Chapter 12 Chapter 10 The Newtonian Revolution

Unlike the scientific and mathematical revolutions we have already examined (which did or were said to have taken place), Newton was thought to have caused a revolution during his lifetime.In his Mathematical Principles of Natural Philosophy, Newton led to a revolution in calculus and the science of mechanics, and as such, he was admired by his contemporaries.Newton is unique in history, and he was a remarkable figure because he made so many very important contributions in so many different fields such as: pure and applied mathematics; optics, and the theory of light and color; The design of scientific instruments; the collation and compilation of mechanics theory and the systematic elaboration of the basic concepts of this subject; the invention of the main concept of physics (mass); the systematic exposition of new scientific methodology, etc.He also worked on heat, on the theory of chemistry and matter, on alchemy, chronology, and the interpretation of the Christian Bible, among other issues.

Newton's mathematical revolution was divided into two aspects: the invention of calculus (which he shared with Leibniz), and the application of mathematics to physics and astronomy.It was this latter aspect that led to the Newtonian revolution in science (as opposed to its mathematical revolution).Of course, among Newton’s predecessors, there were also some great figures who explored using mathematical principles to state natural philosophy, such as Simon Stevens, Galileo, Kepler, Wallis, Hooke, Huygens, etc. .In this sense, the Newtonian Revolution was the culmination of what (going back to the early days of the Scientific Revolution) had produced, rather than some entirely new creation of Newton's, combining Newton's Principia with Kepler's. New Astronomy, Galileo's Two New Sciences, Wallis' Mechanics, Hooke's treatises on the problem of motion, or Huygens (in his treatise on pendulum clocks) on uniformly accelerated motion, etc. The simplest comparison shows that there is a certain difference in depth, scope, and skill. It is because of the sudden increase in overall size that Newton's Principia has become the "new era" of the "physical revolution" "[As Crello (1714) puts it].

It is often asserted that Newton brought together and synthesized the disparate ideas or principles of scientists such as Kepler, Cecillius, or Minck.However, it is difficult to say that Newton's revolutionary science was a synthesis or combination of these ideas, because in fact Newton disclosed their absurdity in his Principia. "True" science cannot simply be the product of absurd ideas or principles.Such misconceptions that Newton displayed in Principia include: Kepler: The "true" description of planetary motion by the three planetary laws; the solar force acting on those bodies decreases with distance and only acts near the ecliptic plane.The sun is certainly a giant magnet; any object in motion, due to its "inherent inertia", will stop moving as soon as the power is no longer applied.

Descartes: The sea of ​​ether carries the planets here and there in great eddies; atoms do not (and cannot) exist, nor does vacuum or void. Galileo: The acceleration of an object falling towards the ground remains constant throughout, even for an object falling away from the Earth towards the Moon; the Moon cannot have any effect on (or be the cause of) the tidal motion of the ocean. Hooke: A concentric force acting on a body (with an inertial component of motion) obeying the inverse square law results in an orbital motion whose velocity is inversely proportional to its distance from the center of the force: this law of motion is the same as Kepler's area law is consistent.

We can further see that Newton denied the existence of "centrifugal" force, which is the basis for the development of Huygens' motion physics.Newton replaced them with the concept of "centripetal" forces, a name Newton chose because of its resemblance to Huygens' "viscentrifugs" (centrifugal forces), although in a different sense and pointing in the opposite direction. Comparing and contrasting Newton's Principia (a title he often used to refer to his writings) with Descartes' Principia reveals the nature of Newton's revolution.A critical reader will find an anomaly in Descartes' Principia that it eschews mathematics in favor of a study of philosophy, physics (or philosophy of nature).Of the four parts of the book, only two are devoted to the physics and development of the vortex system of the universe.Descartes did indeed come up with rules for the number of collisions here, but we already know that these rules are wrong in every instance.Descartes included these rules as a subset in his third law of nature.But when Wallis published the correct rules in the Philosophical Transactions of the Royal Society, they had a stricter and more accurate title: "laws of motion."Newton begins his Principia with a set of definitions, followed by a number of "Axioms or Laws of Motion", the first two of which are roughly equivalent to the first two of Descartes' laws of nature.Newton seems to have transformed Descartes' "regulae quaedam sive leges naturae" ("the rule of quantity or law of nature") into his "axiomata sive leges molus" ("the axiom of motion or the law of motion").Newton's three laws of motion and the axioms of theoretical mechanics he summarized are: (1) Principle of inertia: any object will continue to maintain its state of rest or uniform linear motion unless there is an external force acting on it; The relationship between dynamic effects, that is, a push (or successive) external force will cause the momentum of the object to change along the direction of the external force (for successive forces, it refers to the change in a certain unit of time); ( 3) The action and reaction forces are equal.

Newton also changed Descartes' title "Principia Philosophiae" to "PhilosoPhiae naturalis principia mathematica" (Mathematical Principles of Natural Philosophy), whereby he boasted that in mathematizing the principles he had created a It is a natural philosophy that is different from general philosophy.The mathematic character of Newton's Principia was manifested not only in the formulation of these principles but also in the demonstration and application of propositions; it also illuminated an important new fashion in the use of mathematics in natural philosophy.

Newton's Principia is in many ways a masterpiece.It contains some of the first results of pure mathematics (the theory of limits and the geometry of conic sections), it develops the main concepts of dynamics (mass, momentum, force), it organizes and codifies the principles of dynamics (the three laws of motion ), it also illustrates the dynamic significance of Kepler's three laws of planetary motion and the dynamic significance of Galileo's following experimental conclusion: objects with different weights (at the same position on the earth) have the same acceleration and the same speed.It expounds the laws of curved motion, the analysis of the motion of the pendulum, and the nature of surface-constrained motion. It also shows how to deal with the motion of particles in a continuously changing force field.Newton also pointed out ways to analyze the motion of waves and discussed the ways in which bodies move in various media with resistance.The last part of the book, the third book, is the culmination of the whole book. Here, he reveals Newton's universe subject to the action of gravitation and a generalized force (a special phenomenon is the well-known weight of the earth). system.In this part, Newton discussed the length of the orbits of planets and their satellites, the motion and orbit of comets, and the generation of tidal phenomena in the ocean, etc.

Consider the apparent irregularity of the moon's motion, the treatment of which is an example of the new level of thinking in the book.For the past 1,500 years, astronomers have dealt with the motion of the Moon by constructing geometrical schemes without regard to cause.Now, Newton pointed out that the perturbation phenomenon is the main source of "lunar aberration", and this perturbation is the main result of the sun's gravity and the earth's gravity on the moon.With the publication of the Principia in 1687 it became possible to deal with the problem by the study of effects, starting from first principles, or first causes.As the reviewers of the second edition of Principia have noted, this is an entirely new approach to this type of problem.

Perhaps the greatest of all these achievements was the explanation of the tides, which are caused by the gravitational pull of the sun and moon on the oceans. "The ebb and flow of the ocean tides," asserted Newton (bk. 3, prop. 24), "arises from the action of the sun and the moon." He analyzed the precession and the attraction of the moon to the Earth's presumed equatorial bulge imbalance , on the basis of which, he predicted that the shape of the earth was fan-shaped; from this we can see the significance of Newton's achievements. Some analysts may see the greatness of the Principia in its apparent commitment to the physics of inertia; for Newton, inertia was a property of mass.Newton was the first author to make a clear distinction between mass and weight, and he went on to recognize that the mass of an object has two separate and distinct aspects.Mass is a measure of what an object resists being accelerated or prevented from changing its state of motion or its state of rest; this is its inertia. (Newton sometimes used terms such as "inertial force" or "visinertiae"—a type of force that is distinguished from that of "work of motion" or force that produces acceleration.) However, the mass of an object can also act as a counterweight to A measure of a response to a given gravitational field. Why, then, is there a connection between a body's (inertial) resistance to acceleration and its (gravitational) response to a gravitational field? This is in The answer is not found in classical physics. Newton had the insight to realize that an understanding of this relationship must be based on experiments, so he set out to perform experiments to prove this constant relationship between inertia and gravity. However, the logical necessity of the equivalence of "inertial" mass and "gravitational" mass can only be seen in Einstein's theory of relativity. Einstein greatly admired Newton, because Newton had such profound insights into this problem, and Realized that his reasons for explaining this equivalence relation can only be based on experiments.

The nature of mathematics in Newton's Principia is often misunderstood.If you just flip through the pages one by one in a general way, it will give people the impression that the mathematics used by Newton is geometry, especially the geometry of ancient Greece.Its style seems to be Euclidean or Apollonius.A closer look, however, reveals that Newton was formulating the problem in terms of calculus, using geometric methods to state relationships in terms of different ratios and proportions, and at the same time, seeing "limits" as being equal to zero The (or initial) basic quantity.Thus, although Newton did not detail the system of rules of calculus (or "fluxes") that he later systematically employed, he did make extensive use of the method of limits, which is clearly equivalent to the use of calculus, or, so to speak, The limit method used can be easily converted to the notation of Newton's algorithm or Leibniz's algorithm.Marques de L'Opital recognized this aspect of the Principia when he noted (as Newton smugly mentioned) that the mathematics in the book was almost entirely calculus.For any careful reader, in the elaboration of the limit theory in the first section of the first part of the book, and in the explicit flow number (Newton's term for differentiation) theory in the second section of the second part of the book, this One point is more obvious.In addition, Principia is also famous for being the first to use some other mathematical methods, such as the extensive use of infinite series.

newton style It seems to me that the essence of Newton's scientific revolution can be found in what I have called "Newton's style".This can be easily seen from Newton's discussion of Kepler's laws in Principia.Newton's discussion began with a purely mathematical structure or imaginary system - not just a simplified natural event, but a purely imaginary system that does not exist in the real world.Here, the word "real" refers only to the external world as revealed by experiment and observation.In such a system, a single particle moves around a center of force.Newton mathematically pointed out (bk.1, prop.1), as long as there can be a force in this structure or system from a mass point or particle moving along the orbit to point permanently to the stationary center of force, then Kepler's The law of area (that is, his second law) can be established.He next proved the converse, that if the law of areas holds, then there is a centripetal force, or force pointing towards the center.Therefore, the existence of centripetal force is proved to be both a necessary condition and a sufficient condition for the establishment of Kepler's area law.Then Newton pointed out that if the motion track is elliptical, then the centripetal force must be inversely proportional to the square of the distance from the center.Finally he showed that if under the conditions of such forces there are several orbiting particles, they do not interact with each other—or (with the same result) if the motion of any given particle is compared Comparing motions at different distances—then, Kepler's third law or law of harmony can hold.Incidentally, we may notice that Newton here for the first time indicated the dynamical meaning of each of Kepler's third law.Newton's activities constituted to a large extent the first phase of pure mathematics. In the second stage, Newton compared his mental constructs with the real world.Of course he immediately discovered that in the real world (for example, in our solar system), orbiting bodies do not move around a "mathematical" center of force, but around other real bodies.The moon revolves around the earth and the earth and other planets revolve around the sun.In addition, in order to make his mental construct or imaginary system more in harmony with the real world, Newton improved this system by increasing the number of particles to two.One of the mass points is located in the center and attracts the other mass point moving on the orbit, which is constantly pulling the latter away from the other orbit of linear inertial motion on which it is located.However, according to the principle that any action has an equal and opposite reaction (Newton's third law of motion), it follows that if the central body attracts the orbiting body, then, in Objects in orbit must also attract objects at the center.Thus, this mental construct is extended to systems of two interacting bodies.Newton went on to show that under such conditions it is no longer the case that the orbiting body follows a purely elliptical orbit around a central body at the focus.Instead, he found that both moved in elliptical orbits around their common center of gravity. This two-body system constituted a refined stage in which Newton once again formulated his (now revised) mental construct mathematically.He then compared this improved system with the outside world, which is the second stage of improvement.Of course, he found that this system still did not correspond to the real world around us.In our solar system, for example, there is not just one planet orbiting the sun, but several.In this way, in order to further conform his mental constructs to the external world system, Newton continued to work on another stage.He introduced into the system not one but two or more particles orbiting around a central particle.In this way, using Newton's third law, the following inference is drawn again: every particle moving along the orbit is both attracted by and has an attractive effect on the central object.In other words, the conclusion is that every particle moving along the orbit is not only an attractive object, but also a center of attraction.Any one of these orbiting bodies will have an effect on each of the others, and will be affected by their respective actions.The system consists of objects that interact with each other in perturbations that lead to a slight deviation from Kepler's laws.So Newton went on trying to find a measure of quantities in our solar system that differed from Kepler's laws. In this counterpoint shift between the mathematical structure and the analogy to the real world, and between the first and second stages, Newton developed not only from a single-body system to a multi-body system, but also to orbiting And a multi-object system with satellites, for example, the satellite of the earth is the moon, and Saturn and Jupiter also have their own satellites.Up to this point he had been talking about particles, not physical objects, because he hadn't started thinking about size and shape, but eventually he shifted the discussion from particles to physical entities of a certain size and shape. The process I'm describing is not just a post-hoc analysis of 20th-century people [of the way Newton posed the problem in Principia].It is consistent with the various stages of development of Newton's thought as evidenced by documents. In the autumn of 1684 Newton wrote a pamphlet (On Motion) in which he presented some results of his studies of Kepler's laws and other aspects of the problem.He pointed out in the book that the centripetal force is a necessary and sufficient condition for the establishment of the law of area, and the elliptical orbit implies that this force is inversely proportional to the square of the distance, which is very similar to what he later explained in "Principles".But it was not realized at that time that his proofs were applicable only to the mental constructs of a single system of bodies, so he wrote proudly: "Note: The planets, therefore, in elliptical orbits have a focal point at the center of the sun, Moreover, the area swept by a radius equal to the distance from the sun between the planets is proportional to time, exactly as Kepler postulated." Soon Newton realized that, in fact, it is impossible for a planet to travel along a simple Kepler Le elliptical orbital motion.He saw that his results were applicable only to artificially constructed single-body systems in which the earth was reduced to a mass point and the sun to a fixed center of force. In December 1684, Newton completed a revised draft of On Motion, in which he described the motion of the planets within the context of an interacting system of many bodies.Unlike previous pamphlets, this revised edition concludes that "the planets neither move in perfect elliptical orbits nor appear twice in the same orbit." This conclusion led Newton to the The following results: ktkt is like the motion of the moon, for each planet there are as many orbits as there are motions, and each orbit depends on the combined motion of all these planets, let alone the interaction of all these planets with each other Having said that... the consideration of the causes of so many motions, and the determination of them by exact laws (allowing easy calculations), is, if I am not mistaken, beyond the intellectual power of all mankind. Newton had already noticed that the planets gravitationally interacted with each other.He has expressed this awareness in explicit language in the above quotation: "eorum omnium actions in se invicem" (the interaction of all these planets with each other).From this mutual gravitational attraction, it can be deduced that in the physical world, Kepler's three laws are not all correct, they are only correct in a certain mathematical construction, in which In , the masses that do not interact with each other's orbits are either a mathematical center of force or a fixed gravitational object.Newton's distinction between the realm of mathematics (where Kepler's laws are true laws) and the realm of physics (where those laws are "hypotheses" or approximations) was a revolutionary feature of Newtonian celestial mechanics. In a little booklet he had written before and became Part Three of the Principia, Newton showed how thinking about the third law of motion led to questions about , and the concept that two planets have an interacting force between them.The same thinking led to a revolutionary new idea that some objects in the universe must all be "attracting each other." Proudly stating this conclusion, and explanatory note, he pointed out that on Earth In any pair of bodies on , the amount of gravitational force is so small that it is difficult to observe. "Perhaps," he wrote, "these forces can only be observed on giant planetary bodies." Of all the planets, Jupiter and Saturn are the most massive, so he made a study of the perturbations of their orbits during their motion. explored.With the help of John Flamsteed, Newton discovered that Saturn's orbital motion does indeed perturb when the two planets are very close together. Part III of the Principia deals with cosmic systems, but it is more mathematical than the previous pamphlet.Here, Newton discussed gravity in essentially the same way.First, in what is called the Lunar Experiment, he extended the force of gravity, or that of the Earth, to the Moon, and proved that the magnitude of this force is inversely proportional to the square of the distance.He further believed that this gravitational force of the earth is the same as that of the sun on the planets, and that of a planet on its satellites.He now calls all these forces gravity.With the help of the third law of motion, he transformed the concept of the sun's force acting on the planets into the concept of the interaction force between the sun and the planets.Similarly, he transformed the concept of the force of a planet on a satellite into the concept of the interaction force between a planet and its satellite.In the end, this reformation led to the idea that all objects interact gravitationally. Please do not take my analysis of the development of Newton's thought as an attempt to belittle the part played by his extraordinary creative genius; on the contrary, I think it should be recognized.My analysis illustrates Newton's creative way of thinking about physics, in the ways in which he described the external world mathematically as revealed by experiment and critical observation.Since he did not consider such constructs to be exact representations of the physical world, he was free to explore the properties and effects of mathematical gravity, although he found that the controlling forces "operating at a distance" were not It is both incompatible and not allowed in the kingdom.He then compared his inferences about mathematical constructs with those observed principles and laws of the external world, such as Kepler's law of area and law of elliptical orbits.Wherever this mathematical structure has deficiencies, Newton will improve it.This way of thinking, what I have called the Newtonian style, has attracted attention for the title of his great book "Mathematical Principles of Natural Philosophy". The laws of gravitation explain why the motions of the planets follow Kepler's laws approximately, and why they each deviate from these laws in different ways.It is the law of gravitation that demonstrates why (in the absence of friction) all objects fall at the same speed at any given location on Earth, and why this speed varies with altitude and latitude.The law of universal gravitation also explains the regular and irregular motion of the moon, and provides a physical basis for understanding and predicting tidal motion. What is the relationship between the attraction of the play area.Because of the success of mathematical gravity in explaining and predicting the observed phenomena of the universe, Newton asserted that such a force must "really exist", even though the generally acknowledged philosophy that he himself embraced did not allow nor It is possible to allow such forces to be an integral part of natural systems.Therefore, he advocated to explore how gravitation works. Although Newton sometimes thought that gravitation might be caused by pulses produced by a stream of ether particles colliding with an object, or by some kind of change in a pervasive ether, neither of these views was included in his Principia. mentioned, because, as he eventually pointed out, he never "could invent hypotheses" as explanations for physics.Newton's style led to his mathematical notion of gravitation, and it led him to apply his mathematical results to the physical world, even though it was not the kind of force he could believe in. Some of Newton's contemporaries were so confused by the idea of ​​gravity at a distance that they could not begin to investigate its properties, and they found it difficult to accept Newtonian physics.Newton said that he was no longer capable of explaining how gravitation works, but "it is enough that this gravitation does exist and is sufficient to explain celestial phenomena and tidal phenomena." Some of his contemporaries disagreed with this .Those who admit that Newton's style gives the law of gravitation a sense of reality, show how the law can explain so many phenomena, and look for an explanation of how this force extends through the void of space beyond great distances of.Newton's style allowed Newton to pursue the study of gravitation without the constraints of premature timing that might have prevented his great discoveries. The 18th century biologist G. L． L．De Buffon once wrote that a man's style is inseparable from himself.As far as Newton is concerned, his great discoveries cannot be separated from his style. Confirmation of Newton's Revolution There are many documents that can prove the Newtonian revolution in science. The 18th-century historian of science Jean-Sylvain Bailly wrote that "Newton overturned or transformed all thought": his "philosophy led to a revolution." Newtonian revolution.He noticed that Newton's key to revealing the mysteries of celestial bodies is mathematics: geometry.Baye pointed out: "What is supposed to cause bodies to move does indeed do so; there is ample evidence for this. Only Newton's mathematics (geometry) conjectures the secrets of nature." Insightful, Bailly found that "the advantage of the mathematical explanations is that they are universal." If the planets move according to Kepler's laws, then they must be "propelled by some force that exists in the sun." , this argument depends only on mathematical or geometrical reasons and general principles of motion.Unlike Newton's argument, which did not involve any specific physical properties of the sun, Kepler relied on some specific properties in his argument, such as the sun's magnetic force and the sun's magnetic pole action.Furthermore, the same mathematical argument shows that for Jupiter and Saturn, which also obey the same Kepler's laws, their moons must also be similarly "propelled by the forces existing in the two planets." In other words, Jupiter and Saturn are to their respective satellite systems what the Sun is to its planetary system, the only difference being the extent and magnitude of their control.The same is true of the relationship between the earth and our moon (Bay 1785, VOl. 2, bk. 12, see. 9, pp. 486f.). Bai himself is willing to admit the concept and principle of gravitation, because with the help of gravitation, so many phenomena can be explained: many observation data and empirical laws can be deduced from the properties of gravitation through mathematics (sec.41, pp .555f.).However, he found that at first, many (famous French) scientists divided the Newtonian system into mathematical philosophy and pure natural philosophy.Therefore for P. L． M．De Mauperti—(according to Bayly) "seems to be... the first to use the principle of gravitation in our mathematics," Bayly [vol. 3 ("discourspremier"): 7] Not to mention that "at first he considered the gravitational principle only in terms of its calculable consequences; he recognized gravitation from the mathematician's point of view, not from the physicist's point of view." Also That is to say, Mauperti agrees with Newton's mathematical systems and structures (our first and second stages), but does not admit that Newton is definitely discussing real problems in his system of the universe (third stage). In fact, Mauperti is quite explicit on this point in his treatise entitled "On the Law of Gravitation" (173).He wrote: "I do not consider at all whether gravity is consistent with or contrary to correct philosophy." Instead, "here I only discuss gravity from the point of view of a mathematician [geometry]." Think of gravity as "a quantity, since it is uniformly distributed in all parts of an object, and its action is proportional to its mass, so, however much it may be, many phenomena can be predicted from it. "In other words, Mauperdi recognized Newton's style and was willing to explore the mathematical results of the law of gravitation as a "geometer." From the point of view of a scientist, he asks himself whether there is such a force which is indeed a physical reality, or whether there is any other reason why bodies seem to behave under such a force? If there is such a force A force which necessarily has a cause of its existence; we may perhaps note that his thought is so deeply embedded in mechanistic philosophy that he confines himself to the two material causes of this gravitational action. Middle: some cause originating from a gravitational object, or a cause caused by the motion of some matter other than the object. A similar affirmation of Newton's style can be seen in the writings of Crelow.Craello explains, "Mr. Newton ... made it clear that he used the word gravity only in anticipation of the discovery of its cause; Judgment: Its sole purpose is to establish gravity as a fact" (Crelow 1749, 330). By the end of the 18th century, the concept of universal gravitation was gradually recognized by people.In the preface to his great work Celestial Mechanics (published 1799-1825), Laplace - the second Newton in the discipline - begins (1829, p.xxiii): Towards the end of the seventeenth century, Newton made his discovery of universal gravitation public.Since that time mathematicians have succeeded in attributing to this great law of nature all known phenomena in the cosmic system, and have thereby brought to an unexpected degree of precision theories and astronomical diagrams concerning the celestial bodies.My aim has been to develop a coherent line of thought out of these theories scattered throughout a large body of work.The balance and motion of liquids and solids constitute the solar system and similar systems that exist in infinite space. From this point of view, all the results caused by gravity also constitute the research objects of celestial mechanics, or apply the principles of mechanics to Study the motion and shape of celestial bodies.In the most general sense, astronomy is a great problem of mechanics, where the elements of motion are arbitrary constants.The solution of this problem depends on both the precision of observation and the perfection of analysis. Although there was a shift in Laplace's philosophical outlook, as evident in his Introduction to the Philosophy of Probability published in 1814, he did not feel the need - a century after the publication of the principle - to It is reasonable to discuss whether gravity extends its action across space.In the second "volume" of "Celestial Mechanics", "On the Law of Universal Gravitation and the Motion of the Center of Gravity of Celestial Bodies", the first chapter is "On the Law of Universal Gravitation Deduced from Observation".We are "tempted," he wrote (1829, I:249), "to regard the center of the sun as the center of such a gravitational force extending infinitely in all directions, whose magnitude is the square of the distance Inversely proportional to the change." Since there is no embarrassment at all to use the Newtonian word "gravity," and no longer to be disgusted by the philosophical implications of the word when thinking generally or even beyond Newton's sphere, Laplace came to the conclusion simply and clearly: "The sun and those planets with their own satellites have a kind of attraction. This gravitational force extends infinitely. The magnitude of the force is inversely proportional to the square of the extended distance. All This is true of bodies throughout their sphere of motion" (p. 255).Moreover, "the analogy leads me to the inference that a similar force exists universally in all planets and comets." He concludes quite explicitly that "the observed上的引力，是一条扩展到整个宇宙的普遍定律的一个特例"，这种"引力"并"不完全与总的质量有关"，它对于"组成物的每一个粒子都是相同的"（p ．258）。他欢呼说，牛顿的"万有引力"是一条"伟大的自然原理"，"物质的所有粒子相互吸引，这种作用与质量成正比，而与它们彼此的距离的平方成反比"（p．259）。 这一原理的成功和万有引力的应用，或者爱因斯坦以前的所谓"经典"力学（或牛顿力学）的应用，使这一学科成了所有科学的典范或理想。例如，19世纪中叶和19世纪末大部分关于达尔文革命的争论，都是以方法为中心，而且往往集中在达尔文是坚持还是放弃了牛顿方法这一问题上。在诸如古生物学和生物化学等若干领域中的科学家们，想象有一天他们各自的科学领域中也会有自己的牛顿，而且他们的科学也会达到牛顿的《原理》那样完备的程度。乔治·居维叶在1812年问道，为什么"自然史界不会有朝一日出现它自己的牛顿呢？"在1930年左右，奥托·瓦尔堡叹惜说，化学界中的牛顿（JH．范托夫和威廉F．奥斯特瓦尔德在1887年都曾谈到过化学界需要这样的人物）"还没有出现"（参见科恩1980，294）。 牛顿革命也成了意识形态的一个重大的组成部分，唯一可与之相提并论的则是另一届科学革命，即达尔文革命。艾塞亚.伯林（1980，144）对牛顿的影响作了总结： 牛顿及其同时代的约翰·洛克，是伟大的新思想的代表人物，这些新思想构成了那些"著名的信念和思想习惯中的革命"（兰德尔1940，253），它标志着，随着启蒙运动的发展，现代社会正在出现。今天，在思考这一长达三个世纪之久的影响时，我们也许会发现，很难理解：牛顿实际成就是在创建自然之数学理论方面，但他的成果竟然产生了如此空前的影响。哈雷曾作出过一个牛顿式的预言——1758年（哈雷和牛顿去世以后很久）将会有一颗彗星出现，当这一预言被证实时，恐怕唯有"不同寻常的"、"非凡的"、"令人惊异的"这类形容词才能表达科学家和非科学工作者们内心之中的敬畏之情。无论在哪里，无论是男人还是妇女都发现了这样一种指望，即在所有人类知识和所有人类事物的管理中都会产生出一种类似的合理的演绎和数学推理系统，一种与实验和批判性观察联系在一起的系统。18世纪"显著地"成了一个"信仰科学的时代"（兰德尔1940，276）；牛顿是成功科学的象征，是哲学、心理学、政治学以及社会科学等等所有思想的典范。 18世纪的重农主义者们充分地表述厂对以普遍规律为依据的牛顿式"自然法则"的信仰。按照重农主义者的观点，"根据不可改变的、不可避免的和必然发生的观律，并且以永恒的必然的联系方式"，所有"社会中的事实都连在了一起"（安德烈·纪德和夏尔·里斯特1947，2）"一旦他们认识到了这些规律"，无论是个人还是管理机构就会遵守这些规律。重农主义者不仅相信，人类社会是"受自然规律制约的，"而且还认为，存在着一些"控制着物理世界、动物社会、甚车每一种有机体内部生活的同样的规律"（p．8）。启蒙运动时男人和妇女们抛弃了传统的人类关系和人类社会秩序的概念，他们希望有自己的牛顿，他——他们肯定地说——"即将出现。"这种"社会科学界的牛顿，"按照克兰·布林顿（C．布林顿1950，382）的观点，人概会创造出一种新的"社会科学系统，人们只有遵循〔它们〕才能确保有——不是已成为过去的而是即将在未来出现的——真正的黄金时代，真正的伊甸园。1748年孟德斯鸠出版了《论法的精神》，在这部书中，他把一个运转良好的君主政体与"宇宙系统"作了比较，在宇宙系统中存在着"一种吸引力"，它能够"吸引"所有物体趋向"中心"，孟德斯鸠以《原理》为榜样，"确立了……第一原理"，并且发现广这些原理中自然而然地产生的一些特例。 在可以应用理性原则的思想和活动的几乎每一个可能的层次上，都留下了牛顿革命的重大影响。即使到了今天，在牛顿的时间、空间和质量概念甚至牛顿的引力原理已被爱因斯坦的体系取代了的情况下，牛顿科学仍然在许许多多科学的和日常经验的领域中占据着至高无上的地位。这些领域包括日常生活经验的领域和我们常用的机械（"原子能"装置除外）的领域。本世纪最为壮观的活动——对空间的探索——并不是爱因斯坦相对论的一个例证，它只是经典的引力物理学的直接应用的一个实例。经典的引力物理学是由牛顿在其《原理》中完成的，经过两个多世纪牛顿信徒们的努力，它发展成了理论力学这样一门科学，而且成了大体力学的核心。牛顿革命不仅仅是这场科学革命的顶峰，而且一直是人类思想史中具有最深远意义的革命之一。