"Zero is behind all of the big puzzles in physics. The infinite density of the black hole is a division by zero. The big bang creation from the void is a division by zero. The infinite energy of the vacuum is a division by zero. Yet dividing by zero destroys the fabric of mathematics and the framework of logic - and threatens to undermine the very basis of science. […] The universe begins and ends with zero." (Charles Seife ."Zero, the Biography of a Dangerous Idea", 2000)
"According to quantum theory, the ground state, or lowest energy state, of a pendulum is not just sitting at the lowest energy point, pointing straight down. That would have both a definite position and a definite velocity, zero. This would be a violation of the uncertainty principle, which forbids the precise measurement of both position and velocity at the same time. The uncertainty in the position multiplied by the uncertainty in the momentum must be greater than a certain quantity, known as Planck's constant - a number that is too long to keep writing down, so we use a symbol for it: ħ." (Stephen W Hawking, "The Universe in a Nutshell", 2001)
"Entropy [...] is the amount of disorder or randomness present in any system. All non-living systems tend toward disorder; left alone they will eventually lose all motion and degenerate into an inert mass. When this permanent stage is reached and no events occur, maximum entropy is attained. A living system can, for a finite time, avert this unalterable process by importing energy from its environment. It is then said to create negentropy, something which is characteristic of all kinds of life." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"Expressed in terms of entropy, open systems are negentropic, that is, tend toward a more elaborate structure. As open systems, organisms which are in equilibrium are capable of working for a long time by use of the constant input of matter and energy. Closed systems, however, increase their entropy, tend to run down and can therefore be called ’dying systems’. When reaching a steady state the closed system is not capable of performing any work." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"Information is neither matter nor energy, it is rather an abstract concept of the same kind as entropy, which must be considered a conceptual relative. 'Amount of information' is a metaphorical term and has in fact no numerical properties. " (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"Living systems in general are energy transducers which use information to perform more efficiently, converting one form of energy into another, and converting energy into information. Living species have developed a genius system to overcome entropy by their procreative faculty. […] Storing the surplus energy in order to survive is to reverse the entropic process or to create negentropy. A living being can only resist the degradation of its own structure. The entropic process influencing the structure and environment of the whole system is beyond individual control." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"Potential energy is organized energy, heat is disorganized energy and entropy therefore results in dissolution and disorder. The sum of all the quantities of heat lost in the course of all the activities that have taken place in the universe equals the total accumulation of entropy. A popular analogy of entropy is that it is not possible to warm oneself on something which is colder than oneself. […] Note also that maximun entropy is maximum randomization." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"So the ground state, or lowest energy state, of a pendulum does not have zero energy, as one might expect. Instead, even in its ground state a pendulum or any oscillating system must have a certain minimum amount of what are called zero point fluctuations. These mean that the pendulum won't necessarily be pointing straight down but will also have a probability of being found at a small angle to the vertical. Similarly, even in the vacuum or lowest energy state, the waves in the Maxwell field won't be exactly zero but can have small sizes. The higher the frequency" (the number of swings per minute) of the pendulum or wave, the higher the energy of the ground state." (Stephen W Hawking, "The Universe in a Nutshell", 2001)
"The second law of thermodynamics states that all energy in the universe degrades irreversibly. Thus, differences between energy forms must decrease over time. Everything is spread!" (The principle of degradation of energy with regard to quality.) Translated to the area of systems the law tells us that the entropy of an isolated system always increases. Another consequence is that when two systems are joined together, the entropy of the united system is greater than the sum of the entropies of the individual systems." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"All living organisms must feed on continual flows of matter and energy: from their environment to stay alive, and all living organisms continually produce waste. However, an ecosystem generates no net waste, one species' waste being another species' food. Thus, matter cycles continually through the web of life." (Fritjof Capra, "The Hidden Connections", 2002)
"Lessons from chaos theory show that energy is always needed for reorganization. And for a new order to appear an organization must be willing to allow a measure of chaos to occur; chaos being that which no one can totally control. It means entering a zone where no one can predict the final outcome or be truly confident as to what will happen." (F David Peat, "From Certainty to Uncertainty", 2002)
"To make a quantum observation or to register a measurement in any way, at least one quantum of energy must be exchanged between apparatus and quantum object. But because a quantum is indivisible, it cannot be split or divided. At the moment of observation we cannot know if that quantum came from the measuring apparatus or from the quantum object." (F David Peat, "From Certainty to Uncertainty", 2002)
"In string theory one studies strings moving in a fixed classical spacetime. […] what we call a background-dependent approach. […] One of the fundamental discoveries of Einstein is that there is no fixed background. The very geometry of space and time is a dynamical system that evolves in time. The experimental observations that energy leaks from binary pulsars in the form of gravitational waves - at the rate predicted by general relativity to the […] accuracy of eleven decimal place - tell us that there is no more a fixed background of spacetime geometry than there are fixed crystal spheres holding the planets up." (Lee Smolin, "The New Humanists: Science at the Edge", 2003)
"We don't know what energy is, any more than we know what information is, but as a now robust scientific concept we can describe it in precise mathematical terms, and as a commodity we can measure, market, regulate and tax it." (Hans Christian von Baeyer, "Information, The New Language of Science", 2003)
"Quantum-mechanical effects appear in physical systems that are exceedingly small. A small system means very tiny objects with very tiny amounts of energy, moving around over very short time intervals. Quantum effects show up dramatically once we arrive at length scales the size of the atom, about one ten-thousandth of a millionth of a meter. In fact, we simply cannot understand an atom without quantum mechanics. This is not to say that nature itself suddenly 'switches off'' classical mechanics and 'switches on' quantum mechanics when we enter this new submicroscopic realm. Quantum mechanics is always valid and always holds true at all scales of nature. Rather, quantum effects gradually become more and more pronounced as we descend into the world of atoms. Quantum mechanics is the ultimate set of rules, as far as we know, that governs how nature works" (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)
"At the foundation of classical thermodynamics are the first and second laws. The first law formulates that the total energy of a system is conserved, while the second law states that the entropy of an isolated system can only increase. The second law implies that the free energy of an isolated system is successively degraded by diabatic processes over time, leading to entropy production. This eventually results in an equilibrium state of maximum entropy. In its statistical interpretation, the direction towards higher entropy can be interpreted as a transition to more probable states." (Axel Kleidon & Ralph D Lorenz, "Entropy Production by Earth System Processes" [in "Non- quilibrium Thermodynamics and the Production of Entropy"], 2005)
"In formal terms, the ground state energy" (vacuum energy) of the electromagnetic quantum field is infinite. This causes mathematical trouble in quantum electrodynamics. [2](Eberhard Zeidler, "Quantum Field Theory II: Quantum Electrodynamics", 2006)
"Waves are used in nature in order to transport energy and information. [2](Eberhard Zeidler, "Quantum Field Theory II: Quantum Electrodynamics", 2006)
"Symmetries of the action functional lead to symmetries of the Euler– Lagrange equations. In particular, invariance of the action functional under time translations is responsible for the conservation of energy. Degeneracy of the second variation generates local symmetries also called gauge symmetries. The use of symmetries is basic for modern physics. [3](Eberhard Zeidler, "Quantum Field Theory I: Gauge Theory", 2006)
"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 second law of thermodynamics states that in an isolated system, entropy can only increase, not decrease. Such systems evolve to their state of maximum entropy, or thermodynamic equilibrium. Therefore, physical self-organizing systems cannot be isolated: they require a constant input of matter or energy with low entropy, getting rid of the internally generated entropy through the output of heat" ("dissipation"). This allows them to produce ‘dissipative structures’ which maintain far from thermodynamic equilibrium. Life is a clear example of order far from thermodynamic equilibrium." (Carlos Gershenson,"Design and Control of Self-organizing Systems", 2007)
"The universe is full of energy, but much of it is at equilibrium. At equilibrium no energy can flow, and therefore it cannot be used for work, any more than the level waters of a pond can be used to drive a water-wheel. It is on the flow of energy out of equilibrium - the small fraction of 'useful' energy, 'exergy' - that life depends." (Arthur C Clarke, "Firstborn", 2007)
"We can describe general relativity using either of two mathematically equivalent ideas: curved space-time or metric field. Mathematicians, mystics and specialists in general relativity tend to like the geometric view because of its elegance. Physicists trained in the more empirical tradition of high-energy physics and quantum field theory tend to prefer the field view, because it corresponds better to how we" (or our computers) do concrete calculations." (Frank Wilczek, "The Lightness of Being: Mass, Ether, and the Unification of Forces", 2008)
"Heat is the energy of random chaotic motion, and entropy is the amount of hidden microscopic information." (Leonard Susskind, "The Black Hole War", 2008)
"If universality is one of the observed characteristics of complex dynamical systems in many fields of study, a second characteristic that flows from the study of these systems is that of emergence. As self-organizing systems go about their daily business, they are constantly exchanging matter and energy with their environment, and this allows them to remain in a state that is far from equilibrium. That allows spontaneous behavior to give rise to new patterns." (Terry Cooke-Davies et al, "Exploring the Complexity of Projects", 2009)
"In short, synergy is the consequence of the energy expended in creating order. It is locked up in the viable system created, be it an organism or a social system. It is at the level of the system. It is not discernible at the level of the system. It is not discernible at the level of the system's components. Whenever the system is dismembered to examine its components, this binding energy dissipates." (J-C Spender, "Organizational Knowledge, Collective Practice and Penrose Rents", 2009)
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