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Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
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Home > Category Index for Science Quotations > Category Index E > Category: Everywhere

Everywhere Quotes (24 quotes)

Vacuum voco locum omnem in quo corpora sine resistentia movetur.
Vacuum I call every place in which a body is able to move without resistance.
Original Latin from an unpublished line in a manuscript draft of additions and corrections to the second edition of the Principia held by Cambridge University Library, 'Definition II', MS Add 3965 sec 13 [53-94] Draft No. 3 Folio 422r. As quoted and cited in J.E. McGuire, Tradition and Innovation: Newton’s Metaphysics of Nature (1995, 2011), 139. English translation as given in Isaac Asimov and Jason A. Shulman (eds.), Isaac Asimov’s Book of Science and Nature Quotations (1988), 210.
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Cyberspace consists of transactions, relationships, and thought itself, arrayed like a standing wave in the web of our communications. Ours is a world that is both everywhere and nowhere, but it is not where bodies live. We are creating a world that all may enter without privilege or prejudice accorded by race, economic power, military force, or station of birth. We are creating a world where anyone, anywhere may express his or her beliefs, no matter how singular, without fear of being coerced into silence or conformity.
In 'A Declaration of the Independence of Cyberspace' (8 Feb 1996). Published on Electronic Frontier Foundation website. Reproduced in Lawrence Lessig, Code: Version 2.0) (2008), 303.
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Doubtless the reasoning faculty, the mind, is the leading and characteristic attribute of the human race. By the exercise of this, man arrives at the properties of the natural bodies. This is science, properly and emphatically so called. It is the science of pure mathematics; and in the high branches of this science lies the truly sublime of human acquisition. If any attainment deserves that epithet, it is the knowledge, which, from the mensuration of the minutest dust of the balance, proceeds on the rising scale of material bodies, everywhere weighing, everywhere measuring, everywhere detecting and explaining the laws of force and motion, penetrating into the secret principles which hold the universe of God together, and balancing worlds against worlds, and system against system. When we seek to accompany those who pursue studies at once so high, so vast, and so exact; when we arrive at the discoveries of Newton, which pour in day on the works of God, as if a second fiat had gone forth from his own mouth; when, further, we attempt to follow those who set out where Newton paused, making his goal their starting-place, and, proceeding with demonstration upon demonstration, and discovery upon discovery, bring new worlds and new systems of worlds within the limits of the known universe, failing to learn all only because all is infinite; however we may say of man, in admiration of his physical structure, that “in form and moving he is express and admirable,” it is here, and here without irreverence, we may exclaim, “In apprehension how like a god!” The study of the pure mathematics will of course not be extensively pursued in an institution, which, like this [Boston Mechanics’ Institute], has a direct practical tendency and aim. But it is still to be remembered, that pure mathematics lie at the foundation of mechanical philosophy, and that it is ignorance only which can speak or think of that sublime science as useless research or barren speculation.
In Works (1872), Vol. 1, 180.
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Everything does not happen continuously at any one moment in the universe. Neither does everything happen everywhere in it.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959), 49. Originally published in French as Le Phénomene Humain (1955).
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Everywhere you look in science, the harder it becomes to understand the universe without God.
…...
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Gentlemen, as we study the universe we see everywhere the most tremendous manifestations of force. In our own experience we know of but one source of force, namely will. How then can we help regarding the forces we see in nature as due to the will of some omnipresent, omnipotent being? Gentlemen, there must be a GOD.
As quoted in W. E. Byerly (writing as a Professor Emeritus at Harvard University, but a former student at a Peirce lecture on celestial mechanics), 'Benjamin Peirce: II. Reminiscences', The American Mathematical Monthly (Jan 1925), 32, No. 1, 6.
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Humans everywhere share the same goals when the context is large enough. And the study of the Cosmos provides the largest possible context … . If a human disagrees with you, let him live. In a hundred billion galaxies, you will not find another … . If we are to survive, our loyalties must be broadened further, to include the whole human community, the entire planet Earth.
Cosmos
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If I get the impression that Nature itself makes the decisive choice [about] what possibility to realize, where quantum theory says that more than one outcome is possible, then I am ascribing personality to Nature, that is to something that is always everywhere. [An] omnipresent eternal personality which is omnipotent in taking the decisions that are left undetermined by physical law is exactly what in the language of religion is called God.
As quoted by John D. Barrow in The Universe that Discovered Itself (2000), 171.
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In order to comprehend and fully control arithmetical concepts and methods of proof, a high degree of abstraction is necessary, and this condition has at times been charged against arithmetic as a fault. I am of the opinion that all other fields of knowledge require at least an equally high degree of abstraction as mathematics,—provided, that in these fields the foundations are also everywhere examined with the rigour and completeness which is actually necessary.
In 'Die Theorie der algebraischen Zahlkorper', Vorwort, Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 4.
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In our day grand generalizations have been reached. The theory of the origin of species is but one of them. Another, of still wider grasp and more radical significance, is the doctrine of the Conservation of Energy, the ultimate philosophical issues of which are as yet but dimly seem-that doctrine which “binds nature fast in fate” to an extent not hitherto recognized, exacting from every antecedent its equivalent consequent, and bringing vital as well as physical phenomena under the dominion of that law of causal connexion which, so far as the human understanding has yet pierced, asserts itself everywhere in nature.
'Address Delivered Before The British Association Assembled at Belfast', (19 Aug 1874). Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 2, 1801.
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It [mathematics] is in the inner world of pure thought, where all entia dwell, where is every type of order and manner of correlation and variety of relationship, it is in this infinite ensemble of eternal verities whence, if there be one cosmos or many of them, each derives its character and mode of being,—it is there that the spirit of mathesis has its home and its life.
Is it a restricted home, a narrow life, static and cold and grey with logic, without artistic interest, devoid of emotion and mood and sentiment? That world, it is true, is not a world of solar light, not clad in the colours that liven and glorify the things of sense, but it is an illuminated world, and over it all and everywhere throughout are hues and tints transcending sense, painted there by radiant pencils of psychic light, the light in which it lies. It is a silent world, and, nevertheless, in respect to the highest principle of art—the interpenetration of content and form, the perfect fusion of mode and meaning—it even surpasses music. In a sense, it is a static world, but so, too, are the worlds of the sculptor and the architect. The figures, however, which reason constructs and the mathematic vision beholds, transcend the temple and the statue, alike in simplicity and in intricacy, in delicacy and in grace, in symmetry and in poise. Not only are this home and this life thus rich in aesthetic interests, really controlled and sustained by motives of a sublimed and supersensuous art, but the religious aspiration, too, finds there, especially in the beautiful doctrine of invariants, the most perfect symbols of what it seeks—the changeless in the midst of change, abiding things hi a world of flux, configurations that remain the same despite the swirl and stress of countless hosts of curious transformations.
In 'The Universe and Beyond', Hibbert Journal (1904-1906), 3, 314.
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Let him look at that dazzling light hung aloft as an eternal lamp to lighten the universe; let him behold the earth, a mere dot compared with the vast circuit which that orb describes, and stand amazed to find that the vast circuit itself is but a very fine point compared with the orbit traced by the stars as they roll their course on high. But if our vision halts there, let imagination pass beyond; it will fail to form a conception long before Nature fails to supply material. The whole visible world is but an imperceptible speck in the ample bosom of Nature. No notion comes near it. Though we may extend our thought beyond imaginable space, yet compared with reality we bring to birth mere atoms. Nature is an infinite sphere whereof the centre is everywhere, the circumference nowhere. In short, imagination is brought to silence at the thought, and that is the most perceptible sign of the all-power of God.
Let man reawake and consider what he is compared with the reality of things; regard himself lost in this remote corner of Nature; and from the tiny cell where he lodges, to wit the Universe, weigh at their true worth earth, kingdoms, towns, himself. What is a man face to face with infinity?
Pensées (1670), Section 1, aphorism 43. In H. F. Stewart (ed.), Pascal’s Pensées (1950), 19.
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Nature offers us a thousand simple pleasures—plays of light and color, fragrance in the air, the sun’s warmth on skin and muscle, the audible rhythm of life’s stir and push—for the price of merely paying attention. What joy! But how unwilling or unable many of us are to pay this price in an age when manufactured sources of stimulation and pleasure are everywhere at hand. For me, enjoying nature’s pleasures takes conscious choice, a choice to slow down to seed time or rock time, to still the clamoring ego, to set aside plans and busyness, and to simply to be present in my body, to offer myself up.
In Sisters of the Earth: Women’s Prose and Poetry (1991), 43.
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Nature … is an infinite sphere of which the center is everywhere and the circumference nowhere.
In Pensées (1670), Section 16, No. 26. From Blaise Pascal and W.F. Trotter (trans.), 'Thoughts', collected in Charles W. Eliot (ed.), The Harvard Classics (1910), Vol. 48, 26. From the French, “La nature … est une sphère infinie dont le centre est partout, la circonférence nulle part,” in Pensées de Blaise Pascal (1847), 227-228.
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Nothing is less applicable to life than mathematical reasoning. A proposition in mathematics is decidedly false or true. Everywhere else the true is mingled with the false.
Quoted, without citation, in David Eugene Smith, The Teaching of Elementary Mathematics (1904), 170.
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Science never saw a ghost, nor does it look for any, but it sees everywhere the traces, and it is itself the agent, of a Universal Intelligence.
(2 Dec 1853). In Henry David Thoreau and Bradford Torrey (ed.), The Writings of Henry Thoreau: Journal: VI: December 1, 1853-August 31, 1854 (1906), 4.
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The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. That such is the case a few indications will suffice to show. The mathematical concepts of constant and variable are represented familiarly in life by the notions of fixedness and change. The concept of equation or that of an equational system, imposing restriction upon variability, is matched in life by the concept of natural and spiritual law, giving order to what were else chaotic change and providing partial freedom in lieu of none at all. What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an “ever flying perfect” as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration. The supreme concept of functionality finds its correlate in life in the all-pervasive sense of interdependence and mutual determination among the elements of the world. What is known in mathematics as transformation—that is, lawful transfer of attention, serving to match in orderly fashion the things of one system with those of another—is conceived in life as a process of transmutation by which, in the flux of the world, the content of the present has come out of the past and in its turn, in ceasing to be, gives birth to its successor, as the boy is father to the man and as things, in general, become what they are not. The mathematical concept of invariance and that of infinitude, especially the imposing doctrines that explain their meanings and bear their names—What are they but mathematicizations of that which has ever been the chief of life’s hopes and dreams, of that which has ever been the object of its deepest passion and of its dominant enterprise, I mean the finding of the worth that abides, the finding of permanence in the midst of change, and the discovery of a presence, in what has seemed to be a finite world, of being that is infinite? It is needless further to multiply examples of a correlation that is so abounding and complete as indeed to suggest a doubt whether it be juster to view mathematics as the abstract idealization of life than to regard life as the concrete realization of mathematics.
In 'The Humanization of Teaching of Mathematics', Science, New Series, 35, 645-46.
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The first quality we know in matter is centrality,—we call it gravity,—which holds the universe together, which remains pure and indestructible in each mote, as in masses and planets, and from each atom rays out illimitable influence. To this material essence answers Truth, in the intellectual world,—Truth, whose centre is everywhere, and its circumference nowhere, whose existence we cannot disimagine,—the soundness and health of things, against which no blow can be struck but it recoils on the striker,—Truth, on whose side we always heartily are. And the first measure of a mind is its centrality, its capacity of truth, and its adhesion to it.
In 'Progress of Culture', an address read to the Phi Beta Kappa Society at Cambridge, 18 July 1867. Collected in Works of Ralph Waldo Emerson (1883), 477.
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The sciences are like a beautiful river, of which the course is easy to follow, when it has acquired a certain regularity; but if one wants to go back to the source, one will find it nowhere, because it is everywhere; it is spread so much [as to be] over all the surface of the earth; it is the same if one wants to go back to the origin of the sciences, one will find only obscurity, vague ideas, vicious circles; and one loses oneself in the primitive ideas.
In Essai sur les machines en général (1783), conclusion, as translated in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840 (1990), Vol. 1, 32.
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Thus there is everywhere testimony of the same mind, [there is] no place in creation for the introduction of laws varying from the original design. All is one grand unity.
Sermon (c. 13 Jan. 1895), Mukwonago, Wisconsin, published in Olympia Brown and Gwendolen B. Willis (ed.), Olympia Brown, An Autobiography (1960). Reprinted in Annual Journal of the Universalist Historical Society (1963), vol. 4, 103.
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We lift ourselves by our thought. We climb upon our vision of ourselves. If you want to enlarge your life, you must first enlarge your thought of it and of yourself. Hold the ideal of yourself as you long to be, always everywhere.
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Whenever I get gloomy with the state of the world, I think about the arrivals gate at Heathrow Airport. General opinion’s starting to make out that we live in a world of hatred and greed, but I don’t see that. It seems to me that love is everywhere. Often it’s not particularly dignified or newsworthy, but it’s always there - fathers and sons, mothers and daughters, husbands and wives, boyfriends, girlfriends, old friends. When the planes hit the Twin Towers, as far as I know none of the phone calls from the people on board were messages of hate or revenge - they were all messages of love. If you look for it, I’ve got a sneaky feeling you’ll find that love actually is all around.
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Love Actually (Prime Minister)
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While religion prescribes brotherly love in the relations among the individuals and groups, the actual spectacle more resembles a battlefield than an orchestra. Everywhere, in economic as well as in political life, the guiding principle is one of ruthless striving for success at the expense of one’s fellow men. This competitive spirit prevails even in school and, destroying all feelings of human fraternity and cooperation, conceives of achievement not as derived from the love for productive and thoughtful work, but as springing from personal ambition and fear of rejection.
…...
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[On common water.] Its substance reaches everywhere; it touches the past and prepares the future; it moves under the poles and wanders thinly in the heights of air. It can assume forms of exquisite perfection in a snowflake, or strip the living to a single shining bone cast up by the sea.
From essay 'The Flow of the River', collected in The Immense Journey: An Imaginative Naturalist Explores the Mysteries of Man and Nature (1957, 1959), 16.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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