"Is a random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors? Or are the contributing factors unknowable, and therefore render as random an outcome that can never be determined? Are seemingly random events merely the result of fluctuations superimposed on a determinate system, masking its predictability, or is there some disorderliness built into the system itself?” (Deborah J Bennett, "Randomness", 1998)
"The self-similarity of fractal structures implies that there is some redundancy because of the repetition of details at all scales. Even though some of these structures may appear to teeter on the edge of randomness, they actually represent complex systems at the interface of order and disorder." (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)
"Emergent self-organization in multi-agent systems appears to contradict the second law of thermodynamics. This paradox has been explained in terms of a coupling between the macro level that hosts self-organization (and an apparent reduction in entropy), and the micro level (where random processes greatly increase entropy). Metaphorically, the micro level serves as an entropy 'sink', permitting overall system entropy to increase while sequestering this increase from the interactions where self-organization is desired." (H Van Dyke Parunak & Sven Brueckner, "Entropy and Self-Organization in Multi-Agent Systems", Proceedings of the International Conference on Autonomous Agents, 2001)
"Entropy [...] is the amount of disorder or randomness present in any system. All non-living systems tend toward disorder; left alone they will eventually lose all motion and degenerate into an inert mass. When this permanent stage is reached and no events occur, maximum entropy is attained. A living system can, for a finite time, avert this unalterable process by importing energy from its environment. It is then said to create negentropy, something which is characteristic of all kinds of life." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"If a network is solely composed of neighborhood connections, information must traverse a large number of connections to get from place to place. In a small-world network, however, information can be transmitted between any two nodes using, typically, only a small number of connections. In fact, just a small percentage of random, long-distance connections is required to induce such connectivity. This type of network behavior allows the generation of 'six degrees of separation' type results, whereby any agent can connect to any other agent in the system via a path consisting of only a few intermediate nodes." (John H Miller & Scott E Page, "Complex Adaptive Systems", 2007)
"Although the potential for chaos resides in every system, chaos, when it emerges, frequently stays within the bounds of its attractor(s): No point or pattern of points is ever repeated, but some form of patterning emerges, rather than randomness. Life scientists in different areas have noticed that life seems able to balance order and chaos at a place of balance known as the edge of chaos. Observations from both nature and artificial life suggest that the edge of chaos favors evolutionary adaptation." (Terry Cooke-Davies et al, "Exploring the Complexity of Projects", 2009)
"Most systems in nature are inherently nonlinear and can only be described by nonlinear equations, which are difficult to solve in a closed form. Non-linear systems give rise to interesting phenomena such as chaos, complexity, emergence and self-organization. One of the characteristics of non-linear systems is that a small change in the initial conditions can give rise to complex and significant changes throughout the system. This property of a non-linear system such as the weather is known as the butterfly effect where it is purported that a butterfly flapping its wings in Japan can give rise to a tornado in Kansas. This unpredictable behaviour of nonlinear dynamical systems, i.e. its extreme sensitivity to initial conditions, seems to be random and is therefore referred to as chaos. This chaotic and seemingly random behaviour occurs for non-linear deterministic system in which effects can be linked to causes but cannot be predicted ahead of time." (Robert K Logan, "The Poetry of Physics and The Physics of Poetry", 2010)
"Second Law of thermodynamics is not an equality, but an inequality, asserting merely that a certain quantity referred to as the entropy of an isolated system - which is a measure of the system’s disorder, or ‘randomness’ - is greater (or at least not smaller) at later times than it was at earlier times." (Roger Penrose, "Cycles of Time: An Extraordinary New View of the Universe", 2010)
"[...] a high degree of unpredictability is associated with erratic trajectories. This not only because they look random but mostly because infinitesimally small uncertainties on the initial state of the system grow very quickly - actually exponentially fast. In real world, this error amplification translates into our inability to predict the system behavior from the unavoidable imperfect knowledge of its initial state." (Massimo Cencini, "Chaos: From Simple Models to Complex Systems", 2010)
"Although cascading failures may appear random and unpredictable, they follow reproducible laws that can be quantified and even predicted using the tools of network science. First, to avoid damaging cascades, we must understand the structure of the network on which the cascade propagates. Second, we must be able to model the dynamical processes taking place on these networks, like the flow of electricity. Finally, we need to uncover how the interplay between the network structure and dynamics affects the robustness of the whole system." (Albert-László Barabási, "Network Science", 2016)
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