Today the Department of Astronomy has an important lecture, and the astronomy students all took leave together, so that attendance in class fell to a new low; in the second period, only 3 people were left…… Although I do not require attendance every time, such a dismal turnout is still rather depressing. It seems I need to think of some way around it.
There was a similar phenomenon when I used to take Professor Wu’s class: once the semester had entered its latter half and reached the stage of the Scientific Revolution, attendance actually dropped by quite a lot. Perhaps after half a semester of classes everyone was simply exhausted, but it is a pity to miss the most exciting period. Of course I post the full lecture notes every time, so students who miss class can make up for it, but I do not think that is the main reason for the low attendance. My guess is that students who miss only an occasional class may come to the blog to read the lecture notes, and even students who attend carefully may read them again after class to review; but students who almost never come, I do not really believe they will read the lecture notes every time.
Although I do not require attendance, this course still has regular-course assessment, and for the midterm we require a reading report or an essay, which is more or less due in these next few weeks (I have already received one yesterday). I mention that this assignment is negotiable: if you are confident that you can write a good final paper, or if you simply do not care about grades and absolutely want to slack off, then the midterm assignment can be skipped. If you often engage in discussion in class and your final paper is not bad, I certainly will not be stingy with the grade; but if you almost never show up, do not hand in the midterm assignment, and your final paper is not much good either, then the grade will not look pretty. The premise of everything being negotiable is that you actually have to negotiate with me……
In short, I still hope that those enrolled in the course will come more often to support the class. Although I may not teach very well, in class we can at least discuss things directly, and any questions can be raised at any time.
By next week we should more or less have finished discussing the period of the Scientific Revolution. I am planning to organize a classroom discussion for the week after next. At that time I myself will not have much to say; at most I will add a few supplements and bits of gossip. Even if the students have not completed their reading reports, they should at least have read some books, and after half a semester of lectures they should have some thoughts of their own. Then everyone will have a chance to speak, and I will also have a good chance to memorize everyone’s names again. I hope the students will try their best to be present then~
Last time we talked about the Copernican Revolution, and Copernicus is regarded as the sign that the Scientific Revolution had begun. Of course, as we saw last time, Copernicus himself and his writings were actually very conservative. The significance of Copernicus lies less in what he said than in what he made others say. The problems he left behind were more important than the ones he solved. The boundary between heaven and earth was broken, the universe became unimaginably empty, and then the supposed perfection and imperishability of the heavens, as well as the round crystalline spheres, were one by one shattered.
Thus the impact of the Copernican Revolution went far beyond astronomy, because these cosmological issues had from ancient times been bound up with physics and ethics as well.
This class will focus mainly on the field of physics.
The new astronomical system directly demanded solutions to two physical problems: first, if the earth is moving at high speed every moment, why are people not flung off? Second, if the heavenly bodies are not driven by eternally rotating crystalline spheres, and if the universe is empty, then what is driving their motion? We now know that the answer to the first question is “inertia,” and the answer to the second is “universal gravitation”; these two answers were precisely completed in Newtonian mechanics. So we say that from Copernicus to Newton, from astronomy to physics, from *On the Revolutions of the Heavenly Spheres* in 1543 to *Mathematical Principles of Natural Philosophy* in 1687, there runs the main plotline of the Scientific Revolution.
This is not to say that physicists had to wait until after Copernicus before starting to solve problems. In fact, after Aristotle, his natural philosophy was always the object of scholars’ disputes, and physics and mechanics had their own separate lines of development; it was just that these lines ultimately converged with astronomy during the Scientific Revolution. The “convergence” of these lines is itself an important matter: only the breaking of the distinction between heaven and earth made the convergence of astronomy and physics possible, and the merger of physics and mechanics has an even deeper significance.
That’s right, we need to talk about the merger of physics and mechanics. A lot of histories of science do not discuss this, and even some specialized histories of mechanics do not give it much attention: that is, before modern times, mechanics and physics were completely different concepts, two very different scholarly traditions. Yet when we now speak of modern physics, we mean Newtonian mechanics, as if the two concepts were perfectly identical. Compared with the convergence of astronomy and physics, the convergence of physics and mechanics is not just a convergence; they even seem to have “fused,” and yet we take this for granted. That itself is very strange.
Below, let us first talk about the content that general histories of science usually discuss, namely the theories associated with Galileo and Newton, and then we will turn to the issue of “mechanics.”
In Aristotle’s natural philosophy, an object needs to be pushed in order to move. This is also a fairly commonsense view, but could the natural philosophers in the Aristotelian tradition really not see inertial phenomena? For example, something thrown into the air continues moving for a long time after it leaves the hand; or again, if you jump vertically on a ship moving at constant speed, you still land back in the same place. Of course they did not completely ignore these phenomena, and these phenomena were not entirely inexplicable. For instance, a typical way of explaining them was by the carrying along of air: a moving ship not only carries the passengers on board along with it, but also drags the surrounding air along with it, so as long as you do not jump too high, you are still being carried by the ship and will naturally continue forward together with it. In fact, Copernicus himself adopted this explanation. He believed that the earth’s rotation also carries all objects on the ground and the air along with it in rotation, which is why people do not feel it. As for objects thrown into the air, it is because the thrower not only pushes the object, but also pushes the air around it; after the projectile leaves the hand, layer upon layer of air continues to exert a push on it and on the next layer of air.
This explanation, though not perfect, was by no means wholly unreasonable. The reason for insisting that motion requires an external force to push it is related to Aristotle’s distinction between natural motion and forced motion. Aristotle believed that some motions are natural, such as earth’s sinking and fire’s rising, because each element has its own “natural place”: the natural place of earth is near the center of the universe, while the natural place of fire lies in the highest layer of the sublunar world. Thus the motion by which these elements return to their natural positions does not need to be compelled by external force; therefore the falling of a stone does not require a mover, or one might say that it moves itself by itself. But the motion of things away from their natural place is unnatural. “Natural” means that the cause lies within the thing itself; “unnatural” means that the cause lies outside it. So if a stone is thrown upward, there must be some cause at work outside the stone.
We know that in Newtonian mechanics, an external force is considered the cause of change in motion, not the cause of motion itself. But this is less a new discovery than a new definition, a re-understanding of the concepts of motion and cause. In Aristotle, the concept of “motion” was relatively broad; roughly speaking, it corresponded to what we now call “change.” Aristotle distinguished four kinds of motion, or rather four kinds of change: generation and corruption, quantitative change, qualitative change, and local motion. Today we basically limit the concept of “motion” to local motion, and, as we shall mention later, that is the achievement of mechanistic philosophy. But in Aristotle, local motion was not in a primary or privileged position; he was more concerned with qualitative change, and so were later medieval scholastics. We mentioned earlier the scholar Oresme, who obtained the mean-speed theorem; what they first considered was a graphic method for qualitative change, such as the “rectangle of temperature,” and only later did they extend this method to local motion.
So before the modern law of inertia could be obtained, many concepts needed to be redefined. Only by separating the concept of motion from the concept of change, and by preparing concepts such as speed and acceleration, can we begin to speak of so-called “changes in motion” and the like.
We mentioned last time that the very idea of the Scientific Revolution reminds us that science is not merely a simple accumulation of one new discovery after another; the more crucial matter is the overall transformation of the conceptual framework. When the conceptual framework has not yet been prepared, many things simply will not occur to you to observe, and even when you do see other things, you may understand them differently. So the mechanics revolution we are discussing today is far more than the discovery of a few laws of mechanics; more importantly, the various concepts involved behind it have all changed beyond recognition.
We have said that much of this sorting out of concepts was done by medieval scholastics; however, even by the time of Galileo, Aristotle’s habitual way of thinking was still at work. For example, Galileo still did not completely abandon the distinction between natural motion and forced motion; he believed that free fall is natural motion.
Whenever Galileo is mentioned, people usually think of the famous legendary experiment of dropping objects from the Leaning Tower of Pisa: it is said that Galileo let two balls fall simultaneously from the top of the tower and found that the heavier ball and the lighter ball landed at the same time, thereby refuting the Aristotelian claim that heavier objects fall faster.
We do not know whether Galileo himself really did experiments on the Leaning Tower of Pisa, but examination of Galileo’s manuscripts shows that he probably did conduct similar experiments. Yet the experiment itself is not the most important point. In fact, a little earlier Stevin (1548–1620) also did experiments, and even in the 6th century Byzantine scholars did similar experiments.
These experiments did indeed show that heavy and light balls hit the ground at roughly the same time, but at most this can be said to challenge Aristotelian physics; it is still far from negating Aristotelian physics as a whole. We would say that in many cases the reason heavier objects seem to hit the ground faster is air resistance, but Aristotle could also say that the reason we observe heavy and light balls falling at about the same speed is also due to the medium of air. For instance, we can do another experiment: put two balls in water and let them fall, and we will find that, with equal volume, the heavier ball is indeed faster than the lighter one. In Aristotle’s view, motion has speed in order to overcome the resistance of the medium; if there were no medium, the object should reach its destination directly, that is, with infinite speed. Of course Aristotle denied the existence of a true vacuum, but we can also imagine that the thinner the medium, the more negligible the resistance to motion, and the smaller the speed difference between heavy and light objects.
Therefore, for this free-fall experiment to be regarded as a refutation of Aristotle, it also required a series of conceptual reconstructions, including new understandings of motion and space, including the recognition that air resistance and the buoyancy of water are two different things, and so on. Of course, the most crucial point is that Galileo did not merely refute Aristotle qualitatively; he also gave a quantitative law for free fall, namely that “the distances traversed by objects falling from rest in equal intervals of time are proportional to odd numbers beginning with 1.”
We have mentioned that the mean-speed theorem for quantitatively calculating uniformly accelerated motion had already been given by the scholastic philosophers. But the problem with the scholastics was that they remained at the level of hypothesis and did not connect their theoretical imaginings with the real world. They studied a hypothetical uniformly accelerated motion, but did not consider which motion in the real world it actually corresponded to, let alone connect it with free fall.
Galileo’s contribution was to integrate theoretical imagination and experimental research: he designed experiments on the basis of theoretical conceptions, and then interpreted the results theoretically.
Galileo did not first perform a large number of experiments and only then analyze the quantitative relation. From the start, he concluded that free-fall motion is uniformly accelerated motion, that is, velocity is proportional to time. His reason was that “nature likes simplicity.” He said, “Since nature has already endowed falling heavy bodies with some special acceleration…… in carrying all this out, she is accustomed to use the most ordinary, simplest, and easiest means…… there is nothing simpler than an increase or growth that is repeated forever in exactly the same way.”
We say that Galileo still adhered to Aristotle’s concept of “natural motion,” and since he considered free fall to be natural motion, then because it is natural, it should be accomplished in the simplest and most economical way. Of course it cannot be uniform motion, because the initial velocity is 0. So if it is accelerated motion, it must accelerate in the simplest way, which would be uniformly accelerated motion.
The mean-speed theorem for uniformly accelerated motion had already been obtained by the scholastics, and Galileo also said that everyone knew this, so the problem was how to verify that free-fall motion is uniformly accelerated motion. On the one hand, Galileo grasped this through an intuitive understanding of nature’s simplicity, but on the other hand he certainly also recognized the importance of experimental research; yet Galileo’s experiments were mainly intended to demonstrate, not to expect that one could directly infer laws from them.
So Galileo’s famous “inclined-plane experiment” was meant to confirm that actual free-fall motion is the same as the uniformly accelerated motion of theory, rather than to find the formula for uniformly accelerated motion. By measuring balls rolling down an inclined plane, Galileo proved that this is uniformly accelerated motion, thereby confirming that free-fall motion is also uniformly accelerated motion.
But why does the rolling of a ball along an inclined plane prove that free fall is also uniformly accelerated motion? Galileo reasoned like this: in studying motion on an inclined plane, we find that the ball’s motion law is independent of the slope of the plane. Then we can imagine the limiting case of the inclined plane, one of which is that the plane becomes completely vertical, and that is free fall. The technology of the time could measure motion on gentler inclined planes, but could not precisely measure free fall; Galileo, however, through logical deduction, was convinced that his study of motion on inclined planes could be extended to free fall.
But here Galileo’s reasoning was actually wrong, because on any inclined plane of any slope, the ball is in essence rolling downward; while falling faster and faster, it is also rolling faster and faster, but in free fall the ball is not rolling. Therefore, in motion on an inclined plane, part of the potential energy is transformed, in addition to kinetic energy of the ball’s forward motion, into kinetic energy of the ball’s rotation; but in free fall, all of the potential energy is transformed into kinetic energy, so the results of motion in these two situations are certainly not the same. In fact, Galileo’s data for the free fall of cannonballs, which he claimed to have obtained through repeated experiments, was wrong; this was very likely because he had not in fact directly performed cannonball experiments, but instead extrapolated from the data of inclined-plane experiments.
So we should not overestimate the significance of experiments in early modern science. Galileo and the others’ experiments were more demonstrative than discovery-oriented; thought still came first. But the act of experimenting itself was still of major significance. It marked the unification of theoretical imagination and empirical research, the unification of the mathematical world and the real world. To believe that experiments can “demonstrate” theory, to believe that the mathematical rules of the natural world as conceived can be presented through artificially designed experiments—nature, artifice, and mathematics are unified. This is no small matter. So it is not without reason that philosophers such as Husserl regarded Galileo as a sign of the modern scientific “mathematization of nature.”
The limiting case of motion on an inclined plane is not only one in which the plane becomes completely vertical; there is another in which it becomes completely horizontal. Galileo discovered that a ball runs faster and faster when moving downhill, and slower and slower when moving uphill. So what happens if it neither goes uphill nor downhill? Galileo believed that, if there were no resistance, a ball on an infinite horizontal plane should continue moving indefinitely at its speed.
Here Galileo seems already to have obtained Newton’s first law, but unfortunately he was thinking a bit too much here. Galileo wondered whether such an infinite “horizontal plane” is possible. He noticed that a “horizontal plane” is different from a “plane,” and the two are only approximately identical on very small scales. We know the earth is round: if you walk along a “straight line” at one point, you are in fact continuously ascending. The actual “horizontal plane” should be an arc-shaped surface following the earth’s surface. Thus, the “inertia” in Galileo’s sense is not the tendency to maintain uniform straight-line motion, but the tendency to maintain circular motion around the earth. Galileo’s concept of motion was still, to a large extent, Aristotelian: it was directional, relative, and oriented toward some destination, rather than motion in Newton’s sense within an isotropic infinite space. So Newton’s notion of “absolute space” was not merely a redundant embellishment; precisely because Galileo did not absolutize space, he was unable to free himself from Aristotle’s restraints.
Below we will talk about Newton (1642–1727, old calendar December 25, 1642, new calendar January 4, 1643).
Newton was the synthesizer of the Scientific Revolution. His thought was, to a very large extent, a summation of his predecessors’ ideas, but that in no way diminishes Newton’s place in the history of science, because in the history of science integration itself is often far more important than proposing a single new idea in isolation. For example, the idea of heliocentrism had already been proposed by people in ancient Greece, but that idea was not integrated with other fields of astronomy or physics, and therefore did not spur scientific development at the time. Or again, the mean-speed theorem for uniformly accelerated motion had already been derived by medieval scholars, but it was not combined with actual observational experiments or with the study of falling bodies. In a certain sense, what the entire Scientific Revolution did was “integration” — the integration of heaven and earth, the integration of natural philosophy and mechanics, the integration of theory and experiment… eventually forming a unified, reductionist picture of the world.
Newton was just such an unparalleled master synthesizer, perhaps one who can be matched only by Aristotle of ancient Greece. Newton touched on almost every scientific field of the Scientific Revolution, and in each he attained extraordinary mastery.
In mathematics, he invented calculus; in astronomy, he discovered the law of universal gravitation; in optics, he discovered the composite nature of sunlight and invented the reflecting telescope (technologically); in mechanics, he systematically summed up the three laws of motion; in natural philosophy, he established the mechanical view of nature; in alchemy, too, he was highly productive, and was hailed as the last alchemist (in his later years he was probably afflicted by mercurial poisoning that led to mental depression); in religious theology, he also did a great deal of work, attempting to decipher the “code” of the Bible. In his later years, while serving as head of the British Royal Mint, he also promoted the eventual establishment of the gold standard; while serving as president of the Royal Society, he used his power to suppress opponents such as Hooke and Leibniz, getting bogged down in struggles over priority. For example, when he told the story of how, as a young man, he came to think of universal gravitation from an apple falling to the ground, it was in order to emphasize his independence and originality. In fact, Newton should probably have received many inspirations from Hooke, but his originality is still beyond doubt.
Whether in terms of his great achievements or the work that now seems not so admirable, Newton is highly representative, bringing together in one person the various threads and aspects of the entire Scientific Revolution. If you are interested, you can look for a few well-written biographies of Newton to read. We can see the whole era in each individual person, but a figure of Newton’s stature is obviously an even better window.
But our course in general history of science is mainly organized around problems and ideas, so we cannot talk too much. Especially today, we can only focus on the question of so-called “mechanics.” Later, when we get to alchemy and when we get to mathematics, we may mention Newton again, but we certainly will not be able to cover everything. I hope everyone will spend some time reading on your own outside class.
Let us return to the question raised at the beginning today: what exactly is “mechanics,” and how did it come to be combined with physics?
We know that the English word for 力学 is “mechanics,” and this word does not contain the concept of force. If translated literally, it should be “the study of machines,” and in Greek the word originally meant “machine,” while also carrying meanings like skill, device, and trick.
We have previously discussed Greek “natural philosophy,” and the concept of “nature” discovered by the Greeks: natural things bring themselves into being; nature stands in opposition to the artificial. Machines, skill, tricks, and so on are precisely typical instances of the artificial.
So Greek “mechanics” is precisely a discipline opposed to natural philosophy. A work under Aristotle’s name, the Mechanical Problems, clearly establishes the position of mechanics. The Mechanical Problems was considered a work of Aristotle all the way until the seventeenth century, but later we learned that it was very likely a pseudonymous work written by someone after the Aristotelian school who attached Aristotle’s name to it. Still, it can reflect the Greek concept of mechanics.
The Mechanical Problems begins by stating its theme plainly:
We are puzzled, first, when there occurs an event that is contrary to nature but for which the cause is unknown; second, when an event is brought about by art for the benefit of man and in opposition to nature. For nature’s operation is often not suitable to man’s convenience, because nature always follows the same course without deviation, whereas man’s convenience is always changing. So when it is necessary for us to do something contrary to nature, the difficulty it causes us is puzzling, and therefore we must resort to art. That part of art which helps us deal with these puzzles we call mechanical skill (mechane).[Mechanics, 847a10–847a20, Aristotle 1984, p. 1299] (cited from Zhang Butian: “The Evolution of the Meaning of Mechanics from Ancient Greece to the Early Modern Period”)
However, mechanics was by no means completely unrelated to natural philosophy; rather, it seems to have established some kind of connection between mathematics and natural philosophy.
Archimedes and Hero in the Hellenistic period both had rich studies of mechanics — that is, studies of machine mechanics. Hero classified all machines into five “simple machines”: the lever, wheel-and-axle, pulley, wedge, and screw. Complex machines are composed out of simple machines; for example, gears are made by combining wheel-and-axle and wedge. Hero further reduced the simple machines to a mechanism of two concentric circles.
The image below shows various machines depicted in an encyclopedia from 1728. “Simple machines” seems to be a bit more numerous than Hero’s five, but in any case mechanics is the study of these machine elements and their mathematical principles.
These ancient mechanical texts were not widely circulated in Europe during the Middle Ages, and were only rediscovered in the sixteenth century. Yet in the Middle Ages, the concept of “mechanics” also existed. We know that medieval education included the seven “liberal arts,” which were non-utilitarian, noble disciplines aimed at improving the cultivation of the soul; opposed to them were the so-called “mechanical arts,” namely utilitarian, servile, lowly arts.
The twelfth-century French scholar Hugh of St Victor (约 1078－1141) listed seven “mechanical arts”: “weaving, armament, trade, agriculture, hunting, medicine, and stage performance.”
Although medieval people did not denigrate craft activities in the way the Greeks did, and these mechanical arts were also treated as serious knowledge, compared with the liberal arts their “prestige” was still clearly lower.
It was not until the Renaissance, with the rediscovery of ancient mechanical writings, and perhaps also because of scholars’ attitudes toward craftsmen, that the “prestige” of mechanics rose. It came to be called an “intermediate science” or “mixed mathematics,” some field lying between mathematics and natural philosophy.
Galileo seriously studied the mechanics of Aristotle and Archimedes, but he believed that machines were not, as Aristotle had it, “superior to nature in intelligence,” but rather imitated nature. The lever and pulley were not some anti-natural trick, but instead revealed the ingenious workings of nature itself.
At this point, mechanics still retained the basic meaning of machine mechanics, but its meaning rapidly expanded, and in the end, among mechanistic philosophers such as Descartes and Boyle, it gradually became equated with physics itself.
The French philosophers Pierre Gassendi (1592–1655) and René Descartes (1596-1650) were representative figures of mechanistic philosophy; they tried to explain everything in terms of matter and motion.
In mechanistic philosophy, motion meant nothing more than translational motion; quantitative change and qualitative change were merely surface phenomena, while in essence they were still caused by the mechanical motion of material particles. Mechanists distinguished between primary qualities and secondary qualities. They believed that primary qualities were intrinsic to things, such as shape, extension (spread in space), motion, and impenetrability — which is precisely the property of ordinary machine parts — whereas secondary qualities refer to things like color and odor. They believed that these qualities are not intrinsic to things, but rather are elicited in people’s senses by things, while their essence is still determined by the shape of particles; for example, sharper particles are more likely to produce a spicy taste. Secondary qualities are secondary; as long as we study the external form of things, we can know everything.
In short, mechanistic philosophy regarded the entire universe as a machine, that is, as something wholly external, whose operating mechanism can be grasped simply through the shapes of things and their mutual collisions. From then on, mechanics became physics itself.
We have spoken of the convergence of mechanics and physics, but we find that up to now we still have not touched on the concept of “force.” So what on earth is “force”? Where did it come from?
If the history of science had developed only up to this point, then we would find that translating “mechanics” as “力学” was completely wrong; it would simply be “machine mechanics,” with no “force” involved. Yet we also know that “force” is indeed the core of “Newtonian mechanics.” So much so that when we now see the translation “力学,” we do not feel it is inappropriate at all.
So what on earth is this “force” in “Newtonian mechanics”?
Let us first look at a person named Empedocles, an ancient Greek natural philosopher whom we have not talked much about before. In fact, he was a very interesting figure. Like Pythagoras, he was a legendary person who combined the roles of thinker and religious leader. According to legend, in the end he leapt into a volcanic crater in order to proclaim to his followers that he had become an immortal deity.
Empedocles proposed the theory of the four elements, holding that things are composed of earth, water, air, and fire. The elements themselves are unchanging, while the powers of “love” and “strife” cause the elements to come together or separate from one another, producing various motions and changes.
Empedocles’ doctrine of love and strife sounds absurd today. We know that in modern science, it was Newton’s mechanics, not Empedocles’ doctrine of love, that successfully explained the motion of things.
But hold on: what exactly is the difference between “Newtonian mechanics” and “Empedoclean love theory”?
Let us think about it: if we replace all instances of “force” in Newton’s mechanical system with “love,” change F to L, and define one “Empedoc” as the love that can give a 1 kg object an acceleration of 1 m/s², then instead of saying that there is a force of 1 newton between two bodies, we would say that there is a love of 1 emped between them — and “Empedoclean love theory,” after such substitution, would be completely equivalent to “Newtonian mechanics,” with no difference whatsoever in the precision of explanation.
That is to say, Newtonian “force” is in some sense accidental. It is not that we must use the concept of force to explain natural phenomena; we could have Empedoclean love theory, Zhang San tease theory, Li Si compel theory… We could use any symbol whatsoever to take the place of force.
Newton’s laws are less a matter of Newton having discovered the essence of “force” than of Newton having redefined “force”: force is the cause that makes motion change, and the magnitude of force can be measured by the mass of the object and the extent of the change in its motion — that is, its acceleration. In fact, if we define the cause of change in motion as love or as anything else, whether it is F=ma or L=mb, the effect is the same.
But I must say that, in the history of science, Newtonian mechanics was by no means accidental. Why did Newton succeed not with some other concept, but with the concept of force? There are reasons for that.
First of all, we should note that the concept of force originally was also not closely related to the concept of machine. Whether in Chinese or in Western languages, “force” (vis / force) and “machine” (machine) are neither synonymous nor of the same origin.
In Chinese, the original meaning of 力 is something like “strength” or “physical power,” from which are extended action-images such as “to strive,” “to exert effort,” and “to push with force,” and further extended senses such as power, magic, vitality, and so on. In Western languages, the Latin vis means vigor or vitality, while force leans more toward pressure and coercion. As for the word machine, from the very beginning it meant means, tool, device, equipment.
We notice that force and machine are not merely unrelated; they also evoke mutually conflicting images. The former always refers to something internal, living, and volitional, whereas the latter always refers to something external, cold, and material.
Since “force” and “machine” are so different, how did “mechanics” and “machine mechanics” come to be taken as the same concept so naturally? Something marvelous and important must have happened here — when two similar people end up together, that may be an unremarkable, matter-of-course affair, but when two people utterly incompatible and at odds with each other come together, then there must be a story behind it. Let us see how that story unfolds.
We mentioned that physics and mechanics came together in modern science, and this is a very strange thing. Physics is natural science, which studies the realm of interiority, while mechanics studies purely external things. How could the boundary between interiority and exteriority possibly be broken? We said that among mechanistic philosophers such as Descartes, mechanics and physics had already converged, but this convergence was unsuccessful. Descartes merely made some qualitative imaginings about the mechanical universe, but he did not successfully mathematize the universe’s mechanical mechanism. This was because some stubborn traditional concept still remained outside the mechanical world, and only after Newton stealthily redefined this concept did the mathematization of nature succeed. That concept is force.
The concept of “force” seems from the very beginning to have been a key that opens up the realms of interiority and exteriority alike, precisely because it carries with it some kind of “anthropomorphic association.” Whether “vitality,” “strength,” “energy,” or the derivative images of “exerting force,” “applying force,” and “imparting force,” and so on, the associations this word evokes are often related to humans, or more precisely, to a person’s will or body.
Aside from natural things in the realm of interiority and technical tools or mechanical devices in the realm of exteriority, in the classical world there seems to have been another special domain, namely the existence of “human beings” — human beings are both a kind of “natural thing” that takes itself as its own principle, and also the ultimate source of artificial things. As the maker of artifacts, the human being is the external cause of a machine’s operation; as a natural being, the human being interrupts the pursuit of external causes. In other words, the human seems to be both the end of nature and the beginning of the machine, the link between nature and mechanics. And the concept of “force,” by virtue of its distinctive anthropomorphic associations, achieved precisely this linking of interiority and exteriority: on the one hand, associations like “push,” “exert force,” and “apply force” direct “force” toward the realm of exteriority; on the other hand, associations like “vitality,” “energy,” and “capacity” turn “force” back toward the realm of interiority,
Before Newton, when scientists thought about the concept of force, what they often had in mind was something like “vitality” inherent in the body. This way of thinking of force as an inner power of things is a reverberation of the line of inquiry into interiority that has run from ancient Greek natural philosophy onward.
Thus, Newton’s act of bringing the status of “force” back to the center of science would naturally be regarded by mechanists of the time as a revival of Aristotelian natural philosophy. In Kuhn’s words: “For most seventeenth-century corpuscularians (note: corpuscularism is roughly mechanistic philosophy, reducing all phenomena to the mechanical motion of material particles), the concept of gravitation as an intrinsic principle of attraction seemed too much like the Aristotelian ‘tendency toward motion’ that they had unanimously rejected. The huge advantage of Descartes’ system lay in the fact that it completely eliminated all such ‘occult qualities.’ Descartes’ particles were entirely neutral, and gravity itself was explained as the result of collisions; the concept of an intrinsic principle of attraction at a distance seemed like a retreat to the mysterious ‘sympathies’ and ‘potentialities’ that made medieval science so absurd.”
Indeed, can force really provide a good explanation? For example, why does an apple fall downward? You say it is because there is a mutual force of attraction between the apple and the earth. How is that different from saying that the apple and the earth “love” each other? The concept of “force” looks mysterious; in fact it is mysterious. No wonder mechanistic philosophers at the time were very wary of Newtonian mechanics, whereas we now think nothing of it.
In other words, when Newton brought the concept of “force” to the center of mechanistic science, that too necessarily accompanied the rebirth of some line of thought about the “interiority” of an “inner tendency” or an “inner principle.” Yet this seems to be a kind of strategy of first suppressing and then elevating, a sleight of hand that, by smuggling in a different meaning of the concept of “force,” stripped it of its sense of interiority and thus completely expelled the Aristotelian line of natural philosophy from modern science.
Newton’s transformation of the concept of “force” lay not only in its successful mathematization, or rather its precise definition, but also in the way he reshaped the connection between “force” and “cause”:
On the one hand, Newton removed the interiority of “force.” Definition 4 of the *Principia* plainly states: “An external force is a pressure exerted upon a body, making it change its state of rest or of uniform motion in a straight line. — Such a force exists only while it is acting, and after the action ceases it does not remain in the body, because a body maintains the state it has acquired only by its inertia. External forces have various sources, such as impacts, squeezes, or centripetal force.”
Although Newton still retained expressions such as “inertial force,” the “force” of classical mechanics from then on was nonetheless conceived after the model of “external force”; that is to say, as the cause of changes in a body’s motion, it cannot be within the body itself.
So, is “force” then a kind of external cause? Probably not either; at the very least, it changed the mechanistic tradition’s understanding of external cause. In mechanistic philosophy and in ancient philosophy, “cause” is always understood as another body. Thus the transformation in the status of “force” in Newtonian mechanics is not merely a shift from “the cause of motion” to “the cause of changes in motion.” In fact, in ancient science “force” was never “the cause of motion” either. If A exerts a pushing force on B, thereby causing a change in B’s motion, then as far as the efficient cause is concerned, what matters is not that “pushing force,” but the thing “A” itself.
In short, within the traditional line of thought, if “force” is understood in terms of interiority as “vitality” or “potentiality,” it should be regarded as the cause of motion internal to a thing; whereas if it is understood in terms of exteriority as “push” or “impact,” then “force” is in fact precisely the occurrence of “causal relation” itself—when the acting agent as cause gives a force to the patient as effect, the two become a causal relation; force is the transmission of causality, not cause itself. Newton’s “force,” however, both retained the meaning of “cause” from the line of interiority and was also entirely constructed according to mechanistic thinking in the line of exteriority.
We know that Newton’s third law states that action and reaction are equal in magnitude and opposite in direction. This law seems unremarkable, but in fact it is highly subversive. Given the establishment of Newton’s third law, an external “force” could no longer “transmit” any traditionally imagined causal relation. For what is called a causal relation means that one thing is the cause and another the effect, and the two always have a logical and temporal distinction of priority and posteriority. When Aristotle imagined acts of pushing, he explicitly expressed the difference in status between the two: “To sum up, teaching and learning, or acting and being acted upon (the active and the passive, the pusher and the pushed), are not wholly identical; rather, what underlies them—the motion—is the same. For the activity by which A is realized in B is not the same in definition as the activity by which B, through the action of A, is realized.” And after Newton’s third law, force and reaction force, the one exerting force and the one receiving force, are completely equivalent; “universal gravitation” is everywhere, so do any two objects in the world then become mutual causes and effects? If so, then the concept of causality loses all meaning.
“Force” itself becomes the cause, but what is the point of saying that? What difference is there between saying “the cause of the change in B is that it was subjected to a force” and saying “the cause of the change in B is that it received love”? In other words, is “force” merely an empty word?
The problem had already been noticed in Galileo’s *Dialogues*:
When Simplicio (representing Aristotelian philosophy) answers the question “Why do heavy objects fall?” with “gravity,” Salviati (representing Galileo) says: “‘You are mistaken, Signor Simplicio; you should say: everyone knows that it is called gravity.’ He goes on to say that describing a frequently occurring phenomenon with a specific name can indeed make us imagine that we have attained a certain degree of understanding, but all our so-called explanations of natural phenomena ultimately amount to assigning names to causes that are essentially unknown: ‘gravity,’ ‘force,’ ‘impressed force,’ ‘forming intellect,’ ‘auxiliary intellect,’ or, in general, ‘nature.’”
As Salviati says, if classical mechanics merely makes “force” into a “cause” in order to explain phenomena, then it has explained nothing at all, having merely changed a “name.”
But the explanation offered by classical mechanics is indeed meaningful, because through the mathematical definition of “force,” an explanation in terms of force as cause implies a certain determinate measurement and prediction. When Newton uses “force” to explain things, certainly the name is arbitrary, but the entire set of rules of mathematical calculation and measurement that is given on the basis of this name is not arbitrary.
Therefore, it is not some real “force” that becomes the cause, but rather the mathematical system referred to behind the sign “force” becomes the “cause” explaining the phenomenon. In the development of classical mechanics, the concept of “force” is only a medium, a catalyzing medium. This medium performs a kind of feint or shell game, allowing the tradition of natural philosophy in the realm of interiority and the tradition of mechanics in the realm of exteriority to permeate one another, so that the core concerns of both are ultimately dissolved into nothingness. In the end, all the ambiguity, mystery, and anthropomorphic metaphors of the concept of “force” are hollowed out, and it is mathematics that, under the name of “force,” takes over the new domain of “nature.” Mathematics is no longer merely a tool for studying the mechanisms of natural things; it becomes “nature” itself. It is not merely a language describing causal relations among things, but becomes the “cause” of things—when Aristotle wanted to investigate causes, what he sought was some inner potentiality of a thing or some other thing acting as a mover; when a scholastic philosopher wanted to investigate causes, what he sought was some construct such as a “hidden quality” or “forming intellect”; when a modern scientist wants to investigate causes, he usually seeks, under the name of “force,” a formula written in mathematical language.
But can mathematics as cause satisfy humanity’s questioning of causes? And has the question of “nature” in the tradition of interiority thereby lost its meaning? Although the mathematized mode of inquiry in classical mechanics has achieved tremendous success, the fact that one question has not received a satisfactory answer does not mean the question itself is illegitimate. It is like searching in a dark, dense forest, which makes people confused, while searching for things on an open plain is clear and straightforward. Does that mean one should stay away from the forest and search only in the open? If you searched in the forest for two thousand years and remained dazed and found nothing, while spending two hundred years on the plain and gathering cartloads of things, does that prove that you should never again set foot in the forest? — But the key is not whether the terrain is clear or the harvest abundant; the key is, what exactly are we trying to find? If what we are looking for is still buried deep in the forest, then what is the point of digging up pile after pile of stones on the plain? In the transition from classical science to modern science, we must not only pay attention to how much more precise the new science is conceptually, how much more efficient it is methodologically, and how much richer its results are; we must also pay attention to how the thing we seek has changed.
Further Reading
I. Bernard Cohen: 《The Birth of a New Physics》
Burt: 《The Metaphysical Foundations of Modern Physical Science》
Dijksterhuis: 《The Mechanization of the World Picture》
Translated from the Chinese original with AI assistance. The original text is authoritative.
Leave a Reply