"A second possible approach to general systems theory is through the arrangement of theoretical systems and constructs in a hierarchy of complexity, roughly corresponding to the complexity of the ‘individuals’ of the various empirical fields […] leading towards a ‘system of systems’." (Kenneth E Boulding, "General Systems Theory - The Skeleton of Science", 1956)
"One advantage of exhibiting a hierarchy of systems in this way is that it gives us some idea of the present gaps in both theoretical and empirical knowledge. Adequate theoretical models extend up to about the fourth level, and not much beyond. Empirical knowledge is deficient at practically all levels." (Kenneth E Boulding, "General Systems Theory: The Skeleton of Science", 1956)
"Two possible approaches to the organization of general systems theory suggest themselves, which are to be thought of as complementary rather than competitive, or at least as two roads each of which is worth exploring. The first approach is to look over the empirical universe and to pick out certain general phenomena which are found in many different disciplines, and to seek to build up general theoretical models relevant to these phenomena. The second approach is to arrange the empirical fields in a hierarchy of complexity of organization of their basic 'individual' or unit of behavior, and to try to develop a level of abstraction appropriate to each." (Kenneth E. Boulding, General Systems Theory - The Skeleton of Science, Management Science Vol. 2 (3), 1956)
"Thus, the central theme that runs through my remarks is that complexity frequently takes the form of hierarchy, and that hierarchic systems have some common properties that are independent of their specific content. Hierarchy, I shall argue, is one of the central structural schemes that the architect of complexity uses." (Herbert A Simon, "The Architecture of Complexity", Proceedings of the American Philosophical Society Vol. 106 (6), 1962)
"To model the dynamic behavior of a system, four hierarchies of structure should be recognized: closed boundary around the system; feedback loops as the basic structural elements within the boundary; level variables representing accumulations within the feedback loops; rate variables representing activity within the feedback loops." (Jay W Forrester, "Urban Dynamics", 1969)
"The parallelism of general conceptions or even special laws in different fields therefore is a consequence of the fact that these are concerned with 'systems' and that certain general principles apply to systems irrespective of their nature. Hence principles such as those of wholeness and sum, mechanization, hierarchic order, approached to steady states, equifinality, etc., may appear in quite different disciplines. The isomorphism found in different realms is based of the existence of general system principles, of a more or less well-developed ‘general system theory’." (Ludwig von Bertalanffy, "General System Theory", 1968)
"General systems theory is the scientific exploration of 'wholes' and 'wholeness' which, not so long ago, were considered metaphysical notions transcending the boundaries of science. Hierarchic structure, stability, teleology, differentiation, approach to and maintenance of steady states, goal-directedness - these are a few of such general system properties." (Ervin László, "Introduction to Systems Philosophy", 1972)
"[The] system may evolve through a whole succession of transitions leading to a hierarchy of more and more complex and organized states. Such transitions can arise in nonlinear systems that are maintained far from equilibrium: that is, beyond a certain critical threshold the steady-state regime become unstable and the system evolves into a new configuration." (Ilya Prigogine, Gregoire Micolis & Agnes Babloyantz, "Thermodynamics of Evolution", Physics Today 25 (11), 1972)
"The main object of cybernetics is to supply adaptive, hierarchical models, involving feedback and the like, to all aspects of our environment. Often such modelling implies simulation of a system where the simulation should achieve the object of copying both the method of achievement and the end result. Synthesis, as opposed to simulation, is concerned with achieving only the end result and is less concerned (or completely unconcerned) with the method by which the end result is achieved. In the case of behaviour, psychology is concerned with simulation, while cybernetics, although also interested in simulation, is primarily concerned with synthesis." (Frank H George, "Soviet Cybernetics, the militairy and Professor Lerner", New Scientist, 1973)
"[Hierarchy is] the principle according to which entities meaningfully treated as wholes are built up of smaller entities which are themselves wholes […] and so on. In hierarchy, emergent properties denote the levels." (Peter Checkland, "Systems Thinking, Systems Practice", 1981)
"Systems thinking is a special form of holistic thinking - dealing with wholes rather than parts. One way of thinking about this is in terms of a hierarchy of levels of biological organization and of the different 'emergent' properties that are evident in say, the whole plant (e.g. wilting) that are not evident at the level of the cell (loss of turgor). It is also possible to bring different perspectives to bear on these different levels of organization. Holistic thinking starts by looking at the nature and behaviour of the whole system that those participating have agreed to be worthy of study. This involves: (i) taking multiple partial views of 'reality' […] (ii) placing conceptual boundaries around the whole, or system of interest and (iii) devising ways of representing systems of interest." (C J Pearson and R L Ison, "Agronomy of Grassland Systems", 1987)
"This is why a 'web' of notes with links (like references) between them is far more useful than a fixed hierarchical system. When describing a complex system, many people resort to diagrams with circles and arrows. Circles and arrows leave one free to describe the interrelationships between things in a way that tables, for example, do not. The system we need is like a diagram of circles and arrows, where circles and arrows can stand for anything." (Tim Berners-Lee, "Information Management: A Proposal", 1989)
"Light a fire, build up the steam, turn on a switch, and a linear system awakens. It’s ready to serve you. If it stalls, restart it. Simple collective systems can be awakened simply. But complex swarm systems with rich hierarchies take time to boot up. The more complex, the longer it takes to warm up. Each hierarchical layer has to settle down; lateral causes have to slosh around and come to rest; a million autonomous agents have to acquaint themselves. I think this will be the hardest lesson for humans to learn: that organic complexity will entail organic time." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)
"In a random network the peak of the distribution implies that the vast majority of nodes have the same number of links and that nodes deviating from the average are extremely rare. Therefore, a random network has a characteristic scale in its node connectivity, embodied by the average node and fixed by the peak of the degree distribution. In contrast, the absence of a peak in a power-law degree distribution implies that in a real network there is no such thing as a characteristic node. We see a continuous hierarchy of nodes, spanning from rare hubs to the numerous tiny nodes. The largest hub is closely followed by two or three somewhat smaller hubs, followed by dozens that are even smaller, and so on, eventually arriving at the numerous small nodes."
"Another typical feature of theories of emergence is the layered view of nature. On this view, all things in nature belong to a certain level of existence, each according to its characteristic properties. These levels of existence constitute a hierarchy of increasing complexity that also corresponds to their order of appearance in the course of evolution." (Markus Eronen, "Emergence in the Philosophy of Mind", 2004)
"An ecology provides the special formations needed by organizations. Ecologies are: loose, free, dynamic, adaptable, messy, and chaotic. Innovation does not arise through hierarchies. As a function of creativity, innovation requires trust, openness, and a spirit of experimentation - where random ideas and thoughts can collide for re-creation." (George Siemens, "Knowing Knowledge", 2006)
"Change pressures arise from different sectors of a system. At times it is mandated from the top of a hierarchy, other times it forms from participants at a grass-roots level. Some changes are absorbed by the organization without significant impact on, or alterations of, existing methods. In other cases, change takes root. It causes the formation of new methods (how things are done and what is possible) within the organization." (George Siemens, "Knowing Knowledge", 2006)
"Hierarchy adapts knowledge to the organization; a network adapts the organization to the knowledge." (George Siemens, "Knowing Knowledge", 2006)
"[…] our mental models fail to take into account the complications of the real world - at least those ways that one can see from a systems perspective. It is a warning list. Here is where hidden snags lie. You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long-term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays. You are likely to mistreat, misdesign, or misread systems if you don’t respect their properties of resilience, self-organization, and hierarchy." (Donella H Meadows, "Thinking in Systems: A Primer", 2008)
"A hierarchy is a diagram that shows how various components of a system are related, often with a downward direction (or alternatively a left-to-right direction) that moves from more general to more specific. One way to envision a hierarchy is as an inverted tree: We start with a single component (referred to as the root node or topmost node), typically denoted by a square, and then we draw one or more paths leading from it to other nodes. Each of these nodes, in turn, may subdivide into additional subpaths to other nodes. This process may be repeated any number of times to arrive at a multitiered, tree-like structure." (Robbie T Nakatsu, "Diagrammatic Reasoning in AI", 2010)
"Laws of complexity hold universally across hierarchical scales (scalar, self-similarity) and are not influenced by the detailed behavior of constituent parts." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)
"The notion of emergence is used in a variety of disciplines such as evolutionary biology, the philosophy of mind and sociology, as well as in computational and complexity theory. It is associated with non-reductive naturalism, which claims that a hierarchy of levels of reality exist. While the emergent level is constituted by the underlying level, it is nevertheless autonomous from the constituting level. As a naturalistic theory, it excludes non-natural explanations such as vitalistic forces or entelechy. As non-reductive naturalism, emergence theory claims that higher-level entities cannot be explained by lower-level entities." (Martin Neumann, "An Epistemological Gap in Simulation Technologies and the Science of Society", 2011)
"In other words, the web of life consists of networks within networks. At each scale, under closer scrutiny, the nodes of the network reveal themselves as smaller networks. We tend to arrange these systems, all nesting within larger systems, in a hierarchical scheme by placing the larger systems above the smaller ones in pyramid fashion. But this is a human projection. In nature there is no 'above' or 'below', and there are no hierarchies. There are only networks nesting within other networks." (Fritjof Capra, "The Systems View of Life: A Unifying Vision", 2014)
[the principle of hierarchy:] "Generally, a control system has a hierarchical structure. It must agree with the functional structure of a controlled system and not contradict the hierarchy of (horizontally or vertically) adjacent systems. Tasks and resources supporting the activity of a controlled system must be decomposed according to its structure." (Dmitry A Novikov, "Cybernetics: From Past to Future", 2016)
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