📓On Literature: On Energy (From Fiction to Science-Fiction)

"Hasheesh helped a great deal, and once sent him to a part of space where form does not exist, but where glowing gases study the secrets of existence. And a violet-coloured gas told him that this part of space was outside what he had called infinity. The gas had not heard of planets and organisms before, but identified Kuranes merely as one from the infinity where matter, energy, and gravitation exist." (Howard P Lovecraft, "Celephais", 1922)

"Revolution is everywhere, in everything. It is infinite. There is no final revolution, no final number. The social revolution is only one of an infinite number of numbers; the law of revolution is not a social law, but an immeasurably  greater one. It is a cosmic, universal law - like the laws of the conservation of energy and of the dissipation of energy (entropy)." (Yevgeny Zamiatin, "On Literature, Revolution, Entropy, and Other Matters", 1923)

"Scientific study and reflection had taught us that the known universe of three dimensions embraces the merest fraction of the whole cosmos of substance and energy. In this case an overwhelming preponderance of evidence from numerous authentic sources pointed to the tenacious existence of certain forces of great power and, so far as the human point of view is concerned, exceptional malignancy." (Howard P Lovecraft, "The Shunned House", 1937)

"Science is not a sacred cow - but there are a large number of would-be sacred cowherds busily devoting quantities of time, energy and effort to the task of making it one, so they can be sacred cowherds." (John W Campbell Jr, "Prologue to Analog", [introduction] 1962)

"By squandering nuclear energy, polluting asteroids and planets, ravaging the Preserve, and leaving litter everywhere we go, we shall ruin outer space and turn it into one big dump. It is high time we came to our senses and enforced the laws. Convinced that every minute of delay is dangerous, I sound the alarm: Let us save the Universe." (Stanislaw Lem, "Let Us Save the Universe (An Open Letter from Ijon Tichy, Space Traveller", 1966)

"When they [radio astronomers] grew weary at their electronic listening posts, when their eyes grew dim with looking at unrevealing dials and studying uneventful graphs, they could step outside their concrete cells and renew their dull spirits in communion with the giant mechanism they commanded, the silent, sensing instrument in which the smallest packets of energy, the smallest waves of matter, were detected in their headlong, eternal flight across the universe. It was the stethoscope with which they took the pulse of the all and noted the birth and death of stars, the probe with which, here on an insignificant planet of an undistinguished star on the edge of its galaxy, they explored the infinite." (James Gunn, "The Listeners", 1968)

"The universe is full of matter and force. Yet in all that force, amongst all the bulks and gravities, the rains of cosmic light, the bombardment of energy - how little spirit, how small the decimal points of intelligence." (Ray Bradbury et al, "Mars and the Mind of Man", 1973)

"Webriding. Flowing through stars, points of flame running through hands that aren’t hands, the psychic You bound up in the physical You that’s just a pattern sliding along the web, held together and existing only by the strength of will of the webrider. Sailing on evanescent wings of mind through the energy/matter currents of space." (Jayge Carr, "Webrider", 1985)

"The law of conservation of energy tells us we can't get something for nothing, but we refuse to believe it." (Isaac Asimov, "Isaac Asimov’s Book of Science and Nature Quotations", 1988)

"The second law of thermodynamics!: energy is indestructible in quantity but continually changes in form. And it always runs down like water." (Ernesto Cardenal, "Cosmic Canticle", 1993)

"The universe is driven by the complex interaction between three ingredients: matter, energy, and enlightened self-interest." (Marc S Zicree, "Survivors" [episode of Babylon 5], 1994)

"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)

"Beneath the cylindrical brass shield was an emerald, nearly fifteen centimeters in length and precision-cut into an orthorhombic dipyramidal crystal. It was this shape, combined with the high-energy potentiality of this particular variant of beryl that made time travel possible. It had taken him ten years and most of his inheritance to find and modify the emerald." (Mark Onspaugh, "Time’s Cruel Geometry", [in J W Schnarrv (ed), "Timelines"] 2010)

On Energy (-1849)

"Numbers are the sources of form and energy in the world. They are dynamic and active even among themselves […] almost human in their capacity for mutual influence." (Theon of Symyma, "Mathematics Useful for Understanding Plato" ["Expositio rerum mathematicarum ad legendum Platonem utilem", cca. 100–130)

"The principles of all knowledge are founded in mind; the mind of man, either animated by desire or pressed by necessity, puts in action it’s various energies, and unfolds the seeds of knowledge." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 3, 1794)

"But, as the universe is an extremely complex machine; the arrangement of the various parts of which it is composed, its preservation, and the play and energy of its springs, depend on an infinite number of general as well as particular laws. The most general admit of no exception. The exceptions attach on the detail; their number increases in proportion as the laws are specrfſed and particularized, and thus become more and more limited and restricted by other laws. Hence the exceptions themselves iorm new laws and means employed for a higher end. Apparent disorder in the parts is thus absorbed in the order of the whole, and the small defects gradually vanish in the eye of the philosopher as he proceeds to view nature on a more extended scale." (Johann H Lambert, "The System of the World", 1800)

"In the present state of our knowledge, it would be useless to attempt to speculate on the remote cause of the electrical energy [...] its relation to chemical affinity is, however, sufficiently evident. May it not be identical with it, and an essential property of matter?" (Humphry Davy, "Researches, Chemical and Philosophical, Chiefly Concerning Nitrous Oxide", 1800)

"The imagination […] that reconciling and mediatory power, which incorporating the reason in images of the sense and organizing (as it were) the flux of the senses by the permanence and self-circling energies of the reason, gives birth to a system of symbols, harmonious in themselves, and consubstantial with the truths of which they are the conductors." (Samuel T Coleridge, "The Statesman's Manual", 1816)

"For truth is simple and without fuss, whereas error affords opportunity for dissipating time and energy." (Johann Wolfgang von Goethe, 1829)

"There seems to me to be something analogous to polarized intensity in the pure imaginary part; and to unpolarized energy" (indifferent to direction) in the real part of a quaternion: and thus we have some slight glimpse of a future Calculus of Polarities. This is certainly very vague […]" (Sir William R Hamilton,"On Quaternions; or on a new System of Imaginaries in Algebra", 1844)

"I have long held an opinion, almost amounting to conviction, in common I believe with many other lovers of natural knowledge, that the various forms under which the forces of matter are made manifest have one common origin; or, in other words, are so directly related and mutually dependent, that they are convertible, as it were, one into another, and possess equivalents of power in their action." (Michael Faraday, "On the Magnetization of Light and the Illumination of Magnetic Lines of Force", [Paper read to the Royal Institution] 1845)

On Energy (1850-1874)

"The law of the conservation of energy is already known, viz. that the sum of the actual and potential energies in the universe is unchangeable." (William J M Rankine, "On the General Law of the Transformation of Energy", Philosophical Magazine, 1853)

"Modern civilisation rests upon physical science; take away her gifts to our own country, and our position among the leading nations of the world is gone tomorrow; for it is physical science only that makes intelligence and moral energy stronger than brute force." (Julian Huxley, "A Lobster; or, The Study of Zoology", 1861)

"The law of conservation rigidly excludes both creation and annihilation. Waves may change to ripples, and ripples to waves, - magnitude may be substituted for number, and number for magnitude, - asteroids may aggregate to suns, suns may resolve themselves into florae and faunae, and florae and faunae melt in air, - the flux of power is eternally the same. It rolls in music through the ages, and all terrestrial energy, - the manifestations of life, as well as the display of phenomena, are but the modulations of its rhythm." (John Tyndall, [Conclusion to lecture 12] 1862) 

"The total quantity of all the forces capable of work in the whole universe remains eternal and unchanged throughout all their changes. All change in nature amounts to this, that force can change its form and locality, without its quantity being changed. The universe possesses, once for all, a store of force which is not altered by any change of phenomena, can neither be increased nor diminished, and which maintains any change which takes place on it." (Hermann von Helmholtz, "The Conservation of Energy, from a Lecture", 1863) 

"To Nature nothing can be added; from Nature nothing can be taken away; the sum of her energies is constant, and the utmost man can do in the pursuit of physical truth, or in the applications of physical knowledge, is to shift the constituents of the never-varying total. The law of conservation rigidly excludes both creation and annihilation. Waves may change to ripples, and ripples to waves; magnitude may be substituted for number, and number for magnitude; asteroids may aggregate to suns, suns may resolve themselves into florae and faunae, and floras and faunas melt in air: the flux of power is eternally the same. It rolls in music through the ages, and all terrestrial energy - the manifestations of life as well as the display of phenomena - are but the modulations of its rhythm." (John Tyndall, "Conclusion of Heat Considered as a Mode of Motion: Being a Course of Twelve Lectures Delivered at the Royal Institution of Great Britain in the Season of 1862", 1863)

"[…] the quantities of heat which must be imparted to, or withdrawn from a changeable body are not the same, when these changes occur in a non-reversible manner, as they are when the same changes occur reversibly. In the second place, with each non-reversible change is associated an uncompensated transformation […] I propose to call the magnitude S the entropy of the body […] I have intentionally formed the word entropy so as to be as similar as possible to the word energy […]" (Rudolf Clausius, "The Mechanical Theory of Heat", 1867)

"If for the entire universe we conceive the same magnitude to be determined, consistently and with due regard to all circumstances, which for a single body I have called entropy, and if at the same time we introduce the other and simpler conception of energy, we may express in the following manner the fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat. 1. The energy of the universe is constant. 2. The entropy of the universe tends to a maximum." (Rudolf Clausius, "The Mechanical Theory of Heat - With its Applications to the Steam Engine and to Physical Properties of Bodies", 1867)

"The second fundamental theorem [the second law of thermodynamics], in the form which I have given to it, asserts that all transformations occurring in nature may take place in a certain direction, which I have assumed as positive, by themselves, that is, without compensation […] the entire condition of the universe must always continue to change in that first direction, and the universe must consequently approach incessantly a limiting condition. […] For every body two magnitudes have thereby presented themselves - the transformation value of its thermal content [the amount of inputted energy that is converted to 'work'], and its disgregation [separation or disintegration]; the sum of which constitutes its entropy." (Rudolf Clausius, "The Mechanical Theory of Heat", 1867)

"Any opinion as to the form in which the energy of gravitation exists in space is of great importance, and whoever can make his opinion probable will have, made an enormous stride in physical speculation. The apparent universality of gravitation, and the equality of its effects on matter of all kinds are most remarkable facts, hitherto without exception; but they are purely experimental facts, liable to be corrected by a single observed exception. We cannot conceive of matter with negative inertia or mass; but we see no way of accounting for the proportionality of gravitation to mass by any legitimate method of demonstration. If we can see the tails of comets fly off in the direction opposed to the sun with an accelerated velocity, and if we believe these tails to be matter and not optical illusions or mere tracks of vibrating disturbance, then we must admit a force in that direction, and we may establish that it is caused by the sun if it always depends upon his position and distance." (James C Maxwell, [Letter to William Huggins] 1868)

"The whole science of heat is founded Thermometry and Calorimetry, and when these operations are understood we may proceed to the third step, which is the investigation of those relations between the thermal and the mechanical properties of substances which form the subject of Thermodynamics. The whole of this part of the subject depends on the consideration of the Intrinsic Energy of a system of bodies, as depending on the temperature and physical state, as well as the form, motion, and relative position of these bodies. Of this energy, however, only a part is available for the purpose of producing mechanical work, and though the energy itself is indestructible, the available part is liable to diminution by the action of certain natural processes, such as conduction and radiation of heat, friction, and viscosity. These processes, by which energy is rendered unavailable as a source of work, are classed together under the name of the Dissipation of Energy. " (James C Maxwell, "Theory of Heat", 1871)

"It is difficult, however, for the mind which has once recognised the analogy between the phenomena of self-induction and those of the motion of material bodies, to abandon altogether the help of this analogy, or to admit that it is entirely superficial and misleading. The fundamental dynamical idea of matter, as capable by its motion of becoming the recipient of momentum and of energy, is so interwoven with our forms of thought that, when ever we catch a glimpse of it in any part of nature, we feel that a path is before us leading, sooner or later, to the complete understanding of the subject." (James C Maxwell, "A Treatise on Electricity and Magnetism" Vol. II, 1873)

"In our day grand generalizations have been reached. The theory of the origin of species is but one of them. Another, of still wider grasp and more radical significance, is the doctrine of the Conservation of Energy, the ultimate philosophical issues of which are as yet but dimly seem-that doctrine which “binds nature fast in fate” to an extent not hitherto recognized, exacting from every antecedent its equivalent consequent, and bringing vital as well as physical phenomena under the dominion of that law of causal connexion which, so far as the human understanding has yet pierced, asserts itself everywhere in nature." (John Tyndall, [Address Delivered Before The British Association Assembled at Belfast] 1874) 

On Energy (1910-1919)

"Though the ultimate state of the universe may be its vital and psychical extinction, there is nothing in physics to interfere with the hypothesis that the penultimate state might be the millennium - in other words a state in which a minimum of difference of energy - level might have its exchanges so skillfully canalises that a maximum of happy and virtuous consciousness would be the only result." (William James, [Letter to Henry Adams] 1910)

"The laws expressing the relations between energy and matter are, however, not solely of importance in pure science. They necessarily come first in order [...] in the whole record of human experience, and they control, in the last resort, the rise or fall of political systems, the freedom or bondage of nations, the movements of commerce and industry, the origin of wealth and poverty, and the general physical welfare of the race." (Frederick Soddy, "Matter and Energy", 1912)

"What is the imagination? Only an arm or weapon of the interior energy; only the precursor of the reason." (Ralph W Emerson, "Miscellanies, Natural history of intellect", 1912)

"For thought raised on specialization the most potent objection to the possibility of a universal organizational science is precisely its universality. Is it ever possible that the same laws be applicable to the combination of astronomic worlds and those of biological cells, of living people and the waves of the ether, of scientific ideas and quanta of energy? [...] Mathematics provide a resolute and irrefutable answer: yes, it is undoubtedly possible, for such is indeed the case. Two and two homogenous separate elements amount to four such elements, be they astronomic systems or mental images, electrons or workers; numerical structures are indifferent to any element, there is no place here for specificity." (Alexander Bogdanov, "Tektology: The Universal Organizational Science" Vol. I, 1913)

"There is no force inherent in living matter, no vital force independent of and differing from the cosmic forces; the energy which living matter gives off is counterbalanced by the energy which it receives." (William T Councilman, "Disease and its Causes", 1913

"The miracles of religion are to be discredited, not because we cannot conceive of them, but because they run counter to all the rest of our knowledge; while the mysteries of science, such as chemical affinity, the conservation of energy, the indivisibility of the atom, the change of the non-living into the living […] extend the boundaries of our knowledge, though the modus operandi of the changes remains hidden." (John Burroughs, "Scientific Faith", The Atlantic Monthly, 1915)

"There is a conservation of matter and of energy, there may be a conservation of life; or if not of life, of something which transcends life." (Oliver J Lodge, "Christopher: A Study in Human Personality", 1918)

"If Thought is capable of being classed with Electricity, or Will with chemical affinity, as a mode of motion, it seems necessary to fall at once under the second law of thermodynamics as one of the energies which most easily degrades itself, and, if not carefully guarded, returns bodily to the cheaper form called Heat. Of all possible theories, this is likely to prove the most fatal to Professors of History." (Henry Adams, "The Degradation of the Democratic Dogma", 1919)

"There is a conservation of matter and of energy, there may be a conservation of life; or if not of life, of something which transcends life." (Oliver J Lodge, "Christopher: A Study in Human Personality", 1918)

On Energy (1940-1949)

"Thinking is an experimental dealing with small quantities of energy, just as a general moves miniature figures over a map before setting his troops in action.," (Sigmund Freud, "New Introductory Lectures on Psychoanalysis", 1932)

"True equilibria can occur only in closed systems and that, in open systems, disequilibria called ‘steady states’, or ‘flow equilibria’ are the predominant and characteristic feature. According to the second law of thermodynamics a closed system must eventually attain a time-independent equilibrium state, with maximum entropy and minimum free energy. An open system may, under certain conditions, attain a time-independent state where the system remains constant as a whole and in its phases, though there is a continuous flow of component materials. This is called a steady state. Steady states are irreversible as a whole. […] A closed system in equilibrium does not need energy for its preservation, nor can energy be obtained from it. In order to perform work, a system must be in disequilibrium, tending toward equilibrium and maintaining a steady state, Therefore the character of an open system is the necessary condition for the continuous working capacity of the organism." (Ludwig on Bertalanffy, "Theoretische Biologie: Band 1: Allgemeine Theorie, Physikochemie, Aufbau und Entwicklung des Organismus", 1932)

"A state of equilibrium in a system does not mean, further, that the system is without tension. Systems can, on the contrary, also come to equilibrium in a state of tension" (e.g., a spring under tension or a container with gas under pressure).The occurrence of this sort of system, however, presupposes a certain firmness of boundaries and actual segregation of the system from its environment" (both of these in a functional, not a spatial, sense). If the different parts of the system are insufficiently cohesive to withstand the forces working toward displacement" (i.e., if the system shows insufficient internal firmness, if it is fluid), or if the system is not segregated from its environment by sufficiently firm walls but is open to its neighboring systems, stationary tensions cannot occur. Instead, there occurs a process in the direction of the forces, which encroaches upon the neighboring regions with diffusion of energy and which goes in the direction of an equilibrium at a lower level of tension in the total region. The presupposition for the existence of a stationary state of tension is thus a certain firmness of the system in question, whether this be its own inner firmness or the firmness of its walls." (Kurt Lewin, "A Dynamic Theory of Personality", 1935)

"Essential for any conception of the cell is that it is no static system. It is dynamic. It is energy-cycles, suites of oxidation and reduction, concatenated ferment-actions. It is like a magic hive the walls of whose chambered spongework are shifting veils of ordered molecules, and rend and renew as operations rise and cease. A world of surfaces and streams." (Sir Charles Sherrington, "Man on His Nature", 1940)

"Purposeful active behavior may be subdivided into two classes: ‘feed-back’" (or ‘teleological’) and ‘non-feed-back’" (or ‘non-teleological’). The expression feed-back is used by engineers in two different senses. In a broad sense it may denote that some of the output energy of an apparatus or machine is returned as input; an example is an electrical amplifier with feed-back. The feed-back is in these cases positive - the fraction of the output which reenters the object has the same sign as the original input signal. Positive feed-back adds to the input signals, it does not correct them. The term feed-back is also employed in a more restricted sense to signify that the behavior of an object is controlled by the margin of error at which the object stands at a given time with reference to a relatively specific goal. The feed-back is then negative, that is, the signals from the goal are used to restrict outputs which would otherwise go beyond the goal. It is this second meaning of the term feed-back that is used here." (Arturo Rosenblueth, Norbert Wiener & Julian Bigelow, "Behavior, Purpose and Technology", Philosophy of Science Vol. 10" (1), 1943)

"It seems significant that according to quantum physics the indestructibility of energy on one hand - which expresses its timeless existence - and the appearance of energy in space and time on the other hand correspond to two contradictory" (complementary) aspects of reality. In fact, both are always present, but in individual cases the one or the other may be more pronounced." (Wolfgang Pauli, Moderne Beispiele zur Hintergrundsphysik" ["Modern Examples of Background Physics", 1948)

"In classical physics, most of the fundamental laws of nature were concerned either with the stability of certain configurations of bodies, e.g. the solar system, or else with the conservation of certain properties of matter, e.g. mass, energy, angular momentum or spin. The outstanding exception was the famous Second Law of Thermodynamics, discovered by Clausius in 1850. This law, as usually stated, refers to an abstract concept called entropy, which for any enclosed or thermally isolated system tends to increase continually with lapse of time. In practice, the most familiar example of this law occurs when two bodies are in contact: in general, heat tends to flow from the hotter body to the cooler. Thus, while the First Law of Thermodynamics, viz. the conservation of energy, is concerned only with time as mere duration, the Second Law involves the idea of trend." (Gerald J Whitrow, "The Structure of the Universe: An Introduction to Cosmology", 1949)

"Myth is the secret opening through which the inexhaustible energies of the cosmos pour into human cultural manifestation. Religions, philosophies, arts, the social forms of primitive and historic man, prime discoveries in science and technology, the very dreams that blister sleep, boil up from the basic, magic ring of myth." (Joseph Campbell, "The Hero with a Thousand Faces", 1949

On Energy (2000-2009)

"The second law states that entropy always increases within closed systems. This is really a statement about average behaviour. High entropy means uniformity, differences ('order') are damped by interactions within the system. For water in a tub the water molecules exchange energy via what are essentially elastic collisions. Thus water everywhere in the tub soon acquires the same temperature. What the water does not do is to separate spontaneously into areas of hot and cold water. That would be to decrease the entropy in the system." (David G Green, "Self-organisation in complex systems", 2000)

"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)

"A theory makes certain predictions and allows calculations to be made that can be tested directly through experiments and observations. But a theory such as superstrings talks about quantum objects that exist in a multidimensional space and at incredibly short distances. Other grand unified theories would require energies close to those experienced during the creation of the universe to test their predictions." (F David Peat, "From Certainty to Uncertainty", 2002)

"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)

"For very long pendulums the spurious effects are small, and the main concern is the dissipation of energy as the pendulum gradually losses amplitude. However, for short pendulums the spurious effects are, not negligible. After the following literary divertissement, we note some ways that builders of Foucault pendulums have overcome the complicating effects of these limitations and thereby produced workable pendulums that are much smaller than Foucault’s original giant creation." (Gregory L Baker & Jammes A Blackburn, "The Pendulum: A Case Study in Physics", 2005)

 "Pendulum clocks exemplify important physical concepts. The clock needs to have some method of transferring energy to the pendulum to maintain its oscillation. There also needs to be a method whereby the pendulum regulates the motion of the clock. These two requirements are encompassed in one remarkable mechanism called the escapement. The escapement is a marvelous invention in that it makes the pendulum clock one of the first examples of an automaton with self-regulating feedback." (Gregory L Baker & Jammes A Blackburn, "The Pendulum: A Case Study in Physics", 2005)

"Any technical discussion of noise begins with white noise because white noise is pure or ideal noise. White noise serves as the gold standard of noise. Scientists and engineers have explored hundreds of other noise types but most of these deviate from white noise in some specific way. White noise is noisy because it has a wide and flat band of frequencies if one looks at its spectrum. This reflects the common working definition of noise as a so-called wideband signal. Good signals or wanted signals concentrate their energy on a comparatively narrow band of the frequency spectrum. Hence good signals tend to be so-called narrowband signals at least relative to the wide band of white noise. White noise is so noisy because its spectrum is as wide as possible - it runs the whole infinite length of the frequency spectrum itself. So pure or ideal white noise exists only as a mathematical abstraction. It cannot exist physically because it would require infinite energy." (Bart Kosko, "Noise", 2006)

"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)

"Is the universe noise? That question is not as strange as it sounds. Noise is an unwanted signal. A signal is anything that conveys information or ultimately anything that has energy. The universe consists of a great deal of energy. Indeed a working definition of the universe is all energy anywhere ever. So the answer turns on how one defines what it means to be wanted and by whom." (Bart Kosko, "Noise", 2006)

"Noise is an unwanted signal. A signal is anything that conveys information or ultimately anything that has energy. The universe consists of a great deal of energy. Indeed a working definition of the universe is all energy anywhere ever. So the answer turns on how one defines what it means to be wanted and by whom." (Bart Kosko, "Noise", 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)

"Waves are used in nature in order to transport energy and information. [2](Eberhard Zeidler, "Quantum Field Theory II: Quantum Electrodynamics", 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)

"Mechanics is the science of motion. It describes how things move from om one point to another as time passes, the greater the distance moved each second so the greater is the speed. If something moving hits you, the impact will depend not just on how fast it’s travelling but also how massive it is. It is the momentum that matters: the product of mass and velocity. Mechanics also deals with energy, especially the energy due to motion, ‘kinetic energy’." (Frank Close, "Antimatter", 2009)

"Self-organizing networks suffer various types of random damage. Therefore, if the network remained static, it would soon become dysfunctional. Some networks have developed highly specific screening systems which recognize and repair random damage. On the one hand, this process requires energy, which arrives in the form of perturbations or noise. On the other hand, noise-triggered network restructuring will repeat a few steps of the original self-organization and therefore constitutes a much cheaper way of providing a continuous repair function, with the additional advantage that it is always adaptive with respect to the actual environment of the network." (Péter Csermely, "Weak Links: The Universal Key to the Stabilityof Networks and Complex Systems", 2009)

"There’s matter, like the electron; antimatter, like the positron; and then there are things that are neither matter nor antimatter. The most familiar example of something that is beyond substance is electromagnetic radiation. All electromagnetic radiation, from gamma rays through X-rays and ultra-violet to visible light, infra red, and radio waves, consists of photons of different energies. Matter and antimatter can cancel one another out, their annihilation leaving non-substance in the form of photons; if the conditions are right this sequence can happen in reverse where photons turn into pieces of matter and antimatter." (Frank Close, "Antimatter", 2009)

"Using matrices, Dirac was able to write an equation relating the total energy of a body to a sum of its energy at rest and its energy in motion, all consistent with Einstein’s theory of relativity. The fact that matrices keep account of what happens when things rotate was a bonus, as the maths was apparently saying that an electron can itself rotate: can spin! Furthermore, the fact that he had been able to solve the mathematics by using the simplest matrices, where a single number was replaced by two columns of pairs, implied a ‘two-ness’ to the spin, precisely what the Zeeman effect had implied. The missing ingredi ent in Schrodinger’s theory had miraculously emerged from the mathematics of matrices, which had been forced on Dirac by the requirements of Einstein’s theory of relativity." (Frank Close, "Antimatter", 2009)

On Energy (2010-2019)

"[...] information is just as material as energy, though far less ubiquitous because it involves coding, and codes are conventional as well as artificial. [...] In sum, the concept of information is derivative, nor primary; in particular, it depends upon that of matter. Indeed, all information is transmitted by some physical process, just as every bit of energy is the energy of some material entity, and every energy transfer is a physical process that connects two or more physical entities. " (Mario Bunge, "Matter and Mind: A Philosophical Inquiry", 2010)

"We are beginning to see the entire universe as a holographically interlinked network of energy and information, organically whole and self-referential at all scales of its existence. We, and all things in the universe, are non-locally connected with each other and with all other things in ways that are unfettered by the hitherto known limitations of space and time." (Ervin László, "Cosmos: A Co-creator's Guide to the Whole-World", 2010)

"The laws of thermodynamics tell us something quite different. Economic activity is merely borrowing low-entropy energy inputs from the environment and transforming them into temporary products and services of value. In the transformation process, often more energy is expended and lost to the environment than is embedded in the particular good or service being produced." (Jeremy Rifkin, "The Third Industrial Revolution", 2011)

"The reactions that break down large molecules into small ones do not require an input of energy, but the reactions that build up large molecules require and input of energy. This is consistent with the laws of thermodynamics, which say that large, orderly molecules tend to break down into small, disorderly molecules." (Stanley A Rice, "Life of Earth: Portrait of a Beautiful, Middle-aged Stressed-out World", 2011)

"We can draw several general conclusions. First, because populations of living organisms tend to grow exponentially, numbers can rise very rapidly. This explains the inevitable population pressure that helped Darwin realize the role of natural selection, Second, exponential growth must always be a short-term, temporary phenomenon; for living organisms, the growth typically stops because of predation or a lack of sufficient nutrients or energy. Third, these laws about growth apply to all species- our intelligence cannot make us immune to simple mathematical laws. This is a critical lesson, because human population has been growing exponentially for the past few centuries. Of course, our intelligence gives us one option not available to bacteria. Exponential growth can stop only through some combination of an increase in the death rate and a decrease in the birth rate." (Jeffrey O Bennett & Seth Shostak, "Life in the universe" 3rd Ed., 2012)

"Artificial intelligence is the mimicking of human thought and cognitive processes to solve complex problems automatically. AI uses techniques for writing computer code to represent and manipulate knowledge." (Radian Belu, "Artificial Intelligence Techniques for Solar Energy and Photovoltaic Applications", 2013)

"Chaos provides order. Chaotic agitation and motion are needed to create overall, repetitive order. This ‘order through fluctuations’ keeps dynamic markets stable and evolutionary processes robust. In essence, chaos is a phase transition that gives spontaneous energy the means to achieve repetitive and structural order." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"In essence, chaos is a phase transition that gives spontaneous energy the means to achieve repetitive and structural order." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"Political structures are excessively paternalistic, and to maintain them requires a high level of energy. The massive amounts of energy they consume are unsustainable and invite political meltdowns, bailouts, and fallout. On the other hand, proponents of complexity theory take the paradigm–shattering view that less is more. They understand that, paradoxically enough, the complexity of simplicity is the key to the emergence of systems, repeatable patterns and the social glue that holds community together and creates order. Anyone can make simplicity complicated; it takes a true genius to make the complicated simple." (Lawrence K Samuels, "Defense of Chaos", 2013)

"One of the evident facts about the world is the stability of empty space-time. In classical general relativity we can explain this as a consequence of the positive energy theorem […] the positive energy theorem must extend in some suitable form to any viable quantum theory of gravity." (Lee Smolin "Positive energy in quantum gravity", 2014)

"Before considering the wave equation for mechanical waves, you should understand the difference between the motion of individual particles and the motion of the wave itself. Although the medium is disturbed as a wave goes by, which means that the particles of the medium are displaced from their equilibrium positions, those particles don’t travel very far from their undisturbed positions. The particles oscillate about their equilibrium positions, but the wave does not carry the particles along – a wave is not like a steady breeze or an ocean current which transports material in bulk from one location to another. For mechanical waves, the net displacement of material produced by the wave over one cycle, or over one million cycles, is zero. So, if the particles aren’t being carried along with the wave, what actually moves at the speed of the wave? […] the answer is energy." (Daniel Fleisch & Laura Kinnaman, "A Student’s Guide to Waves", 2015)

"The natural effect of processes going on in the Universe is to move from a state of order to a state of disorder, unless there is an input of energy from outside." (John R Gribbin, "The Time Illusion", 2016)

"The principle of cyclic progression - interconnected systems driven by an external energy source will tend to a cyclic progression in which system variety is generated, dominance emerges to suppress the variety, the dominant mode decays or collapses, and survivors emerge to regenerative variety." (Dmitry A Novikov, "Cybernetics: From Past to Future", 2016)

"A coherent inclusive study of the nature of mathematics would contribute to our understanding of problem-solving in general. Solving problems is how progress is made in all of science and technology. The synthesizing energy to achieve such a result would be a worthy and inspiring task for philosophy." (Reuben Hersh, "Mathematics as an Empirical Phenomenon, Subject to Modeling", 2017)

"The Second Law of Thermodynamics states that in an isolated system" (one that is not taking in energy), entropy never decreases." (The First Law is that energy is conserved; the Third, that a temperature of absolute zero is unreachable.) Closed systems inexorably become less structured, less organized, less able to accomplish interesting and useful outcomes, until they slide into an equilibrium of gray, tepid, homogeneous monotony and stay there." (Steven Pinker, "The Second Law of Thermodynamics", 2017)

"Granularity is ubiquitous in nature: light is made of photons, the particles of light. The energy of electrons in atoms can acquire only certain values and not others. The purest air is granular, and so, too, is the densest matter. Once it is understood that Newton’s space and time are physical entities like all others, it is natural to suppose that they are also granular. Theory confirms this idea: loop quantum gravity predicts that elementary temporal leaps are small, but finite." (Carlo Rovelli, "The Order of Time", 2018)

"[…] Einstein showed, for 'stuff' like space and time, seemingly stable, unchangeable aspects of nature; in truth, it’s the relationship between space and time that always stays the same, even as space contracts and time dilates. Like energy and matter, space and time are mutable manifestations of deeper, unshakable foundations: the things that never vary no matter what." (K C Cole, "The Simple Idea Behind Einstein’s Greatest Discoveries", Quanta Magazine, 2019)

On Energy (1980-1989)

"Thus, in physics, entropy is associated with the possibility of converting thermal energy into mechanical energy. If the entropy does not change during a process, the process is reversible. If the entropy increases, the available energy decreases. Statistical mechanics interprets an increase of entropy as a decrease in order or, if we wish, as a decrease in our knowledge." (John R Pierce, "An Introduction to Information Theory: Symbols, Signals & Noise" 2nd Ed., 1980)

"Time goes forward because energy itself is always moving from an available to an unavailable state. Our consciousness is continually recording the entropy change in the world around us. [...] we experience the passage of time by the succession of one event after another. And every time an event occurs anywhere in this world energy is expended and the overall entropy is increased. To say the world is running out of time then, to say the world is running out of usable energy. In the words of Sir Arthur Eddington, 'Entropy is time's arrow'." (Jeremy Rifkin, "Entropy", 1980)

"The basis of this theory is that in nature there is an inherent uncertainty or unpredictability that manifests itself only on an atomic scale. For example, the position of a subatomic particle such as an electron may not be a well-defined concept at all; it should be envisaged as jiggling around in a random sort of a way. Energy, too, becomes a slightly nebulous concept, subject to capricious and unpredictable changes." (Paul C W Davies, "The Edge of Infinity: Where the Universe Came from and How It Will End", 1981)

"The world's present industrial civilization is handicapped by the coexistence of two universal, overlapping, and incompatible intellectual systems: the accumulated knowledge of the last four centuries of the properties and interrelationships of matter and energy; and the associated monetary culture which has evolved from folkways of prehistoric origin. […] Despite their inherent incompatibilities, these two systems during the last two centuries have had one fundamental characteristic in common, namely exponential growth, which has made a reasonably stable coexistence possible. But, for various reasons, it is impossible for the matter-energy system to sustain exponential growth for more than a few tens of doublings, and this phase is by now almost over. The monetary system has no such constraints, and according to one of its most fundamental rules, it must continue to grow by compound interest." (Marion K Hubbert, "Two Intellectual Systems: Matter-energy and the Monetary Culture", [seminar] 1981)

"A Universal Turing Machine is an ideal mathematical object; it represents a formal manipulation of symbols and owes allegiance to criteria of logical consistency but not to physical laws and constraints. Thus, for example, physical variables play no essential role in the concept of algorithm. In reality, however, every logical operation occurs at a minimum cost of KT of energy dissipation" (where K is Boltzman's constant and T is temperature) and, in fact, occurs at a much higher cost to insure reliability." (Claudia Carello et al, "The Inadequacies of the Computer Metaphor", 1982)

"The difference is that energy is a property of the microstates, and so all observers, whatever macroscopic variables they may choose to define their thermodynamic states, must ascribe the same energy to a system in a given microstate. But they will ascribe different entropies to that microstate, because entropy is not a property of the microstate, but rather of the reference class in which it is embedded. As we learned from Boltzmann, Planck, and Einstein, the entropy of a thermodynamic state is a measure of the number of microstates compatible with the macroscopic quantities that you or I use to define the thermodynamic state." (Edwin T Jaynes, "Papers on Probability, Statistics, and Statistical Physics", 1983)

"There is a fact, or if you wish, a law governing all natural phenomena that are known to date. There is no known exception to this law - it is exact as far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens." (Richard P Feynman et al, "The Feynman Lectures on Physics" Vol. 1, 1983)

"To a considerable degree science consists in originating the maximum amount of information with the minimum expenditure of energy. Beauty is the cleanness of line in such formulations along with symmetry, surprise, and congruence with other prevailing beliefs." (Edward O Wilson,"Biophilia", 1984)

"In the real world, none of these assumptions are uniformly valid. Often people want to know why mathematics and computers cannot be used to handle the meaningful problems of society, as opposed, let us say, to the moon boondoggle and high energy-high cost physics. The answer lies in the fact that we don't know how to describe the complex systems of society involving people, we don't understand cause and effect, which is to say the consequences of decisions, and we don't even know how to make our objectives reasonably precise. None of the requirements of classical science are met. Gradually, a new methodology for dealing with these 'fuzzy' problems is being developed, but the path is not easy." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)

"To a considerable degree science consists in originating the maximum amount of information with the minimum expenditure of energy. Beauty is the cleanness of line in such formulations along with symmetry, surprise, and congruence with other prevailing beliefs." (Edward O Wilson, "Biophilia", 1984)

"The power and glory of symmetry allow us to bypass completely the construction of strong interaction theories of dubious utility. We are able to contain and isolate our ignorance. [...] Symmetry tells us that states in the same multiplet must have the same energy, but it cannot tell us what that energy is." (Anthony Zee, "Fearful Symmetry: The Search for Beauty in Modern Physics", 1986)

"If grand unified theories are correct, we ought to be able to derive the relative power of the strong, weak, and electromagnetic interactions at accessible energies from their presumed equality at much higher energies. When this is attempted, a wonderful result emerges. …in the form first calculated by Howard Georgi, Helen Quinn, and Steven Weinberg […] The couplings of strong-interaction gluons decrease, those of the [weak interaction] W bosons stay roughly constant, and those of the [electromagnetic interaction] photons increase at short distances [or high energies] - so they all tend to converge, as desired." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987)

"What is conserved, in modern physics, is not any particular substance or material but only much more abstract entities such as energy, momentum, and electric charge. The permanent aspects of reality are not particular materials or structures but rather the possible forms of structures and the rules for their transformation." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987)

"The concept of entropy relates to the tendency of things to move toward greater disorder, or disorganization. […] The second law of thermodynamics expresses precisely the same concept. This states that heat dissipates from a central source and the energy becomes degraded, although total energy remains constant" (the first law of thermodynamics). Entropy suggests that organisms, organizations, societies, machines, and so on, will rapidly deteriorate into disorder and death." The reason they do not is because animate things can self-organize and inanimate things may be serviced by man. These are negentropic activities which require energy. Energy, however, can be made available only by further degradation. Ultimately, therefore, entropy wins the day and the attempts to create order can seem rather a daunting task in the entropic scheme of things. Holding back entropy, however, is another of the challenging tasks for the systems scientist." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"Physics is the basic science of matter and energy, and engineering is physics applied to structures and machines. They and chemistry are the sciences that biologists need to explain the structure and mechanism of living things." (R McNeill Alexander, "Dynamics of Dinosaurs and Other Extinct Giants", 1989)

On Energy (1990-1999)

"In physics, there are numerous phenomena that are said to be 'true on all scales', such as the Heisenberg uncertainty relation, to which no exception has been found over vast ranges of the variables involved (such as energy versus time, or momentum versus position). But even when the size ranges are limited, as in galaxy clusters (by the size of the universe) or the magnetic domains in a piece of iron near the transition point to ferromagnetism (by the size of the magnet), the concept true on all scales is an important postulate in analyzing otherwise often obscure observations." (Manfred Schroeder, "Fractals, Chaos, Power Laws Minutes from an Infinite Paradise", 1990)

"Three laws governing black hole changes were thus found, but it was soon noticed that something unusual was going on. If one merely replaced the words 'surface area' by 'entropy' and 'gravitational field' by 'temperature', then the laws of black hole changes became merely statements of the laws of thermodynamics. The rule that the horizon surface areas can never decrease in physical processes becomes the second law of thermodynamics that the entropy can never decrease; the constancy of the gravitational field around the horizon is the so-called zeroth law of thermodynamics that the temperature must be the same everywhere in a state of thermal equilibrium. The rule linking allowed changes in the defining quantities of the black hole just becomes the first law of thermodynamics, which is more commonly known as the conservation of energy." (John D Barrow, "Theories of Everything: The Quest for Ultimate Explanation", 1991)

"What is an attractor? It is the set on which the point P, representing the system of interest, is moving at large times" (i.e., after so-called transients have died out). For this definition to make sense it is important that the external forces acting on the system be time independent" (otherwise we could get the point P to move in any way we like). It is also important that we consider dissipative systems" (viscous fluids dissipate energy by self-friction). Dissipation is the reason why transients die out. Dissipation is the reason why, in the infinite-dimensional space representing the system, only a small set" (the attractor) is really interesting." (David Ruelle, "Chance and Chaos", 1991)

"Symmetry is bound up in many of the deepest patterns of Nature, and nowadays it is fundamental to our scientific understanding of the universe. Conservation principles, such as those for energy or momentum, express a symmetry that" (we believe) is possessed by the entire space-time continuum: the laws of physics are the same everywhere." (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 1992)

"The new information technologies can be seen to drive societies toward increasingly dynamic high-energy regions further and further from thermodynamical equilibrium, characterized by decreasing specific entropy and increasingly dense free-energy flows, accessed and processed by more and more complex social, economic, and political structures." (Ervin László, "Information Technology and Social Change: An Evolutionary Systems Analysis", Behavioral Science 37, 1992)

"The description of the evolutionary trajectory of dynamical systems as irreversible, periodically chaotic, and strongly nonlinear fits certain features of the historical development of human societies. But the description of evolutionary processes, whether in nature or in history, has additional elements. These elements include such factors as the convergence of existing systems on progressively higher organizational levels, the increasingly efficient exploitation by systems of the sources of free energy in their environment, and the complexification of systems structure in states progressively further removed from thermodynamic equilibrium." (Ervin László et al, "The Evolution of Cognitive Maps: New Paradigms for the Twenty-first Century", 1993)

"The universe is driven by the complex interaction between three ingredients: matter, energy, and enlightened self-interest." (Marc S Zicree, "Survivors" [episode of Babylon 5], 1994)

"In contemplating natural phenomena, we frequently have to distinguish between effective complexity and logical depth. For example, the apparently complicated pattern of energy levels of atomic nuclei might easily be misattributed to some complex law at the fundamental level, but it is now believed to follow from a simple underlying theory of quarks, gluons, and photons, although lengthy calculations would be required to deduce the detailed pattern from the basic equations. Thus the pattern has a good deal of logical depth and very little effective complexity." (Murray Gell-Mann, "What is Complexity?", Complexity Vol. 1" (1), 1995)

"It [Living Systems Theory" (LST)] involves observing and measuring important relationships between inputs and outputs of the total system and identifying the structures that perform each of the sub‐system processes. […] The flows of relevant matter, energy, and information through the system and the adjustment processes of subsystems and the total system are also examined. The status and function of the system are analyzed and compared with what is average or normal for that type of system. If the system is experiencing a disturbance in some steady state, an effort is made to discover the source of the strain and correct it." (James G Miller & Jessie L Miller, "Applications of living systems theory", Systemic Practice and Action Research 8, 1995)

"As we explore physics at higher and higher energy, revealing its structure at shorter and shorter distances, we discover more and more symmetry." (David J Gross,"The Role of Symmetry in Fundamental Physics", 1996)

"All systems evolve, although the rates of evolution may vary over time both between and within systems. The rate of evolution is a function of both the inherent stability of the system and changing environmental circumstances. But no system can be stabilized forever. For the universe as a whole, an isolated system, time’s arrow points toward greater and greater breakdown, leading to complete molecular chaos, maximum entropy, and heat death. For open systems, including the living systems that are of major interest to us and that interchange matter and energy with their external environments, time’s arrow points to evolution toward greater and greater complexity. Thus, the universe consists of islands of increasing order in a sea of decreasing order. Open systems evolve and maintain structure by exporting entropy to their external environments." (L Douglas Kiel, "Chaos Theory in the Social Sciences: Foundations and Applications", 1996)

"As we explore physics at higher and higher energy, revealing its structure at shorter and shorter distances, we discover more and more symmetry." (David J Gross, "The Role of Symmetry in Fundamental Physics", 1996)

"Contrary to what happens at equilibrium, or near equilibrium, systems far from equilibrium do not conform to any minimum principle that is valid for functions of free energy or entropy production." (Ilya Prigogine, "The End of Certainty: Time, Chaos, and the New Laws of Nature", 1996)

"The universe would have expanded in a smooth way from a single point. As it expanded, it would have borrowed energy from the gravitational field, to create matter. As any economist could have predicted, the result of all that borrowing, was inflation. The universe expanded and borrowed at an ever-increasing rate. Fortunately, the debt of gravitational energy will not have to be repaid until the end of the universe." (Stephen Hawking," The Beginning of Time", 1996)

"A pendulum swings in a circle, so there is a lowest point that it can possibly reach - hanging vertically downwards. Any change in potential energy must be compensated by an equal and opposite change in kinetic energy: if the bob gets higher, it has to move more slowly; if it gets lower, it has to move faster. Imagine grabbing the pendulum by its bob and raising it to some chosen height. Hold it steady. Your hand did some work, and increased the bob's potential energy. The kinetic energy is zero because the pendulum is not moving. Now let go, and from now on let the pendulum move as it wishes. Gravity pulls the bob downwards, so the potential energy decreases. Kinetic energy must increase to compensate, so the weight starts to fall. At some stage the bob must reach the lowest point of the circle: here its potential energy is zero, so all of the energy has become kinetic. Not only is it moving at this point - it is moving as fast as it can possibly go." (Ian Stewart, "The Magical Maze: Seeing the world through mathematical eyes", 1997)

"These three insights - the network pattern, the flow of energy, and the nutrient cycles—are essential to the new scientific conception of life. Scientists have formulated them in complicated technical language. They speak of 'autopoietic networks', 'dissipative structures', and 'catalytic cycles'. But the basic phenomena described by those technical terms are the web of life, the flow of energy, and the cycles of nature." (Fritjof Capra," Turn, Turn, Turn: Understanding Nature’s Cycles", 1997)

"Complex systems operate under conditions far from equilibrium. Complex systems need a constant flow of energy to change, evolve and survive as complex entities. Equilibrium, symmetry and complete stability mean death. Just as the flow, of energy is necessary to fight entropy and maintain the complex structure of the system, society can only survive as a process. It is defined not by its origins or its goals, but by what it is doing." (Paul Cilliers,"Complexity and Postmodernism: Understanding Complex Systems", 1998)

"In a closed system, the change in entropy must always be 'positive', meaning toward death. However, in open biological or social systems, entropy can be arrested and may even be transformed into negative entropy. - a process of more complete organization and enhanced ability to transform resources. Why? Because the system imports energy and resources from its environment, leading to renewal. This is why education and learning are so important, as they provide new and stimulating input" (termed neg-entropy) that can transform each of us." (Stephen G Haines, "The Managers Pocket Guide to Systems Thinking & Learning", 1998)

"There has to be a constant flow of energy to maintain the organization of the system and to ensure its survival. Equilibrium is another word for death." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)

"Mathematicians have always appreciated clever notations; but symbolism is usually seen as a tool - it's what the tool does that we really care about. Fair enough. But if we want a richer appreciation of mathematics, we should focus some of our energy on this remarkable tool - notation. Besides mathematics, poetry alone works wonders with it." (James R Brown,"Philosophy of Mathematics", 1999)

"[...] 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", 1999)

On Energy (1970-1979)

"Self-organization can be defined as the spontaneous creation of a globally coherent pattern out of local interactions. Because of its distributed character, this organization tends to be robust, resisting perturbations. The dynamics of a self-organizing system is typically non-linear, because of circular or feedback relations between the components. Positive feedback leads to an explosive growth, which ends when all components have been absorbed into the new configuration, leaving the system in a stable, negative feedback state. Non-linear systems have in general several stable states, and this number tends to increase" (bifurcate) as an increasing input of energy pushes the system farther from its thermodynamic equilibrium." (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"Deep in the human nature there is an almost irresistible tendency to concentrate physical and mental energy on attempts at solving problems that seem to be unsolvable." (Ragnar Frisch, "From Utopian Theory to Practical Applications", [Nobel lecture] 1970)

"Questions are the engines of intellect, the cerebral machines which convert energy to motion, and curiosity to controlled inquiry." (David H Fischer, "Historians’ Fallacies", 1970)

"Self-organization can be defined as the spontaneous creation of a globally coherent pattern out of local interactions. Because of its distributed character, this organization tends to be robust, resisting perturbations. The dynamics of a self-organizing system is typically non-linear, because of circular or feedback relations between the components. Positive feedback leads to an explosive growth, which ends when all components have been absorbed into the new configuration, leaving the system in a stable, negative feedback state. Non-linear systems have in general several stable states, and this number tends to increase" (bifurcate) as an increasing input of energy pushes the system farther from its thermodynamic equilibrium." (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"When we know that a physical system is in equilibrium, know the environment, and know the molecular constitution, we are still very far from knowing the quantum-mechanical state that should be used to describe the system. We may conclude that the state should be one of the energy eigenstates, but which of many is still an open question. A statistical description is the best we can hope to achieve. If we supplement our knowledge with information enabling us to force an expectation value calculation of the energy to yield a specified numerical value, we are certainly better off. Nonetheless, this addition still leaves us without a determination of the probability distribution." (Ralph Baierlein, "Atoms and Information Theory: An Introduction to Statistical Mechanics", 1971)

"In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)

"But metaphor is an indispensable tool of thought and expression - a characteristic of all human communication, even of that of the scientist. The conceptual models of cybernetics and the energy theories of psycho-analysis are, after all, only labeled metaphors." (Gregory Bateson, "Steps to an Ecology of Mind", 1972)

"In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)

"What we mean by information - the elementary unit of information - is a difference which makes a difference, and it is able to make a difference because the neural pathways along which it travels and is continually transformed are themselves provided with energy. The pathways are ready to be triggered. We may even say that the question is already implicit in them." (Gregory Bateson, "Steps to an Ecology of Mind", 1972)

"When the phenomena of the universe are seen as linked together by cause-and-effect and energy transfer, the resulting picture is of complexly branching and interconnecting chains of causation. In certain regions of this universe" (notably organisms in environments, ecosystems, thermostats, steam engines with governors, societies, computers, and the like), these chains of causation form circuits which are closed in the sense that causal interconnection can be traced around the circuit and back through whatever position was" (arbitrarily) chosen as the starting point of the description. In such a circuit, evidently, events at any position in the circuit may be expected to have effect at all positions on the circuit at later times." (Gregory Bateson, "Steps to an Ecology of Mind", 1972)

"The universe is full of matter and force. Yet in all that force, amongst all the bulks and gravities, the rains of cosmic light, the bombardment of energy - how little spirit, how small the decimal points of intelligence." (Ray Bradbury et al, "Mars and the Mind of Man", 1973)

"In order to describe meanders, then, we can invoke a model involving scour and centrifugal force, a model that describes the uniform expenditure of energy, or a model based on probability theory. All three models describe the same phenomenon. As far as meanders are concerned, all three models happen to be interrelated - but not out of any fundamental necessity. That is to say, the cross circulation induced by centrifugal force need not necessarily result in a uniform distribution of effort or produce a path that is especially probable. In a world of limited patterns, however, the meander answers several entirely different sets of specifications, so that scour, uniform effort, and probability produce the same design." (Peter B Stevens, "Patterns in Nature", 1974)

"Life, this anti-entropy, ceaselessly reloaded with energy, is a climbing force, toward order amidst chaos, toward light, among the darkness of the indefinite, toward the mystic dream of Love, between the fire which devours itself and the silence of the Cold. Such a Nature does not accept abdication, nor skepticism." (Albert Claude, [Nobel lecture for award received] 1974)

"The analysis of turbulence in terms of probability reveals several interesting things about eddies. For instance, the average eddy moves a distance about equal to its own diameter before it generates small eddies that move, more often than not, in the opposite direction. Those smaller eddies generate still smaller eddies and the process continues until all the energy dissipates as heat through molecular motion." (Peter B Stevens, "Patterns in Nature", 1974)

"There is a distinction between physically embodied machines, whose ultimate function is to transduce energy or deliver power, and abstract machines. i.e., machines that exist only as ideas. The laws which the former embody must be a subset of the laws that govern the real world. The laws that govern the behavior of abstract machines are not necessarily so constrained. One may, for example, design an abstract machine whose internal signals are propagated among its components at speeds greater than the speed of light, in clear violation of physical law. The fact that such a machine cannot actually be built does not prohibit the exploration of its behavior." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"The social dynamics of human history, even more than that of biological evolution, illustrate the fundamental principle of ecological evolution - that everything depends on everything else. The nine elements that we have described in societal evolution of the three families of phenotypes - the phyla of things, organizations and people, the genetic bases in knowledge operating through energy and materials to produce phenotypes, and the three bonding relations of threat, integration and exchange - all interact on each other." (Kenneth E Boulding, "Ecodynamics: A New Theory Of Societal Evolution", 1978)

"Every subatomic interaction consists of the annihilation of the original particles and the creation of new subatomic particles. The subatomic world is a continual dance of creation and annihilation, of mass changing into energy and energy changing into mass. Transient forms sparkle in and out of existence, creating a never-ending, forever newly created reality." (Gary Zukav, "The Dancing Wu Li Masters", 1979)

"The interaction between parts of mind is triggered by difference, and difference is a nonsubstantial phenomenon not located in space or time; difference is related to negentropy and entropy rather than energy." (Gregory Bateson, "Mind and Nature: A Necessary Unity", 1979)

"Thus, an increase in entropy means a decrease in our ability to change thermal energy, the energy of heat, into mechanical energy. An increase of entropy means a decrease of available energy. " (John R Pierce, "An Introduction to Information Theory: Symbols, Signals and Noise", 1979)

On Energy (1960-1969)

"Science is usually understood to depict a universe of strict order and lawfulness, of rigorous economy - one whose currency is energy, convertible against a service charge into a growing common pool called entropy." (Paul A Weiss,"Organic Form: Scientific and Aesthetic Aspects", 1960)

"Entropy is a measure of the heat energy in a substance that has been lost and is no longer available for work. It is a measure of the deterioration of a system." (William B Sill & Norman Hoss" (Eds.), "Popular Science Encyclopedia of the Sciences", 1963)

"'Conservation' (the conservation law) means this […] that there is a number, which you can calculate, at one moment - and as nature undergoes its multitude of changes, this number doesn't change. That is, if you calculate again, this quantity, it'll be the same as it was before. An example is the conservation of energy: there's a quantity that you can calculate according to a certain rule, and it comes out the same answer after, no matter what happens, happens." (Richard P. Feynman, "The Great Conservation Principles", The Messenger Series of Lectures No. 3, Cornell University, 1964) 

"Social organizations are flagrantly open systems in that the input of energies and the conversion of output into further energy input consists of transactions between the organization and its environment." (Daniel Katz, "The motivational basis of organizational behavior", 1964)

"They [archetypes] are, at the same time, both images and emotions. One can speak of an archetype only when these two aspects are simultaneous. When there is merely the image, then there is simply a word picture of little consequence. But by being charged with emotion, the image gains numinosity" (or psychic energy); it becomes dynamic, and consequences of some kind must flow from it." (Carl G Jung,"Man and His Symbols", 1964)

"By squandering nuclear energy, polluting asteroids and planets, ravaging the Preserve, and leaving litter everywhere we go, we shall ruin outer space and turn it into one big dump. It is high time we came to our senses and enforced the laws. Convinced that every minute of delay is dangerous, I sound the alarm: Let us save the Universe." (Stanislaw Lem, "Let Us Save the Universe (An Open Letter from Ijon Tichy, Space Traveller", 1966)

"Higher, directed forms of energy" (e.g., mechanical, electric, chemical) are dissipated, that is, progressively converted into the lowest form of energy, i.e., undirected heat movement of molecules; chemical systems tend toward equilibria with maximum entropy; machines wear out owing to friction; in communication channels, information can only be lost by conversion of messages into noise but not vice versa, and so forth." (Ludwig von Bertalanffy, "Robots, Men and Minds", 1967)

"The general notion in communication theory is that of information. In many cases, the flow of information corresponds to a flow of energy, e. g. if light waves emitted by some objects reach the eye or a photoelectric cell, elicit some reaction of the organism or some machinery, and thus convey information." (Ludwig von Bertalanffy, "General System Theory", 1968)

On Energy (1950-1959)

"It is my thesis that the physical functioning of the living individual and the operation of some of the newer communication machines are precisely parallel in their analogous attempts to control entropy through feedback. Both of them have sensory receptors as one stage of their cycle of operation: that is, in both of them there exists a special apparatus for collecting information from the outer world at low energy levels, and for making it available in the operation of the individual or of the machine. In both cases these external messages are not taken neat, but through the internal transforming powers of the apparatus, whether it be alive or dead. The information is then turned into a new form available for the further stages of performance. In both the animal and the machine this performance is made to be effective on the outer world. In both of them, their performed action on the outer world, and not merely their intended action, is reported back to the central regulatory apparatus." (Norbert Wiener, "The Human Use of Human Beings", 1950)

"To seek not for end but for antecedents is the way of the physicist, who finds causes" in what he has learned to recognise as fundamental properties, or inseparable concomitants, or unchanging laws, of matter and of energy." (Sir D’Arcy W Thompson, "On Growth and Form", 1951)

"The 'cybernetics' of Wiener […] is the science of organization of mechanical and electrical components for stability and purposeful actions. A distinguishing feature of this new science is the total absence of considerations of energy, heat, and efficiency, which are so important in other natural sciences. In fact, the primary concern of cybernetics is on the qualitative aspects of the interrelations among the various components of a system and the synthetic behavior of the complete mechanism." (Qian Xuesen, "Engineering Cybernetics", 1954)

"The 'cybernetics' of Wiener […] is the science of organization of mechanical and electrical components for stability and purposeful actions. A distinguishing feature of this new science is the total absence of considerations of energy, heat, and efficiency, which are so important in other natural sciences. In fact, the primary concern of cybernetics is on the qualitative aspects of the interrelations among the various components of a system and the synthetic behavior of the complete mechanism." (Qian Xuesen, "Engineering Cybernetics", 1954)

"A variety of natural phenomena exhibit what is called the minimum principle. The principle is displayed where the amount of energy expended in performing a given action is the least required for its execution, where the path of a particle or wave in moving from one point to another is the shortest possible, where a motion is completed in the shortest possible time, and so on." (James R Newman, "The World of Mathematics" Vol. II, 1956)

"Cybernetics might, in fact, be defined as the study of systems that are open to energy but closed to information and control-systems that are 'information-tight'." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"In conventional statistical mechanics the energy plays a preferred role among all dynamical quantities because it is conserved both in the time development of isolated systems and in the interaction of different systems. Since, however, the principles of maximum-entropy inference are independent of any physical properties, it appears that in subjective statistical mechanics all measurable quantities may be treated on the same basis, subject to certain precautions." (Edwin T Jaynes, "Information Theory and Statistical Mechanics" I, 1956)

"But in addition to what we decide to do by way of transformation, there are certain tendencies in the way systems behave of their own volition when left to their own devices. The convenient analogy for one of these processes is found in the second law of thermodynamics: an 'ordering' process goes on, for which the name is entropy. This can be explained without technicalities as the tendency of a system to settle down to a uniform distribution of its energy. The dissipation of local pockets of high energy is measured by an increase in entropy, until at maximum entropy all is uniform. According to this model, order is more 'natural' than chaos. This is the reason why it is convenient to discuss cybernetic systems, with their self-regulating tendency to attain stability or orderliness, in terms of entropy - a term which has been taken over to name a key tool of cybernetics." (Stafford Beer, "Cybernetics and Management", 1959)

On Energy (1920-1929)

"For a modern ruler the laws of conservation and transformation of energy, when the vivifing stream takes its source, the ways it wends its course in nature, and how, under wisdom and knowledge, it may be intertwined with human destiny, instead of careering headlong to the ocean, are a study at least as pregnant with consequences to life as any lesson taught by the long unscientific history of man." (Frederick Soddy, "Science and Life", 1920)

"The history of man is dominated by, and reflects, the amount of available energy." (Frederick Soddy, "Science and Life", 1920)

"Revolution is everywhere, in everything. It is infinite. There is no final revolution, no final number. The social revolution is only one of an infinite number of numbers; the law of revolution is not a social law, but an immeasurably greater one. It is a cosmic, universal law - like the laws of the conservation of energy and of the dissipation of energy (entropy)." (Yevgeny Zamiatin, "On Literature, Revolution, Entropy, and Other Matters", 1923)

"Revolution is everywhere, in everything. It is infinite. There is no final revolution, no final number. The social revolution is only one of an infinite number of numbers; the law of revolution is not a social law, but an immeasurably greater one. It is a cosmic, universal law - like the laws of the conservation of energy and of the dissipation of energy" (entropy)." (Yevgeny Zamiatin, "On Literature, Revolution, Entropy, and Other Matters", 1923)

"[Ignorance] of the principle of conservation of energy […] does not prevent inventors without background from continually putting forward perpetual motion machines… Also, such persons undoubtedly have their exact counterparts in the fields of art, finance, education, and all other departments of human activity […] persons who are unwilling to take the time and to make the effort required to find what the known facts are before they become the champions of unsupported opinions - people who take sides first and look up facts afterward when the tendency to distort the facts to conform to the opinions has become well-nigh irresistible." (Robert A Millikan, "Evolution in Science and Religion", 1927) 

"In classical science, it was strange to find that action [...] should yet present the artificial aspect of an energy in space multiplied by a duration. As soon, however, as we realise that the fundamental continuum of the universe is one of space-time and not one of separate space and time, the reason for the importance of the seemingly artificial combination of space with time in the expression for the action receives a very simple explanation. Henceforth, action is no longer energy in a volume of space multiplied by a duration; it is simply energy in a volume of the world, that is to say, in a volume of four-dimensional space-time." (Aram D'Abro, "The Evolution of Scientific Thought from Newton to Einstein", 1927)

"An 'empty world', i. e., a homogeneous manifold at all points at which equations" (1) are satisfied, has, according to the theory, a constant Riemann curvature, and any deviation from this fundamental solution is to be directly attributed to the influence of matter or energy." (Howard P. Robertson, "On Relativistic Cosmology", 1928)

"Social organizations are flagrantly open systems in that the input of energies and the conversion of output into further energy input consists of transactions between the organization and its environment." (Daniel Katz, "The Social Psychology of Organizations", 1929)

On Energy (1900-1909)

"After seeking in vain for the construction of a perpetual motion machine, the relations were investigated which must subsist between the forces of nature if such a machine is to be impossible; and this inverted question led to the discovery of the law of the conservation of energy, which, again, explained the impossibility of perpetual motion in the sense originally intended." (David Hilbert, "Mathematische Probleme", [lecture opening] 1900)

"[...] there is a universal principle, operating in every department of nature and at every stage of evolution, which is conservative, creative and constructive. [...] I have at last fixed upon the word synergy, as the term best adapted to express its twofold character of ‘energy’ and ‘mutuality’ or the systematic and organic ‘working together’ of the antithetical forces of nature. [...] Synergy is a synthesis of work, or synthetic work, and this is what is everywhere taking place. It may be said to begin with the primary atomic collision in which mass, motion, time, and space are involved, and to find its simplest expression in the formula for force, which implies a plurality of elements, and signifies an interaction of these elements." (Lester F Ward, "Pure Sociology", 1903)

"This compromise among the contending forces of nature was effected through organization and the formation of chemical systems, which are so many reservoirs of power, this power being represented by what we call the properties of matter. These systems store up energy and expend it in work, but the work is always a collaboration or cooperation of all the competing forces involved. It is synergy." (Lester F Ward, "Pure Sociology", 1903)

"By laying down the relativity postulate from the outset, sufficient means have been created for deducing henceforth the complete series of Laws of Mechanics from the principle of conservation of energy" (and statements concerning the form of the energy) alone." (Hermann Minkowski, "The Fundamental Equations for Electromagnetic Processes in Moving Bodies", 1907)

"When we study the structure of the atom, we shall arrive at the conclusion that it is an immense reservoir of energy solely constituted by a system of imponderable elements maintained in equilibrium by the rotations, attractions and repulsions of its component parts." (Gustave Le Bon, "The Evolution of Matter", 1907)

"The motive for the study of mathematics is insight into the nature of the universe. Stars and strata, heat and electricity, the laws and processes of becoming and being, incorporate mathematical truths. If language imitates the voice of the Creator, revealing His heart, mathematics discloses His intellect, repeating the story of how things came into being. And the value of mathematics, appealing as it does to our energy and to our honor, to our desire to know the truth and thereby to live as of right in the household of God, is that it establishes us in larger and larger certainties. As literature develops emotion, understanding, and sympathy, so mathematics develops observation, imagination, and reason." (William E Chancellor,"A Theory of Motives, Ideals and Values in Education" 1907)