On Unity (Unsourced)

"As knowledge advances, science ceases to scoff at religion; and religion ceases to frown on science. The hour of mockery by the one, and of reproof by the other, is passing away. Henceforth, they will dwell together in unity and goodwill. They will mutually illustrate the wisdom, power, and grace of God. Science will adorn and enrich religion; and religion will ennoble and sanctify science." (Oliver W Holmes)

"Let us notice first of all, that every generalization implies in some measure the belief in the unity and simplicity of nature." (Henri Poincaré)

"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)

"Nature considered rationally, that is to say, submitted to the process of thought, is a unity in diversity of phenomena; a harmony, blending together all created things, however dissimilar in form and attributes; one great whole animated by the breath of life." (Alexander von Humboldt)

"Nature, despite her seeming diversity, is always a unity, a whole; and thus, when she manifests herself in any part of that whole, the rest must serve as a basis for that particular manifestation, and the latter must have a relationship to the rest of the system." (Johann Wolfgang von Goethe)

"Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity." (Mary Somerville)

"The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena." (David Hilbert)

"The story of scientific discovery has its own epic unity - a unity of purpose and endeavour - the single torch passing from hand to hand through the centuries; and the great moments of science when, after long labour, the pioneers saw their accumulated facts falling into a significant order - sometimes in the form of a law that revolutionised the whole world of thought - have an intense human interest, and belong essentially to the creative imagination of poetry." (Alfred Noyes)

"There is a fundamental error in separating the parts from the whole, the mistake of atomizing what should not be atomized. Unity and complementarity constitute reality." (Werner K Heisenberg)

"We can never achieve absolute truth, but we can live hopefully by a system of calculated probabilities. The law of probability gives to natural and human sciences - to human experience as a whole - the unity of life we seek." (Agnes Meyer)

"Whatever Nature undertakes, she can only accomplish it in a sequence. She never makes a leap. For example she could not produce a horse if it were not preceded by all the other animals on which she ascends to the horse’s structure as if on the rungs of a ladder. Thus every one thing exists for the sake of all things and all for the sake of one; for the one is of course the all as well. Nature, despite her seeming diversity, is always a unity, a whole; and thus, when she manifests herself in any part of that whole, the rest must serve as a basis for that particular manifestation, and the latter must have a relationship to the rest of the system." (Johann Wolfgang von Goethe)

On Unity (-1799)

"If simple unity could be adequately perceived by the sight or by any other sense, then, there would be nothing to attract the mind towards reality any more than in the case of the finger [...] But when it is combined with the perception of its opposite, and seems to involve the conception of plurality as much as unity, then thought begins to be aroused within us, and the soul perplexed and wanting to arrive at a decision asks 'What is absolute unity?' This is the way in which the study of the one has a power of drawing and converting the mind to the contemplation of reality." (Plato, "Republic", cca. 380 BC)

"Things are called continuous when the touching limits of each become one and the same and are contained in each other. Continuity is impossible if these extremities are two. […] Continuity belongs to things that naturally in virtue of their mutual contact form a unity. And in whatever way that which holds them together is one, so too will the whole be one." (Aristotle, "Physics", cca. 350 BC)

"A far greater glory is it to the wise to die for freedom, the love of which stands in very truth implanted in the soul like nothing else, not as a casual adjunct but an essential part of its unity, and cannot be amputated without the whole system being destroyed as a result." (Philo of Alexandria, "Every Good Man is Free", cca. 15 - 45 AD)

"And in the case of superior things like stars, we discover a kind of unity in separation. The higher we rise on the scale of being, the easier it is to discern a connection even among things separated by vast distances." (Marcus Aurelius, "Meditations". cca. 121–180 AD)

"There can only be one wisdom. For if it were possible that there be several wisdoms, then these would have to be from one. Namely, unity is prior to all plurality." (Nicholas of Cusa, "De Pace Fidei" ["The Peace of Faith"], 1453)

"The Fractions which represent the Probabilities of happening and failing, being added together, their Sum will always be equal to Unity, since the Sum of their Numerators will be equal to their common Denominator : now it being a certainty that an Event will either happen or fail, it follows that Certainty, which may be conceived under the notion of an infinitely great degree of Probability, is fitly represented by Unity." (Abraham de Moivre, "The Doctrine of Chances", 1718)

"The schema is in itself always a product of imagination. Since, however, the synthesis of imagination aims at no special intuition, but only at unity in the determination of sensibility, the schema has to be distinguished from the image." (Immanuel Kant," Critique of Pure Reason", 1781)

"Statics is the science of the equilibrium of forces. In general, force or power is the cause, whatever it may be, which induces or tends to impart motion to the body to which it is applied. The force or power must be measured by the quantity of motion produced or to be produced. In the state of equilibrium, the force has no apparent action. It produces only a tendency for motion in the body it is applied to. But it must be measured by the effect it would produce if it were not impeded. By taking any force or its effect as unity, the relation of every other force is only a ratio, a mathematical quantity, which can be represented by some numbers or lines. It is in this fashion that forces must be treated in mechanics." (Joseph-Louis de Lagrange, "Mechanique Analytique", 1788)

"Yet this is attempted by algebraists, who talk of a number less than nothing, of multiplying a negative number into a negative number and thus producing a positive number, of a number being imaginary. Hence they talk of two roots to every equation of the second order, and the learner is to try which will succeed in a given equation: they talk of solving an equation which requires two impossible roots to make it solvable: they can find out some impossible numbers, which, being multiplied together, produce unity. This is all jargon, at which common sense recoils; but, from its having been once adopted, like many other figments, it finds the most strenuous supporters among those who love to take things upon trust, and hate the labour of a serious thought." (William Frend,"The Principles of Algebra", 1796)

On Unity (1800-1849)

"Close observers of nature, however diverse their points of view, will agree that everything of a phenomenal nature must suggest either an original duality capable of being merged in unity, or an original unity capable of becoming a duality. Separating what is united and uniting what is separate is the life of nature. This is the eternal systole and diastole, the eternal synkrisis and diakrisis, the breathing in and out of the world in which we move and have our being." (Johann Wolfgang von Goethe, "On Theory of Color", 1810)

"Only through blind Instinct, in which the only possible guidance of the Imperative is awanting, does the Power in Intuition remain undetermined; where it is schematised as absolute it becomes infinite; and where it is presented in a determinate form, as a principle, it becomes at least manifold. By the above-mentioned act of Intelligising, the Power liberates itself from Instinct, to direct itself towards Unity." (Johann G Fichte, "Outline of the Doctrine of Knowledge", 1810)

"Since it cannot be overlooked by the Doctrine of Knowledge that Actual Knowledge does by no means present itself as a Unity, such as is assumed above but as a multiplicity, there is consequently a second task imposed upon it, - that of setting forth the ground of this apparent Multiplicity. It is of course understood that this ground is not to be derived from any outward source, but must be shown to be contained in the essential Nature of Knowledge itself as such; - and that therefore this problem, although apparently two-fold, is yet but one and the same, - namely, to set forth the essential Nature of Knowledge." (Johann G Fichte, "Outline of the Doctrine of Knowledge", 1810)

"Mathematical analysis […] in the study of all phenomena, interprets them by the same language, as if to attest the unity and simplicity of the plan of the universe, and to make still more evident that unchangeable order which presides over all natural causes. […] There cannot be a language more universal and more simple, more free from errors and obscurities, … more worthy to express the invariable relations of all natural things." (Baron Jean-Baptiste-Joseph Fourier,"Théorie Analytique de la Chaleur", 1822)

"Caught up in the limitless maze, the fragmentation and complication of modern natural science, and yearning for the recapture of simplicity, we must forever ask ourselves: Supposing he had known nature in its present state of complexity, a basic unity withal, how would Plato have coped with it?" (Johann Wolfgang von Goethe, "Maxims and Reflections", 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." (Jean-Baptiste-Joseph Fourier, "Théorie Analytique de la Chaleur", 1822)

"There cannot be a language more universal and more simple, more free from errors and obscurities [...] more worthy to express the invariable relations of all natural things [than mathematics]. [It interprets] all phenomena by the same language, as if to attest the unity and simplicity of the plan of the universe, and to make still more evident that unchangeable order which presides over all natural causes." (Joseph Fourier, "The Analytical Theory of Heat", 1822)

"The more one reflects, the more one acknowledges that necessity governs the world. At each new progress of science ,that which seemed contingent is recognized as being necessary. Multiple relations are established between the branches that we had thought to be separate; we observe laws where we had thought there were only accidental events. We approach more and more the unity of being […]" (Sophie Germain, "Considerations sur l’etat des sciences et lettres, aux differentes epoques de leur culture", 1833)

"Unless my Algebra deceive me, Unity itself divided by Zero will give Infinity." (Thomas Carlyle, "Sartor Resartus", 1836)

"When the whole and the parts are seen at once, as mutually producing and explaining each other, as unity in multeity, there results shapeliness." (Samuel T Coleridge, "Letters", 1836)

"The system becomes more coherent as it is further extended. The elements which we require for explaining a new class of facts are already contained in our system. Different members of the theory run together, and we have thus a constant convergence to unity. In false theories, the contrary is the case." (William Whewell, "Philosophy of the Inductive Sciences", 1840)

"Nature creates unity even in the parts of a whole." (Eugène Delacroix, 1857)

On Unity (1850-1899)

"Simplicity of structure means organic unity, whether the organism be simple or complex; and hence in all times the emphasis which critics have laid upon Simplicity, though they have not unfrequently confounded it with narrowness of range." (George H Lewes, "The Principles of Success in Literature", 1865)

"As systematic unity is what first raises ordinary knowledge to the rank of science, that is, makes a system out of a mere aggregate of knowledge, architectonic is the doctrine of the scientific in our knowledge, and therefore necessarily forms part of the doctrine of method." (Immanuel Kant, "Critique of Pure Reason", 1871)

"The concept of power, which includes as a special case the concept of whole number, that foundation of the theory of number, and which ought to be considered as the most general genuine origin of sets [Moment bei Mannigfaltigkeiten], is by no means restricted to linear point sets, but can be regarded as an attribute of any well-defined collection, whatever may be the character of its elements. [...] Set theory in the conception used here, if we only consider mathematics for now and forget other applications, includes the areas of arithmetic, function theory and geometry. It contains them in terms of the concept of power and brings them all together in a higher unity. Discontinuity and continuity are similarly considered from the same point of view and are thus measured with the same measure." (Georg Cantor, "Ober unendliche, lineare Punktmannichfaltigkeiten", 1879)

"The ignoring of data is, in fact, the easiest and most popular mode of obtaining unity in one's thought." (William James, "The Sentiment of Rationality", Mind Vol. 4, 1879)

"The unity of all science consists alone in its method, not in its material." (Karl Pearson, "The Grammar of Science", 1892)

"Symmetry is evidently a kind of unity in variety, where a whole is determined by the rhythmic repetition of similar." (George Santayana, "The Sense of Beauty: Being the Outlines of Aesthetic Theory", 1896)

On Unity (2000-)

"The calculus is a theory of continuous change - processes that move smoothly and that do not stop, jerk, interrupt themselves, or hurtle over gaps in space and time. The supreme example of a continuous process in nature is represented by the motion of the planets in the night sky as without pause they sweep around the sun in elliptical orbits; but human consciousness is also continuous, the division of experience into separate aspects always coordinated by some underlying form of unity, one that we can barely identify and that we can describe only by calling it continuous." (David Berlinski, "Infinite Ascent: A short history of mathematics", 2005)

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

"By interlinking causes, by searching always for unity in the face of superficial diversity, modern scientific explanations prize depth above breadth. A deep and narrow theory can, and often does, graduate to become a deep and broad one. A broad and shallow theory never does." (John D Barrow, "New Theories of Everything", 2007)

"A science presents us with representations of the phenomena through artifacts, both abstract, such as theories and mathematical models, and concrete such as graphs, tables, charts, and ‘table-top’ models. These representations do not form a haphazard compilation though any unity, in the range of representations made available, is visible mainly at the more abstract levels." (Bas C van Fraassen, "Scientific Representation: Paradoxes of Perspective", 2008)

"Category theory has developed classically, beginning with definitions and axioms and proceeding to a long list of theorems. Category theory is not topology (and so will not be described here), but it can be used to understand some of the relationships that exist among classes of topological spaces. It can be used to bring unity to diversity. [...] the theory of categories is not complete, it may not be completable, but it is a step forward in understanding foundational questions in mathematics." (John Tabak, "Beyond Geometry: A new mathematics of space and form", 2011)

On Unity (1975-1999)

"If physics leads us today to a world view which is essentially mystical, it returns, in a way, to its beginning, 2,500 years ago. […] Eastern thought and, more generally, mystical thought provide a consistent and relevant philosophical background to the theories of contemporary science; a conception of the world in which scientific discoveries can be in perfect harmony with spiritual aims and religious beliefs. The two basic themes of this conception are the unity and interrelation of all phenomena and the intrinsically dynamic nature of the universe. The further we penetrate into the submicroscopic world, the more we shall realize how the modern physicist, like the Eastern mystic, has come to see the world as a system of inseparable, interacting and ever-moving components with the observer being an integral part of this system." (Fritjof Capra, "The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism", 1975)

"In our very distant future we are likely to find that there is only one energy, which has manifold expressions, depending on the state of consciousness that interacts with the energy. However, we presently have a scientific foundation which has already segmented and delineated uniquely different energy characteristics as perceived by our biological senses, and by our extended instrumentation senses. Thus we must continue along the path already laid down by our scientific forebearers, until we have reached the level of consciousness where the unity can be known." (William Tiller, "New Fields, New Laws", 1977) 

"Mathematical physics represents the purest image that the view of nature may generate in the human mind; this image presents all the character of the product of art; it begets some unity, it is true and has the quality of sublimity; this image is to physical nature what music is to the thousand noises of which the air is full […]" (Théophile de Donder, 1977)

"The branch of modern science called cybernetics gives us concepts that describe the evolutionary process at both the level of intracellular structures and the level of social phenomena. The fundamental unity of the evolutionary process at all levels of organization is transformed from a philosophical view to a scientifically substantiated fact." (Valentin F Turchin, "The Phenomenon of Science: A cybernetic approach to human evolution", 1977)

"An autopoietic system is organized (defined as a unity) as a network of processes of production (transformation and destruction) of components that produces the components that: (a) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produce them and, (b) constitute it (the machine) as a concrete unity in the space in which they exist by specifying the topological domain of its realization as such a network." (Francisco Varela, "Principles of Biological Autonomy", 1979)

"Mathematics is not a branch of aesthetics. The mistake, which is common enough, probably stems from the requirement of aesthetic unity but is not identical with that unity." (J K Feibleman,"Assumptions of Grand Logics", 1979)

"An autopoietic system is organized (defined as a unity) as a network of processes of production (transformation and destruction) of components that produces the components that: (a) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produce them and, (b) constitute it (the machine) as a concrete unity in the space in which they exist by specifying the topological domain of its realization as such a network." (Francisco Varela, "Principles of Biological Autonomy", 1979)

"Autopoietic organization simply means processes interlaced in the specific form of a network of productions of components which realizing the network that produced them constitutes it as a unity." (Francisco Varela & Humberto Maturana "Autopoiesis and cognition: The realization of the living", 1980)

"The relations that define a system as a unity, and determine the dynamics of interaction and transformations which it may undergo as such a unity constitute the organization of the machine." (Francisco Varela & Humberto Maturana "Autopoiesis and cognition: The realization of the living", 1980)

"Analogies, metaphors, and emblems are the threads by which the mind holds on to the world even when, absentmindedly, it has lost direct contact with it, and they guarantee the unity of human experience. Moreover, in the thinking process itself they serve as models to give us our bearings lest we stagger blindly among experiences that our bodily senses with their relative certainty of knowledge cannot guide us through." (Hannah Arendt, "The Life of the Mind", 1981)

"By content, therefore, we mean the composition of all the elements of the object in their qualitative determinacy, their interaction and functioning, and the unity of the object's properties, intrinsic processes, relations, contradictions and trends of development. Content is not all that is 'contained' in an object." (Alexander Spirkin, "Dialectical Materialism", 1983)

"The unity of form and content presupposes their relative independence and the active role of the form. The modification of form involves reorganisation of the relations within the object. This process takes place in time and through contradictions." (Alexander Spirkin, "Dialectical Materialism", 1983)

"The ecological principle of unity in diversity grades into a richly mediated social principle; hence my use of the term social ecology." (Murray Bookchin, "What Is Social Ecology?" , 1984)

"The applications of knowledge, especially mathematics, reveal the unity of all knowledge. In a new situation almost anything and everything you ever learned might be applicable, and the artificial divisions seem to vanish." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)

"Organization denotes those relations that must exist among the components of a system for it to be a member of a specific class. Structure denotes the components and relations that actually constitute a particular unity and make its organization real." (Humberto Maturana & Francisco J Varela, "The Tree of Knowledge", 1987)

"The dynamics of any system can be explained by showing the relations between its parts and the regularities of their interactions so as to reveal its organization. For us to fully understand it, however, we need not only to see it as a unity operating in its internal dynamics, but also to see it in its circumstances, i.e., in the context to which its operation connects it. This understanding requires that we adopt a certain distance for observation, a perspective that in the case of historical systems implies a reference to their origin. This can be easy, for instance, in the case of man-made machines, for we have access to every detail of their manufacture. The situation is not that easy, however, as regards living beings: their genesis and their history are never directly visible and can be reconstructed only by fragments." (Humberto Maturana & Francisco J Varela, "The Tree of Knowledge", 1987)

"Autopoietic systems, then, are not only self-organizing systems, they not only produce and eventually change their own structures; their self-reference applies to the production of other components as well. This is the decisive conceptual innovation. […] Thus, everything that is used as a unit by the system is produced as a unit by the system itself. This applies to elements, processes, boundaries, and other structures and, last but not least, to the unity of the system itself." (Niklas Luhmann, "The Autopoiesis of Social Systems", 1990)

"And you should not think that the mathematical game is arbitrary and gratuitous. The diverse mathematical theories have many relations with each other: the objects of one theory may find an interpretation in another theory, and this will lead to new and fruitful viewpoints. Mathematics has deep unity. More than a collection of separate theories such as set theory, topology, and algebra, each with its own basic assumptions, mathematics is a unified whole." (David Ruelle, "Chance and Chaos", 1991)

"Mathematics has deep unity. More than a collection of separate theories such as set theory, topology, and algebra, each with its own basic assumptions, mathematics is a unified whole. Mathematics is a great kingdom, and that kingdom belongs to those who see." (David Ruelle, "Chance and Chaos", 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)

"The unity of mathematics is due to the logical relation between different mathematical theories. The physical theories, by contrast, need not be logically coherent; they have unity because they describe the same physical reality." (David Ruelle, "Chance and Chaos", 1991)

"Every culture has a shared pattern of thinking. It is the cement that holds a culture together, gives it unity. A culture's characteristic way of thinking is imbedded in its concept of the nature of reality, its world view. […] A change of world view not only brings about profound cultural changes, but also is responsible for what historians call a ‘change of age’. An age is a period of time in which the prevailing world view has remained relatively unchanged." (Russell L Ackoff,"Re-Creating the Corporation", 1999)

On Unity (1950-1974)

"Data have an ephemeralness, a rhapsodic spontaneity, a nakedness so utterly at variance with the orderly instincts that pervade our being and with the given unity of our own experience as to be unfit for use in the building of reality. The constructs, on the other hand, are foot-loose, subjective, and altogether too fertile with logical implication to serve in their indiscriminate totality as material for the real world. They do, however, contain the solid logical substance which a stable reality must contain." (Henry Margenau ,"The Nature of Physical Reality: A Philosophy of Modern Physics", 1950)

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

"This continuity of effort is particularly important in mathematics. It is needed to realize the promise of unity which modern mathematics holds. In no science does it appear truer than- in mathematics that the relatively unexplained universe of known facts can be unified by theories of a general character, built of the bricks of current techniques, if only there could rise enough men of talent with a sense of values that would hold them to their task to the very end." (Marston Morse, "Science in the Modern World", Mathematics Magazine Vol. 28 (4), 1955)

"The progress of science is the discovery at each step of a new order which gives unity to what had seemed unlike." (Jacob Bronowski, "Science and Human Values", 1956)

"We can never achieve absolute truth but we can live hopefully by a system of calculated probabilities. The law of probability gives to natural and human sciences - to human experience as a whole - the unity of life we seek." (Agnes E Meyer, "Education for a New Morality", 1957)

"There is beauty in discovery. There is mathematics in music, a kinship of science and poetry in the description of nature, and exquisite form in a molecule. Attempts to place different disciplines in different camps are revealed as artificial in the face of the unity of knowledge. All illiterate men are sustained by the philosopher, the historian, the political analyst, the economist, the scientist, the poet, the artisan, and the musician." (Glenn T Seaborg, 1958)

"Physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods of ordering and surveying human experience. In this respect our task must be to account for such experience in a manner independent of individual subjective judgement and therefor objective in the sense that it can be unambiguously communicated in ordinary human language." (Niels Bohr, "The Unity of Human Knowledge", 1960)

"For Science in its totality, the ultimate goal is the creation of a monistic system in which - on the symbolic level and in terms of the inferred components of invisibility and intangibly fine structure — the world’s enormous multiplicity is reduced to something like unity, and the endless successions of unique events of a great many different kinds get tidied and simplified into a single rational order. Whether this goal will ever be reached remains to be seen. Meanwhile we have the various sciences, each with its own system coordinating concepts, its own criterion of explanation." (Aldous Huxley, "Literature and Science", 1963)

"The 'underlying unity' might mean that everything is made out of the same stuff, and therefore obeys the same equations. That sounds like a good explanation, but let us think. The electrostatic potential, the diffusion of neutrons, heat flow - are we really dealing with the same stuff? Can we really imagine that the electrostatic potential is physically identical to the temperature, or to the density of particles? [...] The displacement of a membrane is certainly not like a temperature. Why, then, is there 'an underlying unity'? [...] Is it possible that this is the clue? That the thing which is common to all the phenomena is the space, the framework into which the physics is put? As long as things are reasonably smooth in space, then the important things that will be involved will be the rates of change of quantities with position in space. That is why we always get an equation with a gradient. [...] What is common to all our problems is that they involve space. "  (Richard Feynman, "Lecture Notes on Physics" Vol. 3, 1964)

"Why are the equations from different phenomena so similar? We might say: ‘It is the underlying unity of nature.’ But what does that mean? What could such a statement mean? It could mean simply that the equations are similar for different phenomena; but then, of course, we have given no explanation. The underlying unity might mean that everything is made out of the same stuff, and therefore obeys the same equations." (Richard P Feynman,"Lecture Notes on Physics", Vol. III, 1964)

On Unity (1925-1949)

"A poem therefore is to be defined as a structure of words whose sound constitutes a rhythmical unity, complete in itself, irrefragable, unanalyzable, completing its symbolic references within the ambit of its sound effects." (Herbert Read, "What is a Poem", 1926)

"It seems to be the impression among students that mathematical physics consists in deriving a large number of partial differential equations and then solving them, individually, by an assortment of special mutually unrelated devices. It has not been made clear that there is any underlying unity of method and one has often been left entirely in the dark as to what first suggested a particular device to the mind of its inventor." (Arthur G Webster, "Partial Differential Equations of Mathematical Physics", 1927)

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

"Science is a system of statements based on direct experience, and controlled by experimental verification. Verification in science is not, however, of single statements but of the entire system or a sub-system of such statements." (Rudolf Carnap, "The Unity of Science", 1934)

"We shall walk together on this path of life, for all things are a part of the universe, and are connected with each other to form one whole unity." (Maria Montessori, "To Educate the Human Potential", 1947)

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

On Unity (1900-1924)

"Let us notice first of all, that every generalization implies in some measure the belief in the unity and simplicity of nature." (Jules H Poincaré, "Science and Hypothesis", 1901)

"For if society lacks the unity that derives from the fact that the relationships between its parts are exactly regulated, that unity resulting from the harmonious articulation of its various functions assured by effective discipline and if, in addition, society lacks the unity based upon the commitment of men's wills to a common objective, then it is no more than a pile of sand that the least jolt or the slightest puff will suffice to scatter." (Émile Durkheim, 1903)    

"From that time, the universe has steadily become more complex and less reducible to a central control. With as much obstinacy as though it were human, it has insisted on expanding its parts; with as much elusiveness as though it were feminine, it has evaded the attempt to impose on it a single will. Modern science, like modern art, tends, in practice, to drop the dogma of organic unity. Some of the mediaeval habit of mind survives, but even that is said to be yielding before the daily evidence of increasing and extending complexity. The fault, then, was not in man, if he no longer looked at science or art as an organic whole or as the expression of unity. Unity turned itself into complexity, multiplicity, variety, and even contradiction." (Henry Adams, "Mont Saint Michel and Chartres", 1904)

"Let us notice first of all, that every generalization implies in some measure the belief in the unity and simplicity of nature." (Jules H Poincaré, "Science and Hypothesis", 1905)

"Mathematicians attach great importance to the elegance of their methods and their results. This is not pure dilettantism. What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details." (Henri Poincaré,"The Future of Mathematics", Monist Vol. 20, 1910)

"It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details." (Henri Poincaré, "The Future of Mathematics", Monist Vol. 20, 1910)

"What is a philosophy? It Is an answer satisfactory to the reason to all the great problems of life. That is what is meant by philosophy. It must satisfy the reason, and it must show the unity underlying the endless diversity of the facts that science observes." (Annie Besant, "The Immediate Future", 1911)

"Theoretical philosophy aimed to discover the unity of experience, namely, in the form of some universal explanation. It strived to yield a world picture, one which is harmoniously integral and completely understandable." (Alexander Bogdanov, "Tektology: The Universal Organizational Science" Vol. I, 1913)

"There is an intellectual function in us which demands unity, connection and intelligibility from any material, whether of perception or thought, that comes within its grasp; and if, as a result of special circumstances, it is unable to establish a true connection, it does not hesitate to fabricate a false one." (Sigmund Freud, 1913-1914)

"Anything at all that can be the object of scientific thought becomes dependent on the axiomatic method, and thereby indirectly on mathematics, as soon as it is ripe for the formation of a theory. By pushing ahead to ever deeper layers of axioms [...] we become ever more conscious of the unity of our knowledge. In the sign of the axiomatic method, mathematics is summoned to a leading role in science." (David Hilbert, "Axiomatisches Denken", 1917)

"By intuition is frequently understood perception, or the knowledge of actual reality, the apprehension of something as real. […] Intuition is the undifferentiated unity of the perception of the real and of the simple image of the possible." (Benedetto Croce, "The Essence of Æsthetic", 1921)

"True artistic experience is never passive, for the spectator is obliged to participate, as it were, in the continuous or discontinuous variations of proportions, positions, lines and planes. Moreover, he must see clearly how this play of repeated or non-repeated changes may give rise to a new harmony of relations which will constitute the unity of the work. Every part becomes organized into a whole with the other parts. All the parts contribute to the unity of the composition, none of them assuming a dominant place in the whole." (Theo van Doesburg, 'Grundbegriffe der neuen Gestaltenden Kunst', 1921-23)

"For tektology the unity of experience is not 'discovered', but actively created by organizational means: ‘philosophers wanted to explain the world, but the main point is it change it’ said the greater precursor of organizational science, Karl Marx. The explanation of organizational forms and methods by tektology is directed not to a contemplation of their unity, but to a practical mastery over them." (Alexander Bogdanov, "Tektology: The Universal Organizational Science", 1922)

"The story of scientific discovery has its own epic unity - a unity of purpose and endeavour - the single torch passing from hand to hand through the centuries; and the great moments of science when, after long labour, the pioneers saw their accumulated facts falling into a significant order - sometimes in the form of a law that revolutionised the whole world of thought - have an intense human interest, and belong essentially to the creative imagination of poetry." (Alfred Noyes, "Watchers of the Sky", 1922)

The Web of Life II

"It is thus that in the universe everything is connected; it is itself but an immense chain of causes and effects, which flow without ceasing one from the other." (Paul-Henri T d'Holbach [Baron d'Holbach], "The System of Nature, Or, Laws of the Moral and Physical World", 1770)

"Brightness and freshness take possession of the mind when it is crossed by the light of principles, shewing the facts of Nature to be organically connected." (John Tyndall, "Six Lectures on Light Delivered in America in 1872-1873" 3rd Ed., 1901) 

"This whole electric universe is a complex maze of similar tensions. Every particle of matter in the universe is separated from its condition of oneness, just as the return ball is separated from the hand, and each is connected with the other one by an electric thread of light which measures the tension of that separateness." (Walter Russell, "The Secret of Light", 1947)

"We shall walk together on this path of life, for all things are a part of the universe, and are connected with each other to form one whole unity." (Maria Montessori, "To Educate the Human Potential", 1947)

"We have since defined Gaia as a complex entity involving the Earth's biosphere, atmosphere, oceans, and soil; the totality constituting a feedback or cybernetic system which seeks an optimal physical and chemical environment for life on this planet." (James Lovelock, "Gaia: A new look at life on Earth", 1981)

"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) 

"In our Gaian world, everything is connected to and influences everything else." (Tim Flannery, "The Weather Makers", 2005)

"I understand that everything is connected, that all roads meet, and that all rivers flow into the same sea." (Paulo Coelho, "Aleph", 2011)

"All the variables we can observe in an ecosystem-population densities, availability of nutrients, weather patterns, and so forth-always fluctuate. This is how ecosystems maintain themselves in a flexible state, ready to adapt to changing conditions. The web of life is a flexible, ever-fluctuating network. The more variables are kept fluctuating, the more dynamic is the system; the greater is its flexibility; and the greater is its ability to adapt to changing conditions." (Fritjof Capra, "The Systems View of Life: A Unifying Vision", 2014)

"Deep ecology does not separate humans - or anything else-from the natural environment. It sees the world not as a collection of isolated objects, but as a network of phenomena that are fundamentally interconnected and interdependent. Deep ecology recognizes the intrinsic value of all living beings and views humans as just one particular strand in the web of life." (Fritjof Capra, "The Systems View of Life: A Unifying Vision", 2014)

On Simplicity XII (Complexity vs Simplicity IV)

"Simplicity of structure means organic unity, whether the organism be simple or complex; and hence in all times the emphasis which critics have laid upon Simplicity, though they have not unfrequently confounded it with narrowness of range." (George H Lewes, "The Principles of Success in Literature", 1865)

"The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, ‘Seek simplicity and distrust it’." (Alfred N Whitehead, "The Concept of Nature", 1919) 

"In products of the human mind, simplicity marks the end of a process of refining, while complexity marks a primitive stage." (Eric Hoffer, 1954)

"The machinery of the world is far too complex for the simplicity of men." (Jorge L Borges, "Dreamtigers", 1960)

"The ideas need not be complex. Most ideas that are successful are ludicrously simple. Successful ideas generally have the appearance of simplicity because they seem inevitable." (Sol LeWitt, "Paragraphs on Conceptual Art", 1967) 

"Simplicity does not precede complexity, but follows it." (Alan Perlis, "Epigrams on Programming", 1982)

"It is important to emphasize the value of simplicity and elegance, for complexity has a way of compounding difficulties and as we have seen, creating mistakes. My definition of elegance is the achievement of a given functionality with a minimum of mechanism and a maximum of clarity." (Fernando J Corbató, "On Building Systems That Will Fail", 1991)

"When a musical piece is too simple we tend not to like it, finding it trivial. When it is too complex, we tend not to like it, finding it unpredictable - we don't perceive it to be grounded in anything familiar. Music, or any art form […] has to strike the right balance between simplicity and complexity […]" (Daniel Levitin, "This is Your Brain on Music", 2006) 

"Most of the world is of great roughness and infinite complexity. However, the infinite sea of complexity includes two islands of simplicity: one of Euclidean simplicity and a second of relative simplicity in which roughness is present but is the same at all scales." (Benoît Mandelbrot, "The Fractalist", 2012)

"I think there is a profound and enduring beauty in simplicity; in clarity, in efficiency. True simplicity is derived from so much more than just the absence of clutter and ornamentation. It's about bringing order to complexity." (Jonathan Ive, 2013) 

From Parts to Wholes (Unsourced)

"By the word symmetry […] one thinks of an external relationship between pleasing parts of a whole; mostly the word is used to refer to parts arranged regularly against one another around a centre. We have […] observed [these parts] one after the other, not always like following like, but rather a raising up from below, a strength out of weakness, a beauty out of ordinariness." (Johann Wolfgang von Goethe)

"Every part is disposed to unite with the whole, that it may thereby escape from its own incompleteness." (Leonardo Da Vinci)

"If nature leads to mathematical forms of great simplicity and beauty - to forms that no one has previously encountered - we cannot help thinking that they are true and that they revealed genuine features of Nature." (Werner K Heisenberg)

"There is a fundamental error in separating the parts from the whole, the mistake of atomizing what should not be atomized. Unity and complementarity constitute reality." (Werner Heisenberg)

"The part always has a tendency to reunite with its whole in order to escape from its imperfection." (Leonardo Da Vinci)

"The whole is simpler than its parts." (Josiah W Gibbs)

"Whatever Nature undertakes, she can only accomplish it in a sequence. She never makes a leap. For example she could not produce a horse if it were not preceded by all the other animals on which she ascends to the horse’s structure as if on the rungs of a ladder. Thus every one thing exists for the sake of all things and all for the sake of one; for the one is of course the all as well. Nature, despite her seeming diversity, is always a unity, a whole; and thus, when she manifests herself in any part of that whole, the rest must serve as a basis for that particular manifestation, and the latter must have a relationship to the rest of the system." (Johann Wolfgang von Goethe)

From Parts to Wholes (1-999 AD)

"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)

"A far greater glory is it to the wise to die for freedom, the love of which stands in very truth implanted in the soul like nothing else, not as a casual adjunct but an essential part of its unity, and cannot be amputated without the whole system being destroyed as a result." (Philo of Alexandria, "Every Good Man is Free",  cca. 15 - 45 AD)

"We can get some idea of a whole from a part, but never knowledge or exact opinion. Special histories therefore contribute very little to the knowledge of the whole and conviction of its truth. It is only indeed by study of the interconnexion of all the particulars, their resemblances and differences, that we are enabled at least to make a general survey, and thus derive both benefit and pleasure from history." (Polybius, "The Histories", cca. 150 BC)

"Either all things proceed from one intelligent source and come together as in one body, and the part ought not to find fault with what is done for the benefit of the whole; or there are only atoms, and nothing else than a mixture and dispersion. Why, then, art thou disturbed? Say to this ruling faculty, Art thou dead, art thou corrupted, art thou playing the hypocrite, art thou become a beast, dost thou herd and feed with the rest?" (Marcus Aurelius, "Meditations". cca. 121–180 AD)

"The other reason is that what happens to the individual is a cause of well-being in what directs the world - of its well-being, its fulfillment, or its very existence, even. Because the whole is damaged if you cut away anything - anything at all - from its continuity and its coherence. Not only its parts, but its purposes. And that's what you're doing when you complain: hacking and destroying." *Marcus Aurelius, "Meditations", cca. 121–180 AD)

"When, therefore, as will be clear to those who read, the passage as a connected whole is literally impossible, whereas the outstanding part of it is not impossible but even true, the reader must endeavor to grasp the entire meaning, connecting by an intellectual process the account of what is literally impossible with the parts that are not impossible but historically true, these being interpreted allegorically in common with the part which, so far as the letter goes, did not happen at all. For our contention with regard to the whole of divine scripture is that it all has a spiritual meaning, but not all a bodily meaning; for the bodily meaning is often proved to be an impossibility." (Origen Adamantius, "On First Principles", cca. 220-230)

From Parts to Wholes (1900-1909)

"And as the ideal in the whole of Nature moves in an infinite process toward an Absolute Perfection, we may say that art is in strict truth the apotheosis of Nature. Art is thus at once the exaltation of the natural toward its destined supernatural perfection, and the investiture of the Absolute Beauty with the reality of natural existence. Its work is consequently not a means to some higher end, but is itself a final aim; or, as we may otherwise say, art is its own end. It is not a mere recreation for man, a piece of by-play in human life, but is an essential mode of spiritual activity, the lack of which would be a falling short of the destination of man. It is itself part and parcel of man's eternal vocation." (George H Howison, "The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Idealism", 1901) 

"Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments." (David Hilbert, "Mathematical Problems", Bulletin American Mathematical Society Vol. 8, 1901-1902)

"For if society lacks the unity that derives from the fact that the relationships between its parts are exactly regulated, that unity resulting from the harmonious articulation of its various functions assured by effective discipline and if, in addition, society lacks the unity based upon the commitment of men's wills to a common objective, then it is no more than a pile of sand that the least jolt or the slightest puff will suffice to scatter.“ (Émile Durkheim, 1903)

"From that time, the universe has steadily become more complex and less reducible to a central control. With as much obstinacy as though it were human, it has insisted on expanding its parts; with as much elusiveness as though it were feminine, it has evaded the attempt to impose on it a single will. Modern science, like modern art, tends, in practice, to drop the dogma of organic unity. Some of the mediaeval habit of mind survives, but even that is said to be yielding before the daily evidence of increasing and extending complexity. The fault, then, was not in man, if he no longer looked at science or art as an organic whole or as the expression of unity. Unity turned itself into complexity, multiplicity, variety, and even contradiction." (Henry Adams, "Mont Saint Michel and Chartres", 1904)

"Reduced to their most pregnant difference, empiricism means the habit of explaining wholes by parts, and rationalism means the habit of explaining parts by wholes. Rationalism thus preserves affinities with monism, since wholeness goes with union, while empiricism inclines to pluralistic views. No philosophy can ever be anything but a summary sketch, a picture of the world in abridgment, a foreshortened bird's-eye view of the perspective of events. And the first thing to notice is this, that the only material we have at our disposal for making a picture of the whole world is supplied by the various portions of that world of which we have already had experience. We can invent no new forms of conception, applicable to the whole exclusively, and not suggested originally by the parts." (William James, "A Pluralistic Universe", 1908)

"A system is a whole which is composed of various parts. But it is not the same thing as an aggregate or heap. In an aggregate or heap, no essential relation exists between the units of which it is composed. In a heap of grain, or pile of stones, one may take away part without the other part being at all affected thereby. But in a system, each part has a fixed and necessary relation to the whole and to all the other parts. For this reason we may say that a building, or a peace of mechanisme, is a system. Each stone in the building, each wheel in the watch, plays a part, and is essential to the whole." (James E Creighton, "An Introductory Logic"‎, 1909)

From Parts to Wholes (1920-1929)

"True artistic experience is never passive, for the spectator is obliged to participate, as it were, in the continuous or discontinuous variations of proportions, positions, lines and planes. Moreover, he must see clearly how this play of repeated or non-repeated changes may give rise to a new harmony of relations which will constitute the unity of the work. Every part becomes organized into a whole with the other parts. All the parts contribute to the unity of the composition, none of them assuming a dominant place in the whole." (Theo van Doesburg, 'Grundbegriffe der neuen Gestaltenden Kunst', 1921-23)

"It has long seemed obvious - and is, in fact, the characteristic tone of European science - that 'science' means breaking up complexes into their component elements. Isolate the elements, discover their laws, then reassemble them, and the problem is solved. All wholes are reduced to pieces and piecewise relations between pieces. The fundamental 'formula' of Gestalt theory might be expressed in this way. There are wholes, the behaviour of which is not determined by that of their individual elements, but where the part-processes are themselves determined by the intrinsic nature of the whole. It is the hope of Gestalt theory to determine the nature of such wholes." (Max Wertheimer, "Gestalt Theory," 1924)

"It seems clear that [set theory] violates against the essence of the continuum, which, by its very nature, cannot at all be battered into a single set of elements. Not the relationship of an element to a set, but of a part to a whole ought to be taken as a basis for the analysis of a continuum." (Hermann Weyl, "Riemanns geometrische Ideen, ihre Auswirkungen und ihre Verknüpfung mit der Gruppentheorie", 1925)

"In all the previous cases of wholes, we have nowhere been able to argue from the parts of the whole. Compared to its parts, the whole constituted by them is something quite different, something creatively new, as we have seen. Creative evolution synthesises from the parts a new entity not only different from them, but quite transcending them. That is the essence of a whole. It is always transcendent to its parts, and its character cannot be inferred from the characters of its parts." (Jan Smuts, "Holism and Evolution", 1926)

"(Holism is) the tendency in nature to form wholes that are greater than the sum of the parts through creative evolution [...]" (Jan Smuts, "Holism and Evolution", 1926)

"The characteristic of the organism is first that it is more than the sum of its parts and second that the single processes are ordered for the maintenance of the whole." (Ludwig von Bertalanffy, 1928)

What in the whole denotes a causal equilibrium process, appears for the part as a teleological event." (Ludwig von Bertalanffy, 1929)

On Symmetry VI (Symmetry and Perception)

“Symmetry is a characteristic of the human mind.” (Alexander Pushkin, 1825)

“Symmetry is what we see at a glance; based on the fact that there is no reason for any difference, and based also on the face of man; whence it happens that symmetry is only wanted in breadth, not in height or depth.” (Blaise Pascal, “Pensées”, 1670)

"It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details." (Henri Poincaré, “The Future of Mathematics”, Monist, Vol. 20)

“[…] admiration for elegant symmetry never dies […]” (Robert Kaplan & Ellen Kaplan, „The Art of the Infinite: The Pleasures of Mathematics”, 2003)

“The word ‘symmetry’ conjures to mind objects which are well balanced, with perfect proportions. Such objects capture a sense of beauty and form. The human mind is constantly drawn to anything that embodies some aspect of symmetry. Our brain seems programmed to notice and search for order and structure. Artwork, architecture and music from ancient times to the present day play on the idea of things which mirror each other in interesting ways. Symmetry is about connections between different parts of the same object. It sets up a natural internal dialogue in the shape.” (Marcus du Sautoy, “Symmetry: A Journey into the Patterns of Nature”, 2008)

“Symmetry is the means by which shape is converted into memory.” (Michael Leyton, “Symmetry, Causality, Mind”, 1992)

“The desire for symmetry, for balance, for rhythm in form as well as in sound, is one of the most inveterate of human instincts.” (Edith Wharton)

On Symmetry III (Mathematicians I)

“To a mathematician, an object possesses symmetry if it retains its form after some transformation. A circle, for example, looks the same after any rotation; so a mathematician says that a circle is symmetric, even though a circle is not really a pattern in the conventional sense - something made up from separate, identical bits. Indeed the mathematician generalizes, saying that any object that retains its form when rotated - such as a cylinder, a cone, or a pot thrown on a potter's wheel - has circular symmetry.” (Ian Stewart & Martin Golubitsky, “Fearful Symmetry: Is God a Geometer?”, 1992)

"Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness." (Eric Temple Bell)

"What makes a great mathematician? A feel for form, a strong sense of what is important. Möbius had both in abundance. He knew that topology was important. He knew that symmetry is a fundamental and powerful mathematical principle. The judgment of posterity is clear: Möbius was right.” (Ian Stewart)

“Mathematicians attach great importance to the elegance of their methods and their results. This is not pure dilettantism. What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.” (Henri Poincaré, “The Future of Mathematics”, Monist Vol. 20, 1910)

“The mathematician has, above all things, an eye for symmetry […]) (James C Maxwell, 1871)
“For the mathematician, the pattern searcher, understanding symmetry is one of the principal themes in the quest to chart the mathematical world.” (Marcus du Sautoy, “Symmetry: A Journey into the Patterns of Nature”, 2008)

“Perhaps the simplest way to explain symmetry is to follow the operational approach used by mathematicians: a symmetry is a motion. That is, suppose you have an object and pick it up, move it around, and set it down. If it is impossible to distinguish between the object in its original and final positions, we say that it has a symmetry.” (Michael Field & Martin Golubitsky, “Symmetry in Chaos: A Search for Pattern in Mathematics, Art, and Nature” 2nd Ed, 2009)

On Symmetry I

“Symmetry is what we see at a glance; based on the fact that there is no reason for any difference, and based also on the face of man; whence it happens that symmetry is only wanted in breadth, not in height or depth.” (Blaise Pascal, “Pensées”, 1670)

“Symmetry is evidently a kind of unity in variety, where a whole is determined by the rhythmic repetition of similar.” (George Santayana, “The Sense of Beauty”, 1896)

“By the word symmetry […] one thinks of an external relationship between pleasing parts of a whole; mostly the word is used to refer to parts arranged regularly against one another around a centre. We have […] observed [these parts] one after the other, not always like following like, but rather a raising up from below, a strength out of weakness, a beauty out of ordinariness.” (Goethe)

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

“In the one sense symmetric means something like well-proportioned, well-balanced, and symmetry denotes that sort of concordance of several parts by which they integrate into a whole. Beauty is bound up with symmetry.” (Hermann Weyl, “Symmetry”, 1952)

“A thing is symmetrical if there is something you can do to it so that after you have finished doing it, it looks the same as before.” (Hermann Weyl, “Symmetry”, 1952)

“[…] a symmetry isn't a thing; it's a transformation. Not any old transformation, though: a symmetry of an object is a transformation that leaves it apparently unchanged.” (Ian Stewart & Martin Golubitsky, “Fearful Symmetry: Is God a Geometer?”, 1992)

“A symmetry is a set of transformations applied to a structure, such that the transformations preserve the properties of the structure.” (Philip Dorrell, “What is Music?: Solving a Scientific Mystery”, 2004)

“Symmetry is the representation of two or more equivalent or balanced elements with respect to a common origin, position, or axis.” (David Smith, “The Symmetry Solution: A Modern View of Biblical Prophecy”, 2009)

“Symmetry is basically a geometrical concept. Mathematically it can be defined as the invariance of geometrical patterns under certain operations. But when abstracted, the concept applies to all sorts of situations. It is one of the ways by which the human mind recognizes order in nature. In this sense symmetry need not be perfect to be meaningful. Even an approximate symmetry attracts one's attention, and makes one wonder if there is some deep reason behind it.” (Eguchi Tohru & ‎K Nishijima , “Broken Symmetry: Selected Papers Of Y Nambu”, 1995)

5 Books 10 Quotes I: Mathematics in Its Creation

Walter W Sawyer, "What is Calculus About?”, 1961
	"In mathematics, a certain surprising thing happens again and again. Someone poses a simple question, a question so simple that it seems no useful result can come from answering it. And yet it turns out that  the answer opens the door to all kinds of interesting developments, and  gives great power to the person who understands it."
"Mathematics also is an exploration. As we push out further, we meet new and unexpected situations and we have to revise our ideas. Rules we have used, theorems we have proved turn out to have unforeseen weaknesses."
Ian Stewart, "In Pursuit of the Unknown", 2012
	“Equations have hidden powers. They reveal the innermost secrets of nature. […] The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us.”
“There are two kinds of equations in mathematics, which on the surface look very similar. One kind presents relations between various mathematical quantities: the task is to prove the equation is true. The other kind provides information about an unknown quantity, and the mathematician’s task is to solve it - to make the unknown known.”
Philip J Davis et al, "The Mathematical Experience", 1995
	“Where is the place of mathematics? Where does it exist? On the printed page, of course, and prior to printing, on tablets or on papyri. Here is a mathematical book - take it in your hand; you have a palpable record of mathematics as an intellectual endeavor. But first it must exist in people's minds, for a shelf of books doesn't create mathematics.”
“The definition of mathematics changes. Each generation and each thoughtful mathematician within a generation formulates a definition according to his lights.”
David Ruelle, "Chance and Chaos", 1991
	"Because mathematical proofs are long, they are also difficult to invent. One has to construct, without making any mistakes, long chains of assertions, and see what one is doing, see where one is going. To see means to be able to guess what is true and what is false, what is useful and what is not. To see means to have a feeling for which definitions one should introduce, and what the key assertions are that will allow one to develop a theory in a natural manner."
"Mathematics has deep unity. More than a collection of separate theories such as set theory, topology, and algebra, each with its own basic assumptions, mathematics is a unified whole. Mathematics is a great  kingdom, and that kingdom belongs to those who see."
James R Brown,"Philosophy of Mathematics", 1999
	"Whatever the ins and outs of poetry, one thing is clear: the manner of expression - notation - is fundamental. It is the same with mathematics - not in the aesthetic sense that the beauty of mathematics is tied up with how it is expressed - but in the sense that mathematical truths are revealed, exploited and developed by various notational innovations."
“In sum, these are a few of the ingredients in the mathematical image: (1) Mathematical results are certain (2) Mathematics is objective (3) Proofs are essential (4) Diagrams are psychologically useful, but prove nothing (5) Diagrams can even be misleading (6) Mathematics is wedded to classical logic (7) Mathematics is independent of sense experience (8) The history of mathematics is cumulative (9) Computer proofs are merely long and complicated regular proofs (10) Some mathematical problems are unsolvable in principle” ||>> Next Post

On Simplicity I (Nature’s Simplicity I)

”[…] it is astonishing and incredible to us, but not to Nature; for she performs with utmost ease and simplicity things which are even infinitely puzzling to our minds, and what is very difficult for us to comprehend is quite easy for her to perform.” (Galileo Galilei, "Dialog Concerning the Two World Systems", 1630)

"The supreme Being is everywhere; but He is not equally visible everywhere. Let us seek Him in the simplest things, in the most fundamental laws of Nature, in the universal rules by which movement is conserved, distributed or destroyed; and let us not seek Him in phenomena that are merely complex consequences of these laws." (Pierre L Maupertuis, "Les Loix du Mouvement et du Repos, déduites d'un Principe Métaphysique", 1746) 

"Men are often led into errors by the love of simplicity, which disposes us to reduce things to few principles, and to conceive a greater simplicity in nature than there really is." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

“Nature does nothing in vain when less will serve; for Nature is pleased with simplicity and affects not the pomp of superfluous causes.“ (Sir Isaac Newton, “The Mathematical Principles of Natural Philosophy”, Voll. II, 1803)

“[…] we must not measure the simplicity of the laws of nature by our facility of conception; but when those which appear to us the most simple, accord perfectly with observations of the phenomena, we are justified in supposing them rigorously exact.” (Pierre S Laplace, "The System of the World", 1809)

”How wonderful it is to me the simplicity of nature when we rightly interpret her laws and how different the convictions which they produce on the mind in comparison with the uncertain conclusions which hypothesis or even theory present.” (Michael Faraday, [letter to A F Svanberg] cca 1854)

”[…] we cannot a priori demand from nature simplicity, nor can we judge what in her opinion is simple.” (Heinrich Hertz, “The Principles of Mechanics Presented in a New Form”, 1894) 

“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)

”The simplicity of nature is not that which may easily be read, but is inexhaustible. The last analysis can no wise be made.” (Ralph W Emerson)