"Clearly, if the state of the system is coupled to parameters of an environment and the state of the environment is made to modify parameters of the system, a learning process will occur. Such an arrangement will be called a Finite Learning Machine, since it has a definite capacity. It is, of course, an active learning mechanism which trades with its surroundings. Indeed it is the limit case of a self-organizing system which will appear in the network if the currency supply is generalized." (Gordon Pask, "The Natural History of Networks", 1960)
"Prediction of the future is possible only in systems that have stable parameters like celestial mechanics. The only reason why prediction is so successful in celestial mechanics is that the evolution of the solar system has ground to a halt in what is essentially a dynamic equilibrium with stable parameters. Evolutionary systems, however, by their very nature have unstable parameters. They are disequilibrium systems and in such systems our power of prediction, though not zero, is very limited because of the unpredictability of the parameters themselves. If, of course, it were possible to predict the change in the parameters, then there would be other parameters which were unchanged, but the search for ultimately stable parameters in evolutionary systems is futile, for they probably do not exist… Social systems have Heisenberg principles all over the place, for we cannot predict the future without changing it." (Kenneth E Boulding, Evolutionary Economics, 1981)
"A conceptual model is a qualitative description of the system and includes the processes taking place in the system, the parameters chosen to describe the processes, and the spatial and temporal scales of the processes." (A Avogadro & R C Ragaini, "Technologies for Environmental Cleanup", 1993)
"Fundamental to catastrophe theory is the idea of a bifurcation. A bifurcation is an event that occurs in the evolution of a dynamic system in which the characteristic behavior of the system is transformed. This occurs when an attractor in the system changes in response to change in the value of a parameter. A catastrophe is one type of bifurcation. The broader framework within which catastrophes are located is called dynamical bifurcation theory." (Courtney Brown, "Chaos and Catastrophe Theories", 1995)
"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)
"Visualizations can be used to explore data, to confirm a hypothesis, or to manipulate a viewer. [...] In exploratory visualization the user does not necessarily know what he is looking for. This creates a dynamic scenario in which interaction is critical. [...] In a confirmatory visualization, the user has a hypothesis that needs to be tested. This scenario is more stable and predictable. System parameters are often predetermined." (Usama Fayyad et al, "Information Visualization in Data Mining and Knowledge Discovery", 2002)
"The existence of equilibria or steady periodic solutions is not sufficient to determine if a system will actually behave that way. The stability of these solutions must also be checked. As parameters are changed, a stable motion can become unstable and new solutions may appear. The study of the changes in the dynamic behavior of systems as parameters are varied is the subject of bifurcation theory. Values of the parameters at which the qualitative or topological nature of the motion changes are known as critical or bifurcation values." (Francis C Moona, "Nonlinear Dynamics", 2003)
"The methodology of feedback design is borrowed from cybernetics (control theory). It is based upon methods of controlled system model’s building, methods of system states and parameters estimation (identification), and methods of feedback synthesis. The models of controlled system used in cybernetics differ from conventional models of physics and mechanics in that they have explicitly specified inputs and outputs. Unlike conventional physics results, often formulated as conservation laws, the results of cybernetical physics are formulated in the form of transformation laws, establishing the possibilities and limits of changing properties of a physical system by means of control." (Alexander L Fradkov, "Cybernetical Physics: From Control of Chaos to Quantum Control", 2007)
"Generally, these programs fall within the techniques of reinforcement learning and the majority use an algorithm of temporal difference learning. In essence, this computer learning paradigm approximates the future state of the system as a function of the present state. To reach that future state, it uses a neural network that changes the weight of its parameters as it learns." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)
"Principle of Equifinality: If a steady state is reached in an open system, it is independent of the initial conditions, and determined only by the system parameters, i.e. rates of reaction and transport." (Kevin Adams & Charles Keating, "Systems of systems engineering", 2012)
"One kind of probability - classic probability - is based on the idea of symmetry and equal likelihood […] In the classic case, we know the parameters of the system and thus can calculate the probabilities for the events each system will generate. […] A second kind of probability arises because in daily life we often want to know something about the likelihood of other events occurring […]. In this second case, we need to estimate the parameters of the system because we don’t know what those parameters are. […] A third kind of probability differs from these first two because it’s not obtained from an experiment or a replicable event - rather, it expresses an opinion or degree of belief about how likely a particular event is to occur. This is called subjective probability […]." (Daniel J Levitin, "Weaponized Lies", 2017)
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