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Who said: “I seem to have been only like a boy playing on the seashore, ... finding a smoother pebble or a prettier shell ... whilst the great ocean of truth lay all undiscovered before me.”
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Mechanics Quotes (131 quotes)

“The Universe repeats itself, with the possible exception of history.” Of all earthly studies history is the only one that does not repeat itself. ... Astronomy repeats itself; botany repeats itself; trigonometry repeats itself; mechanics repeats itself; compound long division repeats itself. Every sum if worked out in the same way at any time will bring out the same answer. ... A great many moderns say that history is a science; if so it occupies a solitary and splendid elevation among the sciences; it is the only science the conclusions of which are always wrong.
In 'A Much Repeated Repetition', Daily News (26 Mar 1904). Collected in G. K. Chesterton and Dale Ahlquist (ed.), In Defense of Sanity: The Best Essays of G.K. Chesterton (2011), 82.
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Lehre von den Ursachen der organischen Gestaltungen.
Developmental mechanics... is the doctrine of the causes of organic forms.
Archiv fur Entwickelungsmechanik der Organismen (1895), 1.
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Qu'une goutee de vin tombe dans un verre d'eau; quelle que soit la loi du movement interne du liquide, nous verrons bientôt se colorer d'une teinte rose uniforme et à partir de ce moment on aura beau agiter le vase, le vin et l'eau ne partaîtront plus pouvoir se séparer. Tout cela, Maxwell et Boltzmann l'ont expliqué, mais celui qui l'a vu plus nettement, dans un livre trop peu lu parce qu'il est difficile à lire, c'est Gibbs dans ses principes de la Mécanique Statistique.
Let a drop of wine fall into a glass of water; whatever be the law that governs the internal movement of the liquid, we will soon see it tint itself uniformly pink and from th at moment on, however we may agitate the vessel, it appears that the wine and water can separate no more. All this, Maxwell and Boltzmann have explained, but the one who saw it in the cleanest way, in a book that is too little read because it is difficult to read, is Gibbs, in his Principles of Statistical Mechanics.
La valeur de la science. In Anton Bovier, Statistical Mechanics of Disordered Systems (2006), 3.
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A system such as classical mechanics may be ‘scientific’ to any degree you like; but those who uphold it dogmatically — believing, perhaps, that it is their business to defend such a successful system against criticism as long as it is not conclusively disproved — are adopting the very reverse of that critical attitude which in my view is the proper one for the scientist.
In The Logic of Scientific Discovery (1959, reprint 2002), 28.
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Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsôt has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.
J. C. Maxwell on Louis Poinsôt (1777-1859) in 'On a Dynamical Top' (1857). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 1, 248.
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After a duration of a thousand years, the power of astrology broke down when, with Copernicus, Kepler, and Galileo, the progress of astronomy overthrew the false hypothesis upon which the entire structure rested, namely the geocentric system of the universe. The fact that the earth revolves in space intervened to upset the complicated play of planetary influences, and the silent stars, related to the unfathomable depths of the sky, no longer made their prophetic voices audible to mankind. Celestial mechanics and spectrum analysis finally robbed them of their mysterious prestige.
Franz Cumont, translated by J.B. Baker, Astrology and Religion Among the Greeks and Romans (1912, 2007), 6.
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All of modern physics is governed by that magnificent and thoroughly confusing discipline called quantum mechanics ... It has survived all tests and there is no reason to believe that there is any flaw in it.... We all know how to use it and how to apply it to problems; and so we have learned to live with the fact that nobody can understand it.
…...
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And there are absolutely no judgments (or rules) in Mechanics which do not also pertain to Physics, of which Mechanics is a part or type: and it is as natural for a clock, composed of wheels of a certain kind, to indicate the hours, as for a tree, grown from a certain kind of seed, to produce the corresponding fruit. Accordingly, just as when those who are accustomed to considering automata know the use of some machine and see some of its parts, they easily conjecture from this how the other parts which they do not see are made: so, from the perceptible effects and parts of natural bodies, I have attempted to investigate the nature of their causes and of their imperceptible parts.
Principles of Philosophy (1644), trans. V. R. and R. P. Miller (1983), 285-6.
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As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D'Alembert's principle for dynamics, the latter is again reduced to statics. Although it is is very much in order that in gradual training of science and in the instruction of the individual the easier precedes the more difficult, the simple precedes the more complicated, the special precedes the general, yet the min, once it has arrived at the higher standpoint, demands the reverse process whereby all statics appears only as a very special case of mechanics.
Collected Works (1877), Vol. 5, 25-26. Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 412.
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As the nineteenth century drew to a close, scientists could reflect with satisfaction that they had pinned down most of the mysteries of the physical world: electricity, magnetism, gases, optics, acoustics, kinetics and statistical mechanics ... all had fallen into order before the. They had discovered the X ray, the cathode ray, the electron, and radioactivity, invented the ohm, the watt, the Kelvin, the joule, the amp, and the little erg.
A Short History of Nearly Everything. In Clifford A. Pickover, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them (2008), 172.
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Bertrand Russell had given a talk on the then new quantum mechanics, of whose wonders he was most appreciative. He spoke hard and earnestly in the New Lecture Hall. And when he was done, Professor Whitehead, who presided, thanked him for his efforts, and not least for “leaving the vast darkness of the subject unobscured.”
Quoted in Robert Oppenheimer, The Open Mind (1955), 102.
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By the 18th century science had been so successful in laying bare the laws of nature that many thought there was nothing left to discover. Immutable laws prescribed the motion of every particle in the universe, exactly and forever: the task of the scientist was to elucidate the implications of those laws for any particular phenomenon of interest. Chaos gave way to a clockwork world. But the world moved on ...Today even our clocks are not made of clockwork. ... With the advent of quantum mechanics, the clockwork world has become a lottery. Fundamental events, such as the decay of a radioactive atom, are held to be determined by chance, not law.
Does God Play Dice?: The New Mathematics of Chaos (2002). xi.
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Can quantum mechanics represent the fact that an electron finds itself approximately in a given place and that it moves approximately with a given velocity, and can we make these approximations so close that they do not cause experimental difficulties?
Physics and Beyond: Encounters and Conversations, trans. Arnold J. Pomerans (1971), 78.
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Cell genetics led us to investigate cell mechanics. Cell mechanics now compels us to infer the structures underlying it. In seeking the mechanism of heredity and variation we are thus discovering the molecular basis of growth and reproduction. The theory of the cell revealed the unity of living processes; the study of the cell is beginning to reveal their physical foundations.
Recent Advances in Cytology (1937), 562.
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Consciously and systematically Klein sought to enthrall me with the problems of mathematical physics, and to win me over to his conception of these problems as developed it in lecture courses in previous years. I have always regarded Klein as my real teacher only in things mathematical, but also in mathematical physics and in my conception of mechanics.
As quoted in Paul Forman and Armin Hermann, 'Sommerfeld, Arnold (Johannes Wilhelm)', Biography in Dictionary of Scientific Biography (1975), Vol. 12, 526. Cited from 'Autobiographische Skizze', Gesammelte Schriften, Vol 4, 673–682.
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Could Hamlet have been written by a committee, or the “Mona Lisa” painted by a club? Could the New Testament have been composed as a conference report? Creative ideas do not spring from groups. They spring from individuals. The divine spark leaps from the finger of God to the finger of Adam, whether it takes ultimate shape in a law of physics or a law of the land, a poem or a policy, a sonata or a mechanical computer.
Baccalaureate address (9 Jun 1957), Yale University. In In the University Tradition (1957), 156.
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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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Einstein never accepted quantum mechanics because of this element of chance and uncertainty. He said: God does not play dice. It seems that Einstein was doubly wrong. The quantum effects of black holes suggests that not only does God play dice, He sometimes throws them where they cannot be seen.
…...
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Engineering is quite different from science. Scientists try to understand nature. Engineers try to make things that do not exist in nature. Engineers stress invention. To embody an invention the engineer must put his idea in concrete terms, and design something that people can use. That something can be a device, a gadget, a material, a method, a computing program, an innovative experiment, a new solution to a problem, or an improvement on what is existing. Since a design has to be concrete, it must have its geometry, dimensions, and characteristic numbers. Almost all engineers working on new designs find that they do not have all the needed information. Most often, they are limited by insufficient scientific knowledge. Thus they study mathematics, physics, chemistry, biology and mechanics. Often they have to add to the sciences relevant to their profession. Thus engineering sciences are born.
Y.C. Fung and P. Tong, Classical and Computational Solid Mechanics (2001), 1.
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Euler could repeat the Aeneid from the beginning to the end, and he could even tell the first and last lines in every page of the edition which he used. In one of his works there is a learned memoir on a question in mechanics, of which, as he himself informs us, a verse of Aeneid gave him the first idea. [“The anchor drops, the rushing keel is staid.”]
In Letters of Euler (1872), Vol. 1, 24.
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Ever since celestial mechanics in the skillful hands of Leverrier and Adams led to the world-amazed discovery of Neptune, a belief has existed begotten of that success that still other planets lay beyond, only waiting to be found.
…...
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Every discoverer of a new truth, or inventor of the method which evolves it, makes a dozen, perhaps fifty, useless combinations, experiments, or trials for one successful one. In the realm of electricity or of mechanics there is no objection to this. But when such rejected failures involve a torture of animals, sometimes fearful in its character, there is a distinct objection to it.
From 'Vivisection', an original paper in Surgical Anaesthesia: Addresses, and Other Papers (1894, 1900), 369-370.
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Every new theory as it arises believes in the flush of youth that it has the long sought goal; it sees no limits to its applicability, and believes that at last it is the fortunate theory to achieve the 'right' answer. This was true of electron theory—perhaps some readers will remember a book called The Electrical Theory of the Universe by de Tunzelman. It is true of general relativity theory with its belief that we can formulate a mathematical scheme that will extrapolate to all past and future time and the unfathomed depths of space. It has been true of wave mechanics, with its first enthusiastic claim a brief ten years ago that no problem had successfully resisted its attack provided the attack was properly made, and now the disillusionment of age when confronted by the problems of the proton and the neutron. When will we learn that logic, mathematics, physical theory, are all only inventions for formulating in compact and manageable form what we already know, like all inventions do not achieve complete success in accomplishing what they were designed to do, much less complete success in fields beyond the scope of the original design, and that our only justification for hoping to penetrate at all into the unknown with these inventions is our past experience that sometimes we have been fortunate enough to be able to push on a short distance by acquired momentum.
The Nature of Physical Theory (1936), 136.
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Geometry is founded in mechanical practice, and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring.
In Principia (1687), Preface, translated by Andrew Motte (1729), in Florian Cajori (ed.), Sir Isaac Newton's Mathematical Principles of Natural Philosophy (1934), xvii.
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Give me a place to stand, and I will move the earth.
F. Hultsch (ed.) Pappus Alexandrinus: Collectio (1876-8), Vol. 3, book 8, section 10, ix.
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He [Lord Bacon] appears to have been utterly ignorant of the discoveries which had just been made by Kepler’s calculations … he does not say a word about Napier’s Logarithms, which had been published only nine years before and reprinted more than once in the interval. He complained that no considerable advance had been made in Geometry beyond Euclid, without taking any notice of what had been done by Archimedes and Apollonius. He saw the importance of determining accurately the specific gravities of different substances, and himself attempted to form a table of them by a rude process of his own, without knowing of the more scientific though still imperfect methods previously employed by Archimedes, Ghetaldus and Porta. He speaks of the εὕρηκα of Archimedes in a manner which implies that he did not clearly appreciate either the problem to be solved or the principles upon which the solution depended. In reviewing the progress of Mechanics, he makes no mention either of Archimedes, or Stevinus, Galileo, Guldinus, or Ghetaldus. He makes no allusion to the theory of Equilibrium. He observes that a ball of one pound weight will fall nearly as fast through the air as a ball of two, without alluding to the theory of acceleration of falling bodies, which had been made known by Galileo more than thirty years before. He proposed an inquiry with regard to the lever,—namely, whether in a balance with arms of different length but equal weight the distance from the fulcrum has any effect upon the inclination—though the theory of the lever was as well understood in his own time as it is now. … He speaks of the poles of the earth as fixed, in a manner which seems to imply that he was not acquainted with the precession of the equinoxes; and in another place, of the north pole being above and the south pole below, as a reason why in our hemisphere the north winds predominate over the south.
From Spedding’s 'Preface' to De Interpretations Naturae Proœmium, in The Works of Francis Bacon (1857), Vol. 3, 511-512. [Note: the Greek word “εὕρηκα” is “Eureka” —Webmaster.]
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I also require much time to ponder over the matters themselves, and particularly the principles of mechanics (as the very words: force, time, space, motion indicate) can occupy one severely enough; likewise, in mathematics, the meaning of imaginary quantities, of the infinitesimally small and infinitely large and similar matters.
In Davis Baird, R.I.G. Hughes and Alfred Nordmann, Heinrich Hertz: Classical Physicist, Modern Philosopher (1998), 159.
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I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect...geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.
Quoted in J Koenderink, Solid Shape (1990).
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I am coming more and more to the conviction that the necessity of our geometry cannot be proved, at least neither by, nor for, the human intelligence … One would have to rank geometry not with arithmetic, which stands a priori, but approximately with mechanics.
From Letter (28 Apr 1817) to Olbers, as quoted in Guy Waldo Dunnington, Carl Friedrich Gauss, Titan of Science: A Study of His Life and Work (1955), 180.
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I can never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model, I can understand it. As long as I cannot make a mechanical model all the way through I cannot understand.
From stenographic report by A.S. Hathaway of the Lecture 20 Kelvin presented at Johns Hopkins University, Baltimore, on 'Molecular Dynamics and the Wave Theory of Light' (1884), 270-271. (Hathaway was a Mathematics fellow there.) This remark is not included in the first typeset publication—a revised version, printed twenty years later, in 1904, as Lord Kelvin’s Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. The original notes were reproduced by the “papyrograph” process. They are excerpted in Pierre Maurice Marie Duhem, Essays in the History and Philosophy of Science (1996), 55.
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I count Maxwell and Einstein, Eddington and Dirac, among “real” mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as “useless” as the theory of numbers.
In A Mathematician's Apology (1940, 2012), 131.
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I don't like it, and I'm sorry I ever had anything to do with it. [About the probability interpretation of quantum mechanics.]
Epigraph, without citation, in John Gribbin, In Search of Schrödinger’s Cat: Quantum Physics and Reality (1984), v, frontispiece.
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I really enjoy good murder mystery writers, usually women, frequently English, because they have a sense of what the human soul is about and why people do dark and terrible things. I also read quite a lot in the area of particle physics and quantum mechanics, because this is theology. This is about the nature of being. This is what life is all about. I try to read as widely as I possibly can.
…...
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I recognize nothing that is not material. In physics, chemistry and biology I see only mechanics. The Universe is nothing but an infinite and complex mechanism. Its complexity is so great that it borders on willfulness, suddenness, and randomness; it gives the illusion of free will possessed by conscious beings.
In Monism of the Universe (1931).
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I should not think of devoting less than 20 years to an Epic Poem. Ten to collect materials and warm my mind with universal science. I would be a tolerable Mathematician, I would thoroughly know Mechanics, Hydrostatics, Optics, and Astronomy, Botany, Metallurgy, Fossilism, Chemistry, Geology, Anatomy, Medicine—then the mind of man—then the minds of men—in all Travels, Voyages and Histories. So I would spend ten years—the next five to the composition of the poem—and the five last to the correction of it. So I would write haply not unhearing of the divine and rightly-whispering Voice, which speaks to mighty minds of predestinated Garlands, starry and unwithering.
Letter to Joseph Cottle, early April 1797. In Earl Leslie Griggs (ed.), The Collected Letters of Samuel Taylor Coleridge (1956), Vol. 1, 320-1.
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I think I can safely say that nobody understands quantum mechanics.
'Probability and Uncertainty—the Quantum Mechanical View of Nature', the sixth of his Messenger Lectures (1964), Cornell University. Collected in The Character of Physical Law (1967), 129. Often misquoted in various ways, for example, “If people say they understand quantum mechanics they’re lying,” in Ari Ben-Menahem, Historical Encyclopedia of Natural and Mathematical Sciences (2009), 5699.
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If it be urged that the action of the potato is chemical and mechanical only, and that it is due to the chemical and mechanical effects of light and heat, the answer would seem to lie in an enquiry whether every sensation is not chemical and mechanical in its operation? Whether those things which we deem most purely spiritual are anything but disturbances of equilibrium in an infinite series of levers, beginning with those that are too small for microscopic detection, and going up to the human arm and the appliances which it makes use of? Whether there be not a molecular action of thought, whence a dynamical theory of the passions shall be deducible?
In Erewhon, Or, Over the Range (1872), 192.
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If we turn to the problems to which the calculus owes its origin, we find that not merely, not even primarily, geometry, but every other branch of mathematical physics—astronomy, mechanics, hydrodynamics, elasticity, gravitation, and later electricity and magnetism—in its fundamental concepts and basal laws contributed to its development and that the new science became the direct product of these influences.
Opening of Presidential Address (27 Apr 1907) to the American Mathematical Society, 'The Calculus in Colleges and Technical Schools', published in Bulletin of the American Mathematical Society (Jun 1907), 13, 449.
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In early life I had felt a strong desire to devote myself to the experimental study of nature; and, happening to see a glass containing some camphor, portions of which had been caused to condense in very beautiful crystals on the illuminated side, I was induced to read everything I could obtain respecting the chemical and mechanical influences of light, adhesion, and capillary attraction.
In preface to Scientific Memoirs (1878), xii.
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In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.
... a l'ouverture du cours de mechanique industrielle á Metz (1827), 2-3, trans. Ivor Grattan-Guinness.
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In general, art has preceded science. Men have executed great, and curious, and beautiful works before they had a scientific insight into the principles on which the success of their labours was founded. There were good artificers in brass and iron before the principles of the chemistry of metals were known; there was wine among men before there was a philosophy of vinous fermentation; there were mighty masses raised into the air, cyclopean walls and cromlechs, obelisks and pyramids—probably gigantic Doric pillars and entablatures—before there was a theory of the mechanical powers. … Art was the mother of Science.
Lecture (26 Nov 1851), to the London Society of Arts, 'The General Bearing of the Great Exhibition on the Progress of Art and Science', collected in Lectures on the Results of the Great Exhibition of 1851' (1852), 7-8.
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In modern times the belief that the ultimate explanation of all things was to be found in Newtonian mechanics was an adumbration of the truth that all science, as it grows towards perfection, becomes mathematical in its ideas.
In An Introduction to Mathematics (1911), 13-14. [To suggest, disclose, or outline partially, produces an “adumbration”, which gives only the main facts and not the details. —Webmaster]
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In order to discover Truth in this manner by observation and reason, it is requisite we should fix on some principles whose certainty and effects are demonstrable to our senses, which may serve to explain the phenomena of natural bodies and account for the accidents that arise in them; such only are those which are purely material in the human body with mechanical and physical experiments … a physician may and ought to furnish himself with, and reason from, such things as are demonstrated to be true in anatomy, chemistry, and mechanics, with natural and experimental philosophy, provided he confines his reasoning within the bounds of truth and simple experiment.
As quoted in selection from the writings of Herman Boerhaave, collected in Oliver Joseph Thatcher (ed.), The Ideas that Have Influenced Civilization, in the Original Documents (1800), Vol. 6, 242.
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In relativity, movement is continuous, causally determinate and well defined; while in quantum mechanics it is discontinuous, not causally determinate and not well defined.
In Wholeness and the Implicate Order (1980), xv.
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In the history of physics, there have been three great revolutions in thought that first seemed absurd yet proved to be true. The first proposed that the earth, instead of being stationary, was moving around at a great and variable speed in a universe that is much bigger than it appears to our immediate perception. That proposal, I believe, was first made by Aristarchos two millenia ago ... Remarkably enough, the name Aristarchos in Greek means best beginning.
[The next two revolutions occurred ... in the early part of the twentieth century: the theory of relativity and the science of quantum mechanics...]
Edward Teller with Judith L. Shoolery, Memoirs: A Twentieth-Century Journey in Science and Politics (2001), 562.
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In the progressive growth of astronomy, physics or mechanical science was developed, and when this had been, to a certain degree, successfully cultivated, it gave birth to the science of chemistry.
Familiar Letters on Chemistry (1851), 2.
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In using the present in order to reveal the past, we assume that the forces in the world are essentially the same through all time; for these forces are based on the very nature of matter, and could not have changed. The ocean has always had its waves, and those waves have always acted in the same manner. Running water on the land has ever had the same power of wear and transportation and mathematical value to its force. The laws of chemistry, heat, electricity, and mechanics have been the same through time. The plan of living structures has been fundamentally one, for the whole series belongs to one system, as much almost as the parts of an animal to the one body; and the relations of life to light and heat, and to the atmosphere, have ever been the same as now.
In Manual of Geology, Treating of the Principles of the Science (1863), 7.
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It is often assumed that because the young child is not competent to study geometry systematically he need be taught nothing geometrical; that because it would be foolish to present to him physics and mechanics as sciences it is useless to present to him any physical or mechanical principles.
An error of like origin, which has wrought incalculable mischief, denies to the scholar the use of the symbols and methods of algebra in connection with his early essays in numbers because, forsooth, he is not as yet capable of mastering quadratics! … The whole infant generation, wrestling with arithmetic, seek for a sign and groan and travail together in pain for the want of it; but no sign is given them save the sign of the prophet Jonah, the withered gourd, fruitless endeavor, wasted strength.
From presidential address (9 Sep 1884) to the General Meeting of the American Social Science Association, 'Industrial Education', printed in Journal of Social Science (1885), 19, 121. Collected in Francis Amasa Walker, Discussions in Education (1899), 132.
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It is possible in quantum mechanics to sneak quickly across a region which is illegal energetically.
In Feynman Lectures on Physics, Vol. 3, 8-12.
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It is probable that the scheme of physics will be enlarged so as to embrace the behaviour of living organisms under the influence of life and mind. Biology and psychology are not alien sciences; their operations are not solely mechanical, nor can they be formulated by physics as it is today; but they belong to a physical universe, and their mode of action ought to be capable of being formulated in terms of an enlarged physics in the future, in which the ether will take a predominant place. On the other hand it may be thought that those entities cannot be brought to book so easily, and that they will always elude our ken. If so, there will be a dualism in the universe, which posterity will find staggering, but that will not alter the facts.
In Past Years: an Autobiography (1932), 350. Quoted in book review, Waldehar Kaempfert, 'Sir Oliver Lodge Stands by the Old Physics', New York Times (21 Feb 1932), BR5.
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It is the structure of the universe that has taught this knowledge to man. That structure is an ever existing exhibition of every principle upon which every part of mathematical science is founded. The offspring of this science is mechanics; for mechanics are no other than the principles of science appplied practically.
In The Age of Reason: Being an Investigation of True and Fabulous Theology (27 Jan O.S. 1794), 42.
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It is therefore easy to see why the churches have always fought science and persecuted its devotees. On the other hand, I maintain that the cosmic religious feeling is the strongest and noblest motive for scientific research. Only those who realize the immense efforts and, above all, the devotion without which pioneer work in theoretical science cannot be achieved are able to grasp the strength of the emotion out of which alone such work, remote as it is from the immediate realities of life, can issue. What a deep conviction of the rationality of the universe and what a yearning to understand, were it but a feeble reflection of the mind revealed in this world, Kepler and Newton must have had to enable them to spend years of solitary labor in disentangling the principles of celestial mechanics! Those whose acquaintance with scientific research is derived chiefly from its practical results easily develop a completely false notion of the mentality of the men who, surrounded by a skeptical world, have shown the way to kindred spirits scattered wide through the world and through the centuries. Only one who has devoted his life to similar ends can have a vivid realization of what has inspired these men and given them the strength to remain true to their purpose in spite of countless failures. It is cosmic religious feeling that gives a man such strength. A contemporary has said, not unjustly, that in this materialistic age of ours the serious scientific workers are the only profoundly religious people.
…...
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It is worthy of note that nearly all that has been done for the improvement of the steam engine has been accomplished, not by men educated in colleges or technical schools, but by laborers, mechanics, and engine-men. There seem to be instances where the mechanical instinct takes precedence over the higher powers of the mind, in efficiency in harnessing the forces of nature and causing them to do our work.
In paper 'Stephenson and Transportation' (1916), collected in Francis Edgar Stanley, Theories Worth Having and Other Papers (1919), 66-67.
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It seems sensible to discard all hope of observing hitherto unobservable quantities, such as the position and period of the electron... Instead it seems more reasonable to try to establish a theoretical quantum mechanics, analogous to classical mechanics, but in which only relations between observable quantities occur.
In Helge Kragh, Quantum Generations: A History of Physics in the Twentieth Century (1999), 161.
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It seems to me, he says, that the test of “Do we or not understand a particular subject in physics?” is, “Can we make a mechanical model of it?” I have an immense admiration for Maxwell’s model of electromagnetic induction. He makes a model that does all the wonderful things that electricity docs in inducing currents, etc., and there can be no doubt that a mechanical model of that kind is immensely instructive and is a step towards a definite mechanical theory of electromagnetism.
From stenographic report by A.S. Hathaway of the Lecture 20 Kelvin presented at Johns Hopkins University, Baltimore, on 'Molecular Dynamics and the Wave Theory of Light' (1884), 132. (Hathaway was a Mathematics fellow there.) This remark is not included in the first typeset publication—a revised version, printed twenty years later, in 1904, as Lord Kelvin’s Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. The original notes were reproduced by the “papyrograph” process. They are excerpted in Pierre Maurice Marie Duhem, Essays in the History and Philosophy of Science (1996), 54-55.
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It was about three o’clock at night when the final result of the calculation [which gave birth to quantum mechanics] lay before me ... At first I was deeply shaken ... I was so excited that I could not think of sleep. So I left the house ... and awaited the sunrise on top of a rock.
[That was “the night of Heligoland”.]
Quoted in Abraham Pais, Niels Bohr’s Times: in Physics, Philosophy, and Polity (1991), 275. Cited in Mauro Dardo, Nobel Laureates and Twentieth-Century Physics (2004), 179.
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Kirchhoff’s whole tendency, and its true counterpart, the form of his presentation, was different [from Maxwell’s “dramatic bulk”]. … He is characterized by the extreme precision of his hypotheses, minute execution, a quiet rather than epic development with utmost rigor, never concealing a difficulty, always dispelling the faintest obscurity. … he resembled Beethoven, the thinker in tones. — He who doubts that mathematical compositions can be beautiful, let him read his memoir on Absorption and Emission … or the chapter of his mechanics devoted to Hydrodynamics.
In Ceremonial Speech (15 Nov 1887) celebrating the 301st anniversary of the Karl-Franzens-University Graz. Published as Gustav Robert Kirchhoff: Festrede zur Feier des 301. Gründungstages der Karl-Franzens-Universität zu Graz (1888), 30, as translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 187. From the original German, “Kirchhoff … seine ganze Richtung war eine andere, und ebenso auch deren treues Abbild, die Form seiner Darstellung. … Ihn charakterisirt die schärfste Präcisirung der Hypothesen, feine Durchfeilung, ruhige mehr epische Fortentwicklung mit eiserner Consequenz ohne Verschweigung irgend einer Schwierigkeit, unter Aufhellung des leisesten Schattens. … er glich dem Denker in Tönen: Beethoven. – Wer in Zweifel zieht, dass mathematische Werke künstlerisch schön sein können, der lese seine Abhandlung über Absorption und Emission oder den der Hydrodynamik gewidmeten Abschnitt seiner Mechanik.” The memoir reference is Gesammelte Abhandlungen (1882), 571-598.
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Look round the world, contemplate the whole and every part of it: you will find it to be nothing but one great machine, subdivided into an infinite number of lesser machines, which again admit of subdivisions to a degree beyond what human senses and faculties can trace and explain. All these various machines, and even their most minute parts, are adjusted to each other with an accuracy which ravishes into admiration all men who have ever contemplated them. The curious adapting of means to ends, throughout all nature, resembles exactly, though it much exceeds, the productions of human contrivance-of human design, thought, wisdom, and intelligence.
Dialogues Concerning Natural Religion (1779), 47-48.
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Modern physics has changed nothing in the great classical disciplines of, for instance, mechanics, optics, and heat. Only the conception of hitherto unexplored regions, formed prematurely from a knowledge of only certain parts of the world, has undergone a decisive transformation. This conception, however, is always decisive for the future course of research.
In Philosophical Problems of Nuclear Science: Eight Lectures (1952), 18.
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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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Mr. [Granville T.] Woods says that he has been frequently refused work because of the previous condition of his race, but he has had great determination and will and never despaired because of disappointments. He always carried his point by persistent efforts. He says the day is past when colored boys will be refused work only because of race prejudice. There are other causes. First, the boy has not the nerve to apply for work after being refused at two or three places. Second, the boy should have some knowledge of mechanics. The latter could be gained at technical schools, which should be founded for the purpose. And these schools must sooner or later be established, and thereby, we should be enabled to put into the hands of our boys and girls the actual means of livelihood.
From William J. Simmons, Men of Mark: Eminent, Progressive and Rising (1887), 108.
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My view, the skeptical one, holds that we may be as far away from an understanding of elementary particles as Newton's successors were from quantum mechanics. Like them, we have two tremendous tasks ahead of us. One is to study and explore the mathematics of the existing theories. The existing quantum field-theories may or may not be correct, but they certainly conceal mathematical depths which will take the genius of an Euler or a Hamilton to plumb. Our second task is to press on with the exploration of the wide range of physical phenomena of which the existing theories take no account. This means pressing on with experiments in the fashionable area of particle physics. Outstanding among the areas of physics which have been left out of recent theories of elementary particles are gravitation and cosmology
In Scientific American (Sep 1958). As cited in '50, 100 & 150 years ago', Scientific American (Sep 2008), 299, No. 3, 14.
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No one can know and understand everything. Even individual scientists are ignorant about most of the body of scientific knowledge, and it is not simply that biologists do not understand quantum mechanics.
From review, 'Billions and Billions of Demons', of the book, The Demon-Haunted World: Science as a Candle in the Dark, by Carl Sagan, in New York Review of Books (9 Jan 1997).
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Nowadays group theoretical methods—especially those involving characters and representations, pervade all branches of quantum mechanics.
Group Theory and its Significance', Proceedings, American Philosophical Society (1973), 117, No. 5, 380.
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One of the most conspicuous and distinctive features of mathematical thought in the nineteenth century is its critical spirit. Beginning with the calculus, it soon permeates all analysis, and toward the close of the century it overhauls and recasts the foundations of geometry and aspires to further conquests in mechanics and in the immense domains of mathematical physics. … A searching examination of the foundations of arithmetic and the calculus has brought to light the insufficiency of much of the reasoning formerly considered as conclusive.
In History of Mathematics in the Nineteenth Century', Congress of Arts and Sciences (1906), Vol. 1, 482. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 113-114.
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Quantum field theory, which was born just fifty years ago from the marriage of quantum mechanics with relativity, is a beautiful but not very robust child.
In Nobel Lecture (8 Dec 1989), 'Conceptual Foundations of the Unified Theory of Weak and Electromagnetic Interactions.'
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Quantum mechanics and relativity, taken together, are extraordinarily restrictive, and they therefore provide us with a great logical machine. We can explore with our minds any number of possible universes consisting of all kinds of mythical particles and interactions, but all except a very few can be rejected on a priori grounds because they are not simultaneously consistent with special relativity and quantum mechanics. Hopefully in the end we will find that only one theory is consistent with both and that theory will determine the nature of our particular universe.
…...
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Quantum mechanics is certainly imposing. But an inner voice tells me that this is not yet the real thing. The theory says a lot, but does not bring us any closer to the secrets of the “Old One.” I, at any rate, am convinced that He is not playing at dice.
Letter to Max Born (4 Dec 1926). Collected in The Born-Einstein Letters: Correspondence between Albert Einstein and Max and Hedwig Born from 1916-1955 (1971), 91. Also seen as “God does not play dice [with the universe].”
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Quantum mechanics is very imposing. … I, at any rate, am convinced that He [God] is not playing at dice.
In letter (4 Dec 1926) to Max Born. From the original German, “Die Quantenmechanik ist sehr achtung-gebietend. … Jedenfalls bin ich überzeugt, daß der nicht würfelt.” English version as in Albert Einstein, Max Born, Hedwig Born and Irene Born (trans.), The Born-Einstein Letters (1971).
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Quantum mechanics provides us with an approximate, plausible, conjectural explanation of what actually is, or was, or may be taking place inside a cyclotron during a dark night in February.
In 'Science and Technology', A Voice Crying in the Wilderness (Vox Clamantis in Deserto) (1989), 91.
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Samuel Pierpoint Langley, at that time regarded as one of the most distinguished scientists in the United States … evidently believed that a full sized airplane could be built and flown largely from theory alone. This resulted in two successive disastrous plunges into the Potomac River, the second of which almost drowned his pilot. This experience contrasts with that of two bicycle mechanics Orville and Wilbur Wright who designed, built and flew the first successful airplane. But they did this after hundreds of experiments extending over a number of years.
In article Total Quality: Its Origins and its Future (1995), published at the Center for Quality and Productivity Improvement.
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Schrodinger’s wave-mechanics is not a physical theory but a dodge—and a very good dodge too.
Gifford Lectures (1927), The Nature of the Physical World (1928), 219.
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Science has taught us to think the unthinkable. Because when nature is the guide—rather than a priori prejudices, hopes, fears or desires—we are forced out of our comfort zone. One by one, pillars of classical logic have fallen by the wayside as science progressed in the 20th century, from Einstein's realization that measurements of space and time were not absolute but observer-dependent, to quantum mechanics, which not only put fundamental limits on what we can empirically know but also demonstrated that elementary particles and the atoms they form are doing a million seemingly impossible things at once.
In op-ed, 'A Universe Without Purpose', Los Angeles Times (1 Apr 2012).
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Science is able to make cooperate catholics and mechanics, students and Nobel prize winners, because a common faith distributes the functions of workmanship despite all differences of rational formulation.
In 'The Scientific Grammar of Michael Faraday’s Diaries', Part I, 'The Classic of Science', A Classic and a Founder (1937), collected in Rosenstock-Huessy Papers (1981), Vol. 1, 8.
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Scientists, therefore, are responsible for their research, not only intellectually but also morally. This responsibility has become an important issue in many of today's sciences, but especially so in physics, in which the results of quantum mechanics and relativity theory have opened up two very different paths for physicists to pursue. They may lead us—to put it in extreme terms—to the Buddha or to the Bomb, and it is up to each of us to decide which path to take.
In The Turning Point: Science, Society, and the Rising Culture (1983), 87.
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Suppose we loosely define a religion as any discipline whose foundations rest on an element of faith, irrespective of any element of reason which may be present. Quantum mechanics for example would be a religion under this definition. But mathematics would hold the unique position of being the only branch of theology possessing a rigorous demonstration of the fact that it should be so classified.
Concluding remark in 'Consistency and Completeness—A Résumé', The American Mathematical Monthly (May 1956), 63, No.5, 305.
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That scientific work should be more useful the more it has been used, while mechanical work is expended in use, may seem strange to us.
From 'The Economy of Science' in The Science of Mechanics: A Critical and Historical Exposition of its Principles (1893), 488.
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The arithmetization of mathematics … which began with Weierstrass … had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics. These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought. But how can we avoid the use of human language? The … symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.
In Tobias Dantzig and Joseph Mazur (ed.), Number: The Language of Science (1930, ed. by Joseph Mazur 2007), 99.
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The basic idea is to shove all fundamental difficulties onto the neutron and to do quantum mechanics in the nucleus.
Letter to Niels Bohr, 20 Jun 1932. Quoted in David C. Cassidy, Uncertainty: The Life and Science of Werner Heisenberg (1992), 292.
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The book of knowledge of ingenious mechanical devices.
The Book of Knowledge of Ingenious Mechanical Devices (c. 1204 or 1206).
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The deepest part of theoretical chemistry must end up in quantum mechanics.
In 'Chemistry', The Feynman Lectures on Physics (1965), Vol. 1, page 3-1.
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The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.
From Principia Mathematica, Book 1, in Author’s Preface to the translation from the Latin by ‎Andrew Motte, as The Mathematical Principles of Natural Philosophy (1729), Vol. 1, second unpaginated page of the Preface.
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The development doctrines are doing much harm on both sides of the Atlantic, especially among intelligent mechanics, and a class of young men engaged in the subordinate departments of trade and the law. And the harm thus considerable in amount must be necessarily more than considerable in degree. For it invariably happens, that when persons in these walks become materialists, they become turbulent subjects and bad men.
The Foot-prints of the Creator: Or, The Asterolepis of Stromness (1850, 1859), Preface, vi.
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THE DYING AIRMAN
A handsome young airman lay dying,
As on the aerodrome he lay,
To the mechanics who round him came sighing,
These last words he did say.
“Take the cylinders out of my kidneys,
The connecting-rod out of my brain,
Take the cam-shaft from out of my backbone,
And assemble the engine again.”
Anonymous
From Edith L. Tiempo, Introduction to Poetry: Poetry Through Image and Statement (1993), 6.
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The experimental investigation by which Ampere established the law of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the 'Newton of Electricity'. It is perfect in form, and unassailable in accuracy, and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electro-dynamics.
A Treatise on Electricity and Magnetism (1873), Vol. 2, 162.
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The following general conclusions are drawn from the propositions stated above, and known facts with reference to the mechanics of animal and vegetable bodies:—
There is at present in the material world a universal tendency to the dissipation of mechanical energy.
Any restoration of mechanical energy, without more than an equivalent of dissipation, is impossible in inanimate material processes, and is probably never effected by means of organized matter, either endowed with vegetable life, or subjected to the will of an animated creature.
Within a finite period of time past the earth must have been, and within a finite period of time to come the earth must again be, unfit for the habitation of man as at present constituted, unless operations have been, or are to be performed, which are impossible under the laws to which the known operations going on at present in the material world are subject.
In 'On a Universal Tendency in Nature to the Dissipation of Mechanical Energy', Proceedings of the Royal Society of Edinburgh, 1852, 3, 141-142. In Mathematical and Physical Papers (1882-1911), Vol. 1, 513-514.
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The genius of Leonardo da Vinci imagined a flying machine, but it took the methodical application of science by those two American bicycle mechanics to create it.
In Time/CBS News, 'The Wright Brothers, People of the Century (1999), 42.
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The highest object at which the natural sciences are constrained to aim, but which they will never reach, is the determination of the forces which are present in nature, and of the state of matter at any given moment—in one word, the reduction of all the phenomena of nature to mechanics.
In Über das Ziel der Naturwissenschaften (1865), 9. As translated in John Bernhard Stallo, The Concepts and Theories of Modern Physics (1882), 18. From the original German, “Das höchste Ziel, welches die Naturwissenschaften zu erstreben haben, ist die Verwirklichung der eben gemachten Voraussetzung, also die Ermittelung der Kräfte, welche in der Natur vorhanden sind, und des Zustandes, in dem die Materie in einem Augenblicke sich befindet, mit einem Worte, die Zurückführung aller Naturerscheinungen auf die Mechanik.”
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The ideas which these sciences, Geometry, Theoretical Arithmetic and Algebra involve extend to all objects and changes which we observe in the external world; and hence the consideration of mathematical relations forms a large portion of many of the sciences which treat of the phenomena and laws of external nature, as Astronomy, Optics, and Mechanics. Such sciences are hence often termed Mixed Mathematics, the relations of space and number being, in these branches of knowledge, combined with principles collected from special observation; while Geometry, Algebra, and the like subjects, which involve no result of experience, are called Pure Mathematics.
In The Philosophy of the Inductive Sciences (1868), Part 1, Bk. 2, chap. 1, sect. 4.
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The kinetic concept of motion in classical theory will have to undergo profound modifications. (That is why I also avoided the term “orbit” in my paper throughout.) … We must not bind the atoms in the chains of our prejudices—to which, in my opinion, also belongs the assumption that electron orbits exist in the sense of ordinary mechanics—but we must, on the contrary, adapt our concepts to experience.
Letter to Niels Bohr (12 Dec 1924), in K. von Meyenn (ed.), Wolfgang Pauli - Wissenschaftliche Korrespondenz (1979), Vol. 1, 188. Quoted and cited in Daniel Greenberger, Klaus Hentschel and Friedel Weinert, Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy (2009), 615.
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The laws of thermodynamics, as empirically determined, express the approximate and probable behavior of systems of a great number of particles, or, more precisely, they express the laws of mechanics for such systems as they appear to beings who have not the fineness of perception to enable them to appreciate quantities of the order of magnitude of those which relate to single particles, and who cannot repeat their experiments often enough to obtain any but the most probable results.
Elementary Principles in Statististical Mechanics (1902), Preface, viii.
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The man who proportions the several parts of a mill, uses the same scientific principles [mechanics], as if he had the power of constructing an universe; but as he cannot give to matter that invisible agency, by which all the component parts of the immense machine of the universe have influence upon each other, and set in motional unison together without any apparent contact, and to which man has given the name of attraction, gravitation, and repulsion, he supplies the place of that agency by the humble imitation of teeth and cogs. All the parts of man’s microcosm must visibly touch.
In The Age of Reason: Being an Investigation of True and Fabulous Theology (27 Jan O.S. 1794), 42-43.
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The mathematician of to-day admits that he can neither square the circle, duplicate the cube or trisect the angle. May not our mechanicians, in like manner, be ultimately forced to admit that aerial flight is one of that great class of problems with which men can never cope… I do not claim that this is a necessary conclusion from any past experience. But I do think that success must await progress of a different kind from that of invention.
[Written following Samuel Pierpoint Langley's failed attempt to launch his flying machine from a catapult device mounted on a barge in Oct 1903. The Wright Brother's success came on 17 Dec 1903.]
'The Outlook for the Flying Machine'. The Independent: A Weekly Magazine (22 Oct 1903), 2509.
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The mechanical speculations of the ancients, particularly of the Greeks, related wholly to statics. Dynamics was founded by Galileo.
In The Science of Mechanics (1893), 128.
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The mechanization of the world picture.
The Mechanization of the World Picture, trans. C. Dikshoorn (1961), 39.
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The person who did most to give to analysis the generality and symmetry which are now its pride, was also the person who made mechanics analytical; I mean Euler.
From History of the Inductive Sciences from the Earliest to the Present (1837), Vol. 2, 93.
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The quantum entered physics with a jolt. It didn’t fit anywhere; it made no sense; it contradicted everything we thought we knew about nature. Yet the data seemed to demand it. ... The story of Werner Heisenberg and his science is the story of the desperate failures and ultimate triumphs of the small band of brilliant physicists who—during an incredibly intense period of struggle with the data, the theories, and each other during the 1920s—brought about a revolutionary new understanding of the atomic world known as quantum mechanics.
Beyond Uncertainty: Heisenberg, Quantum Physics, and the Bomb (2009), 90. Selected and contributed to this website by the author.
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The relationships of free and latent heat set forth in the language of the materialistic theory remain the same if in place of the quantity of matter we put the constant quantity of motion in accordance with the laws of mechanics. The only difference enters where it concerns the generations of heat through other motive forces and where it concerns the equivalent of heat that can be produced by a particular quantity of a mechanical or electrical force.
'Wärme, physiologisch', Handwörterbuch der medicinischen Wissenschaften (1845). In Timothy Lenoir, The Strategy of Life (1982), 203.
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The subsequent course of nature, teaches, that God, indeed, gave motion to matter; but that, in the beginning, he so guided the various motion of the parts of it, as to contrive them into the world he design'd they should compose; and establish'd those rules of motion, and that order amongst things corporeal, which we call the laws of nature. Thus, the universe being once fram'd by God, and the laws of motion settled, and all upheld by his perpetual concourse, and general providence; the same philosophy teaches, that the phenomena of the world, are physically produced by the mechanical properties of the parts of matter; and, that they operate upon one another according to mechanical laws. 'Tis of this kind of corpuscular philosophy, that I speak.
'The Excellence and Grounds of the Mechanical Philosophy', In P. Shaw (ed.), The Philosophical Works of Robert Boyle (1725), Vol. 1, 187.
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The theory of quantum mechanics also explained all kinds of details, such as why an oxygen atom combines with two hydrogen atoms to make water, and so on. Quantum mechanics thus supplied the theory behind chemistry. So, fundamental theoretical chemistry is really physics.
In 'Introduction', QED: The Strange Theory of Light and Matter (1985), 5.
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The thermal agency by which mechanical effect may be obtained is the transference of heat from one body to another at a lower temperature.
'Réflexions sur la puissance motrice du feu' (1824) translated by R.H. Thurston in Reflections on the Motive Power of Fire, and on Machines Fitted to Develop that Power (1890), 139.
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The thing about electronic games is that they are basically repetitive. After a while, the children get bored. They need something different. [Meccano construction toy kits] offer creativity, a notion of mechanics, discovery of the world around you.
As quoted in by Hugh Schofield in web article 'Meccano Revives French Production' (23 Dec 2010).
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The valuable properties of this cement depend in a great measure on the mode of preparing it for use. The mixing should therefore be conducted with care in order to form a perfect union of the powdered cement, sand and water. This can be best accomplished by the use of the New England corn hoe on a board floor or by beating with a hand stamper; not much labour is required if properly applied. Mechanics can judge when the mixture is perfect by the appearance of the mortar, which, when properly prepared, very much resembles putty.
Directions for Using White's Patent Hydraulic Cement.
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The vital act is the act of participation. “Participator” is the incontrovertible new concept given by quantum mechanics. It strikes down the term “observer” of classical theory, the man who stands safely behind the thick glass wall and watches what goes on without taking part. It can’t be done, quantum mechanics says.
In Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, 'Beyond the Edge of Time', Gravitation (1973), Part 3, 1217.
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The worst primary school scolding I ever received was for ridiculing a classmate who asked, ‘What’s an atom?’ To my third grader’s mind, the question betrayed a level of ignorance more befitting a preschooler, but the teacher disagreed and banned me from recess for a week. I had forgotten the incident until a few years ago, while sitting in on a quantum mechanics class taught by a Nobel Prizewinning physicist. Midway through a brutally abstract lecture on the hydrogen atom, a plucky sophomore raised his hand and asked the very same question. To the astonishment of all, our speaker fell silent. He stared out the window for what seemed like an eternity before answering, ‘I don’t know.’
'The Secret Life of Atoms'. Discover (Jun 2007), 28:6, 52.
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There is a strange disparity between the sciences of inert matter and those of life. Astronomy, mechanics, and physics are based on concepts which can be expressed, tersely and elegantly, in mathematical language. They have built up a universe as harmonious as the monuments of ancient Greece. They weave about it a magnificent texture of calculations and hypotheses. They search for reality beyond the realm of common thought up to unutterable abstractions consisting only of equations of symbols. Such is not the position of biological sciences. Those who investigate the phenomena of life are as if lost in an inextricable jungle, in the midst of a magic forest, whose countless trees unceasingly change their place and their shape. They are crushed under a mass of facts, which they can describe but are incapable of defining in algebraic equations.
Man the Unknown (1935), 1.
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These machines [used in the defense of the Syracusans against the Romans under Marcellus] he [Archimedes] had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with king Hiero’s desire and request, some time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry,—which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art.
Plutarch
In John Dryden (trans.), Life of Marcellus.
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This irrelevance of molecular arrangements for macroscopic results has given rise to the tendency to confine physics and chemistry to the study of homogeneous systems as well as homogeneous classes. In statistical mechanics a great deal of labor is in fact spent on showing that homogeneous systems and homogeneous classes are closely related and to a considerable extent interchangeable concepts of theoretical analysis (Gibbs theory). Naturally, this is not an accident. The methods of physics and chemistry are ideally suited for dealing with homogeneous classes with their interchangeable components. But experience shows that the objects of biology are radically inhomogeneous both as systems (structurally) and as classes (generically). Therefore, the method of biology and, consequently, its results will differ widely from the method and results of physical science.
Atom and Organism: A New Approach to Theoretical Biology (1966), 34.
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This whole theory of electrostatics constitutes a group of abstract ideas and general propositions, formulated in the clear and precise language of geometry and algebra, and connected with one another by the rules of strict logic. This whole fully satisfies the reason of a French physicist and his taste for clarity, simplicity and order. The same does not hold for the Englishman. These abstract notions of material points, force, line of force, and equipotential surface do not satisfy his need to imagine concrete, material, visible, and tangible things. 'So long as we cling to this mode of representation,' says an English physicist, 'we cannot form a mental representation of the phenomena which are really happening.' It is to satisfy the need that he goes and creates a model.
The French or German physicist conceives, in the space separating two conductors, abstract lines of force having no thickness or real existence; the English physicist materializes these lines and thickens them to the dimensions of a tube which he will fill with vulcanised rubber. In place of a family of lines of ideal forces, conceivable only by reason, he will have a bundle of elastic strings, visible and tangible, firmly glued at both ends to the surfaces of the two conductors, and, when stretched, trying both to contact and to expand. When the two conductors approach each other, he sees the elastic strings drawing closer together; then he sees each of them bunch up and grow large. Such is the famous model of electrostatic action imagined by Faraday and admired as a work of genius by Maxwell and the whole English school.
The employment of similar mechanical models, recalling by certain more or less rough analogies the particular features of the theory being expounded, is a regular feature of the English treatises on physics. Here is a book* [by Oliver Lodge] intended to expound the modern theories of electricity and to expound a new theory. In it are nothing but strings which move around pulleys, which roll around drums, which go through pearl beads, which carry weights; and tubes which pump water while others swell and contract; toothed wheels which are geared to one another and engage hooks. We thought we were entering the tranquil and neatly ordered abode of reason, but we find ourselves in a factory.
*Footnote: O. Lodge, Les Théories Modernes (Modern Views on Electricity) (1889), 16.
The Aim and Structure of Physical Theory (1906), 2nd edition (1914), trans. Philip P. Wiener (1954), 70-1.
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This [cyanide] poison is for professors of chemistry only. You, as a professor of mechanics, will have to use the rope.
Said during the Nazi occupation of Norway.
Quoted in Kaufman, Industrial Chemist and Chemical Manufacturer, Jan 1988.
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Those who are not shocked when they first come across quantum mechanics cannot possibly have understood it.
…...
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Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not yet assigned a cause to gravity. Indeed, this force arises from some cause that penetrates as far as the centers of the sun and planets without any diminution of its power to act, and that acts not in proportion to the quantity of the surfaces of the particles on which it acts (as mechanical causes are wont to do) but in proportion to the quantity of solid matter, and whose action is extended everywhere to immense distances, always decreasing as the squares of the distances.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), General Scholium, 943.
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Today scientists describe the universe in terms of two basic partial theories—the general theory of relativity and quantum mechanics. They are the great intellectual achievements of the first half of this century. The general theory of relativity describes the force of gravity and the large-scale structure of the universe, that is, the structure on scales from only a few miles to as large as a million million million million (1 with twenty-four zeros after it) miles, the size of the observable universe. Quantum mechanics, on the other hand, deals with phenomena on extremely small scales, such as a millionth of a millionth of an inch. Unfortunately, however, these two theories are known to be inconsistent with each other—they cannot both be correct.
A Brief History of Time: From the Big Bang to Black Holes (1988), 11-2.
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Turbulence is the most important unsolved problem of classical physics.
In The Feynman Lectures on Physics (1964).
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Two extreme views have always been held as to the use of mathematics. To some, mathematics is only measuring and calculating instruments, and their interest ceases as soon as discussions arise which cannot benefit those who use the instruments for the purposes of application in mechanics, astronomy, physics, statistics, and other sciences. At the other extreme we have those who are animated exclusively by the love of pure science. To them pure mathematics, with the theory of numbers at the head, is the only real and genuine science, and the applications have only an interest in so far as they contain or suggest problems in pure mathematics.
Of the two greatest mathematicians of modern tunes, Newton and Gauss, the former can be considered as a representative of the first, the latter of the second class; neither of them was exclusively so, and Newton’s inventions in the science of pure mathematics were probably equal to Gauss’s work in applied mathematics. Newton’s reluctance to publish the method of fluxions invented and used by him may perhaps be attributed to the fact that he was not satisfied with the logical foundations of the Calculus; and Gauss is known to have abandoned his electro-dynamic speculations, as he could not find a satisfying physical basis. …
Newton’s greatest work, the Principia, laid the foundation of mathematical physics; Gauss’s greatest work, the Disquisitiones Arithmeticae, that of higher arithmetic as distinguished from algebra. Both works, written in the synthetic style of the ancients, are difficult, if not deterrent, in their form, neither of them leading the reader by easy steps to the results. It took twenty or more years before either of these works received due recognition; neither found favour at once before that great tribunal of mathematical thought, the Paris Academy of Sciences. …
The country of Newton is still pre-eminent for its culture of mathematical physics, that of Gauss for the most abstract work in mathematics.
In History of European Thought in the Nineteenth Century (1903), 630.
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We are as remote from adequate explanation of the nature and causes of mechanical evolution of the hard parts of animals as we were when Aristotle first speculated on this subject … I think it is possible that we may never fathom all the causes of mechanical evolution or of the origin of new mechanical characters, but shall have to remain content with observing the modes of mechanical evolution, just as embryologists and geneticists are observing the modes of development, from the fertilized ovum to the mature individual, without in the least understanding either the cause or the nature of the process of development which goes on under their eyes every day
From 'Orthogenesis as observed from paleontological evidence beginning in the year 1889', American Naturalist (1922) 56, 141-142. As quoted and cited in 'G.G. Simpson, Paleontology, and the Modern Synthesis', collected in Ernst Mayr, William B. Provine (eds.), The Evolutionary Synthesis: Perspectives on the Unification of Biology (1998), 171.
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We avoid the gravest difficulties when, giving up the attempt to frame hypotheses concerning the constitution of matter, we pursue statistical inquiries as a branch of rational mechanics.
Elementary Principles in Statistical Mechanics (1902), ix.
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We have now got what seems to be definite proof that an X ray which spreads out in a spherical form from a source as a wave through the aether can when it meets an atom collect up all its energy from all round and concentrate it on the atom. It is as if when a circular wave on water met an obstacle, the wave were all suddenly to travel round the circle and disappear all round and concentrate its energy on attacking the obstacle. Mechanically of course this is absurd, but mechanics have in this direction been for some time a broken reed.
Letter to Margery Moseley (2 Feb 1913). In J. L. Heilbron (ed.), H. G. J. Moseley: The Life and Letters of an English Physicist 1887-1915 (1974), 201.
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We know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?
From Nobel Prize Lecture (Dec 1974), 'The Coming Age of the Cell'. Collected in Jan Lindsten (ed.) Nobel Lectures, Physiology or Medicine 1971-1980 (1992).
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We pass with admiration along the great series of mathematicians, by whom the science of theoretical mechanics has been cultivated, from the time of Newton to our own. There is no group of men of science whose fame is higher or brighter. The great discoveries of Copernicus, Galileo, Newton, had fixed all eyes on those portions of human knowledge on which their successors employed their labors. The certainty belonging to this line of speculation seemed to elevate mathematicians above the students of other subjects; and the beauty of mathematical relations and the subtlety of intellect which may be shown in dealing with them, were fitted to win unbounded applause. The successors of Newton and the Bernoullis, as Euler, Clairaut, D’Alembert, Lagrange, Laplace, not to introduce living names, have been some of the most remarkable men of talent which the world has seen.
In History of the Inductive Sciences, Vol. 1, Bk. 4, chap. 6, sect. 6.
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What has been learned in physics stays learned. People talk about scientific revolutions. The social and political connotations of revolution evoke a picture of a body of doctrine being rejected, to be replaced by another equally vulnerable to refutation. It is not like that at all. The history of physics has seen profound changes indeed in the way that physicists have thought about fundamental questions. But each change was a widening of vision, an accession of insight and understanding. The introduction, one might say the recognition, by man (led by Einstein) of relativity in the first decade of this century and the formulation of quantum mechanics in the third decade are such landmarks. The only intellectual casualty attending the discovery of quantum mechanics was the unmourned demise of the patchwork quantum theory with which certain experimental facts had been stubbornly refusing to agree. As a scientist, or as any thinking person with curiosity about the basic workings of nature, the reaction to quantum mechanics would have to be: “Ah! So that’s the way it really is!” There is no good analogy to the advent of quantum mechanics, but if a political-social analogy is to be made, it is not a revolution but the discovery of the New World.
From Physics Survey Committee, U.S. National Academy of Sciences, National Research Council, 'The Nature of Physics', in report Physics in Perspective (1973), 61-62. As cited in I. Bernard Cohen, Revolution in Science (1985), 554-555.
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When Faraday filled space with quivering lines of force, he was bringing mathematics into electricity. When Maxwell stated his famous laws about the electromagnetic field it was mathematics. The relativity theory of Einstein which makes gravity a fiction, and reduces the mechanics of the universe to geometry, is mathematical research.
In 'The Spirit of Research', III, 'Mathematical Research', in The Monist (Oct 1922), 32, No. 4, 542-543.
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With thermodynamics, one can calculate almost everything crudely; with kinetic theory, one can calculate fewer things, but more accurately; and with statistical mechanics, one can calculate almost nothing exactly.
Edward B. Stuart, Alan J. Brainard and Benjamin Gal-Or (eds.), A Critical Review of Thermodynamics (1970), 205.
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You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.
From the recollection of Claude Shannon given in discussion with Myron Tribus (Apr 1961) about the reason Shannon chose the word “entropy” for his information function (first used by Shannon in a 1945 memorandum at Bell Labs). The suggestion from Neumann to use “entropy” dates back to a Neumann-Shannon conversation c.1940. Shannon’s recollection of the Neumann’s recommendation was quoted as recollected by Tribus in Myron Tribus and Edward C. McIrving, 'Energy and Information', Scientific American (1971), 225, 179-88.
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[1155] Mechanics are the Paradise of mathematical science, because here we come to the fruits of mathematics.
Notebook E (1513), folio 8 back. In the original Italian: “La meccanica è il paradiso delle sciētie matematiche, perchè cō quella si viene al frutto matematico.” English and Italian in Jean Paul Richter (trans.), 'Philosophical Maxims: Of Mechanics', The Literary Works of Leonardo da Vinci (1883), Vol. 1, Part 2, 289, Aphorism 1155. [Note: da Vinci wrote ē=en, ō=on] Also translated as “Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics,” in Edward McCurdy, The Notebooks of Leonardo Da Vinci (1939, 1958), Vol. 1, 613.
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[Heisenberg's seminal 1925 paper initiating quantum mechanics marked] one of the great jumps—perhaps the greatest—in the development of twentieth century physics.
In Abraham Pais, Niels Bohr's Times: in Physics, Philosophy, and Polity (1991), 276. Cited in Mauro Dardo, Nobel Laureates and Twentieth-Century Physics (2004), 179.
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[In 18th-century Britain] engineers for the most began as simple workmen, skilful and ambitious but usually illiterate and self-taught. They were either millwrights like Bramah, mechanics like Murdoch and George Stephenson, or smiths like Newcomen and Maudslay.
In Science in History (1969), Vol. 2, 591.
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[Quantum mechanics is] a phenomenon which is impossible, absolutely impossible, to explain in any classical way.
…...
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[T]he laws of quantum mechanics itself cannot be formulated … without recourse to the concept of consciousness.
From essay by Eugene Wigner, 'The Probability of the Existence of a Self-Reproducing Unit', contributed in M. Polanyi, The Logic of Personal Knowledge: Essays Presented to Michael Polanyi on his Seventieth Birthday, 11th March 1961 (1961), 232.
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[W]hen Galileo discovered he could use the tools of mathematics and mechanics to understand the motion of celestial bodies, he felt, in the words of one imminent researcher, that he had learned the language in which God recreated the universe. Today we are learning the language in which God created life. We are gaining ever more awe for the complexity, the beauty, the wonder of God's most devine and sacred gift.
From White House Announcement of the Completion of the First Survey of the Entire Human Genome Project, broadcast on the day of the publication of the first draft of the human genome. Quoted in transcript on the National Archives, Clinton White House web site, 'Text of Remarks on the Completion of the First Survey of the Entire Human Genome Project' (26 Jun 2000).
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“But in the binary system,” Dale points out, handing back the squeezable glass, “the alternative to one isn’t minus one, it’s zero. That’s the beauty of it, mechanically.” “O.K. Gotcha. You’re asking me, What’s this minus one? I’ll tell you. It’s a plus one moving backward in time. This is all in the space-time foam, inside the Planck duration, don’t forget. The dust of points gives birth to time, and time gives birth to the dust of points. Elegant, huh? It has to be. It’s blind chance, plus pure math. They’re proving it, every day. Astronomy, particle physics, it’s all coming together. Relax into it, young fella. It feels great. Space-time foam.”
In Roger's Version: A Novel (1986), 304.
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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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