"It is the principle of necessity towards which, as to their ultimate centre, all the ideas advanced in this essay immediately converge. In abstract theory the limits of this necessity are determined solely by considerations of man’s proper nature as a human being; but in the application we have to regard, in addition, the individuality of man as he actually exists. This principle of necessity should, I think, prescribe the grand fundamental rule to which every effort to act on human beings and their manifold relations should be invariably conformed. For it is the only thing which conducts to certain and unquestionable results. The consideration of the useful, which might be opposed to it, does not admit of any true and unswerving decision." (Wilhelm Von Humboldt, "The Limits of State Action", 1792)
"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)
"The more progress physical sciences makes, the more they tend to enter the domain of mathematics, which is a kind of center to which they all converge. We may even judge of the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation." (Adolphe Quetelet, "Annual Report of the Board of Regents of the Smithsonian Institution", 1874)
"Historical investigation not only promotes the understanding of that which now is, but also brings new possibilities before us, by showing that which exists to be in great measure conventional and accidental. From the higher point of view at which different paths of thought converge we may look about us with freer vision and discover routes before unknown."
"This is the reason why mechanical explanations are better understood than stories, even though they are more difficult to reproduce. The exposition, even if it is faulty, excites analogous schemas already existing in the listener’s mind; so that what takes place is not genuine understanding, but a convergence of acquired schemas of thought. In the case of stories, this convergence is not possible, and the schemas brought into play are usually divergent." (Jean Piaget, "The Language and Thought of the Child", 1926)
"No science has ever been born on a specific day. Each science emerges out of a convergence of an increased interest in some class of problems and the development of scientific methods, techniques, and tools which are adequate to solve these problems." (C West Churchman, "Introduction to Operations Research", 1957)
"Science, philosophy and religion are bound to converge as they draw nearer to the whole." (Pierre T de Chardin, "The Phenomenon of Man", 1959)
"Relativity is inherently convergent, though convergent toward a plurality of centers of abstract truths. Degrees of accuracy are only degrees of refinement and magnitude in no way affects the fundamental reliability, which refers, as directional or angular sense, toward centralized truths. Truth is a relationship." (R Buckminster Fuller, "The Designers and the Politicians", 1962)
"Knowledge is not a series of self-consistent theories that converges toward an ideal view; it is rather an ever increasing ocean of mutually incompatible (and perhaps even incommensurable) alternatives, each single theory, each fairy tale, each myth that is part of the collection forcing the others into greater articulation and all of them contributing, via this process of competition, to the development of our consciousness." (Paul K Feyerabend, "Against Method: Outline of an Anarchistic Theory of Knowledge", 1975)
"Today the world we see outside and the world we see within are converging. This convergence of two worlds is perhaps one of the important cultural events of our age." (Ilya Prigogine, "The Philosophy of Instability", Futures 21 (4), 1989)
"Scientists have discovered many peculiar things, and many beautiful things. But perhaps the most beautiful and the most peculiar thing that they have discovered is the pattern of science itself. Our scientific discoveries are not independent isolated facts; one scientific generalization finds its explanation in another, which is itself explained by yet another. By tracing these arrows of explanation back toward their source we have discovered a striking convergent pattern - perhaps the deepest thing we have yet learned about the universe." (Steven Weinberg, "Dreams of a Final Theory: The Scientist’s Search for the Ultimate Laws of Nature", 1992)
"A great discovery is not a terminus, but an avenue leading to regions hitherto unknown. We climb to the top of the peak and find that it reveals to us another higher than any we have yet seen, and so it goes on. The additions to our knowledge of physics made in a generation do not get smaller or less fundamental or less revolutionary, as one generation succeeds another. The sum of our knowledge is not like what mathematicians call a convergent series […] where the study of a few terms may give the general properties of the whole. Physics corresponds rather to the other type of series called divergent, where the terms which are added one after another do not get smaller and smaller, and where the conclusions we draw from the few terms we know, cannot be trusted to be those we should draw if further knowledge were at our disposal." (Sir Joseph J Thomson)
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