"Newton’s glory was to fulfil, in his Principia of 1687, Galileo's hope of geometrizing gravitation. The ingredients of his solution were Descartes' first law of motion (the principle of inertia), Galileo's rules of and composition of velocities, and Kepler's rules of planetary orbiting. Newton showed that Kepler's rules following form Galileo's, the principle of inertia, and the assumption that a planet falls towards the Sun along the line joining their centres. Since Kepler's rules allowed the substitution of an area for a time, Newton could reduce the problem of the magnitude of gravitational acceleration to a problem in geometry."

"Lex I. Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressi cogitur statum illum mutare. Lex II. Mutationem motus proportionalem esse vi motrici impressa; & fieri secundum lineam rectam qua vis illa imprimatur. Lex III. Actioni contrariam semper & aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales & in partes contrarias dirigi. (English translation: Law I. Every body perseveres in its state of rest or of uniform motion in a straight line, except in so far as it is compelled to change that state by the forces impressed upon it. Law II. The change of motion is proportional to the motive force impressed upon it; and takes place along the straight line on which that force is impressed. Law III. To an action there is always an opposite and equal reaction: or the actions of two bodies on each other are always equal and directed in opposite directions.)"

"Only around the end of the nineteenth century did scientists come across a few observations that did not fit well with Newton's laws, and these led to the net revolution in physics - the theory of relativity and quantum mechanics."

"If 99.99% of the universe is in the plasma state then for the remaining 0.01% must we learn a whole discipline of Fluid Mechanics or Hydrodynamics? The answer is No! More often than not, hydrodynamics provides a first level description of an astrophysical fluid."

"One wonders if the foundations of fluid mechanics or gas dynamics would ever have been secured if Euler or Boltzmann had justified their work to themselves in terms of its contribution to the design of jet aircraft."

"Curiosity about at least two of the branches of fluid mechanics and their applications has a long and distinguished history, for in the Proverbs of Solomon the son of David, king of Israel, it was stated in the words of Agur the son of Jakeh that "There be three things which are too wonderful for me, yea four which I know not," of which two were "The way of an eagle in the air" and "The way of a ship in the midst of the sea," which I take to be questions of aerodynamics and naval architecture, questions that concern us still."

"Fluid mechanics is a part of applied mathematics, of physics, of many branches of engineering, certainly civil, mechanical, chemical, and aeronautical engineering, and of naval architecture and geophysics, with astrophysics and biological and physiological fluid dynamics to be added."

"Although many historians of the new millennium now take issue with the notion of a Scientific Revolution, it is generally agreed that Newton's work culminated the long development of European science, creating a synthesis that opened the way for the scientific culture of the modern age."

"In Newton's time only two kinds of force were available for quantitative investigation. One was the force of gravity; the other the forces of push and pull encountered in everyday life... Newton endeavored to construct a general theory of all forces, both those known in his time and those that might be discovered and investigated later. He intended his theory of gravitation to be one example that he himself could work out fully... Newton formulated his celebrated three laws: (1) In the absence of force, a body will continue at rest or in its present state of uniform rectilinear motion. (2) In the presence of force, a body will be accelerated in the direction of that force, the product of its mass by its acceleration being equal to the force (f = ma). (3) To every force there corresponds an equal counterforce, acting in a direction opposite to that of the force... According to the third law, then, each planet exerts an attractive counterforce to the sun, accelerating it toward the planet... a relatively small acceleration, because the mass of the sun so vastly exceeds... every planet..."

"However far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is that simply by the word "experiment" we refer to a situation where we can tell others what we have done and what we have learned and that, therefore, the account of the experimental arrangement and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics."

"A law explains a set of observations; a theory explains a set of laws. The quintessential illustration of this jump in level is the way in which Newton’s theory of mechanics explained Kepler’s law of planetary motion. Basically, a law applies to observed phenomena in one domain (e.g., planetary bodies and their movements), while a theory is intended to unify phenomena in many domains. Thus, Newton’s theory of mechanics explained not only Kepler’s laws, but also Galileo’s findings about the motion of balls rolling down an inclined plane, as well as the pattern of oceanic tides. Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism. So, for instance, Freud’s theory of mind relies upon the unobservable ego, superego, and id, and in modern physics we have theories of elementary particles that postulate various types of quarks, all of which have yet to be observed."

"From the thick darkness of the middle ages man's struggling spirit emerged as in new birth; breaking out of the iron control of that period; growing strong and confident in the tug and din of succeeding conflict and revolution, it bounded forwards and upwards with restless vigour to the investigation of physical and moral truth; ascending height after height; sweeping afar over the earth, penetrating afar up into the heavens; increasing in endeavour, enlarging in endowment; every where boldly, earnestly out-stretching, til, in the AUTHOR of the PRINCIPIA, one arose, who, grasping the master-key of the universe and treading its celestial paths, opened up to the human intellect the stupendous realities of the material world, and, in the unrolling of its harmonies, gave to the human heart a new song to the goodness, wisdom, and majesty of the all-creating, all-sustaining, all-perfect God."

"Newton then elevates this approximate empirical discovery to the position of a rigorous principle, the principle of inertia, and states that absolutely free bodies hence will cover equal distances in equal times. ...It is the principle of inertia coupled with an understanding of spatial congruence that yields us a definition of congruent stretches of absolute time. ...The principle of inertia, together with the other fundamental principles of mechanics, enables us... to place mechanics on a rigorous mathematical basis, and rational mechanics is the result. ...science, in the case of mechanics, has followed the same course as in geometry. Initially our information is empirical and suffers from all the inaccuracies ...But this empirical information is idealised, then crystallised into axioms, postulates or principles susceptible of direct mathematical treatment. ...If peradventure further experiment were to prove that our mathematical deductions ...were not born out in the world of reality, we should have to modify our initial principles and postulates or else agree that nature is irrational. With mechanics, the necessity of modifying the fundamental principles became imperative when it was recognized that the mass of a body was not the constant magnitude we thought it to be; hence it was experiment that brought about the revolution. On the other hand, in the case of geometry, it was the mathematicians themselves who forsaw the possibility of various non-Euclidean doctrines, prior to any suggestion of this sort being demanded by experiment."

"... Inertia resists acceleration, but acceleration relative to what? Within the frame of classical mechanics the only answer is: Inertia resists acceleration relative to space. This is a physical property of space—space acts on objects, but objects do not act on space. Such is probably the deeper meaning of Newton's assertion spatium est absolutum (space is absolute). But the idea disturbed some, in particular Leibnitz, who did not ascribe an independent existence to space but considered it merely a property of "things" (contiguity of physical objects)."

"I mentally conceive of some moveable [sphere] projected on a horizontal plane, all impediments being put aside. Now it is evident... that equable motion on this plane would be perpetual if the plane were of infinite extent, but if we assume it to be ended, and [situated] on high, the movable, driven to the end of this plane and going on further, adds on to its previous equable and indelible motion, that downward tendency which it has from its heaviness. Thus, there emerges a certain motion, compounded..."

"On the authority of Aristotle... motion in the planetary world was somehow directed by the more perfect motion in higher spheres, and so on, up to the outermost sphere of fixed stars, indistinguishable from the prime mover. This implied a refined animistic and pantheistic world view, incomparably more rational than the ancient world views of Babylonians and Egyptians, among others, but a world view, nonetheless, hardly compatible with the idea of "inertial motion" which is implied in Buridan's concept of "impetus"… a momentous breaking point... which was to bear fruit... in the hands, first of Copernicus and then of Newton."

"Wave functions, probabilities, quantum tunneling, the ceaseless roiling energy fluctuations of the vacuum, the smearing together of space and time, the relative nature of simultaneity, the warping of the spacetime fabric, black holes, the big bang. Who could have guessed that the intuitive, mechanical, clockwork Newtonian perspective would turn out to be so thoroughly parachial—that there would be a whole new mind-boggling world lying just beneath the surface of things as they are ordinarily experienced?"

"Newton's system was for a long time considered as final and the task... seemed simply to be an expansion.... From the theory of the motion of mass points one could go over to the mechanics of solid bodies, to rotatory motions, and one could treat the continuous motion of fluid or the vibrating motion of an elastic body. All these... were gradually developed... with the evolution of mathematics, especially of the differential calculus... checked by experiments. and hydrodynamics became a part of mechanics. Another science... was astronomy. Improvements... led to... more accurate determinations of the motions of the planets... When the phenomena of electricity and magnetism were discovered, the... forces were compared to the gravitational forces... Finally, in the nineteenth century, even the theory of heat could be reduced..."

"The first difficulty arose in the discussion of the electromagnetic field in... Faraday and Maxwell. In Newtonian mechanics the gravitational force had been considered as given... In the work of Faraday and Maxwell... the field of force... became the object of the investigation... they tried to set up equations of motion for the fields, not primarily for the bodies... This change led back to a point of view...held... before Newton. An action could... be transferred... only when the two bodies touched... Newton had introduce a very new and strange hypothesis by assuming a force that acted over a long distance. Now in the theory of fields... action is transferred from one point to a neighboring point... in terms of differential equations. ...the description of the electromagnetic fields... by Maxwell's equations seemed a satisfactory solution of the problem of force. ...The axioms and definitions of Newton had referred to bodies and their motion; but with Maxwell the fields... seemed to have acquired the same degree of reality as the bodies in Newton's theory. This view... was not easily accepted; and to avoid such a change in the concept of reality... many physicists believed that Maxwell's equations actually referred to the deformations of an elastic medium... the ether... the medium was so light and thin that it could penetrate into other matter and could not be seen or felt. ...[H]owever ...it could not explain the complete absence of any longitudinal light waves."

"I shall try to sum up the main obstacles which arrested the progress of science for such an immeasurable time. The first was the splitting of the world into two spheres, and the mental split which resulted from it. The second was the geocentric dogma, the blind eye turned on the promising line of thought which had started with the Pythagoreans and stopped abruptly with Aristarchus of Samos. The third was the dogma of uniform motion in perfect circles. The fourth was the divorcement of science from mathematics. The fifth was the inability to realize that a body at rest tended to stay at rest, a body in motion tended to stay in motion. The main achievement of the first part of the scientific revolution was the removal of these five cardinal obstacles. This was done chiefly by three men: Copernicus, Kepler and Galileo. After that, the road was open to the Newtonian synthesis; from there on the journey led with rapidly gaining speed to the atomic age."

"The history of the development of mechanics is quite indispensable to a full comprehension of the science in its present condition. It also affords a simple and instructive example of the processes by which natural science generally is developed."

"These independent objects of Newtonian physics might move, touch each other, collide, or even, by a certain stretch of the imagination, act at a distance: but nothing could penetrate them except in the limited way that light penetrated translucent substances. This world of separate bodies, unaffected by the accidents of history or geographic location, underwent a profound change with the elaboration of the new concepts of matter and energy that went forward from Faraday and von Mayer through Clerk-Maxwell and Willard Gibbs and Ernest Mach to Planck and Einstein. The discovery that solids, liquids, and gases were phases of all forms of matter modified the very conceptions of substance, while the identification of electricity, light, and heat as aspects of a protean energy, and the final break-up of "solid" matter into particles of this same ultimate energy lessened the gap, not merely between various aspects of the physical world, but between the mechanical and the organic. Both matter in the raw and the more organized and internally self-sustaining organisms could be described as systems of energy in more or less stable, more or less complex, states of equilibrium."

"Galileo's comprehension of the concept of acceleration, which he defined as a change of velocity either in magnitude or direction... was an abstract idea that no one seems to have thought much about before. And in using it to test the still accepted Aristotelian precept that a moving object requires a force to maintain it, Galileo easily demonstrated that it is not motion but rather acceleration which cannot occur without an external force. Deliberately rejecting common sense as a prejudiced witness, he let nature herself speak in the form of a "hard, smooth and very round ball" rolling down a "very straight" ideal groove lined with polished parchment, and then rolling up another groove, clocking each roll "hundreds or times"... he showed that, while downward motion (helped by gravity force) makes speed increase and upward motion (hindered by gravity force) makes speed decrease, there is always a "boundary case" in between... where speed remains constant (without any appreciable force)—and that, by reducing friction, this boundary case can be made to approach a horizontal level where gravity has no effect. Similarly testing... he also drafted a law of falling bodies: "that the distances traversed, during equal intervals of time... stand to one another in the same ratio as the odd numbers beginning with unity." And his beautiful analysis of a cannonball's trajectory into horizontal and vertical components... was one day to be of enormous help to Isaac Newton in solving the riddle of gravity."

"Newton proposed that the particles of the air (we would call them molecules), were motionless in space and were held apart by repulsive forces between them... He assumed that the repulsive force was inversely proportional to the distance between the particles...He showed that, on the basis of this assumption, a collection of static particles in a box would behave exactly as Boyle had found. His model led directly to Boyle's law. Probably the greatest scientist ever, Newton managed to get the right answer from a model that was wrong in every possible way."

"The founders of modern science - for instance, Galileo, Kepler, and Newton - were mostly pious men who did not doubt God’s purposes. Nevertheless they took the revolutionary step of consciously and deliberately expelling the idea of purpose as controlling nature from their new science of nature. They did this on the ground that inquiry into purposes is useless for what science aims at: namely, the prediction and control of events. To predict an eclipse, what you have to know is not its purpose but its causes. Hence science from the seventeenth century onwards became exclusively an inquiry into causes. The conception of purpose in the world was ignored and frowned on. This, though silent and almost unnoticed, was the greatest revolution in human history, far outweighing in importance any of the political revolutions whose thunder has reverberated through the world."

"Newton did not show the cause of the apple falling, but he shewed a similitude between the apple and the stars. By doing so he turned old facts into new knowledge; and was well content if he could bring diverse phenomenon under "two or three Principles of Motion" even "though the Causes of these Principles were not yet discovered.""

"Newtonian mechanics does not apply to all situations. If the speeds of the interacting bodies are very large —an appreciable fraction of the speed of light —we must replace Newtonian mechanics with Einstein’s special theory of relativity, which holds at any speed, including those near the speed of light. If the interacting bodies are on the scale of atomic structure (for example, they might be electrons in an atom), we must replace Newtonian mechanics with quantum mechanics. Physicists now view Newtonian mechanics as a special case of these two more comprehensive theories. Still, it is a very important special case because it applies to the motion of objects ranging in size from the very small (almost on the scale of atomic structure) to astronomical (galaxies and clusters of galaxies)."

"The foundational achievement of classical mechanics is to establish that the first point is faulty. It is fruitful, in that framework, to allow a broader concept of the character of physical reality. To know the state of a system of particles, one must know not only their positions, but also their velocities and their masses. Armed with that information, classical mechanics predicts the system’s future evolution completely. Classical mechanics, given its broader concept of physical reality, is the very model of Einstein Sanity."

"The laws of motion of visible and tangible, or molar, matter had been worked out to a great degree of refinement and embodied in the branches of science known as Mechanics, Hydrostatics, and Pneumatics. These laws had been shown to hold good... throughout the universe on the assumption that all such masses of matter possessed inertia and were susceptible of acquiring motion, in two ways, firstly by impact, or impulse from without; and, secondly, by the operation of certain hypothetical causes of motion termed 'forces,' which were usually supposed to be resident in the particles of the masses themselves, and to operate at a distance, in such a way as to tend to draw any two such masses together, or to separate them more widely."

"The work before us is a proof that the doctrine of mechanics is of the utmost importance to mankind in general, and to civil society in particular, which could hardly subsist without it. The author of this work is Mr. W. Emerson who is well known in the literary world, from several ingenious writings with which he has obliged the public; some of which have passed under our consideration since the commencement of the Review. In this treatise Mr. Emerson has laid down the fundamental principles both of theory and practice, and demonstrated most of them from the common elementary geometry, and the rest from the common rules of algebra; which is certainly the best method of rendering a treatise of this kind useful to the generality of readers, the fluxionary calculus being too difficult for them to understand. The work is divided into thirteen sections: the 1st. contains the general laws of motion. 2. The laws of gravity, the descent of heavy bodies, and the motion of projectiles. 3. The properties of the mechanical powers; the balance, the leaver, the wheel, the pulley, the screw, and the wedge. 4. The descent of bodies upon inclined planes, and in curve surfaces; and the motion of pendulums. 5. The center of gravity, and its properties. 6. The centers of percussion, oscillation, and gyration. 7. The quantity and direction of the pressure of beams of timber, by their weight; and the forces necessary to sustain them. 8. The strength of beams of timber in all positions; and their stress by any weight acting upon them, or by any forces applied to them. 9. The properties of fluids, the principles of hydrostatics, hydraulics, and pneumatics, 10. The resistance of fluids, their forces and actions upon bodies; the motions of ships, and the positions of their fails. 11. Methods of communicating, directing, and regulating any motion in the practice of mechanics. 12. The powers and properties of compound engines; of forces acting within the machines; and concerning friction. 13. The description of compound machines or engines, and the methods of computing their powers or forces; with some account as the advantages or disadvantages of their construction."

"I think I can safely say that nobody understands quantum mechanics."

"To the art of mechanics is owing all sorts of instruments to work with, all engines of war, ships, bridges, mills, curious roofs and arches, stately theatres, columns, pendent galleries, and all other grand works in building. Also clocks, watches, jacks, chariots, carts and carriages, and even the wheel-barrow. Architecture, navigation, husbandry, and military affairs, owe their invention and use to this art."

"Within a certain kind of environment, an activity may be checked so that the only meaning which accrues is of its direct and tangible isolated outcome. One may cook, or hammer, or walk, and the resulting consequences may not take the mind any farther than the consequences of cooking, hammering, and walking in the literal — or physical — sense. But nevertheless the consequences of the act remain far-reaching. To walk involves a displacement and reaction of the resisting earth, whose thrill is felt wherever there is matter. It involves the structure of the limbs and the nervous system; the principles of mechanics. To cook is to utilize heat and moisture to change the chemical relations of food materials; it has a bearing upon the assimilation of food and the growth of the body. The utmost that the most learned men of science know in physics, chemistry, physiology is not enough to make all these consequences and connections perceptible. The task of education, once more, is to see to it that such activities are performed in such ways and under such conditions as render these conditions as perceptible as possible."

"People get a lot of confusion, because they keep trying to think of quantum mechanics as classical mechanics."

"Experimental physics was particularly interested in the processes taking place inside the atom, and in this field the classical mechanics was failing conspicuously and completely. Perhaps its most spectacular failure was with the fundamental problem with the structure of the atom."

"Another conspicuous failure of classical mechanics was with one aspect of the problem of radiation. ...Imagine a crowd of steel balls rolling about on a steel floor. ...There must... be a steady leakage of energy from... causes, such as air resistance and the friction of the floor, so the balls will eventually lose energy, and, after no great length of time, will be found standing at rest on the floor. The energy of their motion seems to have been lost... most of it has been transformed into heat. The classical mechanics predicts that this must happen; it shows that all energy of motion, except possibly a minute fraction of the whole, must be transformed into heat whenever such a transformation is physically possible. It is because of this that perpetual-motion machines are a practical impossibility."

"The need for a fundamentally different approach to the study of physical processes at the molecular level motivated the development of relevant statistical methods, which turned out to be applicable not only to the study of molecular processes (statistical mechanics), but to a host of other areas such as the actuarial profession, design of large telephone exchanges, and the like. In statistical methods, specific manifestations of microscopic entities (molecules, individual telephone sites, etc.) are replaced with their statistical averages, which are connected with appropriate macroscopic variables. The role played in Newtonian mechanics by the calculus, which involves no uncertainty, is replaced in statistical mechanics by probability theory, a theory whose very purpose is to capture uncertainty of a certain type."

"Aristotle's failure in Biology is not less conspicuous than his failure in Mechanics; yet the ideas of Final Cause, Likeness, and Vitality, which are said to be the ideas appropriate to this science, were assuredly possessed by him with a distinctness unsurpassed in modern times."

"Herschel has noticed how the Stagirite obstructed the progress of astronomy by not identifying celestial with terrestrial mechanics, but laying down the principle that celestial motions were regulated by peculiar laws, thus placing them entirely without the pale of experimental research, while at the same time the progress of mechanics was impeded by the [his] assumption of natural and unnatural motions."

"In the beginning was mechanics."

"All this, the positive and physical essence of mechanics, which makes its chief and highest interest for a student of nature, is in existing treatises completely buried and concealed beneath a mass of technical considerations."

"The history of the development of mechanics is quite indispensable to a full comprehension of the science in its present condition. It also affords a simple and instructive example or the processes by which natural science generally is developed."

"Another evil, and one of the worst which arises from the separation of theoretical and practical knowledge, is the fact that a large number of persons, possessed of an inventive turn of mind and of considerable skill in the manual operations of practical mechanics, are destitute of that knowledge of scientific principles which is requisite to prevent their being misled by their own ingenuity. Such men too often spend their money, waste their lives, and it may be lose their reason in the vain pursuits of visionary inventions, of which a moderate amount of theoretical knowledge would be sufficient to demonstrate the fallacy ; and for want of such knowledge, many a man who might have been a useful and happy member of society, becomes a being than whom it would be hard to find anything more miserable. The number of those unhappy persons — to judge from the patent-lists, and from some of the mechanical journals — must be much greater than is generally believed."

"[T]he mere fact that a quantitative majority of causations are of vitalistic type, does not in the least mean that science can neglect the huge, co-existing volume of mechanistic-type causations. Both aspects of causal description are required in all sciences. In physics, for example, which seeks to describe the most ultimate, or elementary reaction tendencies of matter, the attempt is now being made to resolve all complex masses into ultra-simple proton and electron systems. The influence of each proton-electron microcosm, then must be traced in its most far-reaching effects upon the physical behavior of the macrocosmic mass of which it forms a single unit. The causal influences of the total mass, on the other hand, upon its constituent proton-electron systems, and upon other free-lance proton-electron systems, must be described."

"The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for 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; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved."

"Rational mechanics must be the science of the motions which result from any forces, and of the forces which are required for any motions, accurately propounded and demonstrated. For many things induce me to suspect, that all natural phenomena may depend upon some forces by which the particles of bodies are either drawn towards each other, and cohere, or repel and recede from each other: and these forces being hitherto unknown, philosophers have pursued their researches in vain. And I hope that the principles expounded in this work will afford some light, either to this mode of philosophizing, or to some mode which is more true."

"I'm proud to publish this book under my own name, though I don't fully understand the mechanics of its production or the nature of the personality I assume in delivering it. I had no conscious work to do on the book at all. I simply went into trance twice a week, spoke in a "mediumistic" capacity for Seth, or as Seth, and dictated the words to my husband, Robert Butts, who wrote them down."

"Not one word is said here of acausality, wave mechanics, indeterminacy relations, complementarity, … etc. Why doesn’t he talk about what he knows instead of trespassing on the professional philosopher’s preserves? Ne sutor supra crepidam. On this I can cheerfully justify myself: because I do not think that these things have as much connection as is currently supposed with a philosophical view of the world."

"My greatest concern was what to call it. I thought of calling it 'information,' but the word was overly used, so I decided to call it 'uncertainty.' When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, '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.'"

"When he meets a simple geometrical construction, for instance in the honeycomb, he would fain refer it to physical instinct, or to skill and ingenuity, rather than to the operation of physical forces or mathematical laws; when he sees in a snail, or nautilus, or tiny foraminiferal or radiolarian shell a close approach to sphere or spiral, he is prone of old habit to believe that after all it is something more than a spiral or a sphere, and that in this "something more" there lies what neither mathematics nor physics can explain. In short, he is deeply reluctant to compare the living with the dead, or to explain by geometry or by mechanics the things which have their part in the mystery of life."