Chapter 55 Chapter 6 The Rise of Science

Nearly every point of difference between the modern world and previous centuries can be attributed to science, which in the seventeenth century received the most amazing and magnificent success.Although the Italian Renaissance was not in the middle ages, it was not in the modern era either; it was more like the heyday of Greece.The sixteenth century indulged in theology, and the medieval style was heavier than Machiavelli's world.In terms of ideology, modern times began in the seventeenth century.None of the Renaissance Italians would have puzzled Plato or Aristotle; Luther would have terrified Thomas Aquinas, but Aquinas had no trouble understanding Luther.As for the seventeenth century, it was different: Plato and Aristotle, Aquinas and Occam, would have no idea of ​​Newton.

The new concepts brought by science have had a profound impact on modern philosophy.In a sense, Descartes can be said to be the ancestor of modern philosophy, and he himself was a creator of science in the seventeenth century.In order to be able to understand the spiritual atmosphere of the birth period of modern philosophy, it is necessary to talk about the methods and results of astronomy and physics. In the creation of science, there are four extraordinary great men, namely Copernicus, Kepler, Galileo and Newton.Among them, Copernicus belonged to the sixteenth century, but he did not have much prestige during his lifetime.

Copernicus (1473-1543) was a Polish priest of pure orthodoxy.He lived in Italy when he was young, and received some influence of the Renaissance atmosphere. In 1500 he obtained the position of lecturer or professor of mathematics in Rome, but returned to his homeland in 1503 as a member of the monks of Frauenburg Cathedral. A large part of his time seems to have been spent fighting the Germans and reforming the currency, but he devoted his spare time to astronomy.He had long believed that the sun was at the center of the universe, and that the earth had a double motion, that is, its daily rotation and its annual revolution around the sun.Although he also made his personal opinions known, he held back from making them public for fear of condemnation from the Church.His major work, De Revolutionibus Orbium C Blestium (De Revolutionibus Orbium C Blestium) was published in the year of his death (1543), with a preface written by his friend Ossian, in which he stated that the heliocentric theory was nothing more than a hypothesis brought up.To what extent Copernicus endorsed this statement is not known with certainty, but he himself made some similar statements in the text of the book, so the question is irrelevant.Dedicated to the Pope, the book escaped formal condemnation of the Catholic Church until the time of Galileo.The Church at the time of Copernicus was relatively lenient compared with the Church at the time of the Council of Tulent, the Jesuits, and the revived Inquisition.

The atmosphere of Copernicus' work is not a modern atmosphere, but perhaps rather a Pythagorean atmosphere.It was an axiom for him that all celestial bodies must be in constant circular motion; and, like the Greeks, he allowed himself to be swayed by aesthetic motives.In his system there are still "epicycles", but the center is the sun, or rather, near the sun.The fact that the sun was not exactly in the center spoiled the simplicity of his doctrine.Although Copernicus had heard of Pythagoras' theory, he didn't seem to know Aristotle's heliocentric theory, but there was nothing in his theory that the Greek astronomers could not have imagined.The important thing about his achievement is that he knocked the earth off the throne of geometry's dominance.In the long run, it is difficult to attribute the important position in the universe given to human beings in Christian theology.But such consequences of his doctrines Copernicus would not admit; his orthodoxy was sincere, and he rejected the notion that his doctrines contradicted the Bible.

There are some real difficulties in Copernican's theory.The biggest difficulty is not seeing stellar parallax.Suppose the earth at any point in its orbit is 186,000,000 miles from the point where the earth is located half a year later, this should produce a change in the apparent position of the stars, just as a ship on the sea appears to be at a distance from a point on the coast. If it is true north, it must not be true north from another point of view.No parallax phenomenon was observed at that time, and Copernicus made a correct inference: the stars must be farther away than the sun.It wasn't until the nineteenth century that measurement techniques were sophisticated enough to detect stellar parallax, and only a few of the closest stars could be observed at that time.

With regard to falling bodies, another difficulty arises.If the earth keeps rotating from west to east, an object falling from a high place should not land a point directly below the starting point, but should fall a little west, because the earth will have to rotate during the falling time. some distance.This question was answered by Galileo's law of inertia, but in the time of Copernicus, no answer was available. There is an E. A．There is an interesting book by Burtt called The Metaphysical Foundations of Modern Physics (1925), which deals with many of the things done by those who founded modern science. The assumption that is difficult to guarantee is very powerful.

He is quite right to point out that in Copernicus's day there were no facts known which compelled the adoption of his system, but several which were against it. "If contemporary empiricists had been born in the sixteenth century, they would be the first to ridicule this new philosophy of the universe as worthless." A fortuitous accident in the midst of absurd superstition, thereby devaluing modern science.I thought this indicated a misunderstanding of attitudes towards science.What shows the true nature of a scientist is not what he believes, but what attitude he takes to believe it and why he believes it.The belief of a scientist is not an arbitrary belief, but a tentative belief; it is not based on authority, not on intuition, but on the basis of evidence.Copernicus was right in calling his theories hypotheses; his opponents made a mistake in calling new hypotheses undesirable.

Those who founded modern science had two strengths that did not necessarily coexist: great patience in making observations, and intrepidity in making hypotheses.The second of these virtues was previously shared by the earliest Greek philosophers, and the first was also to a considerable degree manifested by the astronomers of late antiquity.But among the ancients, with the possible exception of Aristotle, no one had both, and in the Middle Ages no one had either.Copernicus, like some of his great successors, was both.Concerning the apparent motion of the celestial bodies on the celestial sphere, he knew all that could be known with the instruments available at that time; hypothesis.From the modern point of view, which regards all motion as relative, the only advantage his hypothesis yields is simplicity; but this was not the view of Copernicus, nor that of his contemporaries.With regard to the annual revolution of the earth, there is also a simplification here, but not as pronounced as the simplification of the rotation.

Copernicus still needed epicycles, just less than the Ptolemaic system.The new theory did not acquire sufficient simplicity until Kepler discovered the laws of planetary motion. In addition to its revolutionary impact on people's imagination of the universe, the new astronomy has two great values: first, it admits that what has been believed since ancient times can also be wrong; Combined with a wild guess the laws governing these facts.No matter which of these two points of value, as far as Copernicus is concerned, his successors have not fully utilized them, but in his career, both of these points have been highly expressed.

Copernicus communicated his teachings to some, among them German Lutherans; but when Luther learned of this, he was greatly indignant.He said: "Everyone wants to hear the speech of a sudden fortune-telling astrologer who contrives to prove that the sky or firmament, the sun and the moon do not turn, but the earth does. Whoever wishes to appear clever has to invent some new system which will Naturally the best of all systems. It is a fool who would turn the science of astronomy upside down; but we are told in the Bible that Joshua commanded the sun to stand still, and not the earth."

Similarly, Calvin also took the verse "The world is firm and cannot be shaken" (Psalm 93, verse 1) and scolded Copernicus. He shouted: "Who dares to take Copernicus' prestige over the prestige of the Holy Spirit?" Protestant priests were at least as obstinate as Protestant priests; nevertheless, in Protestant countries soon there was a much greater freedom of thought than in Old ones, because the clergy in Protestant countries For the sake of less power.The important aspect of Protestantism is not to establish heresies, but to split sects; because sectarian splits lead to state churches, and the power of state churches is not enough to control secular regimes.This is entirely an advantage, for the Church has opposed, wherever she can, almost every innovation which tends to increase the happiness and knowledge of the world. Copernicus could not produce any solid evidence to support his hypothesis, so astronomers rejected it for a long time.The next important astronomer was Tycho Brahe (Tycho Brahe, 1546-1601), who took a compromise position: he believed that the sun and the moon circled the earth, but the planets circled the sun.As for theory, Tyko Brah was not very original.However, he gives two valid objections to Aristotle's suggestion that everything above the moon remains the same.One reason is that a new star appeared in 1572, and it was found that this star has no diurnal parallax, so it must be farther than the moon.Another reason is obtained from observing comets, which are also found to be far away.The reader will recall Aristotle's doctrine of transmutation and decay limited to the lower part of the moon; this doctrine, like all the other opinions Aristotle expressed on scientific questions, was in the end an obstacle to progress. Taiko Brah's important position is not that of a theorist, but of an observer; he first engaged in astronomical observations under the auspices of the King of Denmark and later with the auspices of Emperor Rudolph II.He drew up a table of the stars, and recorded the positions of the planets over many years.Shortly before his death, Kepler, then a young man, served as his assistant.To Kepler, Tycho Brah's observations were invaluable. Kepler (1571-1630) is the most striking example of what man can achieve by perseverance without much genius.He was the first important astronomer to adopt the heliocentric theory after Copernicus, but the observation data of Taiko Brah showed that the heliocentric theory would not be quite correct in the form set by Copernicus.Influenced by Pythagorean philosophy, Kepler was a devout Protestant with a somewhat whimsical inclination towards sun worship.These motives certainly gave him a preference for the heliocentric theory.His Pythagorean philosophy led him to follow Plato's Timaeus, assuming that the meaning of the universe must rest on five regular polyhedra.He conceived various hypotheses using these five regular polyhedra; finally, by luck, one of the hypotheses worked. Kepler's great achievement was to discover his three laws of planetary motion.Two of these laws were published by him in 1609, and the third in 1619. His first law states that the planets move in ellipses, and that the sun occupies one focus of the ellipse.The second law says: A connecting line between a planet and the sun sweeps out equal areas in equal times.The third law says: The square of the revolution period of a planet is proportional to the cube of the average distance between the planet and the sun. A few words must be said below to explain the significance of these laws. In the time of Kepler, the first two laws can only be proved according to the situation of Mars; Regarding several other planets, the observation results do not conflict with these two laws, but the observation results are not clear to establish these two laws.Conclusive evidence, however, was soon to be found. The discovery of the first law, which states that planets move in elliptical orbits, required an effort to break away from tradition that is not readily appreciated by modern people.The only thing that all astronomers agree on, without exception, is that all motions of celestial bodies are circular motions, or motions composed of circular motions.When encountering situations where circles are not enough to explain planetary motion, epicycles are used.The so-called epicycle is the curve drawn by a point on the circumference of another circle rolling on the circle.For example: Take a large wheel and fix it on the ground; take a small wheel with a nail pierced through it, let the small wheel (also placed on the ground) roll along the big wheel, and the tip of the nail touches the ground.At this time, the traces of the nails on the ground are drawn as epicyclic circles.The Moon's orbit with respect to the Sun is roughly of this kind: Roughly speaking, the Earth circles the Sun and the Moon circles the Earth.However, this is only an approximation.As the observations became more precise, it became known that no epicycle assembly system would be completely in line with the facts.Kepler found that his hypothesis was much more closely related to the recorded position of Mars than was Ptolemy's, and even more closely than Copernicus'. By substituting an ellipse for a circle, the aesthetic prejudices that have dominated astronomy since Pythagoras had to be abandoned.A circle is a perfect shape, and a celestial body is a perfect object—they are originally gods, and even according to Plato or Aristotle, they have a close relationship with gods.It seems obvious that perfect bodies must move in perfect shape.Moreover, since the celestial bodies move freely without being pushed or pulled, their motion must be "natural."But it is easy to imagine that there is something "natural" about the circle, but it is difficult to imagine it in the ellipse.In this way, many deep-rooted prejudices must be discarded before Kepler's first law can be accepted.No one in antiquity, not even Aristotle of Samoys, foresaw this hypothesis. The second law deals with the change in speed of a planet at different points in its orbit.Let S denote the sun, and P1, P2, P3, P4, P5 denote the successive positions of the planets at equal intervals—say every other month—this law of Kepler says that P1SP2, P2SP3, P3SP4, P4SP5 These pieces are all equal in size.So planets move fastest when they are closest to the sun, and slowest when they are farthest from the sun.This is too shameful; planets should be majestic, and there must be no haste or sluggishness. The first two laws deal with each planet separately, while the third law compares the motions of different planets, so this law is very important.The third law says: Suppose the average distance between a planet and the sun is r, and the period of this planet is T, then the quotient obtained by dividing r3 by T2 is the same in different planets.This law proves Newton's inverse square law of universal gravitation (for the solar system only).But we will talk about this later. Perhaps apart from Newton, Galileo (1564-1642) is the greatest founder of modern science.He was born about the same day as Michelangelo died, and died the year Newton was born.I recommend these two facts to those who still believe in reincarnation (if there is such a person).Galileo was an important astronomer, but he was perhaps even more important as the father of dynamics. Galileo was the first to discover the importance of acceleration in dynamics. "Acceleration" means speed change, no matter the change of speed or the change of speed direction; for example, an object moving at constant speed along the circumference always has an acceleration towards the center of the circle.To use the term used before the time of Galileo, it can be said that whether it is on the ground or in the sky, he regards the constant velocity motion in a straight line as the only "natural" motion.In the early days, it was believed that the celestial bodies moved in a circle and the objects on the ground moved along a straight line, which was "natural".Contrary to this opinion, Galileo believed that if left to itself, all objects would move along a straight line at a uniform speed; any change in the speed of motion or in the direction of motion must be explained as due to a certain "force".This law was announced by Newton as "the first law of motion", also known as the law of inertia.I shall return to its purpose later, but first the details of Galileo's various discoveries must be stated. Galileo was the first person to establish the law of falling bodies.As long as there is the concept of "acceleration", this law is extremely simple.The law says that during the free fall of an object, if the possible influence of air resistance is excluded, its acceleration is consistent; further speaking, all objects, regardless of their weight or size, have the same acceleration.A complete proof of this law was not possible until the invention of the air extractor, about 1654.Since then, it has been possible to observe objects falling in a space almost equal to a vacuum, and it was found that feathers and lead fall as fast.What Galileo was proving at the time was that there was no measurable difference between large and small pieces of the same substance.Until his time, it was always believed that large lead blocks would always fall much faster than small lead blocks, but Galileo proved this to be untrue by experiments.In Galileo's day, measurement techniques were not as sophisticated as they were later; nevertheless, he arrived at a true law of falling bodies.Suppose an object falls in a vacuum, its velocity increases at a certain rate.At the end of the first second the velocity of the object is 32 feet per second; at the end of the second second it is 64 feet per second; at the end of the third second it is 96 feet per second; and so on.The acceleration of the body, the rate of increase in velocity, is always the same; with each passing second, the increase in velocity is (approximately) 32 feet per second. Galileo also studied the problem of bullet flight, which was an important problem for his employer, the Duke of Tuscany.It has always been thought that a bullet fired horizontally moves horizontally for a while, and then suddenly begins to fall vertically.Galileo proved that, disregarding air resistance, the horizontal velocity remains constant in accordance with the law of inertia, but a vertical velocity is added, which increases in accordance with the law of falling bodies.To find out the movement of the bullet in a short period of time (say, one second) after it has been flying for a period of time, the following steps can be taken: First, if the bullet does not fall, it will travel for a period equal to the first second of flight. Horizontal distance equal to the horizontal distance traveled within.Secondly, if the bullet does not move horizontally, but only falls, it will fall vertically at a speed proportional to the time since the flight began.In fact, the position of the bullet changes exactly as it would have been when the bullet moved horizontally for one second with an initial velocity and then fell vertically for a second with a velocity proportional to the elapsed time of flight.It is known from simple calculation that the resulting bullet path is a parabola, excluding the interference part of air resistance, which can be confirmed by observation. What has been said is a simple instance of a principle of dynamics of great utility, that is, the principle that, in the case of several forces acting simultaneously, the effect is the same as if the forces had acted in succession.It's part of a more general principle called the "parallelogram law."For example, suppose you are on the deck of a ship in motion and walk across the deck.When you walk, the boat has already moved forward, so for you, for the water, you have moved forward along the direction of the boat's motion, and also moved across the direction of the boat's motion.If you want to know where you are with respect to the surface of the water, you can imagine that you stand still while the boat is going on, and then, for an equal period of time, walk across the boat without the boat standing still.The same principle applies to forces.In this way, the total effect of several forces can be obtained, and if the respective laws of several forces acting on a moving body are discovered, it is also possible to analyze physical phenomena.The person who initiated this extremely effective method was Galileo. In what I have said above, I have tried to use terms as close to the seventeenth century as possible.Modern terminology differs from this in some important respects, but for the sake of illustrating the achievements of the seventeenth century it is advisable to use the expression of that time for the time being. The law of inertia solved a riddle that the Copernican system could not explain until Galileo.As mentioned earlier, if you drop a stone from the top of the tower, the stone lands at the foot of the tower, not slightly to the west of the foot of the tower; however, if the earth is rotating, it should Turn a certain distance is.So it doesn't, and the reason is that the stone retains the same speed of rotation that it shared with everything else on the ground before it was dropped.In fact, if the tower were really tall enough, it would have had the exact opposite effect as Copernicus' opponents supposed.Because the top of the tower is farther from the center of the earth than the foot of the tower, it moves faster, so the stone should fall slightly east of the foot of the tower.However, this effect is too small to be measured. Galileo enthusiastically adopted the heliocentric system; he corresponded with Kepler, acknowledging his various discoveries.Galileo heard that a Dutchman had recently invented a telescope, built one himself, and soon discovered many important things.He discovered that the Milky Way is composed of thousands of individual stars.He observed the phases of Venus, a phenomenon Copernicus knew to be a necessary corollary of his theory, but which could not be discerned with the naked eye.Galileo discovered the moons of Jupiter and named them "sideramedicea" (Star of the Medicis) in honor of his employer.These satellites are known to obey Kepler's laws.But there is a difficulty.It has always been said that there are five planets, the sun and the moon and seven celestial bodies; "seven" is a sacred number.Isn't the Sabbath the seventh day?Didn’t there used to be seven-branched lampstands and seven churches in Asia?So, what could be more appropriate than that there should be seven celestial bodies?But if one had to add the four moons of Jupiter, it made eleven—a number without mystery.For this reason, the old school denounced the telescope and refused to see through it, asserting that the telescope only makes people see illusions.Galileo wrote to Kepler, wishing they could laugh together at the stupidity of these "crowds"; It is clear from the rest of the letter that the "crowd" are the professors of philosophy who are trying to spell the moons of Jupiter away with "sophistry and sophistry, as if by magic spells." As we all know, Galileo was first convicted secretly by the Inquisition in 1616, and later publicly in 1633; at this second conviction, he declared his repentance and promised never to advocate the rotation or revolution of the earth.The Inquisition did what it wanted and ended science in Italy, where it had not been revived for centuries.But the Inquisition did not prevent scientists from adopting the solar center theory, and caused a lot of damage to the church due to their own ignorance.Happily there are Protestant countries where the clergy, however eager they may be to endanger science, cannot obtain the dominion of the state. Newton (1642-1727) followed the successful path pioneered by Copernicus, Kepler and Galileo to the final complete success.Starting from his own three laws of motion (the first two laws should be attributed to Galileo), Newton proved that Kepler's three laws are equivalent to the following theorem: All planets have an acceleration towards the sun at each moment, and this acceleration varies with The inverse square of the distance between the suns.He pointed out that the acceleration of the moon toward the earth and toward the sun conforms to the same formula, which can explain the motion of the moon; and the acceleration of falling objects on the ground is consistent with the acceleration of the moon according to the inverse square law.Newton defined "force" as the cause of a change in motion, that is, of acceleration.He was thus able to formulate his law of universal gravitation: "All bodies attract all other bodies, and this gravitational force is proportional to the product of the masses of two bodies and inversely proportional to the square of their distance." From this formula he was able to put all the things in the planetary theory, Such as the movement of planets and their satellites, comet orbits, tidal phenomena, etc. are inferred.It was later understood that, even with respect to planets, slight deviations of orbits from ellipses could be deduced from Newton's laws.This success is so consummate that Newton is in danger of becoming a second Aristotle, setting an impenetrable barrier to progress.In England it was not until a century after his death that people sufficiently cast off his authority to do significant creative work on the problems he had studied. The seventeenth century was remarkable not only in astronomy and dynamics, but also in many other aspects of science. First, let's talk about scientific instruments.The compound microscope was invented shortly before the seventeenth century, around 1590. In 1608, a Dutchman named Lippershey invented the telescope, but it was Galileo who first formally used the telescope in science.Galileo also invented the thermometer, which, to say the least, seems very likely. His pupil Torricelli invented the barometer.Guericke (GuerAicke, 1602-86) invented the air extractor.Clocks, while not new, were greatly improved in the seventeenth century, largely by the work of Galileo.Because of these inventions, scientific observation has become infinitely more accurate and far more extensive than ever before. Secondly, in addition to astronomy and dynamics, there have been major achievements in other sciences.Gilbert (1540-1603) published his great work on magnets in 1600.Harvey (1578-1657) discovered the circulation of blood and published his discovery in 1628.Leeuwenhoek (Leeuwenhoek, 1632-1723) discovered sperm cells, but another man named Stephen Hamm (Stephen Hamm) seems to have discovered it a few months earlier.Ravenhoek went on to discover protozoa, single-celled organisms, and even bacteria.Robert Boyle (1627-91) was the "Father of Chemistry, Son of the Earl of Kirk," as I was taught when I was young; This law says: For a certain amount of gas at a certain temperature, the pressure is inversely proportional to the volume. So far I have not spoken of advances in pure mathematics, but advances in this field are indeed very great and are absolutely necessary for much work in the natural sciences.Napier announced the invention of logarithms in 1614.Coordinate geometry was the result of the work of several mathematicians in the seventeenth century, of whom Descartes made the greatest contribution.Calculus was invented independently by Newton and Leibniz; it is the tool of almost all higher mathematics.These are only the most outstanding achievements in pure mathematics, there are countless other major achievements. As a result of the scientific undertakings mentioned above, the vision and views of learned people have been completely changed.At the beginning of the seventeenth century, Sir Thomas Braun was involved in a witch trial; at the end of the century, it would not have happened.In Shakespeare's time, comets were still ominous signs; after the publication of Newton's "Principia" (Principia) in 1687, it was known that he and Halley had calculated the orbits of some comets, and it turned out that comets and planets also obeyed the law of universal gravitation. The governing power of the law has firmly taken root in people's imagination, so that things such as magic and witchcraft cannot be believed. In 1700 the minds of learned men were thoroughly modernized; in 1600, with few exceptions, they were largely medieval. In the remainder of this chapter I want to touch briefly on the philosophical beliefs that appear to have been produced by seventeenth-century science, and on some of the ways in which modern science differs from Newtonian science. The first thing to notice is that almost all traces of biopsy have been eliminated from the laws of physics.The Greeks apparently regarded athletic ability as a sign of life, though they didn't say it explicitly.Observed according to common sense, it seems that animals move by themselves, while dead things only move when they are forced by external forces.According to Aristotle, the soul of an animal has various functions, one of which is to move the animal's body.In Greek thought, the sun and planets were often considered to be gods, or at least to be governed and moved by the gods.Anaxagoras thought otherwise, but he was an impious man.Democritus thought otherwise, but all but the Epicureans despised him in favor of Plato and Aristotle.Aristotle's forty-seven or fifty-five immobile movers are gods, the ultimate source of all motion in the heavens.Any inanimate body, if left to itself, will soon be at rest; and therefore the action of the soul on matter must continue in order for the motion not to cease. All this is changed by the first law of motion.Inanimate matter, once set in motion, will go on forever unless it is stopped by some external cause.Moreover, the external causes of a change in motion are always material in themselves, so far as they can be ascertained with certainty.In any case, the solar system runs on its own momentum and its own laws; there is no need for outside interference.It may still seem that God was needed to set the mechanism in motion; according to Newton, the planets were originally thrown by the hand of God.But when the gods stopped doing this and announced the law of universal gravitation, everything went on by itself without any further intervention from the gods.The place of the gods in the course of nature was again lowered when Laplace suggested that perhaps it was the forces now at work which caused the birth of the planets from the sun.God may still be the Creator; but since it is unclear whether the world had a beginning of time, even this is doubtful.Although most scientists at the time were exemplars of pious faith, theologians were rightly disturbed that the opinions inspired by their careers were detrimental to orthodoxy. Another thing science cites is a profound change in thinking about humanity's place in the universe.In the Middle Ages, when the earth was the center of space, everything had a purpose connected to man.In Newton's time, the earth was a tiny satellite of a star that was not particularly prominent; astronomical distances made it a mere pinpoint in comparison.It seems absolutely impossible, this huge cosmic mechanism is all intentionally arranged for the benefit of some small creatures on this needle point.What's more, "purpose" has been an intrinsic part of the concept of science since Aristotle, and is now expelled from the scientific method.Anyone can still believe that heaven exists to proclaim the glory of God, but no one can let this belief interfere with astronomical calculations. The universe may have a purpose, but "purpose" can no longer have a place in scientific explanation. The Copernican theory, which was supposed to hurt human pride, actually had the opposite effect, because the glorious triumph of science revived human pride.The dying ancient world seemed to be haunted by a sense of guilt, which bequeathed the anguish of guilt to the Middle Ages.It is right and wise to be humble before God, for God always punishes the proud.Plagues, floods, earthquakes, Turks, Tartars, and comets have bewildered gloomy centuries, and it is felt that nothing but humility can avert these present or imminent disasters.But when people sing triumphantly: Nature and its laws are hidden in darkness.God said, "Let there be Newton," and everything will become bright. At this time, it is impossible to remain humble. As for eternal punishment, the Creator of the vast universe must have better things to worry about, so as not to send people to hell for a slight theological mistake.Judas Iscariot may have been condemned forever, but Newton, even if he had been an Arian, would not have been in hell. There are, of course, many other reasons for complacency.The Tatars have been confined to the borders of Asia, and the Turks have gradually become less of a threat.The comet killed Halley's dignity; as for the earthquake, it's still horrific, but it's so interesting that scientists have little regret about it.Western Europeans became rich rapidly, and gradually became the masters of the world: they conquered North and South America, they were powerful in Africa and India; they were respected in China, and feared in Japan.All this, and the glorious triumphs of science, it is no wonder that the man of the seventeenth century felt himself not the despicable sinner he professed to be on Sunday, but the very good man. There are certain aspects in which the concepts of modern theoretical physics differ from those of the Newtonian system.Let me first talk about the concept of "force" which was prominent in the seventeenth century, which is already known to be superfluous.According to Newton, a "force" is the cause of a change in magnitude or direction of motion.The concept of "cause" is important, while "force" is imagined as something that is experienced when something is pushed or pulled.For this reason, the fact that gravitation works over distances was taken as an objection to the theory of universal gravitation, and Newton himself admitted that there must be some medium through which gravitation is transmitted.People gradually discovered that all equations can be written without introducing the concept of "force".What can be observed in the field is a certain relationship between acceleration and orientation configuration; saying that this relationship is caused by "force" as a medium is equivalent to adding nothing to human knowledge.It is known from observation that the planet always has an acceleration towards the sun, and this acceleration varies inversely with the square of the distance between the planet and the sun.说这事起因于万有引力的“力”，正好像说鸦片因为有催眠效能，所以能催人入眠，不过是字句问题。所以现代的物理学家只叙述确定加速度的公式，根本避免“力”字；“力”是关于运动原因方面活力论观点的幽魂发显，这个幽魂逐渐被祓除了。 在量子力学诞生以前，一直没出现任何事情来略微变更头两条运动定律的根本旨趣：就是说，动力学的定律要用加速度来表述。按这点讲，哥白尼与开普勒仍应当和古代人划归一类；他们都寻求表述天体轨道形状的定律。牛顿指明，表述成这种形式的定律决不会超乎近似性定律。行星由于其它行星的吸力所造成的摄动，并不作·准·确·的椭圆运动。同样理由，行星轨道也决不准确地重复。但是关于加速度的万有引力定律非常简洁，牛顿时代以后二百年间一直被当成十分精确。这个定律经过爱因斯坦订正，依旧是关于加速度的定律。 固然，能量守恒定律不是关于加速度而是关于速度的定律；但在应用这条定律的计算中，必须使用的仍旧是加速度。 至于量子力学带来的变革，确实非常深刻，不过多少可说还是争论不定的问题。 有一个加到牛顿哲学上的变革，这里必须提起，就是废弃绝对空间和绝对时间。读者会记得，我们曾结合讲德谟克里特谈到过这个问题。牛顿相信有一个由许多“点”构成的空间，一个由许多“瞬刻”构成的时间，空间和时间不受占据它们的物体及事件影响，独立存在。关于空间，他有一个经验论据支持其个人意见，即物理现象令人能辩认出绝对转动。假如转动桶里的水，水涌上四围桶壁，中央下陷；可是若不让水转动而转动桶，就没有这个效果。在牛顿时代以后，设计出了傅科摆实验，大家一向认为这实验证明了地球自转。即便按最现代的意见，绝对转动问题仍然造成一些困难。 如果一切运动是相对的，地球旋转假说和天空回转假说的差别就纯粹是辞句上的差别；大不过像“约翰是詹姆士的父亲”和“詹姆士是约翰的儿子”之间的差别。但是假若天空回转，星运动得比光还快，这在我们认为是不可能的事。 不能说这个难题的现代解答是完全令人满意的，但这种解答已让人相当满意，因此几乎所有物理学家都同意运动和空间纯粹是相对的这个看法。这点再加上空间与时间融合成“空时”，使我们的宇宙观和伽利略与牛顿的事业带来的宇宙观相比，发生大大改变。但是关于这点也如同关于量子论问题，现在我不再多谈。