"As in a block of marble all possible figures are potentially contained in it, and can be drawn out of it by the movement or by the action of the chisel, so in the same way all intelligible figures are potentially in intelligible extension and are discovered in it according to the different ways in which this extension is represented to the mind, as a consequence of the general laws which God has established according to which he continuously acts in us." (Nicolas Malebranche , "Dialogues On Metaphysics And Religion", 1688)
"If nature could pass from one extremity to another, for example, from rest to movement, from movement to rest, or from a movement in one direction to a movement in the opposite direction, without passing through all the imperceptible movements that lead from the one to the other; the first state must be destroyed, without nature knowing to which new state it must become; for in the end by what reason should one be chosen for preference, and of which one could not ask why this one and not that one? since having no necessary connection between these two states, no passage from movement to rest, from rest to movement, or from a movement [in one direction] to a movement in an opposite direction; no reason at all will determine producing one thing rather than any other." (Johann Bernoulli, "Discours sur les Loix de la Communication du Mouvement", 1727)
"Nature, displayed in its full extent, presents us with an immense tableau, in which all the order of beings are each represented by a chain which sustains a continuous series of objects, so close and so similar that their difference would be difficult to define. This chain is not a simple thread which is only extended in length, it is a large web or rather a network, which, from interval to interval, casts branches to the side in order to unite with the networks of another order." (Comte Georges-Louis Leclerc de Buffon, "Les Oiseaux Qui Ne Peuvent Voler", Histoire Naturelle des Oiseaux Vol. I, 1770)
"There is a certain spiral of a peculiar form on which a point may have been approaching for centuries the center, and have nearly reached it, before we discover that its rate of approach is accelerated. The first thought of the observer, on seeing the acceleration, would be to say that it would reach the center sooner than he had before supposed. But as the point comes near the center it suddenly, although still moving under the same simple law as from the beginning, makes a very short turn upon its path and flies off rapidly almost in a straight line, out to an infinite distance. This illustrates that apparent breach of continuity which we sometimes find in a natural law; that apparently sudden change of character which we sometimes see in man." (Thomas Hill, "Uses of Mathesis", Bibliotheca Sacra Vol. 32, 1875)
"Natura non facit saltum"
"Nature does not undergo discontinuities." (Alfred Marshall, "Principles of Economics", [motto] 1890)
"To use an old analogy - and here we can hardly go except upon analogy - while the building of Nature is growing spontaneously from within, the model of it, which we seek to construct in our descriptive science, can only be constructed by means of scaffolding from without, a scaffolding of hypotheses. While in the real building all is continuous, in our model there are detached parts which must be connected with the rest by temporary ladders and passages, or which must be supported till we can see how to fill in the understructure. To give the hypotheses equal validity with facts is to confuse the temporary scaffolding with the building itself." (John H Poynting, 1899)
"The most violent revolutions in an individual's beliefs leave most of his old order standing. Time and space, cause and effect, nature and history, and one's own biography remain untouched. New truth is always a go-between, a smoother-over of transitions. It marries old opinion to new fact so as ever to show a minimum of jolt, a maximum of continuity." (William James, "What Pragmatism Means", 1907)
"In Continuity, it is impossible to distinguish phenomena at their merging-points, so we look for them at their extremes." (Charles Fort, "The Book of the Damned", 1919)
"The notion that Nature does not proceed by jumps is only one of the budget of plausible lies that we call classical education. Nature always proceeds by jumps. She may spend twenty thousand years making up her mind to jump; but when she makes it up at last, the jump is big enough to take us into a new age." (George B Shaw, "The Gospel of the Brothers Barnabas: Present Day", cca 1920)
"[…] evolution is only one aspect of the order of nature, of the relations of cause and effect, of continuity of space and time, which pervade the universe and enable us to comprehend its simplicity of plan, its complexity of detail." (William D Matthew, Natural History Vol. 25 (2), 1925)
"When we look at a very large number of small objects that are close together the idea of continuum arises within us. […] Even if we believe to perceive a continuum in front of us, a more accurate observation will often convince us that we are only observing a dense succession of small particles." (Felix Klein, "Elementary Mathematics from a Higher Standpoint" Vol III: "Precision Mathematics and Approximation Mathematics", 1928)
"It is easy without any very profound logical analysis to perceive the difference between a succession of favorable deviations from the laws of chance, and on the other hand, the continuous and cumulative action of these laws. It is on the latter that the principle of Natural Selection relies." (Sir Ronald A Fisher, "The Genetical Theory of Natural Selection", 1930)
"The discrete change has only to become small enough in its jump to approximate as closely as is desired to the continuous change. It must further be remembered that in natural phenomena the observations are almost invariably made at discrete intervals; the 'continuity' ascribed to natural events has often been put there by the observer's imagina- tion, not by actual observation at each of an infinite number of points. Thus the real truth is that the natural system is observed at discrete points, and our transformation represents it at discrete points. There can, therefore, be no real incompatibility."
"Where chaos begins, classical science stops. For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the fluctuations of the wildlife populations, in the oscillations of the heart and the brain. The irregular side of nature, the discontinuous and erratic side these have been puzzles to science, or worse, monstrosities." (James Gleick, "Chaos", 1987)
"[…] continuity appears when we try to mathematically express continuously changing phenomena, and differentiability is the result of expressing smoothly changing phenomena." (Kenji Ueno & Toshikazu Sunada, "A Mathematical Gift, III: The Interplay Between Topology, Functions, Geometry, and Algebra", Mathematical World Vol. 23, 1996)
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