"Perhaps the most profound synthesis of physical sciences came from the realization that everything could be understood from 'conservation laws' and symmetry principals." (Didier Sornette, "Why Stock Markets Crash: Critical Events in Complex Systems", 2003)
"According to a 'sociological' view of mathematics, a system, in general, should be able to do whatever is permitted by the laws governing it: the normal state of anarchy is chaos! From this point of view, we should expect that, in the absence of conservation laws, typical motions should be dense in the space available to them; Kolomogorov’s theorem denies this, saying that when the laws are relaxed a bit, the majority of motions stay 'pretty much' where they were, as if in fear of a non-existent police force." (John H Hubbard, "The KAM Theorem", 2004)
"A great deal of the results in many areas of physics are presented in the form of conservation laws, stating that some quantities do not change during evolution of the system. However, the formulations in cybernetical physics are different. Since the results in cybernetical physics establish how the evolution of the system can be changed by control, they should be formulated as transformation laws, specifying the classes of changes in the evolution of the system attainable by control function from the given class, i.e., specifying the limits of control." (Alexander L Fradkov, "Cybernetical Physics: From Control of Chaos to Quantum Control", 2007)
"Each of the most basic physical laws that we know corresponds to some invariance, which in turn is equivalent to a collection of changes which form a symmetry group. […] whilst leaving some underlying theme unchanged. […] for example, the conservation of energy is equivalent to the invariance of the laws of motion with respect to translations backwards or forwards in time […] the conservation of linear momentum is equivalent to the invariance of the laws of motion with respect to the position of your laboratory in space, and the conservation of angular momentum to an invariance with respect to directional orientation [...] discovery of conservation laws indicated that Nature possessed built-in sustaining principles which prevented the world from just ceasing to be." (John D Barrow, "New Theories of Everything", 2007)
"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)
"Entanglement (non-separability) has been interpreted in several non-physical ways, including recourse to telekinesis; it has also been claimed that it refutes realism and confirms holism. In my view, all entanglement does is to confirm the thesis Once a system, always a system. However, this is not an independent postulate, but a consequence of conservation laws." (Mario Bunge, "Matter and Mind: A Philosophical Inquiry", 2010)
"Symmetries are transformations that keep certain parameters (properties, equations, and so on) invariant, that is, the parameters they refer to are conserved under these transformations. It is to be expected, therefore, that the identification of conserved quantities is inseparable from the identification of fundamental symmetries in the laws of nature. Symmetries single out 'privileged' operations, conservation laws single out 'privileged' quantities or properties that correspond to these operations. Yet the specific connections between a particular symmetry and the invariance it entails are far from obvious. For instance, the isotropy of space (the indistinguishability of its directions) is intuitive enough, but the conservation of angular momentum based on that symmetry, and indeed, the concept of angular momentum, are far less intuitive." (Yemima Ben-Menahem, "Causation in Science", 2018)
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