"Symmetry is evidently a kind of unity in variety, where a whole is determined by the rhythmic repetition of similar." (George Santayana, "The Sense of Beauty", 1896)
"To apply the category of cause and effect means to find out which parts of nature stand in this relation. Similarly, to apply the gestalt category means to find out which parts of nature belong as parts to functional wholes, to discover their position in these wholes, their degree of relative independence, and the articulation of larger wholes into sub-wholes." (Kurt Koffka, 1931)
"By a model we thus mean any physical or chemical system which has a similar relation-structure to that of the process it imitates. By ’relation-structure’ I do not mean some obscure non-physical entity which attends the model, but the fact that it is a physical working model which works in the same way as the process it parallels, in the aspects under consideration at any moment." (Kenneth Craik, "The Nature of Explanation", 1943)
"A material model is the representation of a complex system by a system which is assumed simpler and which is also assumed to have some properties similar to those selected for study in the original complex system. A formal model is a symbolic assertion in logical terms of an idealised relatively simple situation sharing the structural properties of the original factual system." (Arturo Rosenblueth & Norbert Wiener, "The Role of Models in Science", Philosophy of Science Vol. 12" (4), 1945)
"Industrial production, the flow of resources in the economy, the exertion of military effort in a war theater-all are complexes of numerous interrelated activities. Differences may exist in the goals to be achieved, the particular processes involved, and the magnitude of effort. Nevertheless, it is possible to abstract the underlying essential similarities in the management of these seemingly disparate systems." (George Dantzig, "Linear programming and extensions", 1963)
"System' is the concept that refers both to a complex of interdependencies between parts, components, and processes, that involves discernible regularities of relationships, and to a similar type of interdependency between such a complex and its surrounding environment." (Talcott Parsons, "Systems Analysis: Social Systems", 1968)
"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic" (that is fixed) rules" (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order" (a pattern) within disorder" (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)
"Chaos demonstrates that deterministic causes can have random effects […] There's a similar surprise regarding symmetry: symmetric causes can have asymmetric effects. […] This paradox, that symmetry can get lost between cause and effect, is called symmetry-breaking. […] From the smallest scales to the largest, many of nature's patterns are a result of broken symmetry; […]" (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 1992)
"The dimensionality and nonlinearity requirements of chaos do not guarantee its appearance. At best, these conditions allow it to occur, and even then under limited conditions relating to particular parameter values. But this does not imply that chaos is rare in the real world. Indeed, discoveries are being made constantly of either the clearly identifiable or arguably persuasive appearance of chaos. Most of these discoveries are being made with regard to physical systems, but the lack of similar discoveries involving human behavior is almost certainly due to the still developing nature of nonlinear analyses in the social sciences rather than the absence of chaos in the human setting. " (Courtney Brown, "Chaos and Catastrophe Theories", 1995)
"From a more general philosophical perspective we can say that we wish to model complex systems because we want to understand them better. The main requirement for our models accordingly shifts from having to be correct to being rich in information. This does not mean that the relationship between the model and the system itself becomes less important, but the shift from control and prediction to understanding does have an effect on our approach to complexity: the evaluation of our models in terms of performance can be deferred. Once we have a better understanding of the dynamics of complexity, we can start looking for the similarities and differences between different complex systems and thereby develop a clearer understanding of the strengths and limitations of different models." (Paul Cilliers,"Complexity and Postmodernism: Understanding Complex Systems", 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)
"[…] swarm intelligence is becoming a valuable tool for optimizing the operations of various businesses. Whether similar gains will be made in helping companies better organize themselves and develop more effective strategies remains to be seen. At the very least, though, the field provides a fresh new framework for solving such problems, and it questions the wisdom of certain assumptions regarding the need for employee supervision through command-and-control management. In the future, some companies could build their entire businesses from the ground up using the principles of swarm intelligence, integrating the approach throughout their operations, organization, and strategy. The result: the ultimate self-organizing enterprise that could adapt quickly - and instinctively - to fast-changing markets." (Eric Bonabeau & Christopher Meyer, "Swarm Intelligence: A Whole New Way to Think About Business", Harvard Business Review, 2001)
"Although the detailed moment-to-moment behavior of a chaotic system cannot be predicted, the overall pattern of its 'random' fluctuations may be similar from scale to scale. Likewise, while the fine details of a chaotic system cannot be predicted one can know a little bit about the range of its 'random' fluctuation." (F David Peat, "From Certainty to Uncertainty", 2002)
"Complexity is the characteristic property of complicated systems we don’t understand immediately. It is the amount of difficulties we face while trying to understand it. In this sense, complexity resides largely in the eye of the beholder - someone who is familiar with s.th. often sees less complexity than someone who is less familiar with it. [...] A complex system is created by evolutionary processes. There are multiple pathways by which a system can evolve. Many complex systems are similar, but each instance of a system is unique." (Jochen Fromm, The Emergence of Complexity, 2004)
"Diverse groups of problem solvers outperformed the groups of the best individuals at solving complex problems. The reason: the diverse groups got stuck less often than the smart individuals, who tended to think similarly." (Scott E Page, [interview in The New York Times] 2008)
"A key discovery of network science is that the architecture of networks emerging in various domains of science, nature, and technology are similar to each other, a consequence of being governed by the same organizing principles. Consequently we can use a common set of mathematical tools to explore these systems. " (Albert-László Barabási, "Network Science", 2016)
"The exploding interest in network science during the first decade of the 21st century is rooted in the discovery that despite the obvious diversity of complex systems, the structure and the evolution of the networks behind each system is driven by a common set of fundamental laws and principles. Therefore, notwithstanding the amazing differences in form, size, nature, age, and scope of real networks, most networks are driven by common organizing principles. Once we disregard the nature of the components and the precise nature of the interactions between them, the obtained networks are more similar than different from each other." (Albert-László Barabási, "Network Science", 2016)
See also the quotes on Similarity in Graphical Representation series
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