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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Category Index for Science Quotations > Category Index C > Category: Connect

Connect Quotes (30 quotes)

1. The First Law of Ecology: Everything is connected to everything else.
In The Closing Circle: Nature, Man, and Technology (2014).
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Omnes scientiae sunt connexae et fovent auxiliis sicut partes ejusdem totius, quarum quaelibet opus suum peragit non propter se sed pro aliis.
All sciences are connected; they lend each other material aid as parts of one great whole, each doing its own work, not for itself alone, but for the other parts; as the eye guides the body and the foot sustains it and leads it from place to place.
Opus Tertium [1266- 1268], chapter 4, Latin text quoted in J. B. Bury, The Idea of Progress (1920), 355 (footnote to page 25). In J. S. Brewer (ed.), Fr. Rogeri Bacon Opera ... inedita (1859), 18.
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A hundred years ago … an engineer, Herbert Spencer, was willing to expound every aspect of life, with an effect on his admiring readers which has not worn off today.
Things do not happen quite in this way nowadays. This, we are told, is an age of specialists. The pursuit of knowledge has become a profession. The time when a man could master several sciences is past. He must now, they say, put all his efforts into one subject. And presumably, he must get all his ideas from this one subject. The world, to be sure, needs men who will follow such a rule with enthusiasm. It needs the greatest numbers of the ablest technicians. But apart from them it also needs men who will converse and think and even work in more than one science and know how to combine or connect them. Such men, I believe, are still to be found today. They are still as glad to exchange ideas as they have been in the past. But we cannot say that our way of life is well-fitted to help them. Why is this?
In 'The Unification of Biology', New Scientist (11 Jan 1962), 13, No. 269, 72.
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Anthropologists are a connecting link between poets and scientists though their fieldwork among primitive peoples has often made them forget the language of science.
From Arthur D. Little Lecture (6 Dec 1963) at the London School of Economics, in Saturday Review (1963), 46, No. 4, 83.
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Endowed with two qualities, which seemed incompatible with each other, a volcanic imagination and a pertinacity of intellect which the most tedious numerical calculations could not daunt, Kepler conjectured that the movements of the celestial bodies must be connected together by simple laws, or, to use his own expression, by harmonic laws. These laws he undertook to discover. A thousand fruitless attempts, errors of calculation inseparable from a colossal undertaking, did not prevent him a single instant from advancing resolutely toward the goal of which he imagined he had obtained a glimpse. Twenty-two years were employed by him in this investigation, and still he was not weary of it! What, in reality, are twenty-two years of labor to him who is about to become the legislator of worlds; who shall inscribe his name in ineffaceable characters upon the frontispiece of an immortal code; who shall be able to exclaim in dithyrambic language, and without incurring the reproach of anyone, “The die is cast; I have written my book; it will be read either in the present age or by posterity, it matters not which; it may well await a reader, since God has waited six thousand years for an interpreter of his words.”
In 'Eulogy on Laplace', in Smithsonian Report for the year 1874 (1875), 131-132.
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For, in mathematics or symbolic logic, reason can crank out the answer from the symboled equations—even a calculating machine can often do so—but it cannot alone set up the equations. Imagination resides in the words which define and connect the symbols—subtract them from the most aridly rigorous mathematical treatise and all meaning vanishes. Was it Eddington who said that we once thought if we understood 1 we understood 2, for 1 and 1 are 2, but we have since found we must learn a good deal more about “and”?
In 'The Biological Basis of Imagination', American Thought: 1947 (1947), 81.
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I should like to draw attention to the inexhaustible variety of the problems and exercises which it [mathematics] furnishes; these may be graduated to precisely the amount of attainment which may be possessed, while yet retaining an interest and value. It seems to me that no other branch of study at all compares with mathematics in this. When we propose a deduction to a beginner we give him an exercise in many cases that would have been admired in the vigorous days of Greek geometry. Although grammatical exercises are well suited to insure the great benefits connected with the study of languages, yet these exercises seem to me stiff and artificial in comparison with the problems of mathematics. It is not absurd to maintain that Euclid and Apollonius would have regarded with interest many of the elegant deductions which are invented for the use of our students in geometry; but it seems scarcely conceivable that the great masters in any other line of study could condescend to give a moment’s attention to the elementary books of the beginner.
In Conflict of Studies (1873), 10-11.
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It is said that the composing of the Lilavati was occasioned by the following circumstance. Lilavati was the name of the author’s daughter, concerning whom it appeared, from the qualities of the ascendant at her birth, that she was destined to pass her life unmarried, and to remain without children. The father ascertained a lucky hour for contracting her in marriage, that she might be firmly connected and have children. It is said that when that hour approached, he brought his daughter and his intended son near him. He left the hour cup on the vessel of water and kept in attendance a time-knowing astrologer, in order that when the cup should subside in the water, those two precious jewels should be united. But, as the intended arrangement was not according to destiny, it happened that the girl, from a curiosity natural to children, looked into the cup, to observe the water coming in at the hole, when by chance a pearl separated from her bridal dress, fell into the cup, and, rolling down to the hole, stopped the influx of water. So the astrologer waited in expectation of the promised hour. When the operation of the cup had thus been delayed beyond all moderate time, the father was in consternation, and examining, he found that a small pearl had stopped the course of the water, and that the long-expected hour was passed. In short, the father, thus disappointed, said to his unfortunate daughter, I will write a book of your name, which shall remain to the latest times—for a good name is a second life, and the ground-work of eternal existence.
In Preface to the Persian translation of the Lilavati by Faizi (1587), itself translated into English by Strachey and quoted in John Taylor (trans.) Lilawati, or, A Treatise on Arithmetic and Geometry by Bhascara Acharya (1816), Introduction, 3. [The Lilavati is the 12th century treatise on mathematics by Indian mathematician, Bhaskara Acharya, born 1114.]
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Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
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Mathematics, among all school subjects, is especially adapted to further clearness, definite brevity and precision in expression, although it offers no exercise in flights of rhetoric. This is due in the first place to the logical rigour with which it develops thought, avoiding every departure from the shortest, most direct way, never allowing empty phrases to enter. Other subjects excel in the development of expression in other respects: translation from foreign languages into the mother tongue gives exercise in finding the proper word for the given foreign word and gives knowledge of laws of syntax, the study of poetry and prose furnish fit patterns for connected presentation and elegant form of expression, composition is to exercise the pupil in a like presentation of his own or borrowed thoughtsand their development, the natural sciences teach description of natural objects, apparatus and processes, as well as the statement of laws on the grounds of immediate sense-perception. But all these aids for exercise in the use of the mother tongue, each in its way valuable and indispensable, do not guarantee, in the same manner as mathematical training, the exclusion of words whose concepts, if not entirely wanting, are not sufficiently clear. They do not furnish in the same measure that which the mathematician demands particularly as regards precision of expression.
In Anleitung zum mathematischen Unterricht in höheren Schulen (1906), 17.
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Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence”.
In 'A Plea for the Mathematician', Nature, 1, 238 in Collected Mathematical Papers, Vol. 2, 655-56.
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Our situation on this earth seems strange. Every one of us appears here involuntarily and uninvited for a short stay, without knowing the whys and the wherefore. In our daily lives we only feel that man is here for the sake of others, for those whom we love and for many other beings whose fate is connected with our own. I am often worried at the thought that my life is based to such a large extent on the work of my fellow human beings and I am aware of my great indebtedness to them.
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Rulers and generals muster their troops. Magnates muster the sums of money which give them power. The fascist dictators muster the irrational human reactions which make it possible for them to attain and maintain their power over the masses. The scientists muster knowledge and means of research. But, thus far, no organization fighting for freedom has ever mustered the biological arsenal where the weapons are to be found for the establishment and the maintenance of human freedom. All precision of our social existence notwithstanding, there is as yet no definition of the word freedom which would be in keeping with natural science. No word is more misused and misunderstood. To define freedom is the same as to define sexual health. But nobody will openly admit this. The advocacy of personal and social freedom is connected with anxiety and guilt feelings. As if to be free were a sin or at least not quite as it should be. Sex-economy makes this guilt feeling comprehensible: freedom without sexual self-determination is in itself a contradiction. But to be sexual means—according to the prevailing human structure—to be sinful or guilty. There are very few people who experience sexual love without guilt feeling. “Free love” has acquired a degrading meaning: it lost the meaning given it by the old fighters for freedom. In films and in books, to be genital and to be criminal are presented as the same thing.
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Science is knowledge certain and evident in itself, or by the principles from which it is deducted, or with which it is certainly connected. It is subjective, as existing in the mind; objective, as embodied in truths; speculative, as leading to do something, as in practical science.
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Siphonophores do not convey the message–a favorite theme of unthinking romanticism–that nature is but one gigantic whole, all its parts intimately connected and interacting in some higher, ineffable harmony. Nature revels in boundaries and distinctions; we inhabit a universe of structure. But since our universe of structure has evolved historically, it must present us with fuzzy boundaries, where one kind of thing grades into another.
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Study the science of art. Study the art of science. Develop your senses - especially learn how to see. Realize that everything connects to everything else.
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Success…seems to be connected with action. Successful men keep moving. They make mistakes, but they don’t quit.
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The difference between an ordinary mind and the mind of Newton consists principally in this, that the one is capable of a more continuous attention than the other,—that a Newton is able, without fatigue, to connect inference with inference in one long series towards a determinate end; while the man of inferior capacity is soon obliged to break or let full the thread which lie had begun to spin.
In Lectures on Metaphysics and Logic (1860), Vol. 1, 178.
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The history of mathematics may be instructive as well as agreeable; it may not only remind us of what we have, but may also teach us to increase our store. Says De Morgan, “The early history of the mind of men with regards to mathematics leads us to point out our own errors; and in this respect it is well to pay attention to the history of mathematics.” It warns us against hasty conclusions; it points out the importance of a good notation upon the progress of the science; it discourages excessive specialization on the part of the investigator, by showing how apparently distinct branches have been found to possess unexpected connecting links; it saves the student from wasting time and energy upon problems which were, perhaps, solved long since; it discourages him from attacking an unsolved problem by the same method which has led other mathematicians to failure; it teaches that fortifications can be taken by other ways than by direct attack, that when repulsed from a direct assault it is well to reconnoiter and occupy the surrounding ground and to discover the secret paths by which the apparently unconquerable position can be taken.
In History of Mathematics (1897), 1-2.
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The prestige of government has undoubtedly been lowered considerably by the prohibition law. For nothing is more destructive of respect for the government and the law of the land than passing laws which cannot be enforced. It is an open secret that the dangerous increase of crime in the United States is closely connected with this.
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The scientific world-picture vouchsafes a very complete understanding of all that happens–it makes it just a little too understandable. It allows you to imagine the total display as that of a mechanical clockwork which, for all that science knows, could go on just the same as it does, without there being consciousness, will, endeavor, pain and delight and responsibility connected with it–though they actually are. And the reason for this disconcerting situation is just this: that for the purpose of constructing the picture of the external world, we have used the greatly simplifying device of cutting our own personality out, removing it; hence it is gone, it has evaporated, it is ostensibly not needed.
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The study of mathematics—from ordinary reckoning up to the higher processes—must be connected with knowledge of nature, and at the same time with experience, that it may enter the pupil’s circle of thought.
In Johann Friedrich Herbart, Henry M. Felkin (trans.) and Emmie Felkin (trans.), Letters and Lectures on Education [Felkin] (1898), 117.
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The succession of individuals, connected by reproduction and belonging to a species, makes it possible for the specific form itself to last for ages. In the end, however, the species is temporary; it has no “eternal life.” After existing for a certain period, it either dies or is converted by modification into other forms.
As translated by Joseph McCabe in Haeckel's The Wonders of Life: a Popular Study of Biological Philosophy (1904), 248.
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There is thus a possibility that the ancient dream of philosophers to connect all Nature with the properties of whole numbers will some day be realized. To do so physics will have to develop a long way to establish the details of how the correspondence is to be made. One hint for this development seems pretty obvious, namely, the study of whole numbers in modern mathematics is inextricably bound up with the theory of functions of a complex variable, which theory we have already seen has a good chance of forming the basis of the physics of the future. The working out of this idea would lead to a connection between atomic theory and cosmology.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 129.
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Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.
In Presidential Address to British Association (19 Aug 1869), 'A Plea for the Mathematician', published in Nature (6 Jan 1870), 1, 262.
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To connect the dinosaurs, creatures of interest to everyone but the veriest dullard, with a spectacular extra­terrestrial event like the deluge of meteors … seems a little like one of those plots that a clever publisher might concoct to guarantee enormous sales. All the Alvarez-Raup theories lack is some sex and the involvement of the Royal family and the whole world would be paying attention to them.
In The Canberra Times (20 May 1984).
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We debase the richness of both nature and our own minds if we view the great pageant of our intellectual history as a compendium of new in formation leading from primal superstition to final exactitude. We know that the sun is hub of our little corner of the universe, and that ties of genealogy connect all living things on our planet, because these theories assemble and explain so much otherwise disparate and unrelated information–not because Galileo trained his telescope on the moons of Jupiter or because Darwin took a ride on a Galápagos tortoise.
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We know enough to be sure that the scientific achievements of the next fifty years will be far greater, more rapid, and more surprising, than those we have already experienced. … Wireless telephones and television, following naturally upon the their present path of development, would enable their owner to connect up to any room similarly equipped and hear and take part in the conversation as well as if he put his head in through the window.
From 'Fifty Years Hence', Strand Magazine (Dec 1931). Reprinted in Popular Mechanics (Mar 1932), 57, No. 3, 394-396.
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Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation.
Fifth Canon of Induction (the Method of Concomitant Variations). In A System of Logic: Ratiocinative and Inductive; Being a Connected View of Principles of Evidence and the Methods of Scientific Investigation (1850), 233.
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While the method of the natural sciences is... analytic, the method of the social sciences is better described as compositive or synthetic. It is the so-called wholes, the groups of elements which are structurally connected, which we learn to single out from the totality of observed phenomena... Insofar as we analyze individual thought in the social sciences the purpose is not to explain that thought, but merely to distinguish the possible types of elements with which we shall have to reckon in the construction of different patterns of social relationships. It is a mistake... to believe that their aim is to explain conscious action ... The problems which they try to answer arise only insofar as the conscious action of many men produce undesigned results... If social phenomena showed no order except insofar as they were consciously designed, there would indeed be no room for theoretical sciences of society and there would be, as is often argued, only problems of psychology. It is only insofar as some sort of order arises as a result of individual action but without being designed by any individual that a problem is raised which demands a theoretical explanation... people dominated by the scientistic prejudice are often inclined to deny the existence of any such order... it can be shown briefly and without any technical apparatus how the independent actions of individuals will produce an order which is no part of their intentions... The way in which footpaths are formed in a wild broken country is such an instance. At first everyone will seek for himself what seems to him the best path. But the fact that such a path has been used once is likely to make it easier to traverse and therefore more likely to be used again; and thus gradually more and more clearly defined tracks arise and come to be used to the exclusion of other possible ways. Human movements through the region come to conform to a definite pattern which, although the result of deliberate decision of many people, has yet not be consciously designed by anyone.
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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
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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