On Principles III (Least Action)

"Nature is thrifty in all its actions." (Pierre L M Maupertuis, Accord de différentes lois de la nature qui avaient jusqu'ici paru incompatibles. Mémoires de l'Académie royale des Sciences, 1744)

"The laws of movement and of rest deduced from this principle being precisely the same as those observed in nature, we can admire the application of it to all phenomena. The movement of animals, the vegetative growth of plants [...] are only its consequences; and the spectacle of the universe becomes so much the grander, so much more beautiful, the worthier of its Author, when one knows that a small number of laws, most wisely established, suffice for all movements." (Pierre L M Maupertuis, "Les Loix du mouvement et du repos déduites d'un principe metaphysique", Histoire de l'Académie Royale des Sciences et des Belles Lettres, 1746)

"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)

"The chief law of physics, the pinnacle of the whole system is, in my opinion, the principle of least action." (Max Planck, “A Survey of Physics”, 1925)

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

"Growth is limited by that necessity which is present in the least amount. And, naturally, the least favorable condition controls the growth rate." (Frank Herbert, "Dune", 1965)

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

"Physicists are all too apt to look for the wrong sorts of generalizations, to concoct theoretical models that are too neat, too powerful, and too clean. Not surprisingly, these seldom fit well with data. To produce a really good biological theory, one must try to see through the clutter produced by evolution to the basic mechanisms. What seems to physicists to be a hopelessly complicated process may have been what nature found simplest, because nature could build on what was already there." (Francis H C Crick, "What Mad Pursuit?: A Personal View of Scientific Discovery", 1988)

"It [science] has as its highest principle and most coveted aim the solution of the problem to condense all natural phenomena which have been observed and are still to be observed into one simple principle, that allows the computation of past and more especially of future processes from present ones. [...] Amid the more or less general laws which mark the achievements of physical science during the course of the last centuries, the principle of least action is perhaps that which, as regards form and content, may claim to come nearest to that ideal final aim of theoretical research." (Max Planck)

"[...] light travels between two given points along the path of shortest time [...]" (Pierre de Fermat)

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)

On Symmetry II (Beauty and Symmetry I)

“Beauty is rather a light that plays over the symmetry of things than that symmetry itself.” (Plotinus)

“Proportion, or symmetry, is the basis of beauty; propriety, of grace.” (Henry Fuseli)

"Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection." (Hermann Weyl, “Symmetry”, 1952)

“Beauty had been born, not, as we so often conceive it nowadays, as an ideal of humanity, but as measure, as the reduction of the chaos of appearances to the precision of linear symbols. Symmetry, balance, harmonic division, mated and mensurated intervals – such were its abstract characteristics.” (Herbert Read, “Icon and Idea: The Function of Art in the Development of Human Consciousness”, 1955)

“The fact is that the beautiful, humanly speaking, is merely form considered in its simplest aspect, in its most perfect symmetry, in its most entire harmony with our make-up.” (Victor Hugo, “Cromwell”, 1909)

“Whereas symmetry can create beauty, its breaking does not necessarily destroy beauty; instead, it may even create another kind of beauty.” (Guozhen Wu, “Nonlinearity and Chaos in Molecular Vibrations”, 2005)

“In the nonmathematical sense, symmetry is associated with regularity in form, pleasing proportions, periodicity, or a harmonious arrangement; thus it is frequently associated with a sense of beauty. In the geometric sense, symmetry may be more precisely analyzed. We may have, for example, an axis of symmetry, a center of symmetry, or a plane of symmetry, which define respectively the line, point, or plane about which a figure or body is symmetrical. The presence of these symmetry elements, usually in combinations, is responsible for giving form to many compositions; the reproduction of a motif by application of symmetry operations can produce a pattern that is pleasing to the senses.” (Hans H Jaffé & ‎Milton Orchin, “Symmetry in Chemistry”, 2002)

“Beauty is our weapon against nature; by it we make objects, giving them limit, symmetry, proportion. Beauty halts and freezes the melting flux of nature.” (Camille Paglia)

“Symmetry creates harmony and beauty in an object.” (Aleksandr P Dubrov, “Symmetry of Biorhythms and Reactivity”, 1989)

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