On Laws (1990-1999)

"A law explains a set of observations; a theory explains a set of laws. […] a law applies to observed phenomena in one domain" (e.g., planetary bodies and their movements), while a theory is intended to unify phenomena in many domains. […] Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism." (John L Casti, "Searching for Certainty: How Scientists Predict the Future", 1990)

"The original purpose and immediate objective in introducing complex numbers into mathematics is to express laws of dependence between variables by simpler operations on the quantities involved. If one applies these laws of dependence in an extended context, by giving the variables to which they relate complex values, there emerges a regularity and harmony which would otherwise have remained concealed." (Heinz-Dieter Ebbinghaus et al,"Numbers", 1990)

"We live in an era when it seems legitimate to try everything conceivable within the known laws of physics, particularly in the absence of data." (Geoffrey Burbridge, "Focal Point", Sky and Telescope Vol. 78 (6), 1990)

"A purely psychological approach to science would miss the importance of the comprehensibility of mathematics, and of 'the unreasonable effectiveness of mathematics in the natural sciences'. In fact, some scientists in the 'soft' sciences seem to miss this as well. But mathematicians and physicists know that they deal with a reality that has laws of its own, a reality above our little psychological problems, a reality that is strange, fascinating, and in some sense beautiful." (David Ruelle, "Chance and Chaos", 1991)

"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)"

"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)

"Order wherever it reigns, brings beauty with it. Theory not only renders the group of physical laws it represents easier to handle, more convenient, and more useful, but also more beautiful." (Pierre Maurice Marie Duhem,"The Aim and Structure of Physical Theory", 1991)

"Somehow the breathless world that we witness seems far removed from the timeless laws of Nature which govern the elementary particles and forces of Nature. The reason is clear. We do not observe the laws of Nature: we observe their outcomes. Since these laws find their most efficient representation as mathematical equations, we might say that we see only the solutions of those equations not the equations themselves. This is the secret which reconciles the complexity observed in Nature with the advertised simplicity of her laws." (John D Barrow, "New Theories of Everything", 1991)

"The letter ‘i’ originally was meant to suggest the imaginary nature of this number, but with the greater abstraction of mathematics, it came to be realized that it was no more imaginary than many other mathematical constructs. True, it is not suitable for measuring quantities, but it obeys the same laws of arithmetic as do the real numbers, and, surprisingly enough, it makes the statement of various physical laws very natural." (John A Paulos,"Beyond Numeracy", 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)

"What causes difficulties is the apparent contradiction between determinism and our free will, introspectively characterized by the fact that several possibilities are open, and we engage our responsibility by choosing one. Introducing chance into the laws of physics does not help us in any way to resolve this contradiction. […] what allows our free will to be a meaningful notion is the complexity of the universe or, more precisely, our own complexity." (David Ruelle, "Chance and Chaos", 1991)

"In everyday language, the words 'pattern' and 'symmetry' are used almost interchangeably, to indicate a property possessed by a regular arrangement of more-or-less identical units […]" (Ian Stewart & Martin Golubitsky,"Fearful Symmetry: Is God a Geometer?", 1992)

"Scientists have discovered many peculiar things, and many beautiful things. But perhaps the most beautiful and the most peculiar thing that they have discovered is the pattern of science itself. Our scientific discoveries are not independent isolated facts; one scientific generalization finds its explanation in another, which is itself explained by yet another. By tracing these arrows of explanation back toward their source we have discovered a striking convergent pattern - perhaps the deepest thing we have yet learned about the universe." (Steven Weinberg, "Dreams of a Final Theory: The Scientist’s Search for the Ultimate Laws of Nature", 1992)

"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 laws of chess are as beautiful as those governing the universe - and as deadly." (Katherine NevilleA Calculated Risk, 1992)

"General evolution theory, based on the integration of the relevant tenets of general system theory, cybernetics, information and communication theory, chaos theory, dynamical systems theory, and nonequilibrium thermodynamics, can convey a sound understanding of the laws and dynamics that govern the evolution of complex systems in the various realms of investigation. […] The basic notions of this new discipline can be developed to give an adequate account of the dynamical evolution of human societies as well. Such an account could furnish the basis of a system of knowledge better able to orient human beings and societies in their rapidly changing milieu." (Ervin Laszlo et al.,"Evolution: The grand synthesis", 1993)

"A deterministic sequence is one in which only one thing can happen next; that is, its evolution is governed by precise laws. Randomness in the broader sense is therefore identical with the absence of determinism." (Edward N Lorenz, "The Essence of Chaos", 1993)

"General evolution theory, based on the integration of the relevant tenets of general system theory, cybernetics, information and communication theory, chaos theory, dynamical systems theory, and nonequilibrium thermodynamics, can convey a sound understanding of the laws and dynamics that govern the evolution of complex systems in the various realms of investigation [...]. The basic notions of this new discipline can be developed to give an adequate account of the dynamical evolution of human societies as well. Such an account could furnish the basis of a system of knowledge better able to orient human beings and societies in their rapidly changing milieu." (Ervin László et al, "The Evolution of Cognitive Maps: New Paradigms for the Twenty-first Century", 1993)

"[…] number theory […] is a field of almost pristine irrelevance to everything except the wondrous demonstration that pure numbers, no more substantial than Plato’s shadows, conceal magical laws and orders that the human mind can discover after all." (Sharon Begley, "New Answer for an Old Question", Newsweek, 5 July, 1993)

"How surprising it is that the laws of nature and the initial conditions of the universe should allow for the existence of beings who could observe it. Life as we know it would be impossible if any one of several physical quantities had slightly different values." (Steven Weinberg, Life in the Quantum Universe", Scientific American, 1995)"

"Arm chair reflections on the concept of causation [are] not going to yield new insights. The grandfather paradox is simply a way of pointing to the fact that if the usual laws of physics are supposed to hold true in a chronology violating spacetime, then consistency constraints emerge. [To understand these constraints] involves solving problems in physics, not armchair philosophical reflections." (John Earman,"Recent Work on Time Travel", 1995)

"How surprising it is that the laws of nature and the initial conditions of the universe should allow for the existence of beings who could observe it. Life as we know it would be impossible if any one of several physical quantities had slightly different values." (Steven Weinberg, "Life in the Quantum Universe", Scientific American, 1995)

"It suggests to me that consciousness and our ability to do mathematics are no mere accident, no trivial detail, no insignificant by-product of evolution that is piggy-backing on some other mundane property. It points to what I like to call the cosmic connection, the existence of a really deep relationship between minds that can do mathematics and the underlying laws of nature that produce them. We have a closed system of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can encode [...] the very laws of physics that gave rise to it." (Paul Davies, "Are We Alone?: Philosophical Implications of the Discovery of Extraterrestrial Life", 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)

"Underpinning everything [...] are the laws of physics. These remarkably ingenious laws are able to permit matter to self-organize to the point where consciousness emerges in the cosmos - mind from matter - and the most striking product of the human mind is mathematics. This is the baffling thing. Mathematics is [...] produced by the human mind. Yet if we ask where mathematics works best, it is in areas like particle physics and astrophysics, areas of fundamental science that are very, very far removed from everyday affairs. [...] at the opposite end of spectrum of complexity from the human brain. [...] a product of the most complex system we know in nature, the human brain, finds a consonance with the underlying, simplest and most fundamental level, the basic building blocks that make up the world." (Paul C W Davies, "Are We Alone?: Philosophical Implications of the Discovery of Extraterrestrial Life", 1995)

"So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand. [...] It is in those outliers and imperfections that the wildness lurks." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"The laws of biology are written in the language of diversity." (Edward O Wilson, "In Search of Nature", 1996)

"To be an engineer, and build a marvelous machine, and to see the beauty of its operation is as valid an experience of beauty as a mathematician's absorption in a wondrous theorem. One is not ‘more’ beautiful than the other. To see a space shuttle standing on the launch pad, the vented gases escaping, and witness the thunderous blast-off as it climbs heavenward on a pillar of flame - this is beauty. Yet it is a prime example of applied mathematics." (Calvin C Clawson,"Mathematical Mysteries", 1996)

"Mathematical beauty and mathematical truth share the fundamental property of objectivity, that of being inescapably context-dependent. Mathematical beauty and mathematical truth, like any other objective characteristics of mathematics, are subject to the laws of the real world, on a par with the laws of physics." (Gian-Carlo Rota,"The Phenomenology of Mathematical Beauty", 1997)

"Shearing away detail is the very essence of model building. Whatever else we require, a model must be simpler than the thing modeled. In certain kinds of fiction, a model that is identical with the thing modeled provides an interesting device, but it never happens in reality. Even with virtual reality, which may come close to this literary identity one day, the underlying model obeys laws which have a compact description in the computer - a description that generates the details of the artificial world." (John H Holland, "Emergence" , Philosophica 59, 1997)

"[…] all tangible phenomena, from the birth of stars to the workings of social institutions, are based on material processes that are ultimately reducible, however long and tortuous the sequences, to the laws of physics." (Edward O Wilson, "Consilience: The Unity of Knowledge", 1998)

"Good theories are the ones that get those predictions right; the best theories enable us to ‘get right’ the calculation of how the Universe came into being and then exploded into its present form. But that doesn’t mean that they convey ultimate truth, or that there ‘really are’ little hard particles rattling around against each other inside the atom. Such truth as there is in any of this work lies in the mathematics; the particle concept is simply a crutch ordinary mortals can use to help them towards an understanding of the mathematical laws." (John R Gribbin, "The Search of Superstrings, Symmetry, and the Theory of Everything", 1998)

"If life on earth is governed by the natural laws of living systems, then a successful participant should learn the concepts and principles." (Stephen G Haines, 1998)

"The beauty of this [systems thinking] mindset is that its mental models are based on natural laws, principles of interrelationship, and interdependence found in all living systems. They give us a new view of ourselves and our many systems, from the tiniest cell to the entire earth; and as our organizations are included in that great range, they help us define organizational problems as systems problems, so we can respond in more productive ways. The systems thinking mindset is a new orientation to life. In many ways it also operates as a worldview - an overall perspective on, and understanding of, the world." (Stephen G Haines, "The Managers Pocket Guide to Systems Thinking & Learning", 1998)

"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)

"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)

"Knowledge is encoded in models. Models are synthetic sets of rules, pictures, and algorithms providing us with useful representations of the world of our perceptions and of their patterns. As argued by philosophers and shown by scientists, we do not have access to 'reality', only to some of its manifestations, whose regularities are used to determine rules, which when widely applicable become 'laws of nature'. These laws are constantly tested in the scientific march, and they evolve, develop and transmute as the frontier of knowledge recedes further away. " (Burton G Malkiel, "A Random Walk Down Wall Street", 1999)

"The laws of nature are rigged not only in favor of complexity, or just in favor of life, but also in favor of mind. To put it dramatically, it implies that mind is written into the laws of nature in a fundamental way." (Paul C W Davies, "The Fifth Miracle: The Search for the Origin and Meaning of Life", 1999)

On Laws (1980-1989)

"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)

"Numbers written on restaurant bills within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe. This single fact took the scientific world by storm." (Douglas N Adams, "Life, the Universe and Everything", 1982)

"The scientific method is a potentiation of common sense, exercised with a specially firm determination not to persist in error if any exertion of hand or mind can deliver us from it. Like other exploratory processes, it can be resolved into a dialogue between fact and fancy, the actual and the possible; between what could be true and what is in fact the case. The purpose of scientific enquiry is not to compile an inventory of factual information, nor to build up a totalitarian world picture of Natural Laws in which every event that is not compulsory is forbidden. We should think of it rather as a logically articulated structure of justifiable beliefs about nature. It begins as a story about a Possible World - a story which we invent and criticise and modify as we go along, so that it ends by being, as nearly as we can make it, a story about real life." (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)

"A model is a work of fiction. Some properties ascribed to objects in the model will be genuine properties of the objects modelled, but others will be merely properties of convenience. […] Some of the properties and relations in a model will be real properties, in the sense that other objects in other situations might genuinely have them. But they are introduced into this model as a convenience, to bring the objects modelled into the range of the mathematical theory." (Nancy Cartwright, "How the Laws of Physics Lie", 1983)"

"In physics it is usual to give alternative theoretical treatments of the same phenomenon. We construct different models for different purposes, with different equations to describe them. Which is the right model, which the 'true' set of equations? The question is a mistake. One model brings out some aspects of the phenomenon; a different model brings out others. Some equations give a rougher estimate for a quantity of interest, but are easier to solve. No single model serves all purposes best." (Nancy Cartwright, "How the Laws of Physics Lie", 1983)

"Physics is like that. It is important that the models we construct allow us to draw the right conclusions about the behaviour of the phenomena and their causes. But it is not essential that the models accurately describe everything that actually happens; and in general it will not be possible for them to do so, and for much the same reasons. The requirements of the theory constrain what can be literally represented. This does not mean that the right lessons cannot be drawn. Adjustments are made where literal correctness does not matter very much in order to get the correct effects where we want them; and very often, as in the staging example, one distortion is put right by another. That is why it often seems misleading to say that a particular aspect of a model is false to reality: given the other constraints that is just the way to restore the representation." (Nancy Cartwright, "How the Laws of Physics Lie", 1983)

"Scientific theories must tell us both what is true in nature, and how we are to explain it. […] Scientific theories are thought to explain by dint of the descriptions they give of reality." (Nancy Cartwright, "How the Laws of Physics Lie", 1983)

"Scientific theories must tell us both what is true in nature, and how we are to explain it. I shall argue that these are entirely different functions and should be kept distinct. […] Scientific theories are thought to explain by dint of the descriptions they give of reality. […] The covering-law model supposes that all we need to know are the laws of nature - and a little logic, perhaps a little probability theory - and then we know which factors can explain which others. " (Nancy Cartwright, "How the Laws of Physics Lie", 1983)

"Structure is the type of connection between the elements of a whole. […] . Structure is a composite whole, or an internally organised content. […] Structure implies not only the position of its elements in space but also their movement in time, their sequence and rhythm, the law of mutation of a process. So structure is actually the law or set of laws that determine a system's composition and functioning, its properties and stability." (Alexander Spirkin, "Dialectical Materialism", 1983)

"The appearance of truth [of fundamental laws] comes from a bad model of explanation, a model that ties laws directly to reality. As an alternative to the conventional picture I propose a simulacrum account of explanation. The route from theory to reality is from theory to model, and then from model to phenomenological law. The phenomenological laws are indeed true of the objects in reality – or might be; but the fundamental laws are true only of objects in the model." (Nancy Cartwright, "How the Laws of Physics Lie", 1983)

"The origin and immediate purpose of the introduction of complex magnitudes into mathematics lie in the theory of simple laws of dependence between variable magnitudes expressed by means of operations on magnitudes. If we enlarge the scope of applications of these laws by assigning to the variables they involve complex values, then there appears an otherwise hidden harmony and regularity." (Heinz-Dieter Ebbinghaus et al.,"Numbers", 1983)

"Science and Art: Two complementary ways of experiencing the natural world – the one analytic, the other intuitive. We have become accustomed to seeing them as opposite poles, yet don’t they depend on one another? The thinker, trying to penetrate natural phenomena with his understanding, seeking to reduce all complexity to a few fundamental laws - isn’t he also the dreamer plunging himself into the richness of forms and seeing himself as part of the eternal play of natural events?" (Benoît Mandelbrot, 1984)

"Scientific laws give algorithms, or procedures, for determining how systems behave. The computer program is a medium in which the algorithms can be expressed and applied. Physical objects and mathematical structures can be represented as numbers and symbols in a computer, and a program can be written to manipulate them according to the algorithms. When the computer program is executed, it causes the numbers and symbols to be modified in the way specified by the scientific laws. It thereby allows the consequences of the laws to be deduced." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)

"Scientific laws have conventionally been constructed in terms of a particular set of mathematical functions and constructs, and they have often been developed as much for their mathematical simplicity as for their capacity to model the salient features of a phenomenon." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)

"The equations of physics have in them incredible simplicity, elegance and beauty. That in itself is sufficient to prove to me that there must be a God who is responsible for these laws and responsible for the universe" (Paul C W Davies, 1984))

"The nothingness ‘before’ the creation of the universe is the most complete void that we can imagine - no space, time, or matter existed. It is a world without place, without duration or eternity, without number - it is what mathematicians call ‘the empty set’. Yet this unthinkable void converts itself into the plenum of existence - a necessary consequence of physical laws. Where are these laws written into that void? What ‘tells’ the void that is pregnant with a possible universe? It would seem that, even the void is subject to law, a logic that exists prior to space and time." (Heinz R Pagels, "Perfect Symmetry: The Search for the Beginning of Time", 1985)

"We expect to learn new tricks because one of our science based abilities is being able to predict. That after all is what science is about. Learning enough about how a thing works so you'll know what comes next. Because as we all know everything obeys the universal laws, all you need is to understand the laws." (James Burke, "The Day the Universe Changed", 1985)

"Science has become a social method of inquiring into natural phenomena, making intuitive and systematic explorations of laws which are formulated by observing nature, and then rigorously testing their accuracy in the form of predictions. The results are then stored as written or mathematical records which are copied and disseminated to others, both within and beyond any given generation. As a sort of synergetic, rigorously regulated group perception, the collective enterprise of science far transcends the activity within an individual brain." (Lynn Margulis & Dorion Sagan, "Microcosmos", 1986)

"The hardest problems we have to face do not come from philosophical questions about whether brains are machines or not. There is not the slightest reason to doubt that brains are anything other than machines with enormous numbers of parts that work in perfect accord with physical laws. As far as anyone can tell, our minds are merely complex processes. The serious problems come from our having had so little experience with machines of such complexity that we are not yet prepared to think effectively about them." (Marvin Minsky, 1986)

"The physicist's problem is the problem of ultimate origins and ultimate natural laws. The biologist's problem is the problem of complexity." (Richard Dawkins, "The Blind Watchmaker", 1986)

"As the idea of permanence of objects has faded, the idea of permanence of physical laws has become better established and more powerful." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987)

"It is the tension between the scientist's laws and his own attempted breaches of them that powers the engines of science and makes it forge ahead." (Willard v O Quine, "Quiddities" , 1987)

"Where chaos begins, classical science stops. For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the fluctuations of the wildlife populations, in the oscillations of the heart and the brain. The irregular side of nature, the discontinuous and erratic side these have been puzzles to science, or worse, monstrosities." (James Gleick,"Chaos", 1987)

"The most abstract conservation laws of physics come into their being in describing equilibrium in the most extreme conditions. They are the most rigorous conservation laws, the last to break down. The more extreme the conditions, the fewer the conserved structures. [...] In a deep sense, we understand the interior of the sun better that the interior of the earth, and the early stages of the big bang best of all." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987)

"Where chaos begins, classical science stops. For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the fluctuations of the wildlife populations, in the oscillations of the heart and the brain. The irregular side of nature, the discontinuous and erratic side these have been puzzles to science, or worse, monstrosities." (James Gleick, "Chaos", 1987)) 

"The principle of maximum diversity operates both at the physical and at the mental level. It says that the laws of nature and the initial conditions are such as to make the universe as interesting as possible. As a result, life is possible but not too easy. Always when things are dull, something new turns up to challenge us and to stop us from settling into a rut. Examples of things which make life difficult are all around us: comet impacts, ice ages, weapons, plagues, nuclear fission, computers, sex, sin and death. Not all challenges can be overcome, and so we have tragedy. Maximum diversity often leads to maximum stress. In the end we survive, but only by the skin of our teeth." (Freeman J Dyson, "Infinite in All Directions", 1988)

"The ‘objective reality’, or the territory itself, is composed of ‘lighthouse’ principles that govern human growth and happiness - natural laws that are woven into the fabric of every civilized society throughout history and comprise the roots of every family and institution that has endured and prospered. The degree to which our mental maps accurately describe the territory does not alter its existence." (Stephen Covey, "The 7 Habits of Highly Effective People", 1989)

"The more closely our maps or paradigms are aligned with these principles or natural laws, the more accurate and functional they will be. Correct maps will infinitely impact our personal and interpersonal effectiveness far more than any amount of effort expended on changing our attitudes and behaviors. [...] Because our attitudes and behaviors flow out of our paradigms, if we use our self-awareness to examine them, we can often see in them the nature of our underlying maps." (Stephen R Covey, "The 7 Habits of Highly Effective People", 1989)

"The view of science is that all processes ultimately run down, but entropy is maximized only in some far, far away future. The idea of entropy makes an assumption that the laws of the space-time continuum are infinitely and linearly extendable into the future. In the spiral time scheme of the timewave this assumption is not made. Rather, final time means passing out of one set of laws that are conditioning existence and into another radically different set of laws. The universe is seen as a series of compartmentalized eras or epochs whose laws are quite different from one another, with transitions from one epoch to another occurring with unexpected suddenness." (Terence McKenna, "True Hallucinations", 1989)

On Laws (1970-1979)

"Accordingly there are two main types of science, exact science [...] and empirical science [...] seeking laws which are generalizations from particular experiences and are verifiable" (or, more strictly, 'probabilities') only by observation and experiment." (Errol E Harris, "Hypothesis and Perception: The Roots of Scientific Method", 1970)

"Both the myths of religion and the laws of science, it is now becoming apparent, are not so much descriptions of facts as symbolic expressions of cosmic truths." (René J Dubos, A God Within, 1972)

"I believe that the present laws of physics are at least incomplete without a translation into terms of mental phenomena." (Eugene P Wigner, "Physics and the Explanation of Life", 1970)

"[...] it seems self-evident that mathematics is not likely to be much help in discovering laws of nature. If a mathematician wants to make a contribution on this" (and I admit it is the highest) level, he will have to master so much experimental material and train himself to think in a way so different from the one he has been accustomed to that he will, in effect, cease to be a mathematician." (Mark Kac, "On Applying Mathematics: Reflections and Examples", Quarterly of Applied Mathematics, 1972)

"Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. Indeed, the beauty and elegance of the physical laws themselves are only apparent when expressed in the appropriate mathematical framework." (Melvin Schwartz, Principles of Electrodynamics, 1972)

"The beauty of physics lies in the extent which seemingly complex and unrelated phenomena can be explained and correlated through a high level of abstraction by a set of laws which are amazing in their simplicity." (Melvin Schwartz, "In Principles of Electrodynamics", 1972)

"A physical theory must accept some actual data as inputs and must be able to generate from them another set of possible data" (the output) in such a way that both input and output match the assumptions of the theory - laws, constraints, etc. This concept of matching involves relevance: thus boundary conditions are relevant only to field-like theories such as hydrodynamics and quantum mechanics. But matching is more than relevance: it is also logical compatibility." (Mario Bunge, "Philosophy of Physics", 1973)

"Modern scientific principle has been drawn from the investigation of natural laws, technology has developed from the experience of doing, and the two have been combined by means of mathematical system to form what we call engineering." (George S Emmerson, "Engineering Education: A Social History", 1973)

"The pre-eminence of astronomy rests on the peculiarity that it can be treated mathematically; and the progress of physics, and most recently biology, has hinged equally on finding formulations of their laws that can be displayed as mathematical models." (Jacob Bronowski, "The Ascent of Man", 1973)

"The mathematically formulated laws of quantum theory show clearly that our ordinary intuitive concepts cannot be unambiguously applied to the smallest particles. All the words or concepts we use to describe ordinary physical objects, such as position, velocity, color, size, and so on, become indefinite and problematic if we try to use them of elementary particles." (Werner K Heisenberg,"Across the Frontiers", 1974)

"Induction is the process of eliciting general laws via observation and the correlation of particular instances. All sciences, including mathematics, make use of the induction method. Now, mathematical induction is applied only by mathematicians in the proof of theorems of a particular kind." (Yakov Khurgin, "Did You Say Mathematics?", 1974)

"It is not always appreciated that the problem of theory building is a constant interaction between constructing laws and finding an appropriate set of descriptive state variables such that laws can be constructed." (Richard C Lewontin, "The Genetic Basis of Evolutionary Change", 1974)

"Laws of nature are human inventions, like ghosts. Laws of logic, or mathematics are also human inventions, like ghosts. The whole blessed thing is a human invention, including the idea that it isn't a human invention." (Robert M Pirsig, "Zen and the Art of Motorcycle Maintenance", 1974)

"Specifically, it seems to me preferable to use, systematically: 'random' for that which is the object of the theory of probability […]; I will therefore say random process, not stochastic process. 'stochastic' for that which is valid 'in the sense of the calculus of probability': for instance; stochastic independence, stochastic convergence, stochastic integral; more generally, stochastic property, stochastic models, stochastic interpretation, stochastic laws; or also, stochastic matrix, stochastic distribution, etc. As for 'chance', it is perhaps better to reserve it for less technical use: in the familiar sense of'by chance', 'not for a known or imaginable reason', or" (but in this case we should give notice of the fact) in the sense of, 'with equal probability' as in 'chance drawings from an urn', 'chance subdivision', and similar examples." (Bruno de Finetti, "Theory of Probability", 1974)

"The mathematically formulated laws of quantum theory show clearly that our ordinary intuitive concepts cannot be unambiguously applied to the smallest particles. All the words or concepts we use to describe ordinary physical objects, such as position, velocity, color, size, and so on, become indefinite and problematic if we try to use them of elementary particles." (Werner K Heisenberg, "Across the Frontiers", 1974)

"To give a causal explanation of an event means to deduce a statement which describes it, using as premises of the deduction one or more universal laws, together with certain singular statements, the initial conditions. [...] We have thus two different kinds of statement, both of which are necessary ingredients of a complete causal explanation." (Karl Popper, "The Philosophy of Karl Popper", 1974)

"We know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?" (Albert Claude, "The Coming Age of the Cell", [Nobel Prize Lecture] 1974)

"Of course, we know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?" (Albert Claude,"The Coming of Age of the Cell", Science, 1975)

"People are entirely too disbelieving of coincidence. They are far too ready to dismiss it and to build arcane structures of extremely rickety substance in order to avoid it. I, on the other hand, see coincidence everywhere as an inevitable consequence of the laws of probability, according to which having no unusual coincidence is far more unusual than any coincidence could possibly be." (Isaac Asimov, "The Planet That Wasn't", 1976)

"A theory is, of course, not merely any grammatically correct text that uses a set of terms somehow symbolically related to reality. It is a systematic aggregate of statements of laws. Its content, its very value as theory, lies at least as much in the structure of the interconnections that relate its laws to one another, as in the laws themselves." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"Machines, when they operate properly, are not merely law abiding; they are embodiments of law. To say that a specific machine is 'operating properly' is to assert that it is an embodiment of a law we know and wish to apply. We expect an ordinary desk calculator, for example, to be an embodiment of the laws of arithmetic we all know." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"The connection between a model and a theory is that a model satisfies a theory; that is, a model obeys those laws of behavior that a corresponding theory explicitly states or which may be derived from it. [...] Computers make possible an entirely new relationship between theories and models. [...] A theory written in the form of a computer program is [...] both a theory and, when placed on a computer and run, a model to which the theory applies." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"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)

"Facts do not ‘speak for themselves’; they are read in the light of theory. Creative thought, in science as much as in the arts, is the motor of changing opinion. Science is a quintessentially human activity, not a mechanized, robot-like accumulation of objective information, leading by laws of logic to inescapable interpretation." (Stephen J Gould,"Ever Since Darwin", 1977)

"It was mathematics, the non-empirical science par excellence, wherein the mind appears to play only with itself, that turned out to be the science of sciences, delivering the key to those laws of nature and the universe that are concealed by appearances." (Hannah Arendt, "The Life of the Mind", 1977)

"Science is a quintessentially human activity, not a mechanized, robot-like accumulation of objective information, leading by laws of logic to inescapable interpretation." (Stephen J Gould, "Ever Since Darwin", 1977)

"[…] the cybernetic approach brings us to another point of view according to which the analogy between society and the organism has a profound meaning, testifying to the existence of extraordinarily general laws of evolution that exist at all levels of the organization of matter and pointing out to us the direction of society's development." (Valentin F Turchin, "The Phenomenon of Science: A cybernetic approach to human evolution", 1977)

"There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers belong to the most arbitrary and ornery objects studied by mathematicians: they grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behaviour, and that they obey these laws with almost military precision." (Don Zagier,"The First 50 Million Prime Numbers", The Mathematical Intelligencer Vol. 0, 1977)

"All mathematical problems are solved by reasoning within a deductive system in which basic laws of logic are embedded." (Martin Gardner,"Aha! Insight", 1978)

"The ideas that are basic to [my work] often bear witness to my amazement and wonder at the laws of nature which operate in the world around us. He who wonders discovers that this is in itself a wonder. By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics." (Maurits C Escher, "The Graphic Work", 1978)

"The unfoldings are called catastrophes because each of them has regions where a dynamic system can jump suddenly from one state to another, although the factors controlling the process change continuously. Each of the seven catastrophes represents a pattern of behavior determined only by the number of control factors, not by their nature or by the interior mechanisms that connect them to the system's behavior. Therefore, the elementary catastrophes can be models for a wide variety of processes, even those in which we know little about the quantitative laws involved." (Alexander Woodcock & Monte Davis, "Catastrophe Theory", 1978)

"Quantum mechanics also uses statistics, but there is a very big difference between quantum mechanics and Newtonian physics. In quantum mechanics, there is no way to predict individual events This is the startling lesson that experiments in the subatomic realm have taught us. [...] Quantum physics abandons the laws which govern individual events and states directly the statistical laws which govern collections of events. Quantum mechanics can tell us how a group of particles will behave, but the only thing that it can say about an individual particle is how it probably will behave. Probability is one of the major characteristics of quantum mechanics." (Gary Zukav, "The Dancing Wu Li Masters", 1979)

Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand nature. Gradually they have become the backbone of our theoretical formulation of physical laws." (Tsung-Dao Lee, "Particle Physics and Introduction to Field Theory", 1981)"

"Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand nature. Gradually they have become the backbone of our theoretical formulation of physical laws." (Tsung-Dao Lee,"Particle Physics and Introduction to Field Theory", 1981)

"Our form of life depends, in delicate and subtle ways, on several apparent ‘coincidences’ in the fundamental laws of nature which make the Universe tick. Without those coincidences, we would not be here to puzzle over the problem of their existence […] What does this mean? One possibility is that the Universe we know is a highly improbable accident, ‘just one of those things’." (John R Gribbin, "Genesis: The Origins of Man and the Universe", 1981)

"Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand nature. Gradually they have become the backbone of our theoretical formulation of physical laws." (Tsung-Dao Lee, "Particle Physics and Introduction to Field Theory", 1981)

"The purpose of scientific enquiry is not to compile an inventory of factual information, nor to build up a totalitarian world picture of Natural Laws in which every event that is not compulsory is forbidden. We should think of it rather as a logically articulated structure of justifiable beliefs about nature. It begins as a story about a Possible World - a story which we invent and criticize and modify as we go along, so that it winds by being, as nearly as we can make it, a story about real life." (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)

"[…] the simplicity of nature which we at present grasp is really the result of infinite complexity; and that below the uniformity there underlies a diversity whose depths we have not yet probed, and whose secret places are still beyond our reach." (William Spottiswoode, 1879)

On Laws (1960-1969)

"Freedom can be manifested only in the void of beliefs, in the absence of axioms, and only where the laws have no more authority than a hypothesis." (Emil Cioran, "History and Utopia", 1960)

"Modern theoretical physics […] has put our thinking about the essence of matter in a different context. It has taken our gaze from the visible-the particles-to the underlying entity, the field. The presence of matter is merely a disturbance of the perfect state of the field at that place; something accidental, one could almost say, merely a ‘blemish’. Accordingly, there are no simple laws describing the forces between elementary particles […] Order and symmetry must be sought in the underlying field." (Walter Thirring "Urbausteine der Materie", 1960)

"[…] no models are [true] = not even the Newtonian laws. When you construct a model you leave out all the details which you, with the knowledge at your disposal, consider inessential. […] Models should not be true, but it is important that they are applicable, and whether they are applicable for any given purpose must of course be investigated. This also means that a model is never accepted finally, only on trial." (Georg Rasch, "Probabilistic Models for Some Intelligence and Attainment Tests", 1960)

"The enormous usefulness of mathematics in natural sciences is something bordering on the mysterious, and there is no rational explanation for it. It is not at all natural that ‘laws of nature’ exist, much less that man is able to discover them. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," 1960)

"The enormous usefulness of mathematics in natural sciences is something bordering on the mysterious, and there is no rational explanation for it. It is not at all natural that ‘laws of nature’ exist, much less that man is able to discover them. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," 1960)

"The first [principle], is that a mathematical theory can only he developed axiomatically in a fruitful way when the student has already acquired some familiarity with the corresponding material - a familiarity gained by working long enough with it on a kind of experimental, or semiexperimental basis, i.e. with constant appeal to intuition. The other principle [...] is that when logical inference is introduced in some mathematical question, it should always he presented with absolute honesty - that is, without trying to hide gaps or flaws in the argument; any other way, in my opinion, is worse than giving no proof at all." (Jean Dieudonné, "Thinking in School Mathematics", 1961)

"Can there be laws of chance? The answer, it would seem should be negative, since chance is in fact defined as the characteristic of the phenomena which follow no law, phenomena whose causes are too complex to permit prediction." (Félix E Borel, "Probabilities and Life", 1962)

"Every isolated determinate dynamic system, obeying unchanging laws, will ultimately develop some sort of organisms that are adapted to their environments." (W Ross Ashby, "Principles of the self-organizing system", 1962)

"Roughly, by a complex system I mean one made up of a large number of parts that interact in a nonsimple way. In such systems, the whole is more than the sum of the parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole." (Herbert Simon, "The Architecture of Complexity", Proceedings of the American Philosophical Society, Vol. 106" (6), 1962)

"Scientists, it should already be clear, never learn concepts, laws, and theories in the abstract and by themselves. Instead, these intellectual tools are from the start encountered in a historically and pedagogically prior unit that displays them with and through their applications." (Thomas Kuhn, "The Structure of Scientific Revolutions", 1962)

"Scientists, it should already be clear, never learn concepts, laws, and theories in the abstract and by themselves. Instead, these intellectual tools are from the start encountered in a historically and pedagogically prior unit that displays them with and through their applications." (Thomas Kuhn, "The Structure of Scientific Revolutions", 1962)

"Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience. The further it goes in this direction, the more it tends to speak the language of mathematics, which is really one of the languages of the imagination, along with literature and music." (Northrop Frye, "The Educated Imagination", 1963)

"Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected." (Richard Feynman, The Feynman Lectures on Physics" Vol. 1, 1963)

"It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better." (Paul Dirac, "The Evolution of the Physicist's Picture of Nature", 1963)

"Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience. The further it goes in this direction, the more it tends to speak the language of mathematics, which is really one of the languages of the imagination, along with literature and music." (Northrop Frye, "The Educated Imagination", 1963)

"We have ceased to expect from physics an explanation of all events, even of the gross structure of the universe, and we aim only at the discovery of the laws of nature, that is the regularities, of the events." (Eugene P Wigner, "Events, Laws of Nature, and Invariance Principles", [Nobel Lecture], 1963)

"We know many laws of nature and we hope and expect to discover more. Nobody can foresee the next such law that will be discovered. Nevertheless, there is a structure in laws of nature which we call the laws of invariance. This structure is so far-reaching in some cases that laws of nature were guessed on the basis of the postulate that they fit into the invariance structure." (Eugene P Wigner, "The Role of Invariance Principles in Natural Philosophy", 1963)

"Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected." (Richard Feynman,"The Feynman Lectures on Physics" Vol. 1,1964)

"Physics can teach us only what the laws of nature are today. It is only Astronomy that can teach us what the initial conditions for these laws are." (Eugene P Wigner,"The Case for Astronomy", Proceedings of the American Philosophical Society Vol. 8" (1), 1964)

"It bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what a tiny piece of space-time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed and the laws will turn out to be simple, like the checker board with all its apparent complexities." (Richard P Feynman, "The Character of Physical Law", 1965)

"So in order to understand the physics one must always have a neat balance and contain in his head all of the various propositions and their interrelationships because the laws often extend beyond the range of their deductions. This will only have no importance when all the laws are known." (Richard Feynman, "The Character of Physical Law", 1965)

"The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way." (Richard Feynman,"The Character of Physical Law", 1965)

"[..] principle of equipresence: A quantity present as an independent variable in one constitutive equation is so present in all, to the extent that its appearance is not forbidden by the general laws of Physics or rules of invariance. […] The principle of equipresence states, in effect, that no division of phenomena is to be laid down by constitutive equations." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"[…] there is perhaps a difference between the ideas which are associated in the sense of their patterns being tired to the original one and available in connexion with it, and being actually associated or aroused. Our mental modelling of the outer world may imitate it and its sequences from moment to moment, but only that which is fairly frequent, or fits into other patterns, will remain for long, and of that only a portion will arise in response to other ideas. " (Kenneth J W Craik, 'Laws of Association',"The Nature of Psychology", 1966)

"[…] mathematics is not portraying laws inherent in the design of the universe but is merely providing man-made schemes or models which we can use to deduce conclusions about our world only to the extent that the model is a good idealization." (Morris Kline,"Mathematics for the Nonmathematician", 1967)

"General systems theory" (in the narrow sense of the term) is a discipline concerned with the general properties and laws of 'systems' . A system is defined as a complex of components in interaction, or by some similar proposition. Systems theory tries to develop those principles that apply to systems in general, irrespective of the nature of the system, of their components, and of the relations or 'forces' between them. The system components need not even be material, as, for example, in the system analysis of a commercial enterprise where components such as buildings, machines, personnel, money and 'good will' of customers enter." (Ludwig von Bertalanffy, "Robots, Men and Minds", 1967)

"It is now natural for us to try to derive the laws of nature and to test their validity by means of the laws of invariance, rather than to derive the laws of invariance from what we believe to be the laws of nature." (Eugene P Wigner, "Symmetries and Reflections", 1967)

"The laws of thought are also the laws of things: of things in the remotest space and the remotest time." (Clive S Lewis, "Christian Reflections", 1967)

"To analyse graphic representation precisely, it is helpful to distinguish it from musical, verbal and mathematical notations, all of which are perceived in a linear or temporal sequence. The graphic image also differs from figurative representation essentially polysemic, and from the animated image, governed by the laws of cinematographic time. Within the boundaries of graphics fall the fields of networks, diagrams and maps. The domain of graphic imagery ranges from the depiction of atomic structures to the representation of galaxies and extends into the spheres of topography and cartography. " (Jacques Bertin, "Semiology of graphics", 1967)

"A structure is a system of transformations. Inasmuch as it is a system and not a mere collection of elements and their properties, these transformations involve laws: the structure is preserved or enriched by the interplay of its transformation laws, which never yield results external to the system nor employ elements that are external to it. In short, the notion of structure is composed of three key ideas: the idea of wholeness, the idea of transformation, and the idea of self-regulation." (Jean Piaget, "Structuralism", 1968)

"Modern theoretical physics […] has put our thinking about the essence of matter in a different context. It has taken our gaze from the visible-the particles-to the underlying entity, the field. The presence of matter is merely a disturbance of the perfect state of the field at that place; something accidental, one could almost say, merely a ‘blemish’. Accordingly, there are no simple laws describing the forces between elementary particles […] Order and symmetry must be sought in the underlying field." (Walter Thirring "‘Urbausteine der Materie", Almanach der bterreichischen Akademie der Wissenschaften Vol. 118, 1968)

"The parallelism of general conceptions or even special laws in different fields therefore is a consequence of the fact that these are concerned with 'systems' and that certain general principles apply to systems irrespective of their nature. Hence principles such as those of wholeness and sum, mechanization, hierarchic order, approached to steady states, equifinality, etc., may appear in quite different disciplines. The isomorphism found in different realms is based of the existence of general system principles, of a more or less well-developed ‘general system theory’." (Ludwig von Bertalanffy, "General System Theory", 1968)

"Thus, there exist models, principles, and laws that apply to generalized systems or their subclasses, irrespective of their particular kind, the nature of their component elements, and the relations or 'forces' between them. It seems legitimate to ask for a theory, not of systems of a more or less special kind, but of universal principles applying to systems in general. In this way we postulate a new discipline called General System Theory. Its subject matter is the formulation and derivation of those principles which are valid for ‘systems’ in general." (Ludwig von Bertalanffy, „General System Theory: Foundations, Development, Applications", 1968)

"We realize, however, that all scientific laws merely represent abstractions and idealizations expressing certain aspects of reality. Every science means a schematized picture of reality, in the sense that a certain conceptual construct is unequivocally related to certain features of order in reality […]" (Ludwig von Bertalanffy, "General System Theory", 1968)

"A theorem is no more proved by logic and computation than a sonnet is written by grammar and rhetoric, or than a sonata is composed by harmony and counterpoint, or a picture painted by balance and perspective." (George Spencer-Brown,"Laws of Form", 1969)

"Discovery always carries an honorific connotation. It is the stamp of approval on a finding of lasting value. Many laws and theories have come and gone in the history of science, but they are not spoken of as discoveries. […] Theories are especially precarious, as this century profoundly testifies. World views can and do often change. Despite these difficulties, it is still true that to count as a discovery a finding must be of at least relatively permanent value, as shown by its inclusion in the generally accepted body of scientific knowledge." (Richard J. Blackwell, "Discovery in the Physical Sciences", 1969)

"How can it be that writing down a few simple and elegant formulae, like short poems governed by strict rules such as those of the sonnet or the waka, can predict universal regularities of Nature? Perhaps we see equations as simple because they are easily expressed in terms of mathematical notation already invented at an earlier stage of development of the science, and thus what appears to us as elegance of description really reflects the interconnectedness of Nature’s laws at different levels." (Murray Gell-Mann, 1969)

"The laws of nature 'discovered' by science are merely mathematical or mechanical models that describe how nature behaves, not why, nor what nature 'actually' is. Science strives to find representations that accurately describe nature, not absolute truths. This fact distinguishes science from religion." (George O Abell, "Exploration of the Universe", 1969)

On Laws (1950-1959)

"It is more important to have a clear understanding of general principles, without, however, thinking of them as fixed laws, than to load the mind with a mass of detailed technical information which can readily be found in reference books or card indexes." (William I B Beveridge, "The Art of Scientific Investigation", 1950)

"In a sense, of course, probability theory in the form of the simple laws of chance is the key to the analysis of warfare; […] My own experience of actual operational research work, has however, shown that its is generally possible to avoid using anything more sophisticated. […] In fact the wise operational research worker attempts to concentrate his efforts in finding results which are so obvious as not to need elaborate statistical methods to demonstrate their truth. In this sense advanced probability theory is something one has to know about in order to avoid having to use it." (Patrick M S Blackett, "Operations Research", Physics Today, 1951) 

"Instead of asking for a cause of the universe, the scientist can ask only for the cause of the present state of the universe; and his task will consist in pushing farther and farther back the date from which he is able to account for the universe in terms of laws of nature." (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)

"[…] observation is not enough, and it seems to me that in science, as in the arts, there is very little worth having that does not require the exercise of intuition as well as of intelligence, the use of imagination as well as of information." (Kathleen Lonsdale,"Facts About Crystals", American Scientist Vol. 39 (4), 1951)

"On the basis of what has been proved so far, it remains possible that there may exist" (and even be empirically discoverable) a theorem-proving machine which in fact is equivalent to mathematical intuition, but cannot be proved to be so, nor even be proved to yield only correct theorems of finitary number theory." (Kurt Gödel, 1951)

"The concept of an average, the equation to a curve, the description of a froth or cellular tissue, all come within the scope of mathematics for no other reason than that they are summations of more elementary principles or phenomena. Growth and Form are throughout of this composite nature; therefore the laws of mathematics are bound to underlie them, and her methods to be peculiarly fitted to interpret them." (D'Arcy W Thompson, "On Growth and Form", 1951)

"The picture of scientific method drafted by modern philosophy is very different from traditional conceptions. Gone is the ideal of a universe whose course follows strict rules, a predetermined cosmos that unwinds itself like an unwinding clock. Gone is the ideal of the scientist who knows the absolute truth. The happenings of nature are like rolling dice rather than like revolving stars; they are controlled by probability laws, not by causality, and the scientist resembles a gambler more than a prophet. He can tell you only his best posits - he never knows beforehand whether they will come true. He is a better gambler, though, than the man at the green table, because his statistical methods are superior. And his goal is staked higher - the goal of foretelling the rolling dice of the cosmos. If he is asked why he follows his methods, with what title he makes his predictions, he cannot answer that he has an irrefutable knowledge of the future; he can only lay his best bets. But he can prove that they are best bets, that making them is the best he can do - and if a man does his best, what else can you ask of him?" (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)

"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)

"Being built on concepts, hypotheses, and experiments, laws are no more accurate or trustworthy than the wording of the definitions and the accuracy and extent of the supporting experiments." (Gerald Holton, "Introduction to Concepts and Theories in Physical Science", 1952)

"In mathematics […] we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials [….] being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency towards intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations." (David Hilbert,"Geometry and the imagination", 1952)

"Statistics is the fundamental and most important part of inductive logic. It is both an art and a science, and it deals with the collection, the tabulation, the analysis and interpretation of quantitative and qualitative measurements. It is concerned with the classifying and determining of actual attributes as well as the making of estimates and the testing of various hypotheses by which probable, or expected, values are obtained. It is one of the means of carrying on scientific research in order to ascertain the laws of behavior of things - be they animate or inanimate. Statistics is the technique of the Scientific Method." (Bruce D Greenschieldsw & Frank M Weida, "Statistics with Applications to Highway Traffic Analyses", 1952)

"The primary fact is that all isolated state-determined dynamic systems are selective: from whatever state they have initially, they go towards states of equilibrium. These states of equilibrium are always characterised, in their relation to the change-inducing laws of the system, by being exceptionally resistant." (W Ross Ashby, "Design for a Brain: The Origin of Adaptive Behavior", 1952)

"All great discoveries in experimental physics have been due to the intuition of men who made free use of models, which were for them not products of the imagination, but representatives of real things." (Max Born,"Physical Reality", Philosophical Quarterly Vol. 3 (11), 1953)

"Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition. It is the hygiene that mathematics practice to keep its ideas healthy and strong. Moreover, the whole structure rests fundamentally on uncertain ground, the intuitions of man." (Morris Kline,"Mathematics in Western Culture", 1953)

"The construction of hypotheses is a creative act of inspiration, intuition, invention; its essence is the vision of something new in familiar material." (Milton Friedman,"Essays in Positive Economics", 1953)

"The world is not made up of empirical facts with the addition of the laws of nature: what we call the laws of nature are conceptual devices by which we organize our empirical knowledge and predict the future." (Richard B Braithwaite, "Scientific Explanation", 1953)

"We cannot define truth in science until we move from fact to law. And within the body of laws in turn, what impresses us as truth is the orderly coherence of the pieces. They fit together like the characters of a great novel, or like the words of a poem. Indeed, we should keep that last analogy by us always, for science is a language, and like a language it defines its parts by the way they make up a meaning. Every word in a sentence has some uncertainty of definition, and yet the sentence defines its own meaning and that of its words conclusively. It is the internal unity and coherence of science which gives it truth, and which makes it a better system of prediction than any less orderly language." (Jacob Bronowski, "The Common Sense of Science", 1953)

"[…] if the aim of physical theories is to explain experimental laws, theoretical physics is not an autonomous science; it is subordinate to metaphysics." (Pierre-Maurice-Marie Duhem, "The Aim and Structure of Physical Theory", 1954)

"Science, then, is the attentive consideration of common experience; it is common knowledge extended and refined. Its validity is of the same order as that of ordinary perception; memory, and understanding. Its test is found, like theirs, in actual intuition, which sometimes consists in perception and sometimes in intent." (George Santayana,"The Life of Reason, or the Phases of Human Progress", 1954)

"The important point for us to observe is that all these constructions and the laws connecting them can be arrived at by the principle of looking for the mathematically simplest concepts and the link between them. In the limited number of mathematically existent simple field types, and the simple equations possible between them, lies the theorist’s hope of grasping the real in all its depth." (Albert Einstein, "Ideas and Opinions", 1954)

"The laws of science are the permanent contribution to knowledge - the individual pieces which are fitted together attempt to form a picture of the physical universe in action." (Edwin P Hubble, "The Nature of Science and Other Lectures", 1954)

"The methods of science may be described as the discovery of laws, the explanation of laws by theories, and the testing of theories by new observations. A good analogy is that of the jigsaw puzzle, for which the laws are the individual pieces, the theories local patterns suggested by a few pieces, and the tests the completion of these patterns with pieces previously unconsidered." (Edwin P Hubble, "The Nature of Science and Other Lectures", 1954)

"It is not only the smallest features of the Universe that are controlled by the laws of physics. The behavior of matter on the very large scale that concerns us in astronomy is also determined by physics. The heavenly bodies dance like puppets on strings. If we are to understand why they dance as they do, it is necessary to find out how the strings are manipulated." (Fred Hoyle, "Frontiers of Astronomy", 1955)

"[…] as every law of nature implies the existence of an invariant, it follows that every law of nature is a constraint. […] Science looks for laws; it is therefore much concerned with looking for constraints. […] the world around us is extremely rich in constraints. We are so familiar with them that we take most of them for granted, and are often not even aware that they exist. […] A world without constraints would be totally chaotic." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"General systems theory is a series of related definitions, assumptions, and postulates about all levels of systems from atomic particles through atoms, molecules, crystals, viruses, cells, organs, individuals, small groups, societies, planets, solar systems, and galaxies. General behavior systems theory is a subcategory of such theory, dealing with living systems, extending roughly from viruses through societies. A significant fact about living things is that they are open systems, with important inputs and outputs. Laws which apply to them differ from those applying to relatively closed systems." (James G Miller, "General behavior systems theory and summary", Journal of Counseling Psychology  (2), 1956)

"The forms of a person’s thoughts are controlled by inexorable laws of pattern of which he is unconscious. These patterns are the unperceived intricate systematizations of his own language - shown readily enough by a candid comparison and contrast with other languages, especially those of a different linguistic family." (Benjamin L Whorf, 1956)

"By some definitions 'systems engineering' is suggested to be a new discovery. Actually it is a common engineering approach which has taken on a new and important meaning because of the greater complexity and scope of problems to be solved in industry, business, and the military. Newly discovered scientific phenomena, new machines and equipment, greater speed of communications, increased production capacity, the demand for control over ever-extending areas under constantly changing conditions, and the resultant complex interactions, all have created a tremendously accelerating need for improved systems engineering. Systems engineering can be complex, but is simply defined as 'logical engineering within physical, economic and technical limits' - bridging the gap from fundamental laws to a practical operating system." (Instrumentation Technology, 1957)

"By the laws of statistics we could probably approximate just how unlikely it is that it would happen. But people forget - especially those who ought to know better, such as yourself - that while the laws of statistics tell you how unlikely a particular coincidence is, they state just as firmly that coincidences do happen." (Robert A Heinlein, "The Door Into Summer", 1957)

"Indeed, the laws of chance are just as necessary as the causal laws themselves." (David Bohm, "Causality and Chance in Modern Physics", 1957)

"[...] the whole course of events is determined by the laws of probability; to a state in space there corresponds a definite probability, which is given by the de Brogile wave associated with the state." (Max Born, "Atomic Physics", 1957)

"If simple perfect laws uniquely rule the universe, should not pure thought be capable of uncovering this perfect set of laws without having to lean on the crutches of tenuously assembled observations? True, the laws to be discovered may be perfect, but the human brain is not. Left on its own, it is prone to stray, as many past examples sadly prove. In fact, we have missed few chances to err until new data freshly gleaned from nature set us right again for the next steps. Thus pillars rather than crutches are the observations on which we base our theories; and for the theory of stellar evolution these pillars must be there before we can get far on the right track." (Erwin Schrödinger & Martin Schwarzschild, "Structure and Evolution of the Stars", 1958)

"Our craving for generality has [as one] source […] our preoccupation with the method of science. I mean the method the method of reducing the explanation of natural phenomena to the smallest possible number of primitive natural laws; and, in mathematics, of unifying the treatment of different topics by using a generalization. Philosophers constantly see the method of science before their eyes, and are irresistibly tempted to ask and answer in the way science does. This tendency is the real source of metaphysics, and leads the philosopher into complete darkness. I want to say here that it can never be our job to reduce anything to anything, or to explain anything. Philosophy really is ‘purely descriptive’." (Ludwig Wittgenstein, "The Blue and Brown Books", 1958)

"The new always happens against the overwhelming odds of statistical laws and their probability, which for all practical, everyday purposes amounts to certainty; the new therefore always appears in the guise of a miracle." (Hannah Arendt, "The Human Condition", 1958)

"Statistical laws are indisputably noncausal, even though some of them may be shown to be partly derivable from laws having a causal component." (Mario Bunge, Causality: The place of the casual principles in modern science, 1959)

"The simplicities of natural laws arise through the complexities of the languages we use for their expression." (Eugene P Wigner, 1959)

On Laws (1940-1949)

"In perception, a knowledge forms itself slowly; in the [mental] image the knowledge is immediate. We see now that the image is a synthetic act which unites a concrete, nonimagined, knowledge to elements which are more actually representative. The image teaches nothing: it is organized exactly like the objects which do produce knowledge, but it is complete at the very moment of its appearance. […] Thus, the object presents itself in the image as having to be apprehended in a multiplicity of synthetic acts. Due to this fact, and because its content retains a sensible opacity, like a phantom, because it does not involve either essences or generating laws but only an irrational quality, it gives the impression of being an object of observation: from this point of view the image appears to be more like a perception than a concept." (Jean-Paul Sartre,"The Psychology of Imagination", 1940)

"Mathematics is an activity governed by the same rules imposed upon the symphonies of Beethoven, the paintings of DaVinci, and the poetry of Homer. Just as scales, as the laws of perspective, as the rules of metre seem to lack fire, the formal rules of mathematics may appear to be without lustre. Yet ultimately, mathematics reaches pinnacles as high as those attained by the imagination in its most daring reconnoiters. And this conceals, perhaps, the ultimate paradox of science. For in their prosaic plodding both logic and mathematics often outstrip their advance guard and show that the world of pure reason is stranger than the world of pure fancy." (Edward Kasner & James R Newman, "Mathematics and the Imagination", 1940)

"The fundamental difference between engineering with and without statistics boils down to the difference between the use of a scientific method based upon the concept of laws of nature that do not allow for chance or uncertainty and a scientific method based upon the concepts of laws of probability as an attribute of nature." (Walter A Shewhart, 1940)

"Thus, the object presents itself in the image as having to be apprehended in a multiplicity of synthetic acts. Due to this fact, and because its content retains a sensible opacity, like a phantom, because it does not involve either essences or generating laws but only an irrational quality, it gives the impression of being an object of observation: from this point of view the image appears to be more like a perception than a concept." (Jean-Paul Sartre, "The Psychology of Imagination", 1940)

"Can there be laws of chance? The answer, it would seem should be negative, since chance is in fact defined as the characteristic of the phenomena which follow no law, phenomena whose causes are too complex to permit prediction." (Félix E Borel, "Probabilities and Life", 1943)

"Exhaustive studies by many investigators have shown that the fundamental laws of nature do not control the phenomena directly. We must picture them as operating in a substratum of which we can form no mental picture unless we are willing to introduce a number of irrelevant and therefore unjustifiable suppositions." (James H Jeans," Physics and Philosophy" 3rd Ed., 1943)

"Good physics is made a priori. Theory precedes fact. Experience is useless because before any experience we are already in possession of the knowledge we are seeking for. Fundamental laws of motion" (and of rest), laws that determine the spatio-temporal behavior of material bodies, are laws of a mathematical nature. Of the same nature as those which govern relations and laws of figures and numbers. We find and discover them not in Nature, but in ourselves, in our mind, in our memory, as Plato long ago has taught us." (Alexander Koyre, "Galileo and the Scientific Revolution of the Seventeenth Century", The Philosophical Review Vol. 52 (3), 1943)

"[…] inner images are rather psychic manifestations of the archetypes which, however, would also have to put forth, create, condition anything lawlike in the behavior of the corporeal world. The laws of this world would then be the physical manifestations of the archetypes. […] Each law of nature should then have an inner correspondence and vice versa, even though this is not always directly visible today." (Wolfgang Pauli, [letter to Markus Fierz] 1948)

"Nothing is left in the world but happenings for which no explanation or interpretation is offered or even attempted, and science has now for its single aim the discovery of the laws to which these happenings conform - the pattern of events." (James H Jeans,"Physics and Philosophy" 3rd Ed., 1943)

"The problem of physics is how the actual phenomena, as observed with the help of our sense organs aided by instruments, can be reduced to simple notions which are suited for precise measurement and used of the formulation of quantitative laws." (Max Born, "Experiment and Theory in Physics", 1944)

"The responsibility for the creation of new scientific knowledge - and for most of its application - rests on that small body of men and women who understand the fundamental laws of nature and are skilled in the techniques of scientific research. We shall have rapid or slow advance on any scientific frontier depending on the number of highly qualified and trained scientists exploring it."(Vannevar Bush, "Science: The Endless Frontier", 1945)

"What now is the answer to the question as to the bridge between the perception of the senses and the concepts, which is now reduced to the question as to the bridge between the outer perceptions and those inner image-like representations. It seems to me one has to postulate a cosmic order of nature - outside of our arbitrariness- to which the outer material objects are subjected as are the inner images […] The organizing and regulating has to be posited beyond the differentiation of physical and psychical […] I am all for it to call this ‘organizing and regulating’ ‘archetypes’. It would then be inadmissible to define these as psychic contents. Rather, the above-mentioned inner pictures" (dominants of the collective unconscious, see Jung) are the psychic manifestations of the archetypes, but which would have to produce and condition all nature laws belonging to the world of matter. The nature laws of matter would then be the physical manifestation of the archetypes." (Wolfgang Pauli, [Letter to Markus Fierz], 1948)

"As the complexity of the structure of matter became revealed through research, its basic simplicity, unity, and dependability became equally evident. So we now see ourselves in a world governed by natural laws instead of by capricious deities and devils. This does not necessarily mean that God has been ruled out of the picture, but it does mean that the architect and engineer of the universe is a far different type of being from the gods assumed by the ancients, and that man lives and dies in a world of logical system and orderly performance." (Karl T Compton, cca. 1930–1949)

"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)

"[In quantum mechanics] we have the paradoxical situation that observable events obey laws of chance, but that the probability for these events itself spreads according to laws which are in all essential features causal laws." (Max Born, Natural Philosophy of Cause and Chance, 1949)

"[…] science, properly interpreted, is not dependent on any sort of metaphysics. It merely attempts to cover a maximum of facts by a minimum of laws." (Herbert Feigl, "Naturalism and Humanism", American Quarterly, Vol. 1, No. 2, 1949)

"The amount of human effort needed to handle information correctly depends very much on the properties of the physical equipment expressing the information, although the laws of correct reasoning are independent of the equipment." (Edmund C Berkeley, "Giant Brains or Machines that Think", 1949)

"[...] the conception of chance enters in the very first steps of scientific activity in virtue of the fact that no observation is absolutely correct. I think chance is a more fundamental conception that causality; for whether in a concrete case, a cause-effect relation holds or not can only be judged by applying the laws of chance to the observation." (Max Born, 1949)

"The outside world is something independent from man, something absolute, and the quest for the laws which apply to this absolute appeared to me as the most sublime scientific pursuit in life." (Max Planck, "A Scientific Autobiography", 1949)

"We have assumed that the laws of nature must be capable of expression in a form which is invariant for all possible transformations of the space-time co-ordinates." (Gerald J Whitrow, "The Structure of the Universe: An Introduction to Cosmology", 1949)

"[...] when the pioneer in science sends for the groping feelers of his thoughts, he must have a vivid intuitive imagination, for new ideas are not generated by deduction, but by an artistically creative imagination. Nevertheless, the worth of a new idea is invariably determined, not by the degree of its intuitiveness - which, incidentally, is to a major extent a matter of experience and habit - but by the scope and accuracy of the individual laws to the discovery of which it eventually leads." (Max Planck, The Meaning and Limits of Exact Science", Science Vol. 110" (2857), 1949)

On Laws (1930-1939)

"In fact, our ordinary description of nature, and the idea of exact laws, rests on the assumption that it is possible to observe the phenomena without appreciably influencing them." (Werner K Heisenberg, "The Physical Principles of the Quantum Theory", 1930)

"It has become increasingly evident in recent times, however, that nature works on a different plan. Her fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies." (Paul A M Dirac, "The Principles of Quantum Mechanics", 1930)

"It is easy without any very profound logical analysis to perceive the difference between a succession of favorable deviations from the laws of chance, and on the other hand, the continuous and cumulative action of these laws. It is on the latter that the principle of Natural Selection relies." (Sir Ronald A Fisher, "The Genetical Theory of Natural Selection", 1930)

"The classical tradition has been to consider the world to be an association of observable objects" (particles, fluids, fields, etc.) moving according to definite laws of force, so that one could form a mental picture in space and time of the whole scheme. This led to a physics whose aim was to make assumptions about the mechanism and forces connecting these observable objects in the simplest possible way. It has become increasingly evident in recent times, however, that nature works on a different plan. Her fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies." (Paul A M Dirac, "The Principles of Quantum Mechanics", 1930)

"The concepts which now prove to be fundamental to our understanding of nature- a space which is finite; a space which is empty, so that one point [of our 'material' world] differs from another solely in the properties of space itself; four-dimensional, seven- and more dimensional spaces; a space which for ever expands; a sequence of events which follows the laws of probability instead of the law of causation - or alternatively, a sequence of events which can only be fully and consistently described by going outside of space and time - all these concepts seem to my mind to be structures of pure thought, incapable of realisation in any sense which would properly be described as material.(James Jeans, "The Mysterious Universe", 1930)

"[…] the main object of physical science is not the provision of pictures, but in the formulation of laws governing phenomena and the application of these laws to the discovery of new phenomena. If a picture exists, so much the better; but whether a picture exists or not is a matter of only secondary importance. In the case of atomic phenomena no picture can be expected to exist in the usual sense of the word ‘picture’, by which is meant to model functioning essentially on classical lines. One may extend the meaning of the word ‘picture’ to include any way of looking at the fundamental laws which make their self-consistency obvious. With this extension, one may acquire a picture of atomic phenomena by becoming familiar with the laws of quantum theory." (Paul A M Dirac, "The Principles of Quantum Mechanics", 1930)

"The methods of progress in theoretical physics have undergone a vast change during the present century. The classical tradition has been to consider the world to be an association of observable objects" (particles, fluids, fields, etc.) moving about according to definite laws of force, so that one could form a mental picture in space and time of the whole scheme. This led to a physics whose aim was to make assumptions about the mechanism and forces connecting these observable objects, to account for their behaviour in the simplest possible way. It has become increasingly evident in recent times, however, that nature works on a different plan. Her fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies." (Paul A M Dirac, The Principles of Quantum Mechanics", 1930)

"Science works by the slow method of the classification of data, arranging the detail patiently in a periodic system into groups of facts, in series like the strata of the rocks. For each series there must be a vocabulary of special words which do not always make good sense when used in another series. But the laws of periodicity seem to hold throughout, among the elements and in every sphere of thought, and we must learn to co-ordinate the whole through our new conception of the reign of relativity." (William H Pallister, "Poems of Science", 1931)

"We have no right to assume that any physical laws exist, or if they have existed up until now, that they will continue to exist in a similar manner in the future." (Max Planck, "The Universe in the Light of Modern Physics", 1931)

"It goes without saying that the laws of nature are in themselves independent of the properties of the instruments with which they are measured. Therefore in every observation of natural phenomena we must remember the principle that the reliability of the measuring apparatus must always play an important role." (Max Planck,"Where is Science Going?", 1932)

"In every important advance the physicist finds that the fundamental laws are simplified more and more as experimental research advances. He is astonished to notice how sublime order emerges from what appeared to be chaos. And this cannot be traced back to the workings of his own mind but is due to a quality that is inherent in the world of perception." (Albert Einstein, 1932)

"It goes without saying that the laws of nature are in themselves independent of the properties of the instruments with which they are measured. Therefore in every observation of natural phenomena we must remember the principle that the reliability of the measuring apparatus must always play an important role." (Max Planck, "Where is Science Going?", 1932)

"The sequence of different positions of the same particle at different times forms a one-dimensional continuum in the four-dimensional space-time, which is called the world-line of the particle. All that physical experiments or observations can teach us refers to intersections of world-lines of different material particles, light-pulsations, etc., and how the course of the world-line is between these points of intersection is entirely irrelevant and outside the domain of physics. The system of intersecting world-lines can thus be twisted about at will, so long as no points of intersection are destroyed or created, and their order is not changed. It follows that the equations expressing the physical laws must be invariant for arbitrary transformations." (Willem de Sitter, "Kosmos", 1932)

"In reality the cycles we have the occasion to observe are generally not damped. How can the maintenance of the swings be explained? Have theses dynamic laws deduced from theory and showing damped oscillations no value in explaining the real phenomena, or in what respect do the dynamic laws need to be completed in order to explain the real happenings? They" (dynamic laws) only form one element of the explanation: they solve the propagation problem. But the impulse problem remains." (Ragnar Frisch, "Propagation problems and impulse problems in dynamic economics", 1933)

"[...] the supreme task of the physicist is the discovery of the most general elementary laws from which the world-picture can be deduced logically. But there is no logical way to the discovery of these elemental laws. There is only the way of intuition, which is helped by a feeling for the order lying behind the appearance, and this Einfühlung [literally, empathy or 'feeling one's way in'] is developed by experience." (Albert Einstein, [Preface to Max Planck's "Where is Science Going?"], 1933)

"Science is not a system of certain, or -established, statements; nor is it a system which steadily advances towards a state of finality […] And our guesses are guided by the unscientific, the metaphysical" (though biologically explicable) faith in laws, in regularities which we can uncover - discover. Like Bacon, we might describe our own contemporary science - 'the method of reasoning which men now ordinarily apply to nature' - as consisting of 'anticipations, rash and premature' and as 'prejudices'." (Karl R Popper, "The Logic of Scientific Discovery", 1934)

"It has become increasingly evident in recent times, however, that nature works on a different plan. Her fundamental laws do not govern the world as it appears in our mental picture in any very direct way, but instead they control a substratum of which we cannot form a mental picture without introducing irrelevancies." (Paul Dirac, "The Principles of Quantum Mechanics", 1935)

"Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature." (Albert Einstein, 1935)

"Science is the attempt to discover, by means of observation, and reasoning based upon it, first, particular facts about the world, and then laws connecting facts with one another and" (in fortunate cases) making it possible to predict future occurrences." (Bertrand Russell, "Religion and Science, Grounds of Conflict", 1935)

"[...] scientists are not a select few intelligent enough to think in terms of 'broad sweeping theoretical laws and principles'. Instead, scientists are people specifically trained to build models that incorporate theoretical assumptions and empirical evidence. Working with models is essential to the performance of their daily work; it allows them to construct arguments and to collect data." (Peter Imhof, Science Vol. 287, 1935–1936)

"Even if all the laws of psychology were known, one could make a prediction about the behavior of a man only if in addition to the laws, the special nature of the particular situation were known." (Kurt Lewin, "Principles of topological psychology", 1936)

"We know, since the theory of relativity at least, that empirical sciences are to some degree free in defining dynamical concepts or even in assuming laws, and that only a system as a whole which includes concepts, coordinating definitions, and laws can be said to be either true or false, to be adequate or inadequate to empirical facts. This 'freedom', however, is a somewhat doubtful gift. The manifold of possibilities implies uncertainty, and such uncertainty can become rather painful in a science as young as psychology, where nearly all concepts are open and unsettled. As psychology approaches the state of a logically sound science, definitions cease to be an arbitrary matter. They become far-reaching decisions which presuppose the mastering of the conceptual problems but which have to be guided entirely by the objective facts." (Kurt Lewin, "Principles of topological psychology", 1936)

"[…] in the world of immediate experience, the world of things is there. Trees grow, day follows night, and death supervenes upon life. One may not say that relations here are external or even internal. They are not relations at all. They are lost in the indescriptibility of things and events, which are what they are. The world which is the test of all observations and all scientific hypothetical reconstruction has in itself no system that can be isolated as a structure of laws, or uniformities, though all laws and formulations of uniformities must be brought to its court for its imprimatur." (Donald C May & George H Mead, "The Philosophy of the Act", 1938)

"The laws of science are the permanent contributions to knowledge - the individual pieces that are fitted together in an attempt to form a picture of the physical universe in action. As the pieces fall into place, we often catch glimpses of emerging patterns, called theories; they set us searching for the missing pieces that will fill in the gaps and complete the patterns. These theories, these provisional interpretations of the data in hand, are mere working hypotheses, and they are treated with scant respect until they can be tested by new pieces of the puzzle." (Edwin P Whipple, "Experiment and Experience", [Commencement Address, California Institute of Technology] 1938)

"Science [...] involves active, purposeful search; it discovers, accumulates, sifts, orders, and tests data; it is a slow, painstaking, laborious activity; it is a search after bodies of knowledge sufficiently comprehensive to lead to the discovery of uniformities, sequential orders or so-called 'laws'; it may be carried on by an individual, but it gains relevance only as it produces data which can be added to and tested by the findings of others." (Constantine Panunzio, "Major Social Institutions", 1939)

"The researcher worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should still take simplicity into consideration in a subordinate way to beauty. […] It often happens that the requirements of simplicity and beauty are the same, but where they clash the latter must take precedence." (Paul A M Dirac, "The Relation Between Mathematics and Physics", Proceedings of the Royal Society , Volume LIX, 1939)