"Zero was at the heart of the battle between East and West. Zero was at the center of the struggle between religion and science. Zero became the language of nature and the most important tool in mathematics. And the most profound problems in physics - the dark core of a black hole and the brilliant flash of the big bang - are struggles to defeat zero." (Charles Seife ."Zero, the Biography of a Dangerous Idea", 2000)
"Physics builds from observations. No physical theory can succeed if it is not confirmed by observations, and a theory strongly supported by observations cannot be denied. (William N Cropper, Great Physicists, 2001)
"What appear to be the most valuable aspects of the theoretical physics we have are the mathematical descriptions which enable us to predict events. These equations are, we would argue, the only realities we can be certain of in physics; any other ways we have of thinking about the situation are visual aids or mnemonics which make it easier for beings with our sort of macroscopic experience to use and remember the equations." (Celia Green, "The Lost Cause", 2003)
"The concept of a random walk is simple but rich for its many applications, not only in finance but also in physics and the description of natural phenomena. It is arguably one of the most founding concepts in modern physics as well as in finance, as it underlies the theories of elementary particles, which are the building blocks of our universe, as well as those describing the complex organization of matter around us." (Didier Sornette, "Why Stock Markets Crash: Critical Events in Complex Systems", 2003)
"Limiting factors in population dynamics play the role in ecology that friction does in physics. They stop exponential growth, not unlike the way in which friction stops uniform motion. Whether or not ecology is more like physics in a viscous liquid, when the growth-rate-based traditional view is sufficient, is an open question. We argue that this limit is an oversimplification, that populations do exhibit inertial properties that are noticeable. Note that the inclusion of inertia is a generalization - it does not exclude the regular rate-based, first-order theories. They may still be widely applicable under a strong immediate density dependence, acting like friction in physics." (Lev Ginzburg & Mark Colyvan, "Ecological Orbits: How Planets Move and Populations Grow", 2004)
"If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future)." (Benoît Mandelbrot, "The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward", 2004)
"At every major step physics has required, and frequently stimulated, the introduction of new mathematical tools and concepts. Our present understanding of the laws of physics, with their extreme precision and universality, is only possible in mathematical terms." (Michael F Atiyah, 2005)
"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)
"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)
"The burgeoning field of computer science has shifted our view of the physical world from that of a collection of interacting material particles to one of a seething network of information. In this way of looking at nature, the laws of physics are a form of software, or algorithm, while the material world - the hardware - plays the role of a gigantic computer." (Paul C W Davies, "Laying Down the Laws", New Scientist, 2007)
"Systematic usage of the methods of modern control theory to study physical systems is a key feature of a new research area in physics that may be called cybernetical physics. The subject of cybernetical physics is focused on studying physical systems by means of feedback interactions with the environment. Its methodology heavily relies on the design methods developed in cybernetics. However, the approach of cybernetical physics differs from the conventional use of feedback in control applications (e.g., robotics, mechatronics) aimed mainly at driving a system to a prespecified position or a given trajectory." (Alexander L Fradkov, "Cybernetical Physics: From Control of Chaos to Quantum Control", 2007)
"Much of the recorded knowledge of physics and engineering is written in the form of mathematical models. These mathematical models form the foundations of our understanding of the universe we live in. Furthermore, nearly all of the existing technology, in one way or another, rests on these models. To the extent that we are surrounded by evidence of the technology working and being reliable, human confidence in the validity of the underlying mathematical models is all but unshakable." (Jerzy A Filar, "Mathematical Models", 2009)
"There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depends heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood." (Paul Lockhart, "A Mathematician's Lament", 2009)
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