; Tadić 2001; PastorSatorras et al. 2001; Capocci et al. 2006),

various transportation structures (Banavar et al. 1999; Guimera et al. 2005; Kühnert et al. 2006),

power grids (Albert et al. 2004),

spontaneous synchronization of systems (GómezGardenes et al. 2007),

 biological systems, e.g.,
 social^{4} and economic realms, e.g.,

diffusion of innovation (Schilling and Phelps 2007; König et al. 2009),

trustbased interactions (Walter et al. 2008),

social affiliation (Brown et al. 2007),

trade relations (Serrano and Boguñá 2003; Garlaschelli and Loffredo 2004a, c; Reichardt and White 2007; Fagiolo et al. 2008, 2009),

shared board directors (Strogatz 2001; Battiston and Catanzaro 2004),

similarity of products (Hidalgo et al. 2007),

price correlation (Bonanno et al. 2003; Onnela et al. 2003),

corporate ownership structures (Glattfelder and Battiston 2009; Vitali et al. 2011; Glattfelder 2013, 2016; GarciaBernardo et al. 2017; Fichtner et al. 2017; Glattfelder and Battiston 2019).

6.3.2 Three Levels of Network Analysis
6.4 Laws of Nature in Complex Systems
Laws of nature can be understood as regularities and structures in a highly complex universe. They critically depend on only a small set of conditions and are independent of many other conditions which could also possibly have an effect (Wigner 1960). Science is the quest to capture fundamental regularities of nature within formal analytical representations (Volume I of the Book of Nature). So then, are there laws of nature to be found for complex systems (Volume II)?
The quest to discover universal laws in complex systems has taken many turns. For instance, the macroscopic theory of thermodynamics allows arbitrary complex systems to be described from a universal point of view. Its foundations lie in statistical physics, explaining the phenomena of irreversible thermodynamics. A different approach, striving for universality, is synergetics (Haken 1977, 1983). In contrast to thermodynamics, this field deals with systems far away from thermal equilibrium. See Haken (2006) for a brief overview of the aforementioned approaches.
In the following, the focus of universality will lie on a purely empirical and descriptive phenomenological investigation. In this context the question “What are the laws of nature for complex systems?” has a clear answer.
6.4.1 Universal Scaling Laws
The empirical analysis of realworld complex systems has revealed an unsuspected regularity which is robust across a great variety of domains. This regularity is captured by what is known as scaling laws, also called power laws (Müller et al. 1990; Mantegna and Stanley 1995; Ghashghaie et al. 1996; West et al. 1997; Gabaix et al. 2003; Guillaume et al. 1997; Galluccio et al. 1997; Amaral et al. 1998; Barabási and Albert 1999; Ballocchi et al. 1999; Albert et al. 1999; Sornette 2000b; PastorSatorras et al. 2001; Dacorogna et al. 2001; Corsi et al. 2001; Newman et al. 2002; Garlaschelli et al. 2003; Newman 2005; Di Matteo et al. 2005; Lux 2006; Kühnert et al. 2006; Di Matteo 2007; Bettencourt et al. 2008; Bettencourt and West 2010; Glattfelder et al. 2011; West 2017). This distinct pattern of organization suggests that universal mechanisms are at work in the structure formation and evolution of many complex systems. Varying origins for these scaling laws have been proposed and insights have been gained from the study of critical phenomena and phase transitions, stochastic processes, richgetricher mechanisms and socalled selforganized criticality (Bouchaud 2001; BarndorffNielsen and Prause 2001; Farmer and Lillo 2004; Newman 2005; Joulin et al. 2008; Lux and Alfarano 2016). Tools and concepts from statistical physics have played a crucial role in discovering and describing these laws (Dorogovtsev and Mendes 2003b; Caldarelli 2007). In essence:
Scaling laws can be understood as laws of nature describing complex systems.
 1.
allometric scaling laws;
 2.
scalinglaw distributions;
 3.
scalefree networks;
 4.
cumulative relations of stochastic processes.
Before presenting these four types of universal scaling, some historical context is given in the following section.
6.4.2 Historical Background: Pareto, Zipf, and Benford
The first study of scaling laws and scaling effects can be traced back to Galileo Galilei. He investigated how ships and animals cannot be naively scaled up, as different physical attributes obey different scaling properties, such as the weight, area, and perimeter (Ghosh 2011). Over 250 years later, the economist and sociologist Vilfredo Pareto brought the concept of scaling laws to prominence (Pareto 1964, originally published in 1896). While investigating the probability distribution of the allocation of wealth among individuals, he discovered the first signs of universal scaling. Put simply, a large portion of the wealth of any society is owned only by a small percentage of the people in that society. Specifically, the Pareto principle says that 20% of the population controls 80% of the wealth. Hence this observation has also been called the 8020 rule. To this day, the Pareto distribution is detected in the distribution of income or wealth. A more detailed treatment of Pareto’s observed inequality was given by the Lorenz curve (Lorenz 1905). This is a graph representing the ranked cumulative income distribution. At any point on the xaxis, corresponding to the bottom \(x\% \) of households, it shows what percentage (\(y\%\)) of the total income they have. A further refinement was the introduction of the Gini coefficient G (Gini 1921). In effect, G is a statistical measure of inequality, capturing how much an observed Lorenz curve deviates from perfect equality \(G=0.0\). Perfect inequality, or \(G=1.0\), corresponds to a stepfunction representing a single household earning all the available income. For the United States, in 1979 \(G=0.346\) and in 2013 \(G=0.41\). The interplay between this rise of the Gini coefficient and the rise of the share of total income going to the top earners, seen beginning at the end of the 1970s, is discussed in Atkinson et al. (2011). In 2011, South Africa saw a maximal \(G=0.634\) and in 2014, Ukraine a minimal \(G=0.241\). The data is available from the World Bank.^{5}
Another popularizer of the universal scaling patterns found in many types of data, analyzed in the physical and social sciences, was the linguist and philologist George Kingsley Zipf. He studied rankfrequency distributions (Zipf 1949), which order distributions of size by rank. In other words, the xaxis shows the ordered ranks, while the yaxis shows the frequency of observations. For instance, the frequency of the use of words in any human language follows a Zipf distribution. For English, unsurprisingly, the most common words are “the”, “of”, and “and”, while all remaining other ones follow Zipf’s law of diminishing frequency. This law, characterized by a scalinglaw probability distribution, is the discrete counterpart of the continuous Pareto probability distribution. See also Newman (2005).
6.4.3 The Types of Universal Scaling
Notwithstanding the spectacular number of occurrences of scalinglaw relations in a vast diversity of complex systems, there are four basic types of scaling laws to be distinguished.
6.4.3.1 Allometric Scaling Laws
Allometric scaling also has medical implications, namely related to drug administration and weight. An example taken from a website^{6} offering a calculator which estimates interspecies dosage scaling between animals of different weights: “If the dosage for a 0.25 kg rat is 0.1 mg, then using an exponent of 0.75, the estimated dosage for a 70 kg human would be 6.8 mg. While the dose to weight ratio for the rat is 0.4 mg/kg, the value for the human is only about 0.1 mg/kg.” In 1962, two psychiatrists decided to test the effects of the psychedelic substance lysergic acid diethylamide (LSD) on an elephant. The animal weighed about 3,000 kg and the researchers estimated that a dose of about 300 mg would be appropriate. Not taking the nonlinear scaling behavior into account, this turned out to be a fatal dose. The elephant died and the ordeal was reported in the prestigious journal Science (West et al. 1962). Knowledge of allometric scaling would have revealed the following. For humans, a standard amount of LSD is 100 micrograms.^{7} Assuming a bodyweight of 70 kg, this dose translates into roughly 1.6 milligrams for an elephant. The administered 300 mg correspond to about 17 mg of LSD for a human. However, there are no verified cases of death by means of an LSD overdose in humans (Passie et al. 2008). See also West (2017).
Allometric scaling laws are also found in the plant kingdom (Niklas 1994). Vascular plants vary in size by about twelve orders of magnitude and scaling laws explain many features. For instance, the selfsimilar and fractal branching architecture follows a scaling relation. There also exist parallels in the characteristics of plants and animals which are described by allometric scaling with respect to mass: the metabolic rate (\(M^{\frac{3}{4}}\)) and the radius of trunk and aorta (\(M^{\frac{3}{8}}\)). See West et al. (1999).
A recent biological scaling law was discovered, describing a universal mathematical relation for folding mammalian brains (Mota and HerculanoHouzel 2015).
6.4.3.2 ScalingLaw Distributions

the size of cities, earthquakes, moon craters, solar flares, computer files, sand particle, wars and price moves in financial markets;

the number of scientific papers written, citations received by publications, hits on webpages and species in biological taxa;

the sales of music, books and other commodities;

the population of cities;

the income of people;

the frequency of words used in human languages and of occurrences of personal names;

the areas burnt in forest fires;
As mentioned, processes following normal distributions have a characteristic scale given by the mean (\(\mu \)) of the distribution. In contrast, scalinglaw distributions lack such a preferred scale, as measurements of scalinglaw processes can yield values distributed across a vast dynamic range, spanning many orders of magnitude. Indeed, for \(\alpha \le 2\) the mean of the scalinglaw distribution can be shown to diverge (Newman 2005). Moreover, analyzing any section of a scalinglaw distribution yields similar proportions of small to large events. In other words, scalinglaw distributions are characterized by scalefree and selfsimilar behavior. Historically, Benoît Mandelbrot observed these properties in the changes of cotton prices, which represented the starting point for his research leading to the discovery of fractal geometry (Mandelbrot 1963, see also Sects. 5.2.2, and 5.1.3). Finally, for normal distributions, events that deviate from the mean by, e.g., 10 standard deviations (10sigma events) are practically impossible to observe. Scaling laws, in contrast, imply that small occurrences are extremely common, whereas large instances become rarer. However, these large events occur nevertheless much more frequently compared to a normal distribution: for scalinglaw distributions, extreme events have a small but very real probability of occurring. This fact is summed up by saying that the distribution has a “fat tail” (Anderson 2004). In the terminology of probability theory and statistics, distributions with fat tails are said to be leptokurtic or to display positive kurtosis. The presence of fat tails greatly impacts risk assessments: although most earthquakes, price moves in financial markets, intensities of solar flares , etc., will be very small most of the time, the possibility that a catastrophic event will happen cannot be neglected.
6.4.3.3 ScaleFree Networks
Scalefree networks are characterized by high robustness against the random failure of nodes, but susceptible to coordinated attacks on the hubs. Theoretically, they are thought to arise from a dynamical growth process, called preferential attachment, in which new nodes favor linking to existing nodes with high degree (Barabási and Albert 1999). AlbertLászló Barabási was highly influential in popularizing the study of complex networks by explaining the ubiquity of scalefree networks with preferential attachment models of network growth. However, the statistician Udny Yule already introduced the notion of preferential attachment in 1925, when he analyzed the powerlaw distribution of the number of species per genus of flowering plants (Udny Yule 1925) . Alternative formation mechanisms for scalefree networks have been proposed, such as fitnessbased models (Caldarelli et al. 2002).
6.4.3.4 Cumulative ScalingLaw Relations
These laws represent the foundation of a new generation of tools for studying volatility, measuring risk, and creating better forecasting (Golub et al. 2016). They also substantially extend the catalog of stylized facts found in financial time series (Guillaume et al. 1997; Dacorogna et al. 2001) and sharply constrain the space of possible theoretical explanations of the market mechanisms. The laws can be used to define an eventbased framework, substituting the passage of physical time with market activity (Guillaume et al. 1997; Glattfelder et al. 2011; Aloud et al. 2011). Consolidating all these building blocks cumulates in a new generation of automated trading algorithms^{11} which not only generate profits, but also provide liquidity and stability to financial markets (Golub et al. 2018). See also Müller et al. (1990), Mantegna and Stanley (1995), Galluccio et al. (1997) for early accounts of the scaling properties in foreign exchange markets.
6.4.3.5 A Word of Caution
Finding laws of nature for complex systems is a challenging task. By design, there exist many levels of organization which interact with each other in theses systems. Moreover, the laws represent idealizations lurking in the murky depths hidden beneath layers of messy data. While the laws of nature relating to Volume I of the Book of Nature are clearcut and orderly, Volume II struggles with this clarity. The importance of the four types of universal scaling laws previously discussed has been challenged by some.
The debate boils down to the following question: How far can one deviate from statistical rigor to detect an approximation of an organizational principle in nature? In the early days of scaling laws, some physicists have been accused of simply plotting their data in a loglog plot and squinting at the screen to declare a scaling law. However, the statistical criteria for a true scaling law to be found in empirical data are quite involved (Clauset et al. 2009). Recently, the ubiquity of scalefree networks has been questioned (Broido and Clauset 2018).
Nonetheless, perhaps the real impediment that network researchers face is far deeper, echoing the poststructural and postmodern sentiment from Sect. 6.2.2. Again Vespignani (Klarreich 2018):In the real world, there is dirt and dust, and this dirt and dust will be on your data. You will never see the perfect power law.
Barabási replied to the accusations in a blog post.^{12} In essence, (Broido and Clauset 2018) utilize a “fictional criterion of scalefree networks,” which “fails the most elementary tests.”There is no general theory of networks.
Footnotes
 1.
However, see Sect. 5.4.1 discussing Langevin and FokkerPlanck equations.
 2.
Accessible online at http://www.artsciencefactory.com/complexitymap_feb09.html.
 3.
The terms mathematical realism and Platonism have been used interchangeably.
 4.
A general reference is VegaRedondo (2007).
 5.
 6.
 7.
See https://erowid.org/chemicals/lsd/lsd_dose.shtml, retrieved February 1, 2018.
 8.
As ranked by www.alexa.com/topsites/, accessed February 2, 2018.
 9.
See http://www.internetlivestats.com/googlesearchstatistics/, accessed February 13, 2018.
 10.
See also Sect. 7.3.2.2.
 11.
The code can be found here: https://github.com/AntonVonGolub/Code.
 12.
Called Love is All You Need—Clauset’s Fruitless Search for ScaleFree Networks , see https://www.barabasilab.com/post/loveisallyouneed/, posted on March 16, 2018.
References
 Ahnert, S., Garlaschelli, D., Fink, T., Caldarelli, G.: Ensemble approach to the analysis of weighted networks. Phys. Rev. E 76(1), 16101 (2007)Google Scholar
 Albert, R., Barabási, A.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47–97 (2002)Google Scholar
 Albert, R., Jeong, H., Barabási, A.: Internet: diameter of the worldwide web. Nature 401(6749), 130–131 (1999)Google Scholar
 Albert, R., Albert, I., Nakarado, G.: Structural vulnerability of the north american power grid. Phys. Rev. E 69(2), 25103 (2004)Google Scholar
 Aloud, M., Tsang, E., Olsen, R.B., Dupuis, A.: A directionalchange events approach for studying financial time series. Economics Discussion Papers (2011–2028) (2011)Google Scholar
 Altamirano, C., Robledo, A.: Possible thermodynamic structure underlying the laws of zipf and benford. Eur. Phys. J. B 81(3), 345 (2011)Google Scholar
 Amaral, L.A.N., Buldyrev, S., Havlin, S., Salinger, M., Stanley, H.: Power law scaling for a system of interacting units with complex internal structure. Phys. Rev. Lett. 80(7), 1385–1388 (1998)Google Scholar
 Anderson, C.: The long tail. Wired Mag. 12(10), 170–177 (2004)Google Scholar
 Anderson, P.W.: More is different. Science 177(4047), 393–396 (1972)Google Scholar
 Atkinson, A.B., Piketty, T., Saez, E.: Top incomes in the long run of history. J. Econ. Lit. 49(1), 3–71 (2011)Google Scholar
 Ballocchi, G., Dacorogna, M.M., Hopman, C.M., Müller, U.A., Olsen, R.B.: The intraday multivariate structure of the eurofutures markets. J. Empir. Financ. 6, 479–513 (1999)Google Scholar
 Banavar, J., Maritan, A., Rinaldo, A.: Size and form in efficient transportation networks. Nature 399(6732), 130–131 (1999)Google Scholar
 Bank of International Settlement: Triennial central bank survey of foreign exchange and otc derivatives markets in 2016. Monetary and Economic Department (2016)Google Scholar
 BarYam, Y.: Dynamics of Complex Systems. AddisonWesley, Reading (1997)Google Scholar
 Barabási, A., Albert, R.: Emergence of scaling in random networks. Science 509, (1999)Google Scholar
 Barabási, A., Albert, R., Jeong, H.: Scalefree characteristics of random networks: the topology of the Worldwide Web. Phys. A 281(1–4), 69–77 (2000)Google Scholar
 Barabási, A.L.: Network Science. Cambridge University Press, Cambridge (2016)Google Scholar
 BarndorffNielsen, O.E., Prause, K.: Apparent scaling. Financ. Stoch. 5(1), 103–113 (2001)Google Scholar
 Barrat, A., Barthelemy, M., PastorSatorras, R., Vespignani, A.: The architecture of complex weighted networks. Proc. Natl. Acad. Sci. 101, 3747 (2004)Google Scholar
 Barthelemy, M., Barrat, A., PastorSatorras, R., Vespignani, A.: Characterization and modeling of weighted networks. Phys. A 346, 34–43 (2004)Google Scholar
 Battiston, S., Catanzaro, M.: Statistical properties of corporate board and director networks. Eur. Phys. J. B 38(2), 345–352 (2004)Google Scholar
 Belsey, C.: Poststructuralism: A Very Short Introduction, vol. 73. Oxford University Press, Oxford (2002)Google Scholar
 Benford, F.: The law of anomalous numbers. In: Proceedings of the American philosophical society, pp. 551–572 (1938)Google Scholar
 Bennett, M., Pang, W., Ostroff, N., Baumgartner, B., Nayak, S., Tsimring, L., Hasty, J.: Metabolic Gene regulation in a dynamically changing environment. Nature 454(7208), 1119–1122 (2008)Google Scholar
 Bettencourt, L., West, G.: A unified theory of urban living. Nature 467(7318), 912 (2010)Google Scholar
 Bettencourt, L.M., Lobo, J., Helbing, D., Kühnert, C., West, G.B.: Growth, innovation, scaling, and the pace of life in cities. Proc. Natl. Acad. Sci. 104(17), 7301–7306 (2007)Google Scholar
 Bettencourt, L.M., Lobo, J., West, G.B.: Why are large cities faster? universal scaling and selfsimilarity in urban organization and dynamics. Eur. Phys. J. BCondens. Matter Complex Syst. 63(3), 285–293 (2008)Google Scholar
 Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm iIntelligence: From Natural to Artificial Systems. 1, Oxford university press, Oxford (1999)Google Scholar
 Bonacich, P.: Power and centrality: a family of measures. Am. J. Sociol. 92(5), 1170–1182 (1987)Google Scholar
 Bonanno, G., Caldarelli, G., Lillo, F., Mantegna, R.: Topology of correlationbased minimal spanning trees in real and model markets. Phys. Rev. E 68(4), 46130 (2003)Google Scholar
 Borgatti, S.P.: Centrality and network flow. Soc. Netw. 27(1), 55–71 (2005)Google Scholar
 Boss, M., Elsinger, H., Summer, M., Thurner, S.: Network topology of the interbank market. Quant. Financ. 4(6), 677–684 (2004)Google Scholar
 Bouchaud, J.P.: Power laws in economics and finance: some ideas from physics. Quant. Financ. 1(1), 105–112 (2001)Google Scholar
 Brazhnik, P., de la Fuente, A., Mendes, P.: Gene networks: how to put the function in genomics. TRENDS Biotechnol. 20(11), 467–472 (2002)Google Scholar
 Brin, S., Page, L.: The anatomy of a largescale hypertextual web search engine. Comput. Netw. ISDN Syst. 30(1–7), 107–117 (1998)Google Scholar
 Broido, A.D., Clauset, A.: Scalefree networks are rare (2018). arXiv:180103400
 Brown, J., Broderick, A., Lee, N.: Word of mouth communication within online communities: conceptualizing the online social network. J. Interact. Mark. 21(3), 2 (2007)Google Scholar
 Buchanan, M.: Nexus: Small Worlds and the Groundbreaking Theory of Networks. WW Norton & Company, New York (2003)Google Scholar
 Bullmore, E., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10(3), 186–198 (2009)Google Scholar
 Caldarelli, G.: ScaleFree Networks: Complex Webs in Nature and Technology. Oxford University Press, Oxford (2007)Google Scholar
 Caldarelli, G., Catanzaro, M.: Networks: A Very Short Introduction. Oxford University Press, Oxford (2012)Google Scholar
 Caldarelli, G., Capocci, A., de Los Rios, P., Muñoz, M.: Scalefree networks from varying vertex intrinsic fitness. Phys. Rev. Lett. 89(22) (2002)Google Scholar
 Cao, T.Y.: Structural realism and the interpretation of quantum field theory. Synthese 136(1), 3–24 (2003)Google Scholar
 Capocci, A., Servedio, V., Colaiori, F., Buriol, L., Donato, D., Leonardi, S., Caldarelli, G.: Preferential attachment in the growth of social networks: the internet encyclopedia Wikipedia. Phys. Rev. E 74(3), 36116 (2006)Google Scholar
 Castellani, B., Hafferty, F.W.: Sociology and Complexity Science: A New Field of Inquiry. Springer Science & Business Media, Heidelberg (2009)Google Scholar
 Chaitin, G.J.: Algorithmic information theory. IBM J. Res. Dev. 21(4), 350–359 (1977)Google Scholar
 Chui, B.: Unified Theory is Getting Closer, Hawking Predicts. San Jose Mercury News (2000). http://www.comdig.com/stephenhawking.php
 Cilliers, P.: Complexity and Postmodernism: Understanding Complex Systems. Routledge, London (1998)Google Scholar
 Cilliers, P., Spurrett, D.: Complexity and postmodernism: Understanding complex systems. S. Afr. J. Philos. 18(2), 258–274 (1999)Google Scholar
 Clauset, A., Shalizi, C.R., Newman, M.E.: Powerlaw distributions in empirical data. SIAM Rev. 51(4), 661–703 (2009)Google Scholar
 Colyvan, M.: An Introduction to the Philosophy of Mathematics. Cambridge University Press, Cambridge (2012)Google Scholar
 Corsi, F., Zumbach, G., Müller, U.A., Dacorogna, M.M.: Consistent highprecision volatility from highfrequency data. Econ. NotesRev. Bank. Financ. Monet. Econ. 30(2), 183–204 (2001)Google Scholar
 Costa, L., Rodrigues, F., Travieso, G., Boas, P.: Characterization of complex networks: a survey of measurements. Adv. Phys. 56(1), 167–242 (2007)Google Scholar
 Dacorogna, M.M., Gençay, R., Müller, U.A., Olsen, R.B., Pictet, O.V.: An Introduction to HighFrequency Finance. Academic Press, San Diego (2001)Google Scholar
 Darley, V.: Emergent phenomena and complexity. Artif. Life 4, 411–416 (1994)Google Scholar
 De Masi, G., Iori, G., Caldarelli, G.: Fitness model for the italian interbank money market. Phys. Rev. E 74(6), 66112 (2006)Google Scholar
 Derrida, J.: Structure, sign, and play in the discourse of the human sciences. In: A postmodern reader, pp. 223–242 (1993)Google Scholar
 Di Matteo, T.: Multiscaling in finance. Quant. Financ. 7(1), 21–36 (2007)Google Scholar
 Di Matteo, T., Aste, T., Dacorogna, M.M.: Long term memories of developed and emerging markets: using the scaling analysis to characterize their stage of development. J. Bank Financ. 29(4), 827–851 (2005)Google Scholar
 Díaz, J., Gallart, J., Ruiz, M.: On the ability of the benford’s law to detect earthquakes and discriminate seismic signals. Seism. Res. Lett. 86(1), 192–201 (2014)Google Scholar
 Dorogovtsev, S., Mendes, J.: Evolution of networks. Adv. Phys. 51(4), 1079–1187 (2002)Google Scholar
 Dorogovtsev, S., Mendes, J.: Evolution of Networks: From Biological Nets to the Internet and WWW. Oxford University Press, Oxford (2003a)Google Scholar
 Dorogovtsev, S., Mendes, J.: Evolution of Networks: From Biological Nets to the Internet and WWW. Oxford University Press, Oxford (2003b)Google Scholar
 Eigen, M.: From Strange Simplicity to Complex Familiarity. Oxford University Press, Oxford (2013)Google Scholar
 Esfeld, M., Lam, V.: Ontic structural realism as a metaphysics of objects. In: Scientific structuralism, pp. 143–159. Springer, Berlin (2010)Google Scholar
 Fagiolo, G., Reyes, J., Schiavo, S.: On the topological properties of the World Trade Web: a weighted network analysis. Phys. A 387, (2008)Google Scholar
 Fagiolo, G., Reyes, J., Schiavo, S.: WorldTrade Web: topological properties, dynamics, and evolution. Phys. Rev. E 79(3), 36115 (2009)Google Scholar
 Falkenburg, B.: Particle Metaphysics: A Critical Account of Subatomic Reality. Springer, Berlin (2007)Google Scholar
 Farmer, J.D., Lillo, F.: On the origin of powerlaw tails in price fluctuations. Quant. Financ. 4(1), C7–C11 (2004)Google Scholar
 Fichtner, J., Heemskerk, E.M., GarciaBernardo, J.: Hidden power of the big three? passive index funds, reconcentration of corporate ownership, and new financial risk. Bus. Polit. 19(2), 298–326 (2017)Google Scholar
 Fisher, L.: The Perfect Swarm. Basic, New York (2009)Google Scholar
 French, S., Ladyman, J.: Remodelling structural realism: Quantum physics and the metaphysics of structure. Synthese 136(1), 31–56 (2003)Google Scholar
 Fryar, C.D., Gu, Q., Ogden, C.L.: Anthropometric reference data for children and adults: United States, 2007–2010. Vital Health Stat.—Ser. 11(252), 1–48 (2012)Google Scholar
 Gabaix, X., Gopikrishnan, P., Plerou, V., Stanley, H.: A theory of powerlaw distributions in financial market fluctuations. Nature 423(6937), 267–270 (2003)Google Scholar
 Galluccio, S., Caldarelli, G., Marsili, M., Zhang, Y.C.: Scaling in currency exchange. Phys. A 245, 423–436 (1997)Google Scholar
 GarciaBernardo, J., Fichtner, J., Takes, F.W., Heemskerk, E.M.: Uncovering offshore financial centers: conduits and sinks in the global corporate ownership network. Sci. Rep. 7(1), 6246 (2017)Google Scholar
 Garlaschelli, D., Loffredo, M.: Fitnessdependent topological properties of the World Trade Web. Phys. Rev. Lett. 93(18), 188701 (2004a)Google Scholar
 Garlaschelli, D., Loffredo, M.: Patterns of link reciprocity in directed networks. Phys. Rev. Lett. 93(1) (2004b)Google Scholar
 Garlaschelli, D., Loffredo, M.: Structure and evolution of the world trade network. Phys. A 355, 138–144 (2004c)Google Scholar
 Garlaschelli, D., Caldarelli, G., Pietronero, L.: Universal Scaling Relations in Food Webs. Nature 423(6936), 165–8 (2003)Google Scholar
 Garlaschelli, D., Battiston, S., Castri, M., Servedio, V., Caldarelli, G.: The scalefree topology of market investments. Phys. A 350, 491–499 (2005)Google Scholar
 Gauss, C.F.: Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium Auctore Carolo Friderico Gauss. Hamburgi sumptibus Frid. Perthes et I. H, Besser (1809)Google Scholar
 Ghashghaie, S., Breymann, W., Peinke, P.T.J., Dodge, Y.: Turbulent cascades in foreign exchange markets. Nature 381, 767–770 (1996)Google Scholar
 Ghosh, A.: Scaling laws. In: Mechanics Over Micro and Nano Scales, pp. 61–94. Springer, Berlin (2011)Google Scholar
 Gini, C.: Measurement of inequality of incomes. Econ. J. 31(121), 124–126 (1921)Google Scholar
 Gladwell, M.: The Tipping Point: How Little Things Can Make a Big Difference. Little Brown and Company, Boston (2000)Google Scholar
 Glattfelder, J.B.: Decoding Complexity: Uncovering Patterns in Economic Networks. Springer, Heidelberg (2013)Google Scholar
 Glattfelder, J.B.: Decoding Financial Networks: Hidden Dangers and Effective Policies. In: Stiftung, B. (ed.) To the Man with a Hammer: Augmenting the Policymaker’s Toolbox for a Complex World. Bertelsmann Stiftung, Gütersloh (2016)Google Scholar
 Glattfelder, J.B.: The bowtie centrality:a novel measure for directed and weighted networks with an intrinsic node property, forthcoming (2019)Google Scholar
 Glattfelder, J.B., Battiston, S.: Backbone of complex networks of corporations: the flow of control. Phys. Rev. E 80(3), 36104 (2009)Google Scholar
 Glattfelder, J.B., Battiston, S.: The architecture of power: Patterns of disruption and stability in the global ownership network, forthcoming (2019)Google Scholar
 Glattfelder, J.B., Dupuis, A., Olsen, R.B.: Patterns in Highfrequency FX data: discovery of 12 empirical scaling laws. Quant. Financ. 11(4), 599 – 614 (2011). http://arxiv.org/abs/0809.1040
 Goldstein, J.: Emergence as a construct: history and issues. Emergence 1(1), 49–72 (1999)Google Scholar
 Golub, A., Chliamovitch, G., Dupuis, A., Chopard, B.: Multi–scale representation of high frequency market liquidity. Algorithmic Financ. 5(1) (2016)Google Scholar
 Golub, A., Glattfelder, J.B., Olsen, R.B.: The alpha engine: designing an automated trading algorithm. In: Dempster, M.A.H., Kanniainen, J., Keane, J., Vynckier, E. (eds.) HighPerformance Computing in Finance: Problems, Methods, and Solutions. Chapman & Hall, London (2018)Google Scholar
 GómezGardenes, J., Moreno, Y., Arenas, A.: Paths to synchronization on complex networks. Phys. Rev. Lett. 98(3), 34101 (2007)Google Scholar
 Gonze, D., Bernard, S., Waltermann, C., Kramer, A., Herzel, H.: Spontaneous synchronization of coupled circadian oscillators. Biophys. J. 89(1), 120–129 (2005)Google Scholar
 Green, D.G.: The Unexpected Side Effects of Complexity in Society. Springer, New York (2014)Google Scholar
 Guillaume, D.M., Dacorogna, M.M., Davé, R.D., Müller, U.A., Olsen, R.B., Pictet, O.V.: From the Bird’s Eye to the microscope: a survey of new stylized facts of the intradaily foreign exchange markets. Financ. Stoch. 1, 95–129 (1997)Google Scholar
 Guimera, R., Mossa, S., Turtschi, A., Amaral, L.: The Worldwide air transportation network: anomalous centrality, community structure, and cities’ global roles. Proc. Natl. Acad. Sci. 102(22), 7794 (2005)Google Scholar
 Haken, H.: Synergetics: An introduction. Springer, Berlin (1977)Google Scholar
 Haken, H.: Advanced Synergetics. Springer, Berlin (1983)Google Scholar
 Haken, H.: Information and SelfOrganization: A Macroscopic Approach to Complex Systems, 3rd edn. Springer, Heidelberg (2006)Google Scholar
 Helbing, D., Yu, W.: The outbreak of cooperation among successdriven individuals under noisy conditions. Proc. Natl. Acad. Sci. 106(10), 3680–3685 (2009)Google Scholar
 Helbing, D., Farkas, I., Vicsek, T.: Simulating dynamical features of escape panic. Nature 407(6803), 487–490 (2000)Google Scholar
 Hidalgo, C.: Why Information Grows. Basic, New York (2015)Google Scholar
 Hidalgo, C.A., Klinger, B., Barabási, A.L., Hausmann, R.: The product space conditions the development of nations. Science 317(5837), 482–487 (2007)Google Scholar
 Hill, T.P.: A statistical derivation of the significantdigit law. Stat. Sci. 354–363, (1995)Google Scholar
 Holland, J.: Hidden Order: How Adaptation Builds Complexity. Basic, New York (1995)Google Scholar
 Holland, J.: Emergence: From Chaos to Order. Helix Books, New York (1998)Google Scholar
 Holland, J.: Studying complex adaptive systems. J. Syst. Sci. Complex. 19(1), 1–8 (2006)Google Scholar
 Hubbell, C.: An inputoutput approach to clique identification. Sociometry 28(4), 377–399 (1965)Google Scholar
 Huggett, S., Mason, L., Tod, K., Tsou, S., Woodhouse, N.: The Geometric Universe: Science. Geometry and the Work of Roger Penrose. Oxford University Press, Oxford (1998)Google Scholar
 Iori, G., De Masi, G., Precup, O., Gabbi, G., Caldarelli, G.: A network analysis of the italian overnight money market. J. Econ. Dyn. Control. 32(1), 259–278 (2008)Google Scholar
 ISDA: Central clearing in the equity derivatives market (2014)Google Scholar
 James, G., Witten, D., Hastie, T., Tibshirani, R.: An Introduction to Statistical Learning. Springer, Heidelberg (2013)Google Scholar
 Johnson, N.: Simply Complexity: A Clear Guide to Complexity Theory. Oneworld, London (2009)Google Scholar
 Johnson, S.: Emergence: The Connected Lives of Ants, Brains, Cities, and Software. Scribner, New York (2001)Google Scholar
 Joulin, A., Lefevre, A., Grunberg, D., Bouchaud, J.P.: Stock price jumps: news and volume play a minor role. Wilmott Mag. 46, 1 – 6 (2008). www.arxiv.org/abs/0803.1769
 Katz, L.: A new status index derived from sociometric analysis. Psychometrika 18(1), 39–43 (1953)Google Scholar
 Kauffman, S.: The Origins of Order. Oxford University Press, Oxford (1993)Google Scholar
 Kauffman, S.: Reinventing the Sacred: A New View of Science, Reason, and Religion. Basic, New York (2008)Google Scholar
 Kitano, H.: Systems biology: a brief overview. Science 295(5560), 1662–1664 (2002)Google Scholar
 Klarreich, E.: Scant evidence of power laws found in realworld networks. Quanta Magazine. https://www.quantamagazine.org/scantevidenceofpowerlawsfoundinrealworldnetworks20180215/, 15 February 2018
 Kleiber, M.: Body size and metabolism. ENE 1(9), (1932)Google Scholar
 König, M., Battiston, S., Schweitzer, F.: Modeling Evolving Innovation Networks. In: Innovation Networks, p. 187 (2009)Google Scholar
 Kuhlmann, M.: The Ultimate Constituents of the Material World. In Search of an Ontology for Fundamental Physics. Ontos Verlag, Heusenstamm (2010)Google Scholar
 Kuhlmann, M.: Physicists Debate Whether the World Is Made of Particles or Fields–or Something Else Entirely. Scientific American. https://www.scientificamerican.com/article/physicistsdebatewhetherworldmadeofparticlesfieldsorsomethingelse/, 24 July 2013
 Kuhlmann, M.: Quantum field theory. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, summer, 2015th edn. Stanford University, Metaphysics Research Lab (2015)Google Scholar
 Kühnert, C., Helbing, D., West, G.: Scaling laws in urban supply networks. Phys. A 363, 96–103 (2006)Google Scholar
 Ladyman, J.: What is structural realism? Stud. Hist. Philos. Sci. Part A 29(3), 409–424 (1998)Google Scholar
 Ladyman, J.: Structural realism. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, winter, 2016th edn. Stanford University, Metaphysics Research Lab (2016)Google Scholar
 Ladyman, J., Lambert, J., Wiesner, K.: What is a complex system? Eur. J. Philos. Sci. 3(1), 33–67 (2013)Google Scholar
 Langton, C.G.: Computation at the edge of chaos: phase transitions and emergent computation. Phys. D: Nonlinear Phenom. 42(1–3), 12–37 (1990)Google Scholar
 Lorenz, M.O.: Methods of measuring the concentration of wealth. Publ. Am. Stat. Assoc. 9(70), 209–219 (1905)Google Scholar
 Luque, B., Lacasa, L.: The firstdigit frequencies of prime numbers and riemann zeta zeros. Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci., R. Soc. 465, 2197–2216 (2009)Google Scholar
 Lux, T.: Financial power laws: empirical evidence, models, and mechanisms. In: Power Laws in Social Sciences (2005)Google Scholar
 Lux, T.: Financial power laws: Empirical evidence, models, and mechanism. Technical report, Economics Working Paper (2006)Google Scholar
 Lux, T., Alfarano, S.: Financial power laws: Empirical evidence, models, and mechanisms. Chaos, Solitons Fractals 88, 3–18 (2016)Google Scholar
 Mandelbrot, B.B.: The variation of certain speculative prices. J. Bus. 36, 394–419 (1963)Google Scholar
 Mantegna, R.N., Stanley, H.E.: Scaling behavior in the dynamics of an economic index. Nature 376, 46–49 (1995)Google Scholar
 McKane, A., Drossel, B.: Models of Food Web Evolution (2005)Google Scholar
 Meyers, L., Pourbohloul, B., Newman, M., Skowronski, D., Brunham, R.: Network theory and SARS: predicting outbreak diversity. J. Theor. Biol. 232(1), 71–81 (2005)Google Scholar
 Morganti, M.: Is there a compelling argument for ontic structural realism? Philos. Sci. 78(5), 1165–1176 (2011)Google Scholar
 Moses, M., Bezerra, G., Edwards, B., Brown, J., Forrest, S.: Energy and time determine scaling in biological and computer designs. Philso. Trans. R. Soc. B 371(1701), 20150446 (2016)Google Scholar
 Mota, B., HerculanoHouzel, S.: Cortical folding scales universally with surface area and thickness, not number of neurons. Science 349(6243), 74–77 (2015)Google Scholar
 Moussaïd, M., Perozo, N., Garnier, S., Helbing, D., Theraulaz, G.: The walking behaviour of pedestrian social groups and its impact on crowd dynamics. PloS One 5(4), e10047 (2010)Google Scholar
 Müller, U.A., Dacorogna, M.M., Olsen, R.B., Pictet, O.V., Schwarz, M., Morgenegg, C.: Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis. J. Bank Financ. 14, 1189–1208 (1990)Google Scholar
 Newcomb, S.: Note on the frequency of use of the different digits in natural numbers. Am. J. Math. 4(1), 39–40 (1881)Google Scholar
 Newman, M.: Scientific collaboration networks. I. network construction and fundamental results. Phys. Rev. E 64(1), 16131 (2001a)Google Scholar
 Newman, M.: Scientific collaboration networks. II. shortest paths, weighted networks, and centrality. Phys. Rev. E 64(1), 16132 (2001b)Google Scholar
 Newman, M.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)Google Scholar
 Newman, M.: Analysis of weighted networks. Phys. Rev. E 70(5), 56131 (2004)Google Scholar
 Newman, M., Barabási, A., Watts, D.: The Structure and Dynamics of Networks. Princeton University Press, Princeton (2006)Google Scholar
 Newman, M.E.J.: Power laws, pareto distributions and Zipf’s law. Contemp. Phys. 46(5), 323–351 (2005)Google Scholar
 Newman, M.E.J., Watts, D.J., Strogatz, S.H.: Random graph models of social networks. Proc. Natl. Acad. Sci. 99(90001), 2566–2572 (2002)Google Scholar
 Niklas, K.J.: Plant Allometry: The Scaling of Form and Process. University of Chicago Press, Chicago (1994)Google Scholar
 Onnela, J.P., Chakraborti, A., Kaski, K., Kertész, J., Kanto, A.: Dynamics of market correlations: taxonomy and portfolio analysis. Phys. Rev. E 68(5), 56110 (2003)Google Scholar
 Onnela, J.P., Saramäki, J., Kertész, J., Kaski, K.: Intensity and coherence of motifs in weighted complex networks. Phys. Rev. E 71(6), 065103.1–065103.4 (2005)Google Scholar
 Papadimitriou, C.H.: Computational Complexity. Wiley, New York (2003)Google Scholar
 Pareto, V.: Cours d’économie Politique, vol. 1. Droz, Geneva (1964)Google Scholar
 Passie, T., Halpern, J.H., Stichtenoth, D.O., Emrich, H.M., Hintzen, A.: The pharmacology of lysergic acid diethylamide: a review. CNS Neurosci. Ther. 14(4), 295–314 (2008)Google Scholar
 PastorSatorras, R., Vázquez, A., Vespignani, A.: Dynamical and correlation properties of the internet. Phys. Rev. Lett. 87(25), 258701 (2001)Google Scholar
 Pietronero, L., Tosatti, E., Tosatti, V., Vespignani, A.: Explaining the uneven distribution of numbers in nature: the laws of benford and zipf. Phys. A: Stat. Mech. Its Appl. 293(1–2), 297–304 (2001)Google Scholar
 Prigogine, I.: From Being to Becoming. W.H. Freeman, San Francisoco (1980)Google Scholar
 Prigogine, I., Nicolis, G.: SelfOrganization in Nonequilibrium Systems. Wiley, New York (1977)Google Scholar
 Prigogine, I., Stengers, I., Prigogine, I.: Order out of Chaos: Man’s New Dialogue With Nature. Bantam Books, New York (1984)Google Scholar
 Quax, R., Apolloni, A., Sloot, P.M.: Towards understanding the behavior of physical systems using information theory. Eur. Phys. J. Spec. Top. 222(6), 1389–1401 (2013)Google Scholar
 Reichardt, J., White, D.: Role models for complex networks. Eur. Phys. J. B 60(2), 217–224 (2007)Google Scholar
 Ripley, B.: Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge (2008)Google Scholar
 Schilling, M., Phelps, C.: Interfirm collaboration networks: the impact of largescale network structure on firm innovation. Manag. Sci. 53(7), 1113–1126 (2007)Google Scholar
 Sen De, A., Sen, U.: Benford’s law detects quantum phase transitions similarly as earthquakes. EPL (Europhysics Letters) 95(5), 50008 (2011). http://stacks.iop.org/02955075/95/i=5/a=50008
 Serrano, M., Boguñá, M.: Topology of the World Trade Web. Phys. Rev. E 68(1), 15101 (2003)Google Scholar
 Servedio, V., Buttà, P., Caldarelli, G.: Vertex intrinsic fitness: How to produce arbitrary scalefree networks. Phys. Rev. E 70, (2004)Google Scholar
 Simon, H.A.: The organization of complex systems. In: Models of Discovery, pp. 245–261. Springer, Heidelberg (1977)Google Scholar
 Smolin, L.: Three Roads to Quantum Gravity. Basic Books, New York (2001)Google Scholar
 Sornette, A., Sornette, D.: Selforganized criticality and earthquakes. EPL (Europhysics Letters) 9(3), 197 (1989)Google Scholar
 Sornette, D.: Critical Phenomena in Natural Sciences. Springer, New York (2000a)Google Scholar
 Sornette, D.: Fokkerplanck equation of distributions of financial returns and power laws. Phys. A 290(1), 211–217 (2000b)Google Scholar
 Strogatz, S.: Exploring complex networks. Nature 410(6825), 268–276 (2001)Google Scholar
 Strogatz, S.H.: Sync: The Emerging Science of Spontaneous Order. Penguin, London (2004)Google Scholar
 Tadić, B.: Dynamics of dDrected graphs: The WorldWide Web. Phys. A 293(1–2), 273–284 (2001)Google Scholar
 Tasić, V.: Mathematics and the Roots of Postmodern Thought. Oxford University Press, Demand (2001)Google Scholar
 Treiber, M., Hennecke, A., Helbing, D.: Congested traffic states in empirical observations and microscopic simulations. Phys. Rev. E 62(2), 1805 (2000)Google Scholar
 Turchin, P.: Complex Population Dynamics: A Theoretical/Empirical Synthesis, vol. 35. Princeton University Press (2003)Google Scholar
 Turing, A.M.: Computing machinery and intelligence. Mind 59(236), 433–460 (1950)Google Scholar
 Udny Yule, G.: A mathematical theory of evolution, based on the conclusions of dr. jc willis, frs. Philos. Trans. R. Soc. Lond. Ser. B 213, 21–87 (1925)Google Scholar
 VegaRedondo, F.: Complex Social Networks. Cambridge University Press, Cambridge (2007)Google Scholar
 Vitali, S., Glattfelder, J.B., Battiston, S.: The network of global corporate control. PLoS One 6(10), e25995 (2011). http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0025995
 Voit, J.: The Statistical Mechanics of Financial Markets. Springer, Heidelberg (2005)Google Scholar
 Von Bertalanffy, L.: General System Theory. George Braziller, New York (1969)Google Scholar
 Walter, F., Battiston, S., Schweitzer, F.: A model of a trustbased recommendation system on a social network. Auton. Agents MultiAgent Syst. 16(1), 57–74 (2008)Google Scholar
 Watts, D., Strogatz, S.: Collective dynamics of smallworld networks. Nature 393(440), 440–442 (1998)Google Scholar
 West, G.: Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Lifein Organisms, Cities, Economies, and Companies. Penguin, New York (2017)Google Scholar
 West, G.B., Brown, J.H.: The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization. J. Exp. Biol. 208(9), 1575–1592 (2005)Google Scholar
 West, G.B., Brown, J.H., Enquist, B.J.: A general model for the origin of allometric scaling laws in biology. Science 276(5309), 122–126 (1997)Google Scholar
 West, G.B., Brown, J.H., Enquist, B.J.: A general model for the structure and allometry of plant vascular systems. Nature 400(6745), 664 (1999)Google Scholar
 West, L.J., Pierce, C.M., Thomas, W.D.: Lysergic acid diethylamide: Its effects on a male asiatic elephant. Science 138(3545), 1100–1103 (1962)Google Scholar
 Wiener, N.: Cybernetics. Sci. Am. 179(5), 14–19 (1948)Google Scholar
 Wigner, E.: The unreasonable effectiveness of mathematics in the natural sciences. Commun. Pure Appl. Math. 13(1), 222–237 (1960)Google Scholar
 Wittgenstein, L.: Tractatus LogicoPhilosophicus. Brace and Co., New York, Harcourt (1922)Google Scholar
 Woermann, M.: Bridging Complexity and PostStructuralism. Springer, Switzerland (2016)Google Scholar
 Wolfram, S.: A New Kind of Science. Wolfram Media Inc, Champaign (2002)Google Scholar
 Zipf, G.K.: Human Behaviour and the Principle of LeastEffort. AddisonWesley, Reading (1949)Google Scholar
Copyright information
Open Access This chapter is licensed under the terms of the Creative Commons AttributionNonCommercial 2.5 International License (http://creativecommons.org/licenses/bync/2.5/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.