Barry R Parker - Collected Quotes

"Chaos appears in both dissipative and conservative systems, but there is a difference in its structure in the two types of systems. Conservative systems have no attractors. Initial conditions can give rise to periodic, quasiperiodic, or chaotic motion, but the chaotic motion, unlike that associated with dissipative systems, is not self-similar. In other words, if you magnify it, it does not give smaller copies of itself. A system that does exhibit self-similarity is called fractal. [...] The chaotic orbits in conservative systems are not fractal; they visit all regions of certain small sections of the phase space, and completely avoid other regions. If you magnify a region of the space, it is not self-similar." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"Geometry gives us a way of turning numbers into pictures." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"General relativity, one of the most famous theories, is formulated in terms of a nonlinear equation. This makes us wonder if some of the phenomena described by general relativity, namely black holes, objects orbiting black holes, and even the universe itself, can become chaotic under certain circumstances. [...] The problem is the equation itself, namely the equation of general relativity; it is so complex that the most general solution has never been obtained. It has, of course, been solved for many simple systems; if the system has considerable symmetry (e.g., it is spherical) the equation reduces to a number of ordinary equations that can be solved, but chaos does not occur in these cases. In more realistic cases—situations that actually occur in nature - chaos may occur, but the equations are either unsolvable or very difficult to solve. This presents a dilemma. If we try to model the system using many simplifications it won't exhibit chaos, but if we model it realistically we can't solve it." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"Most of us use the word 'chaos' rather loosely to represent anything that occurs randomly, so it is natural to think that the motion described by the erratic pendulum above is completely random. Not so. The scientific definition of chaos is different from the one you may be used to in that it has an element of determinism in it. This might seem strange, as determinism and chaos are opposites of one another, but oddly enough they are also compatible." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"Noise is a problem in most signals. [...] It's easy to see that noise is random; it fluctuates erratically with no pattern." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"Nonlinear equations have many properties and difficulties that linear equations do not have. If a nonlinear equation, for example, describes a collection of objects and we want to find the collective effect of these objects, we cannot merely add their individual effects. Because source and effect are independent of one another, their sum does not give the overall effect. With nonlinear phenomena there are strong interactions between the bodies and the contribution from each is modified by the others. Mathematically this means if we change a variable on one side of the equation it doesn't cause a proportional change in the variable on the other side." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"Nonlinearity is important because it can lead to chaos. That's not to say that we get chaos all the time with nonlinear equations; in practice it only occurs under certain conditions." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"One of the major problems with general relativity is that it is not a theory in the usual sense. In the case of most theories you have a stable background, or frame of reference, and you look for solutions within it. In general relativity the solution is the background - the space-time - and it is not necessarily stable," (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"One of the reasons we deal with the pendulum is that it is easy to plot its motion in phase space. If the amplitude is small, it's a two-dimensional problem, so all we need to specify it completely is its position and its velocity. We can make a two-dimensional plot with one axis (the horizontal), position, and the other (the vertical), velocity." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"The problems associated with the initial singularity of the universe bring us to what is called the theory of everything. It is an all-encompassing theory that would completely explain me origin of the universe and everything in it. It would bring together general relativity and quantum mechanics, and explain everything there is to know about the elementary particles of the universe, and the four basic forces of nature (gravitational, electromagnetic, weak, and strong nuclear forces). Furthermore, it would explain the basic laws of nature and the fundamental constants of nature such as the speed of light and Planck's constant." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"The reason general relativity cannot be unified with electromagnetic theory seems to be related to its nonlinearity. To unify the two fields properly we have to construct a "quantized" version of relativity; in other words, we have to quantize it, and so far no one has." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"What chaos implies is not catastrophes, but rather our inability to make long-range predictions [...]" (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"What is chaos? Everyone has an impression of what the word means, but scientifically chaos is more than random behavior, lack of control, or complete disorder. [...] Scientifically, chaos is defined as extreme sensitivity to initial conditions. If a system is chaotic, when you change the initial state of the system by a tiny amount you change its future significantly." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"What is renormalization? First of all, if scaling is present we can go to smaller scales and get exactly the same result. In a sense we are looking at the system with a microscope of increasing power. If you take the limit of such a process you get a stability that is not otherwise present. In short, in the renormalized system, the self-similarity is exact, not approximate as it usually is. So renormalization gives stability and exactness." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

Gerald J Whitrow - Collected Quotes

"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)

"Space-time is curved in the neighborhood of material masses, but it is not clear whether the presence of matter causes the curvature of space-time or whether this curvature is itself responsible for the existence of matter." (Gerald J Whitrow, "The Structure of the Universe: An Introduction to Cosmology", 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)

"The basic objection to attempts to deduce the unidirectional nature of time from concepts such as entropy is that they are attempts to reduce a more fundamental concept to a less fundamental one." (Gerald J Whitrow, "The Natural Philosophy of Time", 1961)

"[Time is not] a mysterious illusion of the intellect. [...] It is an essential feature of the universe." (Gerald J Whitrow, "The Natural Philosophy of Time", 1961)

"Our conscious appreciation of the fact that one event follows another is of a different kind from our awareness of either event separately. If two events are to be represented as occurring in succession, then - paradoxically - they must also be thought of simultaneously." (Gerald J Whitrow, "The Natural Philosophy of Time", 1961)

"Language itself inevitably introduced an element of permanence into the world. For, although speech itself is transitory, the conventionalized sound symbols of language transcended time." (Gerald J Whitrow, "Time in History: Views of Time from Prehistory to the Present Day", 1988)

"Man must have been conscious of memories and purposes long before he made any explicit distinction between past, present, and future." (Gerald J Whitrow, "Time in History: Views of Time from Prehistory to the Present Day", 1988)

"The development of rational thought actually seems to have impeded man's appreciation for the significance of time. [...] Belief that the ultimate reality is timeless is deeply rooted in human thinking, and the origin of rational investigation of the world was the search for permanent factors that lie behind the ever-changing pattern of events." (Gerald J Whitrow, "Time in History: Views of Time from Prehistory to the Present Day", 1988)

Arthur Koestler - Collected Quotes

"The ultimate truth is penultimately always a falsehood. He who will be proved right in the end appears to be wrong and harmful before it." (Arthur Koestler, "Darkness at Noon", 1940)

"Artists treat facts as stimuli for the imagination, while scientists use their imagination to coordinate facts." (Arthur Koestler, "Insight and Outlook: An Inquiry into the Common Foundations of Science, Art and Social Ethics", 1949)

"Men cannot be treated as units in operations of political arithmetic because they behave like the symbols for zero and the infinite, which dislocate all mathematical operations." (Arthur Koestler, "Crossman", 1949)

"If time is treated in modern physics as a dimension on a par with the dimensions of space, why should we a priori exclude the possibility that we are pulled as well as pushed along its axis? The future has, after all, as much or as little reality as the past, and there is nothing logically inconceivable in introducing, as a working hypothesis, an element of finality, supplementary to the element of causality, into our equations. It betrays a great lack of imagination to believe that the concept of “purpose” must necessarily be associated with some anthropomorphic deity." (Arthur Koestler, "The Sleepwalkers: A History of Man’s Changing Vision of the Universe", 1959)

"Myths grow like crystals, according to their own, recurrent pattern; but there must be a suitable core to start their growth." (Arthur Koestler, "The Sleepwalkers: A History of Man’s Changing Vision of the Universe", 1959)

"We can add to our knowledge, but we cannot subtract from it." (Arthur Koestler, "The Sleepwalkers: A History of Man’s Changing Vision of the Universe", 1959) 

"It has been said that discovery consists in seeing an analogy which nobody had seen before." (Arthur Koestler, "The Act of Creation", 1964) 

"The moment of truth, the sudden emergence of new insight, is an act of intuition. Such intuitions give the appearance of miraculous flashes, or short circuits of reasoning. In fact they may be likened to an immersed chain, of which only the beginning and the end are visible above the surface of consciousness. The diver vanishes at one end of the chain and comes up at the other end, guided by invisible links." (Arthur Koestler, "The Act of Creation", 1964)

"The principle mark of genius is not perfection, but originality, the opening of new frontiers; once this is done, the conquered territory becomes common property." (Arthur Koestler, "The Act of Creation", 1964)

"True creativity often starts where language ends." (Arthur Koestler, "The Act of Creation", 1964)

"Without the hard little bits of marble which are called 'facts' or 'data' one cannot compose a mosaic; what matters, however, are not so much the individual bits, but the successive patterns into which you arrange them, then break them up and rearrange them." (Arthur Koestler, "The Act of Creation", 1964)

"Creative activity could be described as a type of learning process where teacher and pupil are located in the same individual." (Arthur Koestler, "Drinkers of Infinity: Essays 1955-1967", 1967)

"The progress of science is strewn, like an ancient desert trail, with the bleached skeletons of discarded theories which once seemed to possess eternal life." (Arthur Koestler, "The Ghost in the Machine", 1967)

"Creativity in science could be described as the art of putting two and two together to make five. In other words, it consists in combining previously unrelated mental structures in such a way that you get more out of the emergent whole than you have put in." (Arthur Koestler, "Janus: A Summing Up", 1978)

"The more original a discovery, the more obvious it seems afterwards." (Arthur Koestler)

Freeman J Dyson - Collected Quotes

"The reason why new concepts in any branch of science are hard to grasp is always the same; contemporary scientists try to picture the new concept in terms of ideas which existed before." (Freeman J Dyson, "Innovation in Physics" , Scientific American, 1958)

"It has been generally believed that only the complex numbers could legitimately be used as the ground field in discussing quantum-mechanical operators. Over the complex field, Frobenius' theorem is of course not valid; the only division algebra over the complex field is formed by the complex numbers themselves. However, Frobenius' theorem is relevant precisely because the appropriate ground field for much of quantum mechanics is real rather than complex." (Freeman Dyson, "The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics" , Journal of Mathematical Physics Vol. 3, 1962)

"For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created." (Freeman J Dyson, "Mathematics in the Physical Sciences", Scientific American, 1964)

"Mathematical intuition is more often conservative than revolutionary, more often hampering than liberating." (Freeman J Dyson, "Mathematics in the Physical Sciences", Scientific American Vol,. 211 (3), 1964)

"The trouble with group theory is that it leaves so much unexplained that one would like to explain. It isolates in a beautiful way those aspects of nature that can be understood in terms of abstract symmetry alone. It does not offer much hope of explaining the messier facts of life, the numerical values of particle lifetimes and interaction strengths - the great bulk of quantitative experimental data that is now waiting for explanation. The process of abstraction seems to have been too drastic, so that many essential and concrete features of the real world have been left out of consideration. Altogether group theory succeeds just because its aims are modest. It does not try to explain everything, and it does not seem likely that it will grow into a complete or comprehensive theory of the physical world." (Freeman J Dyson, "Mathematics in the Physical Sciences", Scientific American Vol. 211 (3), 1964)

"A good scientist is a person with original ideas. A good engineer is a person who makes a design that works with as few original ideas as possible. There are no prima donnas in engineering." (Freeman J Dyson, "Disturbing the Universe", 1979)

"In the long run, qualitative changes always outweigh quantitative ones. Quantitative predictions of economic and social trends are made obsolete by qualitative changes in the rules of the game. Quantitative predictions of technological progress are made obsolete by unpredictable new inventions. I am interested in the long run, the remote future, where quantitative predictions are meaningless. The only certainty in that remote future is that radically new things will be happening." (Freeman J Dyson, "Disturbing the Universe", 1979)

"I have found a universe growing without limit in richness and complexity, a universe of life surviving forever and making itself known to its neighbors across unimaginable gulfs of space and time. Whether the details of my calculations turn out to be correct or not, there are good scientific reasons for taking seriously the possibility that life and intelligence can succeed in molding this universe of ours to their own purposes." (Freeman J Dyson, "Infinite in All Directions", 1988)

"If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed. I would feel that the Creator had been uncharacteristically lacking in imagination." (Freeman J Dyson, "Infinite in All Directions", 1988)

"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)

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

"The bottom line for mathematicians is that the architecture has to be right. In all the mathematics that I did, the essential point was to find the right architecture. It's like building a bridge. Once the main lines of the structure are right, then the details miraculously fit. The problem is the overall design." (Freeman J Dyson, [interview] 1994)

"I see some parallels between the shifts of fashion in mathematics and in music. In music, the popular new styles of jazz and rock became fashionable a little earlier than the new mathematical styles of chaos and complexity theory. Jazz and rock were long despised by classical musicians, but have emerged as art-forms more accessible than classical music to a wide section of the public. Jazz and rock are no longer to be despised as passing fads. Neither are chaos and complexity theory. But still, classical music and classical mathematics are not dead. Mozart lives, and so does Euler. When the wheel of fashion turns once more, quantum mechanics and hard analysis will once again be in style." (Freeman J Dyson, "Book Review of ‘Nature’s Numbers’", The American Mathematical Monthly, Vol. 103 (7), 1996)

"The total disorder in the universe, as measured by the quantity that physicists call entropy, increases steadily steadily as we go from past to future. On the other hand, the total order in the universe, as measured by the complexity and permanence of organized structures, also increases steadily as we go from past to future." (Freeman J Dyson, [Page-Barbour lecture], 2004)

"The progress of science requires the growth of understanding in both directions, downward from the whole to the parts and upward from the parts to the whole." (Freeman J Dyson, "The Scientist As Rebel", 2006)

"The total disorder in the universe, as measured by the quantity that physicists call entropy, increases steadily as we go from past to future. On the other hand, the total order in the universe, as measured by the complexity and permanence of organized structures, also increases steadily as we go from past to future." (Freeman J Dyson, "A Many-Colored Glass: Reflections on the Place of Life in the Universe", 2007)

"Recreational mathematics is a splendid hobby which young and old can equally enjoy. The popularity of Sudoku shows that an aptitude for recreational mathematics is widespread in the population. From Sudoku it is easy to ascend to mathematical pursuits that offer more scope for imagination and originality." (Freeman Dyson, 2011)

"The whole point of science is that most of it is uncertain. That’s why science is exciting–because we don’t know. Science is all about things we don’t understand. The public, of course, imagines science is just a set of facts. But it’s not. Science is a process of exploring, which is always partial. We explore, and we find out things that we understand. We find out things we thought we understood were wrong. That’s how it makes progress." (Freeman Dyson,  [interview] 2014)

"A model is done when nothing else can be taken out." (Freeman J Dyson)

"Much of the history of science, like the history of religion, is a history of struggles driven by power and money. And yet, this is not the whole story. Genuine saints occasionally play an important role, both in religion and science. For many scientists, the reward for being a scientist is not the power and the money but the chance of catching a glimpse of the transcendent beauty of nature." (Freeman J Dyson)

"It often happens that understanding of the mathematical nature of an equation is impossible without a detailed understanding of its solution." (Freeman J Dyson)

"One factor that has remained constant through all the twists and turns of the history of physics is the decisive importance of the mathematical imagination." (Freeman J Dyson)

Douglas N Adams - Collected Quotes

"It is impossible to import things into an infinite area, there being no outside to import things in from." (Douglas N Adams, "The Original Hitchhiker Radio Script, Fit the Fifth" , 1978)

"The simple truth is that interstellar distances will not fit into the human imagination." (Douglas N Adams, "The Hitchhiker's Guide to the Galaxy", 1979)

"The Universe, as has been observed before, is an unsettlingly big place, a fact which for the sake of a quiet life most people tend to ignore." (Douglas N Adams, "The Restaurant at the End of the Universe", 1980)

"The whole fabric of the space-time continuum is not merely curved, it is in fact totally bent." (Douglas N Adams, "The Restaurant at the End of the Universe", 1980) 

"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 complexities of cause and effect defy analysis." (Douglas N Adams, "Dirk Gently's Holistic Detective Agency", 1987) 

"Words used carelessly, as if they did not matter in any serious way, often allowed otherwise well-guarded truths to seep through." (Douglas N Adams, "The Long Dark Tea-Time of the Soul", 1988)

"The most misleading assumptions are the ones you don’t even know you’re making." Douglas N Adams, "Last Chance to See", 1990)

"The system of life on this planet is so astoundingly complex that it was a long time before man even realized that it was a system at all and that it wasn't something that was just there." (Douglas N Adams, "Last Chance to See", 1990)

"A computer terminal is not some clunky old television with a typewriter in front of it. It is an interface where the mind and body can connect with the universe and move bits of it about." (Douglas N Adams, "Mostly Harmless", 1992)

"Anything that happens, happens. Anything that, in happening, causes something else to happen, causes something else to happen. Anything that, in happening, causes itself to happen again, happens again. It doesn't necessarily do it in chronological order though." (Douglas N Adams, "Mostly Harmless", 1992)

"Everything you see or hear or experience in any way at all is specific to you. You create a universe by perceiving it, so everything in the universe you perceive is specific to you." (Douglas N Adams, "Mostly Harmless", 1992)

"All opinions are not equal. Some are a very great deal more robust, sophisticated and well supported in logic and argument than others." (Douglas N Adams, "The Salmon of Doubt", 2002)

"We are stuck with technology when what we really want is just stuff that works." (Douglas N Adams, "The Salmon of Doubt", 2002)

"Deep in the fundamental heart of mind and Universe there is a reason." (Douglas N Adams, "The Hitchhiker's Guide to the Galaxy Radio Scripts" Vol. 2, 2012)

"The world is a thing of utter inordinate complexity and richness and strangeness that is absolutely awesome. I mean the idea that such complexity can arise not only out of such simplicity, but probably absolutely out of nothing, is the most fabulous extraordinary idea. And once you get some kind of inkling of how that might have happened, it's just wonderful." (Douglas N Adams)

On Universe (-1699)

"[...] because the origin of arts and sciences is to be considered according to the present revolution of the universe, we must affirm, in conformity with the most general tradition, that geometry was first invented by the Egyptians, deriving its origin from the mensuration of their fields: since this, indeed, was necessary to them, on account of the inundation of the Nile washing away the boundaries of land belonging to each. Nor ought It to seem wonderful, that the invention of this as well as of other sciences, should receive its commencement from convenience and opportunity. Since whatever is carried in the circle of generation proceeds from the imperfect to the perfect." (Proclus Lycaeus, cca 5th century)

"Everything existing in the universe is the fruit of chance." (Democritus, 4th century BC)

"The infinite […] happens to subsist in a way contrary to what is asserted by others: for the infinite is not that beyond which there is nothing, but it is that of which there is always something beyond. […] But that pertaining to which there is nothing beyond is perfect and whole. […] that of which nothing is absent pertaining to the parts […] the whole is that pertaining to which there is nothing beyond. But that pertaining to which something external is absent, that is not all […] But nothing is perfect which has not an end; and the end is a bound. On this account […] Parmenides spoke better than Melissus: for the latter says that the infinite is a whole; but the former, that the whole is finite, and equally balanced from the middle: for to conjoin the infinite with the universe and the whole, is not to connect line with line." (Aristotle, "Physics", cca. 4th century BC)

"For verily not by design did the first-beginnings of things station themselves each in its right place guided by keen intelligence, nor did they bargain sooth to say what motions each should assume, but because many in number and shifting about in many ways throughout the universe they are driven and tormented by blows during infinite time past, after trying motions and unions of every kind at length they fall into arrangements such as those out of which our sum of things has been formed […]" (Lucretius, "On the Nature of Things", 1st century BC)

"I say, then, that the universe and all its parts both received their first order from divine providence, and are at all times administered by it." (Marcus T Cicero, "De Natura Deorum" ["On the Nature of the Gods"], 45 BC)

"No species remains constant: that great renovator of matter Nature, endlessly fashions new forms from old: there’s nothing in the whole universe that perishes, believe me; rather it renews and varies its substance. What we describe as birth is no more than incipient change from a prior state, while dying is merely to quit it. Though the parts may be transported hither and thither, the sum of all matter is constant." (Publius Ovidius Naso [Ovid], "Metamorphoses", 8 AD)

"Constantly regard the universe as one living being, having one substance and one soul; and observe how all things have reference to one perception, the perception of this one living being; and how all things act with one movement; and how all things are the cooperating causes of all things which exist; observe too the continuous spinning of the thread and the contexture of the web." (Marcus Aurelius, "Meditations". cca. 121–180 AD)

"Those who devised the eccentrics seen thereby in large measure to have solved the problem of apparent motions with approximate calculations. But meanwhile they introduced a good many ideas which apparently contradict the first principles of uniform motion. Nor could they elicit or deduce from the eccentrics the principal consideration, that is, the structure of the universe and the true symmetry of its parts."  (Nicolaus Copernicus, "De revolutionibus orbium coelestium", 1543)

"Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth." (Galileo Galilei, "The Assayer", 1623)

"I tell you that if natural bodies have it from Nature to be moved by any movement, this can only be circular motion, nor is it possible that Nature has given to any of its integral bodies a propensity to be moved by straight motion. I have many confirmations of this proposition, but for the present one alone suffices, which is this. I suppose the parts of the universe to be in the best arrangement, so that none is out of its place, which is to say that Nature and God have perfectly arranged their structure. This being so, it is impossible for those parts to have it from Nature to be moved in straight, or in other than circular motion, because what moves straight changes place, and if it changes place naturally, then it was at first in a place preternatural to it, which goes against the supposition. Therefore, if the parts of the world are well ordered, straight motion is superfluous and not natural, and they can only have it when some body is forcibly removed from its natural place, to which it would then return by a straight line, for thus it appears that a part of the earth does [move] when separated from its whole. I said 'it appears to us', because I am not against thinking that not even for such an effect does Nature make use of straight line motion." (Galileo Galilei, [Letter to Francesco Ingoli] 1624)

"I will prove that there are infinite worlds in an infinite world. Imagine the universe as a great animal, and the stars as worlds like other animals inside it. These stars serve in turn as worlds for other organisms, such as ourselves, horses and elephants. We in our turn are worlds for even smaller organisms such as cankers, lice, worms and mites. And they are earths for other, imperceptible beings. Just as we appear to be a huge world to these little organisms, perhaps our flesh, blood and bodily fluids are nothing more than a connected tissue of little animals that move and cause us to move. Even as they let themselves be led blindly by our will, which serves them as a vehicle, they animate us and combine to produce this action we call life." (Cyrano de Bergerac,"The Other World", 1657)

"The nature, mother of the eternal diversities, or the divine spirit, are zaelous of her variety by accepting one and only one pattern for all things, By these reasons she has invented this elegant and admirable proceeding. This wonder of Analysis, prodigy of the universe of ideas, a kind of hermaphrodite between existence and non-existence, which we have named imaginary root?" (Gottfried W Leibniz, "De Bisectione Latereum", 1675)

On Universe (1800-1849)

"The Author of nature has not given laws to the universe, which, like the institutions of men, carry in themselves the elements of their own destruction. He has not permitted, in his works, any symptom of infancy or of old age, or any sign by which we may estimate either their future or their past duration. He may put an end, as he no doubt gave a beginning, to the present system, at some determinate period; but we may safely conclude, that this great catastrophe will not be brought about by any of the laws now existing, and that it is not indicated by anything which we perceive." (John Playfair, "Illustrations of the Huttonian Theory of the Earth", 1802)

"It is contrary to the usual order of things, that events so harmonious as those of the system of the world, should depend on such diversified agents as are supposed to exist in our artificial arrangements; and there is reason to anticipate a great reduction in the number of undecompounded bodies, and to expect that the analogies of nature will be found conformable to the refined operations of art. The more the phenomena of the universe are studied, the more distinct their connection appears, and the more simple their causes, the more magnificent their design, and the more wonderful the wisdom and power of their Author." (Sir Humphry Davy, "Elements of Chemical Philosophy", 1812)

"We ought then to consider the present state of the universe as the effect of its previous state and as the cause of that which is to follow. An intelligence that, at a given instant, could comprehend all the forces by which nature is animated and the respective situation of the beings that make it up, if moreover it were vast enough to submit these data to analysis, would encompass in the same formula the movements of the greatest bodies of the universe and those of the lightest atoms. For such an intelligence nothing would be uncertain, and the future, like the past, would be open to its eyes." (Pierre-Simon de Laplace, "Essai philosophique sur les probabilités", 1814)

"It is probable that what we call thought is not an actual being, but no more than the relation between certain parts of that infinitely varied mass, of which the rest of the universe is composed, and which ceases to exist as soon as those parts change their position with regard to each other." (Percy B Shelley, "On a Future State", 1815)

"Genius and science have burst the limits of space, and few observations, explained by just reasoning, have unveiled the mechanism of the universe. Would it not also be glorious for man to burst the limits of time, and, by a few observations, to ascertain the history of this world, and the series of events which preceded the birth of the human race?" (Georges Cuvier, "Essays on the Theory of the Earth", 1822)

"Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes." (Baron Jean-Baptiste-Joseph Fourier, "Théorie Analytique de la Chaleur", 1822)

""God puts his finger in the other scale, And up we bounce, a bubble. Nought is great Nor small, with God; for none but he can make The atom imperceptible, and none But he can make a world; he counts the orbs, He counts the atoms of the universe, And makes both equal; both are infinite.""  (Philip James Bailey, "Festus", 1845)

On Universe (1850-1874)

"A human being, what is a human being? Everything and nothing. Through the power of thought it can mirror everything it experiences. Through memory and knowledge it becomes a microcosm, carrying the world within itself. A mirror of things, a mirror of facts. Each human being becomes a little universe within the universe!" (Guy de Maupassant, [in "The Journal of a Madman"] 1851)

"The more man inquires into the laws which regulate the material universe, the more he is convinced that all its varied forms arise from the action of a few simple principles. These principles themselves converge, with accelerating force, towards some still more comprehensive law to which all matter seems to be submitted. Simple as that law may possibly be, it must be remembered that it is only one amongst an infinite number of simple laws: that each of these laws has consequences at least as extensive as the existing one, and therefore that the Creator who selected the present law must have foreseen the consequences of all other laws." (Charles Babbage, "Passages From the Life of a Philosopher", 1864)

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

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

"The world of ideas which it discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest grounds of the title of mathematics to human regard, and would remain unimpeached and unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance." (James J Sylvester, "The Study That Knows Nothing of Observation", 1869)

"I cannot look at the universe as the result of blind chance, yet I can see no evidence of beneficent design, or indeed of design of any kind, in the details." (Charles Darwin, [Letter to Joseph D Hooker, 1870)

"The mind of man may be compared to a musical instrument with a certain range of notes, beyond which in both directions we have an infinitude of silence. The phenomena of matter and force lie within our intellectual range, and as far as they reach we will at all hazards push our inquiries. But behind, and above, and around all, the real mystery of this universe [Who made it all?] lies unsolved, and, as far as we are concerned, is incapable of solution." (John Tyndall, "Fragments of Science for Unscientific People", 1871)

"One microscopic glittering point; then another; and another, and still another; they are scarcely perceptible, yet they are enormous. This light is a focus; this focus, a star; this star, a sun; this sun, a universe; this universe, nothing. Every number is zero in the presence of the infinite." (Victor Hugo, "The Toilers of the Sea", 1874)

On Universe (1875-1899)

"The moral universe is so closely linked to the physical universe that it is scarcely likely that they are not one and the same machine." (Denis Diderot, "Eléments de Physiologie", 1875)

"The strongest use of the symbol is to be found in its magical power of doubling the actual universe, and placing by its side an ideal universe, its exact counterpart, with which it can be compared and contrasted, and, by means of curiously connecting fibres, form with it an organic whole, from which modern analysis has developed her surpassing geometry." (Benjamin Peirce, "On the Uses and Transformations of Linear Algebra", 1875)"The history of thought should warn us against concluding that because the scientific theory of the world is the best that has yet been formulated, it is necessarily complete and final. We must remember that at bottom the generalizations of science or, in common parlance, the laws of nature are merely hypotheses devised to explain that ever-shifting phantasmagoria of thought which we dignify with the high-sounding names of the world and the universe." (Sir James G Frazer, "The Golden Bough: A Study in Magic and Religion", 1890)

"The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe." (Karl Pearson, "The Grammar of Science", 1892)

"There is no short cut to truth, no way to gain a knowledge of the universe except through the gateway of scientific method." (Karl Pearson, "The Grammar of Science", 1892)

"Harmonious order governing eternally continuous progress - the web and woof of matter and force interweaving by slow degrees, without a broken thread, that veil which lies between us and the Infinite - that universe which alone we know or can know; such is the picture which science draws of the world, and in proportion as any part of that picture is in unison with the rest, so may we feel sure that it is rightly painted." (Thomas H Huxley, "Darwiniana", 1893–94)

"The universe is infinite in all directions, not only above us in the large but also below us in the small. If we start from our human scale of existence and explore the content of the universe further and further, we finally arrive, both in the large and in the small, at misty distances where first our senses and then even our concepts fail us." (Emil Wiechert, 1896)

"The whole aspect of the universe changes with this new conception. The idea of force governing the world, of pre-established law, preconceived harmony, disappears to make room for the harmony that [Charles] Fourier had caught a glimpse of: the one which results from the disorderly and incoherent movements of numberless hosts of matter, each of which goes its own way and all of which hold each other in equilibrium." (Peter Kropotkin, "Anarchism: Its Philosophy and Ideal", 1896)

On Universe (Unsourced)

"[…] if one really understood the central point and its necessity in the construction of the world, one ought to be able to state it in one clear, simple sentence. Until we see the quantum principle with this simplicity we can well believe that we do not know the first thing about the universe, about ourselves, and about our place in the universe." (John A Wheeler)

"Everything you’ve learned in school as 'obvious' becomes less and less obvious as you begin to study the universe." (Richard B Fuller)

"Exploring Pi is like exploring the universe." (David Chudnovsky)

"God may not play dice with the universe, but something strange is going on with the prime numbers." (Paul Erdos)

"Human thought, flying on the trapezes of the star-filled universe, with mathematics stretched beneath, was like an acrobat working with a net but suddenly noticing that in reality there is no net." (Vladimir Nabokov)

"I find it as difficult to understand a scientist who does not acknowledge the presence of a superior rationality behind the existence of the universe as it is to comprehend a theologian who would deny the advances of science." (Wernher von Braun)

"It is Proportion that beautifies everything, the whole Universe consists of it, and Musicke is measured by it." (Orlando Gibbons)

"Just as the constant increase of entropy is the basic law of the universe, so it is the basic law of life to be ever more highly structured and to struggle against entropy." (Václav Havel, [Letter to Gustáv Husák])

"Man is not born to solve the problems of the universe, but to find out where the problems begin, and then to take his stand within the limits of the intelligible." (Johann Wolfgang von Goethe)

"Man’s first glance at the universe discovers only variety, diversity, multiplicity of phenomena. Let that glance be illuminated by science - by the science which brings man closer to God, - and simplicity and unity shine on all sides." (Louis Pasteur)

"Math is the language of the universe. So the more equations you know, the more you can converse with the cosmos." (Neil deGrasse Tyson)

"Mathematics is not only real, but it is the only reality. [The] entire universe is made of matter, obviously. And matter is made of particles. It's made of electrons and neutrons and protons. So the entire universe is made out of particles. Now what are the particles made out of? They're not made out of anything. The only thing you can say about the reality of an electron is to cite its mathematical properties. So there's a sense in which matter has completely dissolved and what is left is just a mathematical structure." (Martin Gardner)

"Nothing in the universe is contingent, but all things are conditioned to exist and operate in a particular manner by the necessity of the divine nature." (Baruch Spinoza)

"Number rules the universe." (Pythagoras)

"One might describe the mathematical quality in Nature by saying that the universe is so constituted that mathematics is a useful tool in its description. However, recent advances in physical science show that this statement of the case is too trivial. The connection between mathematics and the description of the universe goes far deeper than this, and one can get an appreciation of it only from a thorough examination of the various facts that make it up." (Paul A M Dirac)

"Our sunsets have been reduced to wavelengths and frequencies. The complexities of the universe have been shredded into mathematical equations. Even our self-worth as human beings has been destroyed." (Dan Brown)

"Science and poetry are, in fact, inseparable. By providing a vision of life, of Earth, of the universe in all its splendor, science does not challenge human values; it can inspire human values. It does not negate faith; it celebrates faith." (Jacques-Yves Cousteau)

"Science is opposed to theological dogmas because science is founded on fact. To me, the universe is simply a great machine which never came into being and never will end. The human being is no exception to the natural order. Man, like the universe, is a machine." (Nikola Tesla)

"Scientific understanding is an essential step to our finding a home for ourselves in the universe. Through understanding the universe, we become at home in it. In a certain sense we have made this universe out of human concepts and human discoveries. It ceases to be a lonely place, because we can to some extent actually navigate in it." (Isidor Isaac Rabi)

"Since primes are the basic building blocks of the number universe from which all the other natural numbers are composed, each in its own unique combination, the perceived lack of order among them looked like a perplexing discrepancy in the otherwise so rigorously organized structure of the mathematical world." (H Peter Aleff, "Prime Passages to Paradise")

"Ten decimal places of pi are sufficient to give the circumference of the earth to a fraction of an inch, and thirty decimal places would give the circumference of the visible universe to a quantity imperceptible to the most powerful microscope." (Simon Newcomb)

"That deep emotional conviction of the presence of a superior reasoning power, which is revealed in the incomprehensible universe, forms my idea of God." (Albert Einstein)

"The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not thereby discovering the fundamental principles of the universe nor becoming acquainted with the ideas of God." (John W N Sullivan)

"The present state of the system of nature is evidently a consequence of what is in the preceding moment, and if we conceive of an intelligence which at a given instant knew all the forces acting in nature and the position of every object in the universe - if endowed with a brain sufficiently vast to make all necessary calculations - could describe with a single formula the motions of the largest astronomical bodies and those of the smallest atoms. To such an intelligence, nothing would be uncertain; the future, like the past, would be an open book." (Pierre-Simon Laplace)

"The universe is an enormous direct product of representations of symmetry groups." (Steven Weinberg)

"The universe is built on a plan the profound symmetry of which is somehow present in the inner structure of our intellect." (Paul Valery)

"The whole universe is one mathematical and harmonic expression, made up of finite representations of the infinite." (Fritz L Kunz)

"To those of us who spend our lives working on scientific problems, science is a great intellectual adventure of such interest that nothing else we ever do can compare with it. We are attempting to understand the order of a physical universe, vast in extent in space and time, and most complicated and beautiful in its details." (Harold Urey)

"[...] we and our models are both part of the universe we are describing. Thus a physical theory is self referencing, like in Gödel’s theorem. One might therefore expect it to be either inconsistent or incomplete. The theories we have so far are both inconsistent and incomplete." (Stephen Hawking, "Gödel and the End of the Universe" )

"We find, therefore, under this orderly arrangement, a wonderful symmetry in the universe, and a definite relation of harmony in the motion and magnitude of the orbs, of a kind that is not possible to obtain in any other way." (Johannes Kepler)

"What you can show using physics, forces this universe to continue to exist. As long as you're using general relativity and quantum mechanics you are forced to conclude that God exists." (Frank Tipler)

"When confronted with the order and beauty of the universe and the strange coincidences of nature, it's very tempting to take the leap of faith from science into religion. I am sure many physicists want to. I only wish they would admit it." (Tony Rothman)

On Universe (2010-2019)

"The objectivist view is that probabilities are real aspects of the universe - propensities of objects to behave in certain ways - rather than being just descriptions of an observer’s degree of belief. For example, the fact that a fair coin comes up heads with probability 0.5 is a propensity of the coin itself. In this view, frequentist measurements are attempts to observe these propensities. Most physicists agree that quantum phenomena are objectively probabilistic, but uncertainty at the macroscopic scale - e.g., in coin tossing - usually arises from ignorance of initial conditions and does not seem consistent with the propensity view." (Stuart J Russell & Peter Norvig, "Artificial Intelligence: A Modern Approach", 2010)

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

"With each theory or model, our concepts of reality and of the fundamental constituents of the universe have changed." (Stephen Hawking & Leonard Mlodinow, "The Grand Design", 2010)

"All the ideas in the universe can be described by words. Therefore, if you simply take all the words and rearrange them randomly enough times, you’re bound to hit upon at least a few great ideas eventually."  (Jarod Kintz, "The Days of Yay are Here! Wake Me Up When They're Over", 2011)

"Science has revealed a universe that is vast, ancient, violent, strange, and beautiful, a universe of almost infinite variety and possibility one in which time can end in a black hole, and conscious beings can evolve from a soup of minerals." (Leonard Mlodinow, "War of the Worldviews: Where Science and Spirituality Meet - and Do Not", 2011)

?"You do not study mathematics because it helps you build a bridge. You study mathematics because it is the poetry of the universe. Its beauty transcends mere things." (Jonathan D Farley, 2011)

"Complexity is the prodigy of the world. Simplicity is the sensation of the universe. Behind complexity, there is always simplicity to be revealed. Inside simplicity, there is always complexity to be discovered." (Gang Yu, "in Data Warehousing in the Age of Big Data", 2013)

"It's pretty much a fact that our entire universe is a mental construct. We don't actually deal with reality directly. We simply compose a picture of reality from what's going on in our retinas, in the timpani of our ears, and in our nerve endings." (Alan Moore, The Believer No. 99, [interview] 2013)

"The universe of all things that exist may be understood as a universe of systems where a system is defined as any set of related and interacting elements. This concept is primitive and powerful and has been used increasingly over the last half-century to organize knowledge in virtually all domains of interest to investigators. As human inventions and social interactions grow more complex, general conceptual frameworks that integrate knowledge among different disciplines studying those emerging systems grow more important. Living systems theory (LST) instructs integrative research among biological and social sciences and related academic disciplines." (G. A. Swanson & James G Miller, "Living Systems Theory", 2013)

"Without precise predictability, control is impotent and almost meaningless. In other words, the lesser the predictability, the harder the entity or system is to control, and vice versa. If our universe actually operated on linear causality, with no surprises, uncertainty, or abrupt changes, all future events would be absolutely predictable in a sort of waveless orderliness." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"The process of thinking itself requires us to view the universe in the direction of entropy, since an abstraction always involves information loss, since symbols 'abstract' complexity from observed objects." (John C Wright, "Awake in the Night Land", 2014)

"A part is always too limited to explain the whole. You might picture a worldview as trying to stuff the entire universe into a box. Invariably, something will stick out of the box. Its categories are too ‘small’ to explain the world." (Nancy Pearcey, "Finding Truth: 5 Principles for Unmasking Atheism, Secularism, and Other God Substitutes", 2015)

"Religion claims to help us understand things about the universe, but, unlike science has no way to test or verify its claims. Both science and religion compete to understand reality, but only science has the method to verify its findings, while religion merely buttresses emotional and epistemic commitments made in advance, commitments impervious to evidence." (Jerry Coyne, 2015)

"The passage of time and the action of entropy bring about ever-greater complexity - a branching, blossoming tree of possibilities. Blossoming disorder (things getting worse), now unfolding within the constraints of the physics of our universe, creates novel opportunities for spontaneous ordered complexity to arise." (D J MacLennan, "Frozen to Life", 2015)

"Without chaos there would be no creation, no structure and no existence. After all, order is merely the repetition of patterns; chaos is the process that establishes those patterns. Without this creative self-organizing force, the universe would be devoid of biological life, the birth of stars and galaxies - everything we have come to know." (Lawrence K Samuels, "Chaos Gets a Bad Rap: Importance of Chaology to Liberty", 2015)

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

"Images are generally resistant to change and ignore messages that do not conform to their internal settings. Sometimes, however, they do react and can alter in an incremental or even revolutionary manner. Humans can talk about and share their images and, in the symbolic universe they create, reflect upon what is and what might be." (Michael C Jackson, "Critical Systems Thinking and the Management of Complexity", 2019)

"Just by looking at accelerating complexification of the Universe of which we are an integral part, we can conclude that we are not subjected to a random walk of evolution, nor are we subjected to a deterministic script of Nature, the truth lies somewhere in between – we are part of teleological evolution." (Alex M Vikoulov, "The Syntellect Hypothesis: Five Paradigms of the Mind's Evolution", 2019)

On Universe (2000-2009)

"A more extreme form of exponential growth was probably responsible for the start of the universe. Astronomer and physicists now generally accept the Big Bang theory, according to which the universe started at an unimaginably small size and then doubled in a split second 100 times, enough to make it the size of a small grapefruit. This period of 'inflation' or exponential growth then ended, and linear growth took over, with an expanding fireball creating the universe that we know today." (Richar Koch, "The Power Laws", 2000)

"The passion and beauty and joy of science is that we humans have invented a process to understand the universe in a way that is true for everyone. We are finding universal truths." (Bill Nye, 2000)

"Theoretical physicists are like pure mathematicians, in that they are often interested in the hypothetical behaviour of entirely imaginary objects, such as parallel universes, or particles traveling faster than light, whose actual existence is not being seriously proposed at all." (John Ziman," Real Science: What it Is, and what it Means", 2000)

"Zero is behind all of the big puzzles in physics. The infinite density of the black hole is a division by zero. The big bang creation from the void is a division by zero. The infinite energy of the vacuum is a division by zero. Yet dividing by zero destroys the fabric of mathematics and the framework of logic - and threatens to undermine the very basis of science. […] The universe begins and ends with zero." (Charles Seife ."Zero, the Biography of a Dangerous Idea", 2000)

"One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?" (Stephen W Hawking, "The Universe in a Nutshell", 2001).

"'There is an old debate', Erdos liked to say, 'about whether you create mathematics or just discover it. In other words, are the truths already there, even if we don't yet know them?' Erdos had a clear answer to this question: Mathematical truths are there among the list of absolute truths, and we just rediscover them. Random graph theory, so elegant and simple, seemed to him to belong to the eternal truths. Yet today we know that random networks played little role in assembling our universe. Instead, nature resorted to a few fundamental laws [...]. Erdos himself created mathematical truths and an alternative view of our world by developing random graph theory." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"When we look at the world around us, we find that we are not thrown into chaos and randomness but are part of a great order, a grand symphony of life. Every molecule in our body was once a part of previous bodies-living or nonliving-and will be a part of future bodies. In this sense, our body will not die but will live on, again and again, because life lives on. We share not only life's molecules but also its basic principles of organization with the rest of the living world. Arid since our mind, too, is embodied, our concepts and metaphors are embedded in the web of life together with our bodies and brains. We belong to the universe, we are at home in it, and this experience of belonging can make our lives profoundly meaningful." (Fritjof Capra, "The Hidden Connections", 2002)

"Nothing exists in the universe that is separate from anything else. Everything is intrinsically connected, irrevocably interdependent, interactive, interwoven into the fabric of all of life." (Neale D Walsch, "Conversations With God: An Uncommon Dialogue", 2003)

"The concept of a random walk is simple but rich for its many applications, not only in finance but also in physics and the description of natural phenomena. It is arguably one of the most founding concepts in modern physics as well as in finance, as it underlies the theories of elementary particles, which are the building blocks of our universe, as well as those describing the complex organization of matter around us." (Didier Sornette, "Why Stock Markets Crash: Critical Events in Complex Systems", 2003)

"Metaphor is evidence of the human ability to visualize the universe as a coherent organism. Proof of our capacity, not just to see one thing in another but to change the very nature of things. When a metaphor is accepted as fact, it enters groupthink, taking on an existence in the real world. [...] Metaphor is the default form of thought, providing many angles from which to literally 'see' the world." (Marcel Danesi, "Poetic Logic: The Role of Metaphor in Thought, Language, and Culture", 2004)

"The total disorder in the universe, as measured by the quantity that physicists call entropy, increases steadily steadily as we go from past to future. On the other hand, the total order in the universe, as measured by the complexity and permanence of organized structures, also increases steadily as we go from past to future." (Freeman J Dyson, [Page-Barbour lecture], 2004)

"We tackle a multifaceted universe one face at a time, tailoring our models and equations to fit the facts at hand. Whatever mechanical conception proves appropriate, that is the one to use. Discovering worlds within worlds, a practical observer will deal with each realm on its own terms. It is the only sensible approach to take." (Michael Munowitz, "Knowing: The Nature of Physical Law", 2005)

"Although fiction is not fact, paradoxically we need some fictions, particularly mathematical ideas and highly idealized models, to describe, explain, and predict facts.  This is not because the universe is mathematical, but because our brains invent or use refined and law-abiding fictions, not only for intellectual pleasure but also to construct conceptual models of reality." (Mario Bunge, "Chasing Reality: Strife over Realism", 2006)

"The standard big bang model doesn’t explain the smoothness and flatness of the universe, so it’s been embellished by an additional component: inflation. A minuscule fraction of a second after the big bang, the universe was propelled into an exponential expansion that increased its size from a proton to a grapefruit. […] Moreover, if we accept the theory that the universe emerged from a quantum seed and exponentially expanded in the big bang, there is the possibility that other regions of space-time exist, remote in time or space from our universe. Due to the random nature of quantum processes, these parallel universes could have wildly different properties. This extravagant concept is called the multiverse." (Chris Impey, "The Living Cosmos: Our search for life in the universe", 2007)

"The total disorder in the universe, as measured by the quantity that physicists call entropy, increases steadily as we go from past to future. On the other hand, the total order in the universe, as measured by the complexity and permanence of organized structures, also increases steadily as we go from past to future." (Freeman J Dyson, "A Many-Colored Glass: Reflections on the Place of Life in the Universe", 2007)

"[chaos theory] presents a universe that is at once deterministic and obeys the fundamental physical laws, but is capable of disorder, complexity, and unpredictability. It shows that predictability is a rare phenomenon operating only within the constraints that science has filtered out from the rich diversity of our complex world." (Ziauddin Sardar & Iwona Abrams, "Introducing Chaos: A Graphic Guide", 2008)

"Let's face it, the universe is messy. It is nonlinear, turbulent, and chaotic. It is dynamic. It spends its time in transient behavior on its way to somewhere else, not in mathematically neat equilibria. It self-organizes and evolves. It creates diversity, not uniformity. That's what makes the world interesting, that's what makes it beautiful, and that's what makes it work." (Donella H Meadow, "Thinking in Systems: A Primer", 2008)

"Yet, in the end, entropy will always emerge victorious, snuffing out the very last glimmer of heat and light. After that there is only darkness. When that state is reached even eternity will cease to exist, for one moment will be like every other and nothingness will claim the universe." (Peter F Hamilton, "The Temporal Void", 2008)

"[…] if all sentient beings in the universe disappeared, there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime, even if no one had proved them prime." (Martin Gardner, "When You Were a Tadpole and I Was a Fish", 2009)

"Much of the recorded knowledge of physics and engineering is written in the form of mathematical models. These mathematical models form the foundations of our understanding of the universe we live in. Furthermore, nearly all of the existing technology, in one way or another, rests on these models. To the extent that we are surrounded by evidence of the technology working and being reliable, human confidence in the validity of the underlying mathematical models is all but unshakable." (Jerzy A Filar, "Mathematical Models", 2009)

"There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depends heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood." (Paul Lockhart, "A Mathematician's Lament", 2009)

On Universe (1990-1999)

"On this view, we recognize science to be the search for algorithmic compressions. We list sequences of observed data. We try to formulate algorithms that compactly represent the information content of those sequences. Then we test the correctness of our hypothetical abbreviations by using them to predict the next terms in the string. These predictions can then be compared with the future direction of the data sequence. Without the development of algorithmic compressions of data all science would be replaced by mindless stamp collecting - the indiscriminate accumulation of every available fact. Science is predicated upon the belief that the Universe is algorithmically compressible and the modern search for a Theory of Everything is the ultimate expression of that belief, a belief that there is an abbreviated representation of the logic behind the Universe's properties that can be written down in finite form by human beings." (John D Barrow, New Theories of Everything", 1991)

"Probability does pervade the universe, and in this sense, the old chestnut about baseball imitating life really has validity. The statistics of streaks and slumps, properly understood, do teach an important lesson about epistemology, and life in general. The history of a species, or any natural phenomenon, that requires unbroken continuity in a world of trouble, works like a batting streak. All are games of a gambler playing with a limited stake against a house with infinite resources. The gambler must eventually go bust. His aim can only be to stick around as long as possible, to have some fun while he's at it, and, if he happens to be a moral agent as well, to worry about staying the course with honor!" (Stephen J Gould, 1991)

"The inflationary period of expansion does not smooth out irregularity by entropy-producing processes like those explored by the cosmologies of the seventies. Rather it sweeps the irregularity out beyond the Horizon of our visible Universe, where we cannot see it . The entire universe of stars and galaxies on view to us. […] on this hypothesis, is but the reflection of a minute, perhaps infinitesimal, portion of the universe's initial conditions, whose ultimate extent and structure must remain forever unknowable to us. A theory of everything does not help here. The information contained in the observable part of the universe derives from the evolution of a tiny part of the initial conditions for the entire universe. The sum total of all the observations we could possibly make can only tell us about a minuscule portion of the whole." (John D Barrow, "Theories of Everything: The Quest for Ultimate Explanation", 1991)

"The scope of Theories of Everything is infinite but bounded; they are necessary parts of a full understanding of things but they are far from sufficient to reveal everything about a Universe like ours. In the pages of this book, we have seen something of what a Theory of Everything might hope to teach us about the unity of the Universe and the way in which it may contain elements that transcend our present compartmentalized view of Nature's ingredients. But we have also learnt that there is more to Everything than meets the eye. Unlike many others that we can imagine, our world contains prospective elements. Theories of Everything can make no impression upon predicting these prospective attributes of reality; yet, strangely, many of these qualities will themselves be employed in the human selection and approval of an aesthetically acceptable Theory of Everything. There is no formula that can deliver all truth, all harmony, all simplicity. No Theory of Everything can ever provide total insight. For, to see through everything, would leave us seeing nothing at all." (John D Barrow, "New Theories of Everything", 1991)

"Indeed, except for the very simplest physical systems, virtually everything and everybody in the world is caught up in a vast, nonlinear web of incentives and constraints and connections. The slightest change in one place causes tremors everywhere else. We can't help but disturb the universe, as T.S. Eliot almost said. The whole is almost always equal to a good deal more than the sum of its parts. And the mathematical expression of that property - to the extent that such systems can be described by mathematics at all - is a nonlinear equation: one whose graph is curvy." (M Mitchell Waldrop, "Complexity: The Emerging Science at the Edge of Order and Chaos", 1992)

"Scientists use mathematics to build mental universes. They write down mathematical descriptions - models - that capture essential fragments of how they think the world behaves. Then they analyse their consequences. This is called 'theory'. They test their theories against observations: this is called 'experiment'. Depending on the result, they may modify the mathematical model and repeat the cycle until theory and experiment agree. Not that it's really that simple; but that's the general gist of it, the essence of the scientific method." (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 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 voyage of discovery into our own solar system has taken us from clockwork precision into chaos and complexity. This still unfinished journey has not been easy, characterized as it is by twists, turns, and surprises that mirror the intricacies of the human mind at work on a profound puzzle. Much remains a mystery. We have found chaos, but what it means and what its relevance is to our place in the universe remains shrouded in a seemingly impenetrable cloak of mathematical uncertainty." (Ivars Peterson, "Newton’s Clock", 1993)

"We have found chaos, but what it means and what its relevance is to our place in the universe remains shrouded in a seemingly impenetrable cloak of mathematical uncertainty." (Ivars Peterson, "Newton’s Clock", 1993)

"A religion old or new, that stressed the magnificence of the universe as revealed by modern science, might be able to draw forth reserves of reverence and awe hardly tapped by the conventional faiths. Sooner or later such a religion will emerge." (Carl Sagan, "Pale Blue Dot: a Vision of the Human Future in Space", 1994)

"If we imagine mathematics as a grand orchestra, the system of whole numbers could be likened to a bass drum: simple, direct, repetitive, providing the underlying rhythm for all the other instruments. There surely are more sophisticated concepts - the oboes and French horns and cellos of mathematics - and we examine some of these in later chapters. But whole numbers are always at the foundation." (William Dunham, "The Mathematical Universe", 1994)

"Minkowski, building on Einstein's work, had now discovered that the Universe is made of a four-dimensional ‘spacetime’ fabric that is absolute, not relative." (Kip S Thorne, "Black Holes and Time Warps: Einstein's Outrageous Legacy" , 1994)

"A fuzzy set can be defined mathematically by assigning to each possible individual in the universe of discourse a value representing its grade of membership in the fuzzy set. This grade corresponds to the degree to which that individual is similar or compatible with the concept represented by the fuzzy set. Thus, individuals may belong in the fuzzy act to a greater or lesser degree as indicated by a larger or smaller membership grade. As already mentioned, these membership grades are very often represented by real-number values ranging in the closed interval between 0 and 1." (George J Klir & Bo Yuan, "Fuzzy Sets and Fuzzy Logic: Theory and Applications", 1995)

"An essential element of dynamics systems is a positive feedback that self-enhances the initial deviation from the mean. The avalanche is proverbial. Cities grow since they attract more people, and in the universe, a local accumulation of dust may attract more dust, eventually leading to the birth of a star. Earlier or later, self-enhancing processes evoke an antagonistic reaction. A collapsing stock market stimulates the purchase of shares at a low price, thereby stabilizing the market. The increasing noise, dirt, crime and traffic jams may discourage people from moving into a big city." (Hans Meinhardt, "The Algorithmic Beauty of Sea Shells", 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)

"Humans may crave absolute certainty; they may aspire to it; they may pretend, as partisans of certain religions do, to have attained it. But the history of science - by far the most successful claim to knowledge accessible to humans - teaches that the most we can hope for is successive improvement in our understanding, learning from our mistakes, an asymptotic approach to the Universe, but with the proviso that absolute certainty will always elude us. We will always be mired in error. The most each generation can hope for is to reduce the error bars a little, and to add to the body of data to which error bars apply." (Carl Sagan, "The Demon-Haunted World: Science as a Candle in the Dark", 1995)

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

"The Law of Entropy Nonconservation required that life be lived forward, from birth to death. […] To wish for the reverse was to wish for the entropy of the universe to diminish with time, which was impossible. One might as well wish for autumn leaves to assemble themselves in neat stacks just as soon as they had fallen from trees or for water to freeze whenever it was heated." (Michael Guillen, "Five Equations That Changed the World", 1995)

"Yet everything has a beginning, everything comes to an end, and if the universe actually began in some dense explosion, thus creating time and space, so time and space are themselves destined to disappear, the measure vanishing with the measured, until with another ripple running through the primordial quantum field, something new arises from nothingness once again." (David Berlinski, "A Tour of the Calculus", 1995)

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

"Numbers, in fact, are the atoms of the universe, combining with everything else." (Calvin C Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers", 1996)

"Our mental model of the way the world works must shift from images of a clockwork, machinelike universe that is fixed and determined, to the model of a universe that is open, dynamic, interconnected, and full of living qualities." (Joseph Jaworski, "Synchronicity: The Inner Path of Leadership", 1996)

"Science is distinguished not for asserting that nature is rational, but for constantly testing claims to that or any other affect by observation and experiment." (Timothy Ferris, "The Whole Shebang: A State-of-the Universe’s Report", 1996)

"In many ways, the mathematical quest to understand infinity parallels mystical attempts to understand God. Both religions and mathematics attempt to express the relationships between humans, the universe, and infinity. Both have arcane symbols and rituals, and impenetrable language. Both exercise the deep recesses of our mind and stimulate our imagination. Mathematicians, like priests, seek ‘ideal’, immutable, nonmaterial truths and then often try to apply theses truth in the real world." (Clifford A Pickover, "The Loom of God: Mathematical Tapestries at the Edge of Time", 1997)

"Intriguingly, the mathematics of randomness, chaos, and order also furnishes what may be a vital escape from absolute certainty - an opportunity to exercise free will in a deterministic universe. Indeed, in the interplay of order and disorder that makes life interesting, we appear perpetually poised in a state of enticingly precarious perplexity. The universe is neither so crazy that we can’t understand it at all nor so predictable that there’s nothing left for us to discover." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1997)

"Is God a mathematician? Certainly, the world, the universe, and nature can be reliably understood using mathematics. Nature is mathematics." (Clifford A Pickover, "The Loom of God", 1997)

"Math has its own inherent logic, its own internal truth. Its beauty lies in its ability to distill the essence of truth without the messy interference of the real world. It’s clean, neat, above it all. It lives in an ideal universe built on the geometer’s perfect circles and polygons, the number theorist’s perfect sets. It matters not that these objects don’t exist in the real world. They are articles of faith." (K C Cole, "The Universe and the Teacup: The Mathematics of Truth and Beauty", 1997)

"There is no end to discoveries in mathematics just as there is no end to the mystery of the universe. Both are boundless. Hence mathematics is not so much a body of knowledge as a way of thought with inexhaustible possibilities." (Karma V Mital, "Understanding Mathematics And Computers" , 1997)

"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)

"In an infinite universe, every point in space-time is the center." (David Zindell, "War in Heaven", 1998)

"Mathematics is a product - a discovery - of the human mind. It enables us to see the incredible, simple, elegant, beautiful, ordered structure that lies beneath the universe we live in. It is one of the greatest creations of mankind - if it is not indeed the greatest." (Keith Devlin, "Life By the Numbers", 1998)

"Often, we use the word random loosely to describe something that is disordered, irregular, patternless, or unpredictable. We link it with chance, probability, luck, and coincidence. However, when we examine what we mean by random in various contexts, ambiguities and uncertainties inevitably arise. Tackling the subtleties of randomness allows us to go to the root of what we can understand of the universe we inhabit and helps us to define the limits of what we can know with certainty." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"Partial models, imperfect as they may be, are the only means developed by science for understanding the universe. This statement does not imply an attitude of defeatism but the recognition that the main tool of science is the human mind and that the human mind is finite." (Nancy Cartwright, "The Dappled World: A Study of the Boundaries of Science", 1999)

"The classic example of chaos at work is in the weather. If you could measure the positions and motions of all the atoms in the air at once, you could predict the weather perfectly. But computer simulations show that tiny differences in starting conditions build up over about a week to give wildly different forecasts. So weather predicting will never be any good for forecasts more than a few days ahead, no matter how big (in terms of memory) and fast computers get to be in the future. The only computer that can simulate the weather is the weather; and the only computer that can simulate the Universe is the Universe." (John Gribbin, "The Little Book of Science", 1999)

On Universe (1980-1989)

"[…] mathematics can never prove anything. No mathematics has any content. All any mathematics can do is – sometimes – turn out to be useful in describing some aspects of our so-called ‘physical universe’. That is a bonus; most forms of mathematics are as meaning-free as chess." (Robert A Heinlein, "The Number of the Beast", 1980)

"In natural science we are concerned ultimately, not with convenient arrangements of observational data which can be generalized into universal explanatory form, but with movements of thought, at once theoretical and empirical, which penetrate into the intrinsic structure of the universe in such a way that there becomes disclosed to us its basic design and we find ourselves at grips with reality.… We cannot pursue natural science scientifically without engaging at the same time in meta-scientific operations." (Thomas F Torrance, "Divine and Contingent Order", 1981)

"In the initial stages of research, mathematicians do not seem to function like theorem-proving machines. Instead, they use some sort of mathematical intuition to ‘see’ the universe of mathematics and determine by a sort of empirical process what is true. This alone is not enough, of course. Once one has discovered a mathematical truth, one tries to find a proof for it." (Rudy Rucker, "Infinity and the Mind: The science and philosophy of the infinite", 1982)

"The vision of the Universe that is so vivid in our minds is framed by a few iron posts of true observation - themselves resting on theory for their meaning - but most of all the walls and towers in the vision are of papier-mâché, plastered in between those posts by an immense labor of imagination and theory." (John A Wheeler & Wojciech H Zurek, "Quantum Theory and Measurement", 1983)

"Mathematical research should be as broad and as original as possible, with very long range-goals. We expect history to repeat itself: we expect that the most profound and useful future applications of mathematics cannot be predicted today, since they will arise from mathematics yet to be discovered." (Arthur Jaffe, "Ordering the universe: the role of mathematics", SIAM Review Vol 26. No 4, 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)

"Nature is disordered, powerful and chaotic, and through fear of the chaos we impose system on it. We abhor complexity, and seek to simplify things whenever we can by whatever means we have at hand. We need to have an overall explanation of what the universe is and how it functions. In order to achieve this overall view we develop explanatory theories which will give structure to natural phenomena: we classify nature into a coherent system which appears to do what we say it does." (James Burke, "The Day the Universe Changed", 1985)

"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)

"Mathematics is more than doing calculations, more than solving equations, more than proving theorems, more than doing algebra, geometry or calculus, more than a way of thinking. Mathematics is the design of a snowflake, the curve of a palm frond, the shape of a building, the joy of a game, the frustration of a puzzle, the crest of a wave, the spiral of a spider's web. It is ancient and yet new. Mathematics is linked to so many ideas and aspects of the universe." (Theoni Pappas, "More Joy of Mathematics: Exploring Mathematics All Around You", 1986)

"Science is not a given set of answers but a system for obtaining answers. The method by which the search is conducted is more important than the nature of the solution. Questions need not be answered at all, or answers may be provided and then changed. It does not matter how often or how profoundly our view of the universe alters, as long as these changes take place in a way appropriate to science. For the practice of science, like the game of baseball, is covered by definite rules." (Robert Shapiro, "Origins: A Skeptic’s Guide to the Creation of Life on Earth", 1986)

"Somehow, after all, as the universe ebbs toward its final equilibrium in the featureless heat bath of maximum entropy, it manages to create interesting structures." (James Gleick, "Chaos: Making a New Science", 1987)

"The increase of disorder or entropy with time is one example of what is called an arrow of time something that gives a direction to time and distinguishes the past from the future. There are at least three different directions of time. First, there is the thermodynamic arrow of time - the direction of time in which disorder or entropy increases. Second, there is the psychological arrow of time. This is the direction in which we feel time passes - the direction of time in which we remember the past, but not the future. Third, there is the cosmological arrow of time. This is the direction of time in which the universe is expanding rather than contracting." (Stephen W. Hawking, "The Direction of Time", New Scientist 46, 1987)

"Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?" (Stephen W Hawking, "A Brief History of Time: From the Big Bang to Black Holes", 1988)

"In an infinite number universe, every point can be regarded as the center, because every point has an infinite of stars on each side of it." (Stephen Hawking, "A Brief History of Time", 1988)

"Science doesn't purvey absolute truth. Science is a mechanism. It's a way of trying to improve your knowledge of nature. It's a system for testing your thoughts against the universe and seeing whether they match. And this works, not just for the ordinary aspects of science, but for all of life. I should think people would want to know that what they know is truly what the universe is like, or at least as close as they can get to it." (Isaac Asimov, [Interview by Bill Moyers] 1988)

"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 usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?" (Stephen Hawking, "A Brief History of Time", 1988)

"The world of science lives fairly comfortably with paradox. We know that light is a wave and also that light is a particle. The discoveries made in the infinitely small world of particle physics indicate randomness and chance, and I do not find it any more difficult to live with the paradox of a universe of randomness and chance and a universe of pattern and purpose than I do with light as a wave and light as a particle. Living with contradiction is nothing new to the human being." (Madeline L'Engle, "Two-Part Invention: The Story of a Marriage", 1988)

"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 Universe (1970-1979)

"Engineers, as a rule are not and do not pretend to be philosophers in the sense of building up consistent systems of thought following logically from certain premises. If anything, they pride themselves on being hard-headed practical men concerned only with facts, disdaining mere speculation or opinion. In practice, however, engineers do make many assumptions about the nature of the universe, of man, and of society." (Edwin T Layton Jr., "The Revolt of the Engineers", 1971)

"When things don't change any longer, that's the end result of entropy, the heat-death of the universe. The more things go on moving, interrelating, conflicting, changing, the less balance there is - and the more life." (Ursula K Le Guin, "The Lathe of Heaven", 1971)

"One of the central problems studied by mankind is the problem of the succession of form. Whatever is the ultimate nature of reality (assuming that this expression has meaning). it is indisputable that our universe is not chaos. We perceive beings, objects, things to which we give names. These beings or things are forms or structures endowed with a degree of stability: they take up some part of space and last for some period of time." (René Thom, "Structural Stability and Morphogenesis", 1972)

"The line between inner and outer landscapes is breaking down. Earthquakes can result from seismic upheavals within the human mind. The whole random universe of the industrial age is breaking down into cryptic fragments." (William S Burroughs, [preface] 1972)

"There is no reason to assume that the universe has the slightest interest in intelligence -  or even in life. Both may be random accidental by-products of its operations like the beautiful patterns on a butterfly's wings. The insect would fly just as well without them […]" (Arthur C Clarke, "The Lost Worlds of 2001", 1972)

"[...] everything is inter-linked. And therefore everything has numberless causes. The entire universe contributes to the least thing. A thing is as it is because the world is as it is." (Nisargadatta Maharaj, "I am That", 1973)

"Science is systematic organisation of knowledge about the universe on the basis of explanatory hypotheses which are genuinely testable. Science advances by developing gradually more comprehensive theories; that is, by formulating theories of greater generality which can account for observational statements and hypotheses which appear as prima facie unrelated." (Francisco J Ayala, "Studies in the Philosophy of Biology: Reduction and Related Problems", 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)

"Symbols, formulae and proofs have another hypnotic effect. Because they are not immediately understood, they, like certain jokes, are suspected of holding in some sort of magic embrace the secret of the universe, or at least some of its more hidden parts." (Scott Buchanan, "Poetry and Mathematics", 1975)

"We have reversed the usual classical notion that the independent 'elementary parts' of the world are the fundamental reality, and that the various systems are merely particular contingent forms and arrangements of these parts. Rather, we say that inseparable quantum interconnectedness of the whole universe is the fundamental reality, and that relatively independent behaving parts are merely particular and contingent forms within this whole." (David Bohm, "On the Intuitive Understanding of Nonlocality as Implied by Quantum Theory", Foundations of Physics Vol 5 (1), 1975)

"If entropy must constantly and continuously increase, then the universe is remorselessly running down, thus setting a limit (a long one, to be sure) on the existence of humanity. To some human beings, this ultimate end poses itself almost as a threat to their personal immortality, or as a denial of the omnipotence of God. There is, therefore, a strong emotional urge to deny that entropy must increase." (Isaac Asimov," Asimov on Physics", 1976)

"It is tempting to wonder if our present universe, large as it is and complex though it seems, might not be merely the result of a very slight random increase in order over a very small portion of an unbelievably colossal universe which is virtually entirely in heat-death." (Isaac Asimov, 1976)

"A model of the universe does not require faith, but a telescope. If it is wrong, it is wrong." (Paul C W Davies, "Space and Time in the Modern Universe", 1977)

"Her dance spoke of nothing more and nothing less than the tragedy of being alive, and being human. It spoke, most eloquently, of pain. It spoke, most knowingly, of despair. It spoke of the cruel humor of limitless ambition yoked to limited ability, of eternal hope invested in an ephemeral lifetime, of the driving need to try and create an inexorably predetermined future. It spoke of fear, and of hunger, and, most clearly, of the basic loneliness and alienation of the human animal. It described the universe through the eyes of man: a hostile environment, the embodiment of entropy, into which we are all thrown alone, forbidden by our nature to touch another mind save secondhand, by proxy. It spoke of the blind perversity which forces man to strive hugely for a peace which, once attained, becomes boredom. And it spoke of folly, of the terrible paradox by which man is simultaneously capable of reason and unreason, forever unable to cooperate even with himself." Spider Robinson and Jeanne Robinson, "Stardance", 1977)

"Luck was not probability, but it acted through probability. It was, so to speak, quantities of probability, a quantitative average throughout the universe. And like any other fixed quantity, it could only be concentrated or increased at the cost of a diminution elsewhere." (Barrington J Bayley, "The Grand Wheel", 1977)

"The structure of space-time, taken as a whole, is the subject matter of the science called cosmology. Since you are asking about all space and all time in cosmology, you are interested in the entire universe, everywhere and everywhen, viewed as a static geometrical object." (Rudolf B Rucker," Geometry, Relativity and the Fourth Dimension", 1977)

"The evolutionary vision is agnostic in regard to systems in the universe of greater complexity than those of which human beings have clear knowledge. It recognizes aesthetic, moral, and religious ideas and experiences as a species, in this case of mental structures or of images, which clearly interacts with other species in the world's great' ecosystem." (Kenneth Boulding," Ecodynamics: A New Theory of Societal Evolution", 1978)

"It is hard for us today to assimilate all the new ideas that are being suggested in response to the new information we have. We must remember that our picture of the universe is based not only on our scientific knowledge but also on our culture and our philosophy. What new discoveries lie ahead no one can say. There may well be civilizations in other parts of our galaxy or in other galaxies that have already accomplished much of what lies ahead for mankind. Others may just be beginning. The universe clearly presents an unending challenge." (Necia H Apfel & J Allen Hynek, "Architecture of the Universe", 1979)

"It is unscientific to say that within the many billions of galactic systems, ours is the only planet that supports life in advanced form. Nature shuns one of a kind as much as it abhors a vacuum. Given infinite time and space, anything that occurs at one place or time in the universe will occur elsewhere or ‘elsewhen’." (Norman Cousins, "Rendezvous with Infinity", Cosmic Search Magazine Vol. 1 (1), 1979)

"The ultimate metaphysical secret, if we dare state it so simply, is that there are no boundaries in the universe. Boundaries are illusions, products not of reality but of the way we map and edit reality. And while it is fine to map out the territory, it is fatal to confuse the two." (Ken Wilber, "No Boundary: Eastern and Western Approaches to Personal Growth", 1979)

"We see the universe as it is, Father Damien, and these naked truths are cruel ones. We who believe in life, and treasure it, will die. Afterward there will be nothing, eternal emptiness, blackness, nonexistence. In our living there has been no purpose, no poetry, no meaning. Nor do our deaths possess these qualities. When we are gone, the universe will not long remember us, and shortly it will be as if we had never lived at all. Our worlds and our universe will not long outlive us. Ultimately entropy will consume all, and our puny efforts cannot stay that awful end." (George R R Martin, "The Way of Cross and Dragon", 1979)