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

"Above them Phileas Fogg moved in majestic indifference. He was following his own rational orbit around the world, without bothering at all about the asteroids gravitating around him." (Jules Verne, "Around the World in Eighty Days", 1873)

"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." (H P Lovecraft, "Celephais", 1922)

"Earth - it was a place where you could stop being afraid, a place where fear of suffocation was not, where fear of blowout was not, where nobody went berserk with the chokers or dreamed of poisoned air or worried about shorthorn cancer or burn blindness or meteorite dust or low-gravity muscular atrophy. A place where there was wind to blow your sweat away." (Walter M Miller Jr, "The Lineman", 1957)

"We’re free out here, really free for the first time. We’re floating, literally. Gravity can’t bow our backs or break our arches or tame our ideas. You know, it’s only out here that stupid people like us can really think. The weightlessness gets our thoughts and we can sort them. Ideas grow out here like nowhere else - it’s the right environment for them. Anyone can get into space, if he wants to hard enough. The ticket is a dream." (Fritz Leiber," The Beat Cluster", 1961)

"His vessel found itself between two vortices of gravitation called Bakhrida and Scintilla; Bakhrida speeds up time, Scintilla on the other hand slows it down, and between them lies a zone of stagnation, in which the present, becalmed, flows neither backward nor forward. There Heptodius froze alive, and remains to this day, along with the countless frigates and galleons of other astromariners, pirates, and spaceswashers, not aging in the least, suspended in the silence and excruciating boredom that is Eternity." (Stanislaw Lem, "How Erg the Self-Inducing Slew a Paleface", 1965)

"Every so often some idiot tries to abolish marriage. Such attempts work as well as repealing the law of gravity, making pi equal to three point zero, or moving mountains by prayer. Marriage is not something thought up by priests and inflicted on mankind; marriage is as much a part of mankind’s evolutionary equipment as his eyes, and as useful to the race as eyes are to an individual." (Robert A Heinlein, "Time Enough for Love", 1973)

"The force of gravity-though it is the first force with which we are acquainted, and though it is always with us, and though it is the one with a strength we most thoroughly appreciate-is by far the weakest known force in nature. It is first and rearmost." (Isaac Asimov, 1976)

"A rocket is the most lavishly expensive transportation ever invented. In a typical rocketship mission half the effort is spent fighting gravity to go up and the other half is spent fighting gravity in letting down - as crashing is considered an unsatisfactory end to a mission." (Robert A Heinlein, "The Cat Who Walks through Walls", 1985)

"Belief is a force. It’s a weak force, by comparison with gravity; when it comes to moving mountains, gravity wins every time. But it still exists." (Terry Pratchett, "Pyramids", 1989)

"Of all the forces in the universe, the hardest to overcome is the force of habit. Gravity is easy-peasy by comparison." (Terry Pratchett, "Johnny and the Dead", 1993)

On Physics: On Gravity (1850-1899)

"It is no valid objection that science as yet throws no light on the far higher problem of the essence or origin of life. Who can explain gravity? No one now objects to following out the results consequent on this unknown element of attraction" (Charles Darwin, "The Origin of Species", 1859)

"Newton's law is nothing but the statistics of gravitation, it has no power whatever. Let us get rid of the idea of power from law altogether. Call law tabulation of facts, expression of facts, or what you will; anything rather than suppose that it either explains or compels."(Florence Nightingale, "Suggestions for Thought", 1860)

"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)

"Economic laws are statements with regard to the tendencies of man's action under certain conditions. They are hypothetical only in the same sense as are the laws of the physical sciences: for those laws also contain or imply conditions. But there is more difficulty in making the conditions clear, and more danger in any failure to do so, in economics than in physics. The laws of human action are not indeed as simple, as definite or as clearly ascertainable as the law of gravitation; but many of them may rank with the laws of those natural sciences which deal with complex subject-matter." (Alfred Marshall, "Principles of Economics", 1890)

"Everything in physical science, from the law of gravitation to the building of bridges, from the spectroscope to the art of navigation, would be profoundly modified by any considerable inaccuracy in the hypothesis that our actual space is Euclidean. The observed truth of physical science, therefore, constitutes overwhelming empirical evidence that this hypothesis is very approximately correct, even if not rigidly true." (Bertrand Russell, "Foundations of Geometry", 1897)

On Physics: On Gravity (1925-1949)

"The essence of Riemann's discoveries consists in having shown that there exist a vast number of possible types of spaces, all of them perfectly self-consistent. When, therefore, it comes to deciding which one of these possible spaces real space will turn out to be, we cannot prejudge [...] Experiment and observation alone can yield us a clue. To a first approximation, experiment and observation prove space to be Euclidean, and this accounts for our natural belief [...] merely by force of habit. But experiment is necessarily innacurate, and we cannot foretell whether our opinions will not have to be modified when our experiments are conducted with greater accuracy. Riemann's views thus place the problem of space on an empirical basis excluding all a priori assertions on the subject [...] the relativity theory is very intimately connected with this empirical philosophy; for. [...] Einstein is compelled to appeal to a varying non-Euclideanism of four-dimensional space-time in order to account with extreme simplicity for gravitation. [...] had the extension of the universe been restricted on a priori grounds [...] to three dimensional Euclidean space, Einstein's theory would have been rejected on first principles. [...] as soon as we recognise that the fundamental continuum of the universe and its geometry cannot be posited a priori [...] a vast number of possibilities are thrown open. Among these the four-dimensional space-time of relativity, with its varying degrees of non-Euclideanism, finds a ready place." (Aram D'Abro,  "The Evolution of Scientific Thought from Newton to Einstein", [Forward] 1927)

"Light-waves in passing a massive body such as the sun are deflected through a small angle. This is additional evidence that the Newtonian picture of gravitation as a tug is inadequate. You cannot deflect waves by tugging at them, and clearly another representation of the agency which deflects them must be found." (Arthur Eddington, "The Nature of the Physical World", 1928)

"The force acting on the pendulum is proportional to its active mass, its inertia is proportional to its passive mass, so that the period will depend on the ratio of the passive and the active mass. Consequently the fact that the period of all these different pendulums was the same, proves that this ratio is a constant, and can be made equal to unity by a suitable choice of units, i. e., the inertial and the gravitational mass are the same." (Willem de Sitter, "The Astronomical Aspect of the Theory of Relativity", 1933)

"In electromagnetism [...] the law of the inverse square had been supreme, but, as a consequence of the work of Faraday and Maxwell, it was superseded by the field. And the same change took place in the theory of gravitation. By and by the material particles, electrically charged bodies, and magnets which are the things that we actually observe come to be looked upon only as 'singularities' in the field. So far this transformation from the force to the potential, from the action at a distance to the field, is only a purely mathematical operation." (Willem de Sitter,"Kosmos", 1932)

"Two points should be specially emphasized in connection with the general theory of relativity. First, it is a purely physical theory, invented to explain empirical physical facts, especially the identity of gravitational and inertial mass, and to coordinate and harmonize different chapters of physical theory, especially mechanics and electromagnetic theory. It has nothing metaphysical about it. Its importance from a metaphysical or philosophical point of view is that it aids us to distinguish in the observed phenomena what is absolute, or due to the reality behind the phenomena, from what is relative, i.e. due to the observer.S econd, it is a pure generalization, or abstraction, like Newton's system of mechanics and law of gravitation. It contains no hypothesis, as contrasted with the atomic theory or the theory of quanta, which are based on hypothesis. It may be considered as the logical sequence and completion of Newton's Principia. The science of mechanics was founded by Archimedes, who had a clear conception of the relativity of motion, and may be called the first relativist. Galileo, who was inspired by the reading of the works of Archimedes, took the subject up where his great predecessor had left it. His fundamental discovery is the law of inertia, which is the backbone of Newton's classical system of mechanics, and retains the same central position in Einstein's relativistic system. Thus one continuous line of thought can be traced through the development of our insight into the mechanical processes of nature... characterized by the sequence [...] Archimedes, Galileo, Newton, Einstein." (Willem de Sitter, "The Astronomical Aspect of the Theory of Relativity", 1933)

"There are necessities and impossibilities in reality which do not obtain in fiction, any more than the law of gravity to which we are subject controls what is represented in a picture. [...] It is the same with pure good; for a necessity as strong as gravity condemns man to evil and forbids him any good, or only within the narrowest limits and laboriously obtained and soiled and adulterated with evil. [...] The simplicity which makes the fictional good something insipid and unable to hold the attention becomes, in the real good, an unfathomable marvel." (Simone Weil, "Morality and Literature", cca. 1941)

"Any region of space-time that has no gravitating mass in its vicinity is uncurved, so that the geodesics here are straight lines, which means that particles move in straight courses at uniform speeds (Newton's first law). But the world-lines of planets, comets and terrestrial projectiles are geodesics in a region of space-time which is curved by the proximity of the sun or earth. […] No force of gravitation is […] needed to impress curvature on world-lines; the curvature is inherent in the space […]" (James H Jeans," The Growth of Physical Science", 1947)

"The first forces brought into mathematical formulation were gravitational forces, as seen in planetary motion. Next were elastic forces. Then followed electric and magnetic forces... Their [electric and magnetic forces] study was mostly a product of the nineteenth century. [...] electromagnetic forces are of a far wider application than was first supposed. It has become evident that, instead of being active only in electrostatic and electromagnetic applications such as the telegraph, dynamo, and radio, the forces between the nuclei and electrons of single atoms, the chemical forces between atoms and molecules, the forces of cohesion and elasticity holding solids together, are all of an electric nature. [...] electromagnetic theory [...] carries us rather far into the structure of matter [...] The equations underlying the theory, Maxwell's equations, are relatively simple, but not nearly so simple as Newton's Newton's laws of motion." (John C Slater & Nathaniel H Frank, "Electromagnetism", 1947)

"Although the Special Theory of Relativity does not account for electromagnetic phenomena, it explains many of their properties. General Relativity, however, tells us nothing about electromagnetism. In Einstein's space-time continuum gravitational forces are absorbed in the geometry, but the electromagnetic forces are quite unaffected. Various attempts have been made to generate the geometry of space-time so as to produce a unified field theory incorporating both gravitational and electromagnetic forces." (Gerald J Whitrow, "The Structure of the Universe: An Introduction to Cosmology", 1949)

On Physics: On Gravity (2010-)

"Starting with Einstein’s general relativity, differential geometry has started playing a major role in physics. General relativity describes the gravitational fields as a metric property of the spacetime manifold. More precisely, spacetime (i.e., the manifold the points of which are events; we may intuitively say that an event is ‘something that happens in a given point in space at a certain time’) is supposed to be endowed with a Lorentzian metric. This means that spacetime has pointwise the same structure as the Minkowski space of special relativity but in general is not flat, as on the contrary Minkowski space is. Indeed, out of the metric tensor one can construct another tensor field, the curvature field, which measures how far the geometry of spacetime is from that of a flat space. The celebrated Einstein equations prescribe how the matter in our universe determines the curvature of spacetime, and in turn the curvature determines how matter (particles, light rays, extended bodies…) moves." (Claudio Bartocci & Ugo Bruzzo, [Claudio Bartocci et al (Eds), "New Trends in Geometry: Their tole in the natural and social sciences"], 2011)

"The Newtonian universe is material in the sense that the world was viewed as being made up of stuff - tangible, real objects. It was argued that even forces like gravity that appear to act across empty stretches of space are conveyed by tiny particles, or corpuscles. Moreover, since the universe is material, its behavior can be predicted or understood. Things are they way they are for a reason or a cause. The Newtonian world is mathematical, in that it was viewed that the regularities or laws that describe or govern the world are mathematical in nature." (David P Feldman,"Chaos and Fractals: An Elementary Introduction", 2012)

"[…] there’s atomic physics - electrons and protons and neutrons, all the stuff of which atoms are made. At these very, very, very small scales, the laws of physics are much the same, but there is also a force you ignore, which is the gravitational force. Gravity is present everywhere because it comes from the entire mass of the universe. It doesn’t cancel itself out, it doesn’t have positive or negative value, it all adds up." (Michael F Atiyah, [interview] 2013)

"The most familiar manifold, however, is the space-time manifold, which has 4 dimensions. It is described by a time coordinate and three spatial coordinates. In addition to being a differentiable manifold, space-time has much more additional structure. It is at the level of this additional structure, which will be the subject of later chapters, that the space-time of Newtonian physics differs from the space-time of special relativity and from the space-times of Einstein’s theory of gravity (also called general relativity)." (José G Vargas, "Differential Geometry for Physicists and Mathematicians: Moving frames and differential forms from Euclid past Riemann", 2014)

"String theory today looks almost fractal. The more closely people explore any one corner, the more structure they find. Some dig deep into particular crevices; others zoom out to try to make sense of grander patterns. The upshot is that string theory today includes much that no longer seems stringy. Those tiny loops of string whose harmonics were thought to breathe form into every particle and force known to nature (including elusive gravity) hardly even appear anymore on chalkboards at conferences." (K C Cole, "The Strange Second Life of String Theory", Quanta Magazine", 2016) [source]

"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)

"[...] one thing that's worth mentioning, though, it that apart from the dream of understanding physics at a deeper level involving gravity, work in string theory has been useful in shedding lights on more conventional problems in quantum field theory and even in condensed matter physics and as well with applications to mathematics. Apart from its intrinsic interest, those successes are one of the things that tend to give us confidence that we're on the right track. Because, speaking personally, I find it implausible that a completely wrong new physics theory would give rise to useful insights about so many different areas." (Edward Witten, [in "Dirac Conversation: Edward Witten". Interview at Int'l Center for Theoretical Physics], 2024) [source] 

On Physics: On Gravity (1950-1999)

"As soon as matter took over, the force of Newtonian gravity, which represents one of the most important characteristics of 'ponderable' matter, came into play." (George Gamow, "Conclusion of The Creation of the Universe", 1952)

"The second law of thermodynamics is, without a doubt, one of the most perfect laws in physics. Any reproducible violation of it, however small, would bring the discoverer great riches as well as a trip to Stockholm. The world’s energy problems would be solved at one stroke. […] Not even Maxwell’s laws of electricity or Newton’s law of gravitation are so sacrosanct, for each has measurable corrections coming from quantum effects or general relativity. The law has caught the attention of poets and philosophers and has been called the greatest scientific achievement of the nineteenth century." (Ivan P. Bazarov, "Thermodynamics", 1964)

"The force of gravity - though it is the first force with which we are acquainted, and though it is always with us, and though it is the one with a strength we most thoroughly appreciate - is by far the weakest known force in nature. It is first and rearmost." (Isaac Asimov, "Asimov On Physics", 1976)

"So much of science consists of things we can never see: light ‘waves’ and charged ‘particles’; magnetic ‘fields’ and gravitational ‘forces’; quantum ‘jumps’ and electron ‘orbits’. In fact, none of these phenomena is literally what we say it is. Light waves do not undulate through empty space in the same way that water waves ripple over a still pond; a field is only a mathematical description of the strength and direction of a force; an atom does not literally jump from one quantum state to another, and electrons do not really travel around the atomic nucleus in orbits. The words we use are merely metaphors." (K C Cole, "On Imagining the Unseeable", Discover Magazine, 1982)

"Electromagnetic fields [...] are neither charged nor magnetized and thus cannot contribute to their own source. The general theory does reveal a new feature of electromagnetic fields... Since they have energy, they produce gravitational effects and thus affect the structure of space-time, which, in turn, means that an electromagnetic field can affect the motion of non-charged matter." (Nancy Nersessian, "Faraday to Einstein: Constructing Meaning in Scientific Theories", 1984)

"Until now, physical theories have been regarded as merely models with approximately describe the reality of nature. As the models improve, so the fit between theory and reality gets closer. Some physicists are now claiming that supergravity is the reality, that the model and the real world are in mathematically perfect accord." (Paul C W Davies, "Superforce", 1984)

"For the advancing army of physics, battling for many a decade with heat and sound, fields and particles, gravitation and spacetime geometry, the cavalry of mathematics, galloping out ahead, provided what it thought to be the rationale for the natural number system. Encounter with the quantum has taught us, however, that we acquire our knowledge in bits; that the continuum is forever beyond our reach. Yet for daily work the concept of the continuum has been and will continue to be as indispensable for physics as it is for mathematics." (John A Wheeler, "Hermann Weyl and the Unity of Knowledge", American Scientist Vol. 74, 1986)

"In deterministic geometry, structures are defined, communicated, and analysed, with the aid of elementary transformations such as affine transfor- transformations, scalings, rotations, and congruences. A fractal set generally contains infinitely many points whose organization is so complicated that it is not possible to describe the set by specifying directly where each point in it lies. Instead, the set may be defined by "the relations between the pieces." It is rather like describing the solar system by quoting the law of gravitation and stating the initial conditions. Everything follows from that. It appears always to be better to describe in terms of relationships." (Michael Barnsley, "Fractals Everwhere", 1988)

"To build matter itself from geometry - that in a sense is what string theory does. It can be thought of that way, especially in a theory like the heterotic string which is inherently a theory of gravity in which the particles of matter as well as the other forces of nature emerge in the same way that gravity emerges from geometry. Einstein would have been pleased with this, at least with the goal, if not the realization. [...] He would have liked the fact that there is an underlying geometrical principle - which, unfortunately, we don’t really yet understand." (David Gross, [interview] 1988)

"In contrast to gravitation, interatomic forces are typically modeled as inhomogeneous power laws with at least two different exponents. Such laws (and exponential laws, too) are not scale-free; they necessarily introduce a characteristic length, related to the size of the atoms. Power laws also govern the power spectra of all kinds of noises, most intriguing among them the ubiquitous (but sometimes difficult to explain)." (Manfred Schroeder, "Fractals, Chaos, Power Laws Minutes from an Infinite Paradise", 1990)

"Scaling invariance results from the fact that homogeneous power laws lack natural scales; they do not harbor a characteristic unit (such as a unit length, a unit time, or a unit mass). Such laws are therefore also said to be scale-free or, somewhat paradoxically, 'true on all scales'. Of course, this is strictly true only for our mathematical models. A real spring will not expand linearly on all scales; it will eventually break, at some characteristic dilation length. And even Newton's law of gravitation, once properly quantized, will no doubt sprout a characteristic length." (Manfred Schroeder, "Fractals, Chaos, Power Laws Minutes from an Infinite Paradise", 1990)

"In practice, the intelligibility of the world amounts to the fact that we find it to be algorithmically compressible. We can replace sequences of facts and observational data by abbreviated statements which contain the same information content. These abbreviations we often call 'laws of Nature.' If the world were not algorithmically compressible, then there would exist no simple laws of nature. Instead of using the law of gravitation to compute the orbits of the planets at whatever time in history we want to know them, we would have to keep precise records of the positions of the planets at all past times; yet this would still not help us one iota in predicting where they would be at any time in the future. This world is potentially and actually intelligible because at some level it is extensively algorithmically compressible. At root, this is why mathematics can work as a description of the physical world. It is the most expedient language that we have found in which to express those algorithmic compressions." (John D Barrow, "New Theories of Everything", 1991)

"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)

"The Feynman method has the virtue that it provides us with a vivid picture of nature’s quantum trickery at work. The idea is that the path of a particle through space is not generally well defined in quantum mechanics. […] So when an electron arrives at a point in space - say a target screen - many different histories must be integrated together to create this one event. Feynman’s so-called path-integral, or sum-over-histories approach to quantum mechanics, set this remarkable concept out as a mathematical procedure. It remained more or less a curiosity for many years, but as physicists pushed quantum mechanics to its limits - applying it to gravitation and even cosmology - so the Feynman approach turned out to offer the best calculational tool for describing a quantum universe. History may well judge that, among his many outstanding contributions to physics, the path-integral formulation of quantum mechanics is the most significant." (Paul Davies , [Introduction to Richard P Feynman's"Six Easy Pieces"] 1994)

"No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level. […] because any unified field theory first must absorb the Riemannian geometry of Einstein’s theory and the Lie groups coming from quantum field theory. […] The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity." (Michio Kaku, "Hyperspace", 1995)

"Riemann concluded that electricity, magnetism, and gravity are caused by the crumpling of our three-dimensional universe in the unseen fourth dimension. Thus a 'force' has no independent life of its own; it is only the apparent effect caused by the distortion of geometry. By introducing the fourth spatial dimension, Riemann accidentally stumbled on what would become one of the dominant themes in modern theoretical physics, that the laws of nature appear simple when expressed in higher-dimensional space. He then set about developing a mathematical language in which this idea could be expressed." (Michio Kaku, "Hyperspace", 1995)

"Much of what the universe had been, was, and would be, Newton had disclosed, was the outcome of an infinity of material particles all pulling on one another simultaneously. If the result of all that gravitational tussling had appeared to the Greeks to be a cosmos, it was simply because the underlying equation describing their behavior had itself turned out to be every bit a cosmos-orderly, beautiful, and decent." (Michael Guillen," Five Equations That Changed the World", 1995)

"The laws of Nature are based upon the existence of a pattern, linking one state of affairs to another; and where there is pattern, there is symmetry. Yet. [...] the symmetries that the laws enshrine are broken in [...] outcomes. Suppose that we balance a needle on its point and then release it. The law of gravity, which governs its subsequent motion, is perfectly democratic. It has no preference for any particular direction in the Universe: it is symmetrical in this respect. Yet, when the needle falls, it must fall in a particular direction. The directional symmetry of the underlying law is broken, therefore [...] By the same token, the fallen needle hides the symmetry of the law. [...] Such 'symmetry-breaking' governs much of what we see in the Universe... It allows a Universe governed by a small number of symmetrical laws to manifest an infinite diversity of complex, asymmetrical states. This is how the Universe can be at once, simple and complicated." (John D Barrow, "The Artful Universe", 1995)

"The problems associated with the initial singularity of the universe bring us to what is called the theory of everything. It is an all-encompassing theory that would completely explain me origin of the universe and everything in it. It would bring together general relativity and quantum mechanics, and explain everything there is to know about the elementary particles of the universe, and the four basic forces of nature (gravitational, electromagnetic, weak, and strong nuclear forces). Furthermore, it would explain the basic laws of nature and the fundamental constants of nature such as the speed of light and Planck's constant." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 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)

"Discovery of supersymmetry would be one of the real milestones in physics, made even more exciting by its close links to still more ambitious theoretical ideas. Indeed, supersymmetry is one of the basic requirements of 'string theory', which is the framework in which theoretical physicists have had some success in unifying gravity with the rest of the elementary particle forces. Discovery of supersymmetry would would certainly give string theory an enormous boost." (Edward Witten, [preface to (Gordon Kane, "Supersymmetry: Unveiling the Ultimate Laws of Nature", 2000)] 1999)

On Physics: On Gravity (1800-1849)

"The law of gravitation extends universally over all matter. The fixed stars obeying central forces move in orbits. The milky way comprehends several systems of fixed stars; those that appear out of the tract of the milky way form but one system which is our own. The sun being of the number of fixed stars, revolves round a centre like the rest. Each system has its centre, and several systems taken together have a common centre, Assemblages of their assemblages have likewise theirs. In fine, there is à universal centre for the whole world round which all things revolve." (Johann H Lambert, "The System of the World", 1800)

"Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom: to it nothing would be uncertain, and the future as the past would be present to its eyes. The human mind offers a feeble outline of that intelligence, in the perfection which it has given to astronomy. Its discoveries in mechanics and in geometry, joined to that of universal gravity, have enabled it to comprehend in the same analytical expressions the past and future states of the world system." (Pierre-Simon Laplace, "Analytical Theory of Probability", 1812)

"Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity." (Pierre-Simon Laplace, "Philosophical Essay on Probabilities”, 1814)

"Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy. Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics." (Jean-Baptiste-Joseph Fourier, "The Analytical Theory of Heat", 1822)

"In order that a pendulum may continue to make the same number of oscillations in a given time, it must be shortened as it is carried towards the equator; and the variation of its length in different latitudes affords an accurate measurement of the force of gravity. But the force of gravity has known relation to the figure of the earth, which, therefore, may be determined, by observing the length of the seconds pendulum at different points on its surface." (David Brewster, [in "The Edinburgh Encyclopaedia"] 1830) 

"Science and knowledge are subject, in their extension and increase, to laws quite opposite to those which regulate the material world. Unlike the forces of molecular attraction, which cease at sensible distances; or that of gravity, which decreases rapidly with the increasing distance from the point of its origin; the farther we advance from the origin of our knowledge, the larger it becomes, and the greater power it bestows upon its cultivators, to add new fields to its dominions." (Charles Babbage, "On the Economy of Machinery and Manufactures", 1832)

"It is a mathematical fact that the casting of this pebble from my hand alters the centre of gravity of the universe." (Thomas Carlyle, "Sartor Resartus", 1836)

"Gravity. Surely this force must be capable of an experimental relation to electricity, magnetism, and the other forces, so as to bind it up with them in reciprocal action and equivalent effect." (Michael Faraday, [Notebook entry] 1849) 

On Physics: On Gravity (2000-2009)

"In the language of mental models, such past experience provided the default assumptions necessary to fill the gaps in the emerging and necessarily incomplete framework of a relativistic theory of gravitation. It was precisely the nature of these default assumptions that allowed them to be discarded again in the light of novel information - provided, for instance, by the further elaboration of the mathematical formalism - without, however, having to abandon the underlying mental models which could thus continue to function as heuristic orientations." (Jürgen Renn, "Before the Riemann Tensor: The Emergence of Einstein’s Double Strategy", [in "The Universe of General Relativity"] 2000)

"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, "Loop Quantum Gravity", The New Humanists: Science at the Edge, 2003)

"It was found [in the 1970s], unexpectedly and without anyone really having a concept for it, that the rules of perturbation theory can be changed in a way that makes relativistic quantum gravity inevitable rather than impossible. The change is made by replacing point particles by strings. Then Feynman graphs are replaced by Riemann surfaces, which are smooth - unlike the graphs, which have singularities at interaction vertices. The Riemann surfaces can degenerate to graphs in many different ways. In field theory, the interactions occur at the vertices of a Feynman graph. By contrast, in string theory, the interaction is encoded globally, in the topology of a Riemann surface, any small piece of which is like any other. This is reminiscent of how non-linearities are encoded globally in twistor theory." (Edward Witten,"The Past and Future of String Theory", [in  W Gibbons et al, "The Future of Theoretical Physics and Cosmology: Celebrating Stephen Hawking's Contributions to Physics", 2003)

"General relativity explains gravitation as a curvature, or bending, or warping, of the geometry of space-time, produced by the presence of matter. Free fall in a space shuttle around Earth, where space is warped, produces weightlessness, and is equivalent from the observer's point of view to freely moving in empty space where there is no large massive body producing curvature. In free fall we move along a 'geodesic' in the curved space-time, which is essentially a straight-line motion over small distances. But it becomes a curved trajectory when viewed at large distances. This is what produces the closed elliptical orbits of planets, with tiny corrections that have been correctly predicted and measured. Planets in orbits are actually in free fall in a curved space-time!" (Leon M Lederman & Christopher T Hill, "Symmetry and the Beautiful Universe", 2004)

"Combine general relativity and quantum theory into a single theory that can claim to be the complete theory of nature. This is called the problem of quantum gravity." (Lee Smolin, "The Trouble with Physics: The Rise of String Theory, The Fall of a Science and What Comes Next", 2006)

"String theory was not invented to describe gravity; instead it originated in an attempt to describe the strong interactions, wherein mesons can be thought of as open strings with quarks at their ends. The fact that the theory automatically described closed strings as well, and that closed strings invariably produced gravitons and gravity, and that the resulting quantum theory of gravity was finite and consistent is one of the most appealing aspects of the theory." (David Gross, "Einstein and the Search for Unification", 2005)

"Mathematical theories have sometimes been used to predict phenomena that were not confirmed until years later. For example, Maxwell’s equations, named after physicist James Clerk Maxwell, predicted radio waves. Einstein’s field equations suggested that gravity would bend light and that the universe is expanding. Physicist Paul Dirac once noted that the abstract mathematics we study now gives us a glimpse of physics in the future. In fact, his equations predicted the existence of antimatter, which was subsequently discovered. Similarly, mathematician Nikolai Lobachevsky said that “there is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world." (Clifford A Pickover, "The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics", 2009)

"The concept of symmetry is used widely in physics. If the laws that determine relations between physical magnitudes and a change of these magnitudes in the course of time do not vary at the definite operations (transformations), they say, that these laws have symmetry (or they are invariant) with respect to the given transformations. For example, the law of gravitation is valid for any points of space, that is, this law is in variant with respect to the system of coordinates." (Alexey Stakhov et al, "The Mathematics of Harmony", 2009)

On Gravity (-1799)

"The weight of any heavy body of known weight at a particular distance from the center of the world varies according to the variation of its distance therefrom: so that as often as it is removed from the center, it becomes heavier, and when brought near to it, is lighter. On this account, the relation of gravity to gravity is as the relation of distance to distance from the center." (Al Khazini, "Book of the Balance of Wisdom", cca. 12th century)

"I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy." (Sir Isaac Newton, "Philosophiæ Naturalis Principia Mathematica" ["The Mathematical Principles of Natural Philosophy"], 1687)

"It is inconceivable, that inanimate brute matter should, without the mediation of something else, which is not material, operate upon and affect other matter without mutual contact [...]That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent, acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers." (Sir Isaac Newton, [letter to Bentley] 1693)

"And thus Nature will be very conformable to her self and very simple, performing all the great Motions of the heavenly Bodies by the Attraction of Gravity which intercedes those Bodies, and almost all the small ones of their Particles by some other attractive and repelling Powers which intercede the Particles. The Vis inertiae is a passive Principle by which Bodies persist in their Motion or Rest, receive Motion in proportion to the Force impressing it, and resist as much as they are resisted. By this Principle alone there never could have been any Motion in the World. Some other Principle was necessary for putting Bodies into Motion; and now they are in Motion, some other Principle is necessary for conserving the Motion." (Sir Isaac Newton, "Opticks", 1704)

"Moreover, force, gravity, and words of that kind, are often, and not unwisely, used in the concrete; in such a way that they know the movement of the body, the difficulty of resistance, etc. But when they are used by philosophers to signify certain natures, precise and abstract from all these, which are neither subject to the senses, nor can be understood by any power of the mind, nor can they be shaped by the imagination, they in turn give rise to errors and confusion." (George Berkeley, "De Motu", 1721)

"Especially when we investigate the general laws of Nature, induction has very great power; & there is scarcely any other method beside it for the discovery of these laws. By its assistance, even the ancient philosophers attributed to all bodies extension, figurability, mobility, & impenetrability; & to these properties, by the use of the same method of reasoning, most of the later philosophers add inertia & universal gravitation. Now, induction should take account of every single case that can possibly happen, before it can have the force of demonstration; such induction as this has no place in establishing the laws of Nature. But use is made of an induction of a less rigorous type ; in order that this kind of induction may be employed, it must be of such a nature that in all those cases particularly, which can be examined in a manner that is bound to lead to a definite conclusion as to whether or no the law in question is followed, in all of them the same result is arrived at; & that these cases are not merely a few. Moreover, in the other cases, if those which at first sight appeared to be contradictory, on further & more accurate investigation, can all of them be made to agree with the law; although, whether they can be made to agree in this way better than in any Other whatever, it is impossible to know directly anyhow. If such conditions obtain, then it must be considered that the induction is adapted to establishing the law." (Roger J Boscovich, "De Lege Continuitatis" ["On the law of continuity"], 1754)

On Gravity (1900-1924)

"There is not in Nature any system perfectly isolated, perfectly abstracted from all external action; but there are systems which are nearly isolated. If we observe such a system, we can study not only the relative motion of its different parts with respect to each other, but the motion of its centre of gravity with respect to the other parts of the universe." (Henri Poincaré, "Science and Hypothesis", 1902)

"In astronomy, the law of gravitation is plainly better worth knowing than the position of a particular planet on a particular night, or even on every night throughout a year. There are in the law a splendor and simplicity and sense of mastery which illuminate a mass of otherwise uninteresting details [...]" (Bertrand Russell, "On History,  Independent Review, 1904)

"The mathematical formula is the point through which all the light gained by science passes in order to be of use to practice; it is also the point in which all knowledge gained by practice, experiment, and observation must be concentrated before it can be scientifically grasped. The more distant and marked the point, the more concentrated will be the light coming from it, the more unmistakable the insight conveyed. All scientific thought, from the simple gravitation formula of Newton, through the more complicated formulae of physics and chemistry, the vaguer so called laws of organic and animated nature, down to the uncertain statements of psychology and the data of our social and historical knowledge, alike partakes of this characteristic, that it is an attempt to gather up the scattered rays of light, the different parts of knowledge, in a focus, from whence it can be again spread out and analyzed, according to the abstract processes of the thinking mind. But only when this can be done with a mathematical precision and accuracy is the image sharp and well-defined, and the deductions clear and unmistakable. As we descend from the mechanical, through the physical, chemical, and biological, to the mental, moral, and social sciences, the process of focalization becomes less and less perfect, - the sharp point, the focus, is replaced by a larger or smaller circle, the contours of the image become less and less distinct, and with the possible light which we gain there is mingled much darkness, the sources of many mistakes and errors. But the tendency of all scientific thought is toward clearer and clearer definition; it lies in the direction of a more and more extended use of mathematical measurements, of mathematical formulae." (John T Merz, "History of European Thought in the 19th Century" Vol. 1, 1904)

"If we turn to the problems to which the calculus owes its origin, we find that not merely, not even primarily, geometry, but every other branch of mathematical physics - astronomy, mechanics, hydrodynamics, elasticity, gravitation, and later electricity and magnetism - in its fundamental concepts and basal laws contributed to its development and that the new science became the direct product of these influences. [...] The calculus is the greatest aid we have to the appreciation of physical truth in the broadest sense of the word." (William Osgood,"The Calculus in Colleges in Colleges and Technical Schools", Bulletin of the American Mathematical Society, 1907)

"A new theory by the author has been added, which draws the physical inferences consequent on the extension of the foundations of geometry beyond Reimann... and represents an attempt to derive from world-geometry not only gravitational but also electromagnetic phenomena. Even if this theory is still only in its infant stage, I feel convinced that it contains no less truth than Einstein's Theory of Gravitation—whether this amount of truth is unlimited or, what is more probable, is bounded by the Quantum Theory." (Albert Einstein, "The Meaning of Relativity", 1922)

"When Faraday filled space with quivering lines of force, he was bringing mathematics into electricity. When Maxwell stated his famous laws about the electromagnetic field it was mathematics. The relativity theory of Einstein which makes gravity a fiction, and reduces the mechanics of the universe to geometry, is mathematical research." (James B Shaw, "The Spirit of Research", The Monist No. 4, 1922)

Lee Smolin - Collected Quotes

"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, "Loop Quantum Gravity", The New Humanists: Science at the Edge, 2003)

"Spacetime […] turns out to be discrete, described by a structure called spin foam." (Lee Smolin, “The New Humanists: Science at the Edge”, 2003)

"Neither space nor time has any existence outside the system of evolving relationships that comprises the universe. Physicists refer to this feature of general relativity as background independence."  (Lee Smolin, "Three Roads to Quantum Gravity", 2000)

"The relational picture of space and time has implications that are as radical as those of natural selection, not only for science but for our perspective on who we are and how we came to exist in this evolving universe of relations." (Lee Smolin, "Three Roads to Quantum Gravity", 2000)

"Time is described only in terms of change in the network of relationships that describes space." (Lee Smolin, "Three Roads to Quantum Gravity", 2000)

"String theory seems to be incompatible with a world in which a cosmological constant has a positive sign, which is what the observations indicate." (Lee Smolin, "The New Humanists: Science at the Edge", 2003)

"Combine general relativity and quantum theory into a single theory that can claim to be the complete theory of nature. This is called the problem of quantum gravity." (Lee Smolin, "The Trouble with Physics: The Rise of String Theory, The Fall of a Science and What Comes Next", 2006)

"From the beginning of physics, there have been those who imagined they would be the last generation to face the unknown. Physics has always seemed to its practitioners to be almost complete. This complacency is shattered only during revolutions, when honest people are forced to admit that they don't know the basics." (Lee Smolin, "The Trouble with Physics: The Rise of String Theory, The Fall of a Science and What Comes Next", 2006)

"In both quantum theory and general relativity, we encounter predictions of physically sensible quantities becoming infinite. This is likely the way that nature punishes impudent theorists who dare to break her unity. […] If infinities are signs of missing unification, a unified theory will have none. It will be what we call a finite theory." (Lee Smolin, "The Trouble with Physics: The Rise of String Theory, The Fall of a Science and What Comes Next", 2006)

"In science, for a theory to be believed, it must make a prediction - different from those made by previous theories - for an experiment not yet done. For the experiment to be meaningful, we must be able to get an answer that disagrees with that prediction. When this is the case, we say that a theory is falsifiable - vulnerable to being shown false. The theory also has to be confirmable, it must be possible to verify a new prediction that only this theory makes. Only when a theory has been tested and the results agree with the theory do we advance the statement to the rank of a true scientific theory." (Lee Smolin, "The Trouble with Physics: The Rise of String Theory, The Fall of a Science and What Comes Next", 2006)

"Quantum theory can be described as a new kind of language to be used in a dialogue between us and the systems we study with our instruments. [...] It tells us nothing about what the world would be like in our absence." (Lee Smolin, "The Trouble with Physics: The Rise of String Theory, The Fall of a Science and What Comes Next", 2006)

"Some string theorists prefer to believe that string theory is too arcane to be understood by human beings, rather than consider the possibility that it might just be wrong." (Lee Smolin, "The Trouble with Physics: The Rise of String Theory, The Fall of a Science and What Comes Next", 2006)

"If we believe that the task of physics is the discovery of a timeless mathematical equation that captures every aspect of the universe, then we believe that the truth about the universe lies outside the universe." (Lee Smolin, "Time Reborn: From the Crisis in Physics to the Future of the Universe", 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)

String Theory I

"The odd thing about string theory was very odd indeed. It required that the universe have at least ten dimensions. As we live in a universe of only four dimensions, the theory postulated that the other dimensions [...] had collapsed into structures so tiny that we do not notice them. (Timothy Ferris, "Coming of Age in the Milky Way", 1988)

"Theoretical physicists are accustomed to living in a world which is removed from tangible objects by two levels of abstraction. From tangible atoms we move by one level of abstraction to invisible fields and particles. A second level of abstraction takes us from fields and particles to the symmetry-groups by which fields and particles are related. The superstring theory takes us beyond symmetry-groups to two further levels of abstraction. The third level of abstraction is the interpretation of symmetry-groups in terms of states in ten-dimensional space-time. The fourth level is the world of the superstrings by whose dynamical behavior the states are defined." (Freeman J Dyson, "Infinite in All Directions", 1988)

"No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level. […] because any unified field theory first must absorb the Riemannian geometry of Einstein’s theory and the Lie groups coming from quantum field theory. […] The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity." (Michio Kaku, "Hyperspace", 1995)

"Discovery of supersymmetry would be one of the real milestones in physics, made even more exciting by its close links to still more ambitious theoretical ideas. Indeed, supersymmetry is one of the basic requirements of 'string theory', which is the framework in which theoretical physicists have had some success in unifying gravity with the rest of the elementary particle forces. Discovery of supersymmetry would would certainly give string theory an enormous boost." (Edward Witten, [preface to (Gordon Kane, "Supersymmetry: Unveiling the Ultimate Laws of Nature", 2000) 1999)

"For string theory to make sense, the universe should have nine spatial dimensions and one time dimension, for a total of ten dimensions." (Brian Greene, "The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory", 1999)

"If string theory is right, the microscopic fabric of our universe is a richly intertwined multidimensional labyrinth within which the strings of the universe endlessly twist and vibrate, rhythmically beating out the laws of the cosmos." (Brian Greene, "The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory", 1999)

"To appreciate string theory, one must understand what it is that is being generalized." (Edward Witten, "Physical Law and the Quest for Mathematical Understanding", Bulletin of the American Mathematical Society Vol. 40 (1), 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, "Loop Quantum Gravity", The New Humanists: Science at the Edge, 2003)

"String theory is extremely attractive because gravity is forced upon us. All known consistent string theories include gravity, so while gravity is impossible in quantum field theory as we have known it, it is obligatory in string theory." (Edward Witten)

"[The discovery of string theory is like] wandering around the desert and then stumbling on a tiny pebble. But when we examine it carefully, we find that it is the tip of a gigantic pyramid." (Michio Kaku)

🌡️Thermodynamics II

"Everywhere […] in the Universe, we discern that closed physical systems evolve in the same sense from ordered states towards a state of complete disorder called thermal equilibrium. This cannot be a consequence of known laws of change, since […] these laws are time symmetric- they permit […] time-reverse. […] The initial conditions play a decisive role in endowing the world with its sense of temporal direction. […] some prescription for initial conditions is crucial if we are to understand […]" (John D Barrow, "Theories of Everything: The Quest for Ultimate Explanation", 1991)

"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)

"The second law of thermodynamics, which requires average entropy (or disorder) to increase, does not in any way forbid local order from arising through various mechanisms of self-organization, which can turn accidents into frozen ones producing extensive regularities. Again, such mechanisms are not restricted to complex adaptive systems." (Murray Gell-Mann, "What is Complexity?", Complexity Vol 1 (1), 1995)

"Emergent self-organization in multi-agent systems appears to contradict the second law of thermodynamics. This paradox has been explained in terms of a coupling between the macro level that hosts self-organization (and an apparent reduction in entropy), and the micro level (where random processes greatly increase entropy). Metaphorically, the micro level serves as an entropy 'sink', permitting overall system entropy to increase while sequestering this increase from the interactions where self-organization is desired." (H Van Dyke Parunak & Sven Brueckner, "Entropy and Self-Organization in Multi-Agent Systems", Proceedings of the International Conference on Autonomous Agents, 2001)

"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)

"Thermodynamics is about those properties of systems that are true independent of their mechanism. This is why there is a fundamental asymmetry in the relationship between mechanistic descriptions of systems and thermodynamic descriptions of systems. From the mechanistic information we can deduce all the thermodynamic properties of that system. However, given only thermodynamic information we can deduce nothing about mechanism. This is in spite of the fact that thermodynamics makes it possible for us to reject classes of models such as perpetual motion machines." (Carlos Gershenson, “Design and Control of Self-organizing Systems”, 2007)

"Second Law of thermodynamics is not an equality, but an inequality, asserting merely that a certain quantity referred to as the entropy of an isolated system - which is a measure of the system’s disorder, or ‘randomness’ - is greater (or at least not smaller) at later times than it was at earlier times." (Roger Penrose, "Cycles of Time: An Extraordinary New View of the Universe", 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)

"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)

On Topology IV (More on Topology)

"The young mathematical disciple 'topology' might be of some help in making psychology a real science." (Kurt Lewin, Principles of topological psychology, 1936)

"Topology provides the synergetic means of ascertaining the values of any system of experiences. Topology is the science of fundamental pattern and structural relationships of event constellations." (R Buckminster Fuller, "Operating Manual for Spaceship Earth", 1969)

"Topology is not ‘designed to guide us’ in structure. It is this structure." (Jacques Lacan, "L’Étourdit", 1972)

"No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level. […] because any unified field theory first must absorb the Riemannian geometry of Einstein’s theory and the Lie groups coming from quantum field theory. […] The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity." (Michio Kaku, "Hyperspace", 1995)

"Topology makes it possible to explain the general structure of the set of solutions without even knowing their analytic expression." (Michael I. Monastyrsky, "Riemann, Topology, and Physics" 2nd Ed., 2008)

"At the basis of the distance concept lies, for example, the concept of convergent point sequence and their defined limits, and one can, by choosing these ideas as those fundamental to point set theory, eliminate the notions of distance." (Felix Hausdorff)

"In every subject one looks for the topological and algebraic structures involved, since these structures form a unifying core for the most varied branches of mathematics." (K Weise and H Noack, "Aspects of Topology")

"Mathematicians do not study objects, but relations between objects. Thus, they are free to replace some objects by others so long as the relations remain unchanged. Content to them is irrelevant: they are interested in form only." (Henri Poincaré)

"Poetry and code - and mathematics - make us read differently from other forms of writing. Written poetry makes the silent reader read three kinds of pattern at once; code moves the reader from a static to an active, interactive and looped domain; while algebraic topology allows us to read qualitative forms and their transformations." (Stephanie Strickland)

"Topology is the study of the modal relations of spatial figures and the laws of connectivity, mutual position, and ordering of points, lines, surfaces, and solids and their parts independently of measure and magnitude relations." (Johann B Listing)