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Thought Experiments and Inertial Motion: A Golden Thread in the Development of Mechanics

Mark Shumelda e James Robert Brown
p. 71-96

Abstract

The history of mechanics has been extensively investigated in a number of historical works. The full story from the Greeks and medievals through the Scientific Revolution to the modern era is long and complex. But it is also incomplete. Studies to date have been admirably thorough in putting empirical discoveries into proper perspective and in making clear the great importance of mathematical innovations. But there has been surprisingly little regard for the role of thought experiments in the development of mechanics. We attempt to rectify this, at least in part. After a brief account of Greek ideas of space and motion, we focus on late medieval and early modern physics, especially the development of inertial motion. In particular, we examine the thought experiments of Buridan, Oresme, and Galileo, which did so much to undermine Aristotle’s account of motion and lead the way to the modern concept of inertia.

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1The history of mechanics has been extensively investigated in a number of historical works, including classic books such as Mach (1960), Dugas (1988), and Clagett (1961), and scores of articles in various academic journals. The full story from the Greeks and medievals through the Scientific Revolution to the modern era is long and complex. It is also incomplete. Studies to date have been admirably thorough in putting empirical discoveries into proper perspective and in making clear the great importance of mathematical innovations. But there has been surprisingly little regard for the role of thought experiments in the development of mechanics. Of course, many historians have rightly stressed the importance of reconceptualization in the history of science and further noted that this process was something different than the observation of new facts. But the focus has not been on thought experiments as the driving force behind such conceptual developments. In neither kinematics nor dynamics have thought experiments received their historical due in their ancient, medieval, classical (Newtonian) or modern (Relativity and Quantum Theory) forms, in spite of their obvious importance in the development of each. We hope, at least in part, to rectify this.

2Needless to say, we cannot hope to be exhaustive. We focus on only one theme – thought experiments in connection with inertia and relative motion. Even in this we are not starting from scratch. Ernst Mach, in the book cited above, paid homage to gedanken experimenten, as he called them. And Alexandre Koyré (1968) claimed that Galileo was primarily a thought experimenter. But these studies are only an important beginning. We hope to go beyond, but we are under no illusion of completeness, not even in the relatively narrow topic of thought experiments and motion. A full study of even a single period in the history of mechanics would, of course, include hard won empirical data, the development of instruments such as the telescope, and relevant mathematical innovations, as well as thought experiments. Again, we will focus only on the last. In short, our aim is to present a brief history of one aspect of mechanics via thought experiments.

3Readers might want us first to define thought experiments. We think it best to satisfy ourselves with only a rough characterization. Thought experiments are performed in the “laboratory of the mind.” They are imagined situations in which we typically set things up, let them run, and see what happens. Physicists often entertain hypothetical situations and reason about them, but thought experiments are more specialized – the hypothetical situation must be visualizable; it has an experimental character. As with real experiments, the result of a thought experiment could refute one theory, support another, or perhaps illustrate some difficult conceptual issue. And again like real experiments, they are fallible.

4Our history, narrow though it is, will be further truncated. It should start with the Greeks and finish with relativity, but we will confine ourselves, after some Greek preliminaries, to the late medieval period and the early Scientific Revolution, years that were crucial in the development of classical mechanics and the idea of inertial motion.

1. The ancient Greek worldview

1.1 The Presocratics

5As with so many things, there is no better place to start than with the Greeks. Early thinking about space was confused and confusing – but often ingenious. According to Aristotle (on whom we rely for much of our knowledge of the pre-Socratics),

  • 1 1 Aristotle, Metaphysics, A4, 985b4.

Leucippus and his associate Democritus hold that the elements are the full and the void; they call them being and not-being, respectively. Being is full and solid, not-being is void and rare. Since the void exists no less than body, it follows that not-being exists no less than being. The two together are the Material causes of existing things1.

6One can immediately see why the void was so controversial for the Greeks. The very expression of the idea is problematic. The void is nothing, it is non-being. So, one might naturally conclude that, since the void is nothing at all, it does not and cannot exist. That’s exactly what many, including Parmenides, did conclude. The idea of the void was dismissed as illogical nonsense. Yet, for many others, the void was necessary, for how otherwise could things move if they did not have empty room to move into?

7Parmenides and his followers flourished at about the same time as the early Atomists (5th century BCE). Their objection was simple: The void is nothing and nothing cannot exist as a thing. Whatever does exist must be a continuous, undifferentiated whole. Change requires things moving about, but this would be impossible, since there is no place for anything to move into. Consequently, the universe is unchanging, and the appearance of change and difference is an utter illusion – reality is wildly different than it seems.

8Zeno’s contribution to the Parmenidean outlook was generated by several famous thought experiments. They took the form of paradoxes in which he would show that the common sense supposition of motion leads to absurdities. In one of these paradoxes Zeno argues that it is impossible to traverse a stadium. Before getting to the other side, one must get to the mid-point. But before reaching the mid-point, one must get one quarter of the way, and so on ad infinitum. Thus, to traverse the stadium, one would have to pass through infinitely many distances in a finite time, and this was taken to be impossible.

9Another of Zeno’s paradoxes shows that Achilles cannot catch the tortoise, if the tortoise has a head start. It matters not how fast Achilles can run, how slow the tortoise moves, or how short the gap between them. If Achilles runs the distance to where the tortoise started in a given time interval, then the tortoise has moved ahead a bit. Achilles must now run that second distance, but during that time the tortoise has moved ahead a bit more. Though the gap between them is getting smaller, there are infinitely many such gaps to be covered, and this will be impossible for Achilles to achieve in a finite time.

10The conclusion that Zeno wants us to draw from his paradoxes is that our ordinary notions of space, time, and motion are confused and contradictory. His thought experiments support Parmenides by showing that the contrary view is absurd – even though it is unshakable common sense. Appearance and reality sharply diverge.

11As is so often the case in fundamental differences of opinion, one side’s modus ponens is the other side’s modus tollens. Parmenides and his followers thought the void is absurd, so they drew the conclusion that motion is impossible. The Atomists turned this around, claiming that motion is manifestly possible, and so they concluded that the void must exist, after all. What the two sides shared is the common premiss: motion requires the void. Greek thought about space and motion seemed at an impasse, at least until Aristotle (384-322 BCE).

1.2 Aristotle

12Space and time are part of Aristotle’s general theory of motion and change. Not only was he concerned with how an object changes from one spatial location to another, Aristotle was also interested in how an acorn changes into an oak tree. He was, in short, concerned with motion or change in a very general sense, and he made use of the concepts of potentiality and actuality in his explanation. There are a number of important ingredients in Aristotle’s account.

  • 2 2 The distinction between actual and potential infinity is central to all so-called constructive ac (...)

13First, the non-existence of the infinite. It’s a commonplace to say there are infinitely many points on a line. The great success of analytic geometry (which puts the real numbers into one-one correspondence with the points on a line) no doubt accounts for this widespread view. It has become unquestioned common sense. But is it true? Aristotle certainly thought not. There are no points on a line (or on a plane or in space), except those we make. The line, according to Aristotle, is a true continuum. It is infinitely divisible in the sense that it can be divided again and again without limit. If we make a cut in a line (say with a compass), then we construct a point. We may do this repeatedly and without limit; that is, we never arrive at a situation where we cannot do it again. But at any given stage in the process of constructing points, we have made only finitely many cuts in the line, never a so-called actual (or completed) infinity. The only infinity for Aristotle is the potential infinity2.

14With this account of the infinite in mind, Aristotle could tackle Zeno’s paradoxes. The crucial premiss in Zeno’s arguments is the assumption that space consists in an actual infinity of points and time in an actual infinity of moments. Aristotle’s theory of the potential infinite flatly denies this. So, Zeno’s arguments can’t even get started, since the necessary preconditions for the thought experiments do not exist.

  • 3 3 Aristotle, Physics, 212a20.

15Second, natural place and natural motion. Nature, according to Aristotle, is the cause of motion and change. Place is defined as “the innermost motionless boundary of that which it contains”3. The place of the wine is in the bottle; the place of the boat is in the water that immediately surrounds it. This is a relativistic view of spatial location, especially when motion is considered. But there is a hierarchy of locations. The place of the moving boat is in the water; the place of the flowing water is in the river banks; the place of the river banks is…, and so on. In the ultimate scheme of things there is the stationary centre of the universe, the ultimate frame of reference.

16These ideas are used in Aristotle’s elaborate and far-reaching doctrine of natural place. The Universe is finite in size (since space cannot be actually infinite), but it is not in any place (since there is no container). There is a centre of the Universe and that is where the Earth is. There is an objective “up” and “down,” defined in terms of radial lines from the centre of the Universe. Nature directs things to their natural place. A rock falls toward the centre of the Earth, not because of the action of the Earth, but because the rock strives to get to its natural place, the centre of the Universe. If we could somehow move the Earth away a few thousand kilometres and then drop the rock, we would not see it fall to the Earth, but rather it would move toward the centre of the Universe. Similarly, there is a natural place for water which is just above the natural place for earth, air above that, and fire, yet again is naturally above air. When removed from their natural places, they strive to return to them.

17Just as Aristotle appeals to ‘naturalness’ in his definition of place, so he has a corresponding idea of motion. Material objects are more or less defined by Aristotle in terms of their natural motion. This may sound foreign to modern ears, but we should remind ourselves that properties like this are present in current physics. While electrons are not defined in terms of velocities (any below the velocity of light being allowed), photons, for example, are characterized by the fact that in every inertial reference frame they always move at velocity c, a motion which is ‘natural’ for them. In Newtonian mechanics, as long as no force is acting on it, a body moves in a straight line at a constant speed. This motion, inertial motion, is natural for any body. Aristotle’s distinction between natural and non-natural motions (which he called violent) is crucial. Even though we differ greatly in detail with Aristotle, we do adopt something similar in distinguishing kinematics (free motion) from dynamics (motion under a force).

18There are four elements in the Aristotelian universe: earth, water, air, and fire, and their natural places are in concentric rings around the centre of the universe. Beyond these elements is a fifth, the aether. The natural motion for the four elements is along radial lines through the centre of the universe, toward its natural place. Natural motion for the aether is circular, again around the centre of the universe.

19Why is aether’s natural motion circular? Aristotle’s answer would have rung true to any intelligent listener until the 17th century. Circular motion, he said, is perfect. Not only is it perfect, but circular motion is unique in leaving the perfect celestial realm perfectly unchanged. It rotates around the earth (remember, that’s the centre of the Universe), as a rigid, unchanging whole.

20Third, non-existence of the void. Aristotle denied the existence of the void, empty space. The Universe is full; there is stuff of one sort or another everywhere. He offered several arguments in various places against a void or a true vacuum. One runs as follows: there is no difference of any sort among the various regions of a void; it is completely homogeneous. But a rock, for example, moves to its natural place, and in order for this to happen, one place must be objectively different from another. Since one place is not different from another within a void, motion in a void must be problematic, if not impossible. A rock in a void would be completely disoriented; it wouldn’t know which way is down, and so wouldn’t know which way to move, or whether to move at all. Aristotelian place has a kind of causal power, or at least the power to tell an object how to move; the void has no such power.

21Aristotle had a very big problem to worry about. Remember the dispute between the Atomists and Parmenides. Both agreed that the void is necessary for motion, but Parmenides thought the void absurd, so motion must be impossible, while the Atomists thought motion is obvious so the void must exist. Aristotle wanted it both ways: there is motion and it happens in a full space.

22It seemed, of course, that if everywhere were to be filled with stuff, then there would be no room for anything to move. Aristotle countered that motion is possible in a plenum so long as one body moves aside for another. The idea is really quite simple. Think of a fish swimming through the water which is displaced in front and moves in behind as the fish swims along. We’ll come back to this momentarily.

23Fourth, natural vs. violent motion. When a rock is thrown up, it is certainly moving, but not naturally, in Aristotle’s sense. Such motion was called “violent motion” and making sense of it was horribly difficult for Aristotle and his followers through the middle ages. When a rock or spear leaves our hands, why does it persist for a while in its unnatural motion and why does natural motion eventually overtake it? As we just mentioned, the account that Aristotle seemed to favour claimed that the air, which got out of the way of the moving object, rushed around to the back (to prevent a vacuum) and this gave the object a push. Thus the object would be kept in violent motion even after it left our hands. The process is called antiperistasis.

24Finally, we should point out too that Aristotle’s universe is finite in spatial extent. The Atomists, both early and late, took the void, to be infinite. Lucretius (De rerum natura) offered the following clever thought experiment to prove it. Suppose space is only finite. Then, if we come to the edge or boundary, we could throw a javelin. If it flies past the supposed edge, then it is not the edge after all. On the other hand, if the javelin bounces back, then there must be something beyond the edge that makes it bounce back. So, once again, the supposed edge is not really an edge after all. Thus, space has no edge; it is infinite.

25Elegant thought experiments like this one are always a delight, even if they don’t work. The most Lucretius has shown is that space is unbounded, that is, it has no edge. A two-dimensional being could work its way around a sphere (such as the surface of the earth) throwing the lance ahead and never coming to an edge. The sphere is unbounded. But it is not infinite. What Lucretius failed to take into account is possibility of a different topology. It is, of course, anachronistic to point this out. In his day, Lucretius’s argument was rightly persuasive.

1.3 Summary

26The point of this brief section on Greek thinking about space and motion has been to set the stage for the medieval and early modern period. The difficulties they faced and the conceptual tools they employed are the legacy of the Greeks. The medievals were in the grip of Aristotle and the Aristotelian framework. To summarize, the chief ingredients of the medieval framework inherited from Aristotle include:

 

  • The objects we see around us consist of a mix of four elements, earth, water, air, and fire. The heavens are made entirely of aether (the fifth element or quintessence).

  • Each element has a natural place and strives to move to it.

  • Natural motion for the four elements is in radial lines through the centre of the Universe. Natural motion for aether is circular.

  • Violent motion is explained by antiperistasis – whereby the medium through which an object travels is actively responsible for keeping the object in motion.

  • The Universe is full; there is no vacuum.

  • Everything that moves requires a mover. There is nothing akin to conservation of energy or momentum; things naturally come to rest in their natural place.

  • God (the unmoved mover or movers), is constantly injecting motion into the universe.

 

27We will expand on some of these points below. For now we stress that there is nothing here in the way of a concept of relative motion or inertia. We will take a liberal view of what inertia is, but to be a reasonable approximation to our modern concept, it should include the possibility of motion as well as rest as a “natural state” of being.

2. Challenges to Aristotelian dynamics

2.1 Natural vs. Violent Motion

28Why does a rock thrown horizontally continue in its horizontal motion after it has left the thrower’s hand? This was a serious puzzle, since its motion is not natural. It should, in the Aristotelian view, move down, toward its natural place at the centre of the universe. Such non-natural motion is called “violent,” and its explanation was one of the central problems in Aristotle’s physics. Why does violent motion continue after an object has been detached from the source of its motion?

29According to Aristotelian dynamics, every motion presupposes a mover. In order to satisfy this requirement for the case of detached motion, Aristotle explains that the original cause of motion imparts a moving power not only to the projectile itself, but also to the medium surrounding the moving object:

  • 4 Aristotle, Physics VIII.10.266b,27-267a.20, Clagett (trans.) 506.

If it is true that everything that is moved… is moved by something, how comes it that some things are moved continuously, though that which has caused them to move is no longer in contact with them, as, for instance, things thrown?… We must, therefore, hold that the original movement gives the power of causing motion to air, or water, or anything else which is naturally adapted for being a movent [i.e., mover] as well as for being moved4.

  • 5 Aristotle, Physics VIII.10.266b,27-267a.20, Clagett (trans.) 507.
  • 6 Aristotle, Physics VIII.10.266b,27-267a.20, Clagett (trans.) 506.
  • 7 Aristotle, Physics VIII.10.266b,27-267a.20, Clagett (trans.) 507.

30Aristotle’s theory of antiperistasis supposes that while the medium remains stationary during the object’s movement through it, it nevertheless ‘simultaneously [along with the object] receives the power or force to act as a movent’5. So the particles of air closest to the original mover, for example, receive the full amount of motive force – some of which they pass onto their neighbouring particles, which then pass a reduced amount of motive force onto yet further particles, and so on. Each successive ‘wave’ of air actively pushes the projectile, thanks to the ‘the power to cause motion’6 which it receives from its neighbouring wave of air. Resistance causes this motive force to be gradually expended. The motion of the object ‘finally ceases when the member of the series [of particles in the medium] immediately preceding no longer makes the next a movent but only causes it to be moved’7.

31It is important to note that in Aristotelian dynamics, resistance plays a fundamental role. Without it, no motion could take place.

  • 8 An Anonymous Treatment of Peripatetic Dynamics, 460, Clagett (trans.) 451.

Without resistance, motion does not take place, and the absence of resistance is the cause of why a simple body is not moved in a vacuum. Because a simple body does not have intrinsic resistance, and there is no extrinsic resistance in a vacuum, and [further] there is no resistance except intrinsic or extrinsic [resistance], it follows that a simple body does not have resistance, and consequently is not moved in a vacuum. Because without resistance motion does not take place – except one that is infinitely fast – it follows that a pure, simple body is not mobile in a vacuum unless it should be mobile infinitely fast; because if this were the case, it would traverse space immediately, which is impossible8.

32The dynamics of antiperistasis (in violent motion the medium pushes the moving body), remained dominant well into the high middle ages, but was plagued with conceptual and empirical problems. Some of the most effective and influential criticisms came in the form of thought experiments, especially those advanced by Jean Buridan.

2.2 Violent Motion

  • 9 Some go so far as to say, ‘It can scarcely be doubted that impetus is analogous to the later inerti (...)

33Natural philosophy in the fourteenth century was marked by a period of transition. Thinkers such as Jean Buridan (ca.1300 – ca.1361) and his student, Nicole Oresme (1323 – 1382), raised serious criticisms against the prevailing Aristotelian theory of dynamics. In its stead they proposed the theory of impetus, which explains that the source of motion is not to be found in the medium (i.e. moving to natural place or the medium pushing) but rather in the moving object itself. In some ways, this development prefigures the discovery of the laws of inertia9 by Galileo Galilei (1564 – 1642) and René Descartes (1596-1650) two centuries later. What draws Buridan, Oresme, and Galileo together is their shared use of thought experiments, many of which are among the most brilliant ever conceived.

34Each of the thought experiments we will discuss identifies some instance of detached (i.e. violent) motion (whether projectile or circular) which is presumably derived from experience and yet fails to be explained by the tenets of Aristotelian dynamics. In each case, the reader is supposed to conclude that Aristotle’s theory is seriously deficient.

35Buridan’s commentary on Aristotle’s Physics contains the following devastating thought experiments, some of which are close to reports of actual experience, while others are more hypothetical. They are all directed against Aristotle’s theory of antiperistasis.

  • 10 Buridan, Questions on the Physics of Aristotle, VIII.12.2, Clagett (trans.) 533.

A lance having a conical posterior as sharp as its anterior would be moved after projection just as swiftly as it would be without a sharp conical posterior. But surely the air following could not push a sharp end in this way, because the air would be easily divided by the sharpness10.

  • 11 Buridan, Questions on the Physics of Aristotle, VIII.12.2, Clagett (trans.) 533.

A ship drawn swiftly in the river even against the flow of the river, after the drawing has ceased, cannot be stopped quickly, but continues to move for a long time. And yet a sailor on deck does not feel any air from behind pushing him. He feels only the air from the front resisting him11.

  • 12 Buridan, Questions on the Physics of Aristotle, VIII.12.2, Clagett (trans.) 533.

36Again, suppose that the said ship were loaded with grain or wood and a man were situated to the rear of the cargo. Then if the air were of such an impetus that it could push the ship along so strongly, the man would be pressed very violently between that cargo and the air following it. Experience shows this to be false12.

  • 13 Buridan, Questions on the Physics of Aristotle, VIII.12.2, Clagett (trans.) 533.

Or, at least, if the ship were loaded with grain or straw, the air following and pushing would fold over the stalks which were in the rear. This is all false13.

37The moral is clear. In each case, the air cannot be moving the very objects it is purported to move. If it did, we would notice effects plainly contrary to common experience and expectation. Antiperistasis cannot explain these cases of violent motion.

38Another thought experiment by Buridan makes use of a very straight-forward analogy between launching a projectile together with its surrounding air and pushing the surrounding air by itself.

  • 14 Buridan, Questions on the Physics of Aristotle, VIII.12.3, Clagett (trans.) 534.

You could, by pushing your hand, move the adjacent air, if there is nothing in your hand, just as fast or faster than if you were holding in your hand a stone which you wish to project. If, therefore, that air by reason of the velocity of its motion is of a great enough impetus to move the stone swiftly, it seems that if I were to impel air toward you equally as fast, the air ought to push you impetuously and with sensible strength. [Yet] we would not perceive this14.

39With this thought experiment Buridan makes the case against antiperistasis even more devastating. If I throw a big stone at you, it will hurt. But if I throw the same amount of air that is pushing the stone, it seems as nothing to you. This thought experiment has the same experiential flavour as any great experiment, but the conclusion is so obviously absurd, that we feel no need to carry it out.

40The structure of these thought experiments is a common one. We set up the conditions, but we find that things do not go as the theory demands. The conclusion we draw is that the theory is false. Many of Galileo’s famous thought experiments, as we shall see, have this form. And some of Einstein’s, too. He famously imagined chasing a light beam to see what an electromagnetic wave front would look like. It led to an absurdity. Such negative thought experiments are often very effective in telling us what is false, but they do not tell us what is true. And this is the case with Buridan so far. We can see what is wrong, but not yet what is right. This will continue to be the case with the next few examples. Later we will see thought experiments that play a positive role in coming to a new theory.

41We will now turn to circular motion, which presents a particularly difficult challenge to antiperistasis. In this thought experiment we are to consider a spinning top and a smith’s mill (a heavy stone wheel for grinding grain),

  • 15 Buridan, Questions on the Physics of Aristotle, VIII.12.2, Clagett (trans.) 533.

which are moved for a long time and yet do not leave their places. Hence, it is not necessary for the air to follow along to fill up the place of departure of a top of this kind and a smith’s mill. So it cannot be said [that the top and the smith’s mill are moved by the air] in this manner15.

42There is no need for the air to fill in the places vacated by a rotating object, since those places are filled in by other parts of the object itself. And yet the wheel moves. Antiperistasis is gratuitous at best in such cases and downright false at worst.

43Another thought experiment that deals with detached motion is particularly intriguing, because, like others it would seem to be do-able, but in fact would be quite challenging to carry out. Nevertheless, the result seems perfectly evident, from merely visualizing the situation.

  • 16 Buridan, Questions on the Physics of Aristotle, VIII.12.3, Clagett (trans.) 534.

If you cut off the air on all sides near the smith’s mill by a cloth, the mill does not on this account stop but continues to move for a long time. Therefore it is not moved by the air16.

44This thought experiment differs from the previous examples insofar as it represents Buridan’s attempt to create an idealized or fully ‘controlled’ experimental scenario. All of the thought experiments we have encountered thus far argue against the theory that the air (or the medium in general) is responsible for projectile or circular motion. All that Buridan’s previous counter-examples accomplish, however, is to demonstrate that the air does not visibly ‘push’ or ‘mutually replace’ itself behind a moving object. The examples, however, are quite realistic and assume that the objects remain immersed in the air. A clever Aristotelian could, therefore, come up with some kind of dynamical theory that still involves the medium – possibly as a mysterious ‘unperceived’ or ‘unobserved’ mover. Buridan’s last thought-experiment is the only one which can counter this neo-Aristotelian rejoinder. This is because it actually proposes removing the air altogether from the scenario – thus rendering it impossible for the medium to be responsible for sustaining detached motion. Unlike the previous thought-experiments, which involve common, everyday occurrences like throwing lances and observing passing ships, Buridan proposes that we abstract from the ordinary scenario of a ‘merely’ spinning wheel. Admittedly, it is far from clear what ‘cut[ting] off the air on all sides near the smith’s mill by a cloth’ would entail. Does Buridan intend for us to imagine the wheel spinning in a complete vacuum? Perhaps all he means is that the cloth is to enclose the spinning wheel as tightly as possible without actually touching it. In any event, what is clear is that Buridan constructs this last thought experiment so that the air can play no role whatsoever in the motion of the wheel. This move to an idealization removes all doubt as to the failure of Aristotelian dynamics.

45Jumping ahead to Galileo, we see the same sort of response to antiperistasis. In the following thought experiment, Galileo uses an analogy to set up a reductio ad absurdum argument against Aristotle’s theory of projectile motion.

  • 17 Galileo, Dialogue, 153.

SAGREDO: If I were to place two arrows upon that table when a strong wind was blowing, one in the direction of the wind and the other across it, the wind would quickly carry away the latter and leave the former. Now apparently the same ought to happen with two shots from a bow, if Aristotle’s doctrine were true, because the one going sideways would be spurred on by a great quantity of air moved by the bowstring – as much as the whole length of the arrow – whereas the other arrow would receive the impulse from only as much air as there is in the tiny circle of its thickness.
SIMPLICIO: I have never seen an arrow shot sideways, but I think it would not go even one-twentieth the distance of one shot point first17.

46This thought experiment could just as easily have come from Buridan. And Galileo would feel perfectly at home with any of Buridan’s examples. In attacking Aristotle, they are largely interchangeable. But how they responded to the problems with Aristotle, as we shall see, is quite different.

47Still on the theme of the air being responsible for motion, Galileo points out another type of problem, this time concerning relative weights of various things and the fact that air itself has the least weight of all.

  • 18 Galileo, Dialogue, 152.

SALVIATI: [Consider what would happen] if two strings of equal length were suspended…with a lead ball attached to the end of one and a cotton ball to the other. Which of these pendulums do you believe would continue to move the longer before stopping vertically?
SIMPLICIO: The lead ball would go back and forth a great many times; the cotton ball, two or three at most.
SALVIATI: If the pendulums have just shown us that the less a moving body partakes of weight, the less apt it is to conserve motion, how can it be that the air, which has no weight at all in air, is the only thing that does conserve the motion acquired?18

48Galileo provides us with the beginnings of a positive explanation for why a heavy pendulum swings longer than a light one (and what causes violent motion in general). According to the above analogy, dense, solid objects are capable of “conserving motion” while the gaseous air is not. Galileo thus posits that whatever might be the source of projectile motion, it is not to be found within the medium through which the object travels, but within the object itself. The thought experiment not only presents a plausible phenomenon with which to refute the rival dynamical theory of Aristotle, but begins to develop a positive account of projectile motion.

3. Motion of the heavens and earth

  • 19 Galileo, Dialogue, 154.

49Some of Galileo’s most important thought experiments on the subject of inertial motion are to be found within the context of his discussion of the diurnal rotation of the earth. In fact, the Dialogue Concerning the Two Chief World Systems is chiefly concerned with refuting Aristotle’s theory that the earth stands still and that the heavens revolve around it. Galileo’s discussion is prefaced somewhat in Oresme’s Le Livre du ciel et du monde, where the author likewise confronts Ptolemy’s geocentric, stationary-earth model of the universe. It turns out that both Ptolemy and Aristotle argue their case by way of thought experiments which involve analogies. Oresme and Galileo thus have their work cut out for them. Each points out the fallacy in his predecessors’ analogies and revises their thought experiments to explicitly incorporate what later became known as the principle of Galilean relativity (i.e. the laws of motion are the same in all reference frames which are moving in a uniform, non-accelerated, manner). The end result, in the words of Galileo’s Salviati, is somewhat inconclusive: “[I have claimed] only to show that nothing can be deduced from the experiments offered by [the Aristotelians] as one argument for [the earth’s] motionlessness”19. Because the local kinematic behaviour of objects would be unaffected by the uniform rotation of the earth (strictly speaking, since the earth is accelerating by rotating it cannot be considered an inertial frame), we cannot use thought experiments to settle the question one way or the other. Although Oresme and Galileo fail to provide us with a successful, positive argument for the earth’s rotation, by drawing on the principle of Galilean relativity, they implicitly adopt a new dynamical theory: the law of inertia.

50Here are two analogy-type thought experiments which claim to prove the immobility of the earth. In the first example, Ptolemy draws an analogy between a moving ship and the earth.

  • 20 Oresme, Le Livre du ciel et du monde, Sambursky (trans.) 161.

If one were in a ship which was moving rapidly towards the east and if one were to fire an arrow straight upwards, it would not fall in the ship, but very far away, towards the west. And similarly, if the earth is moved very quickly in turning from west to east, supposing that one were to throw a stone directly upwards, it would not fall in the place from which it started but far away towards the west; and the contrary indeed happens20.

51And, thus, the Earth cannot move. In its day, this thought experiment was as impressive as it was simple.

52The second thought experiment, which Galileo attributes to Aristotle’s followers, is somewhat more thorough in drawing out the very same conclusion.

  • 21 Galileo, Dialogue, 126.
  • 22 Galileo, Dialogue, 144.

SALVIATI: [Here is what] is considered an irrefutable argument for the earth being motionless. For if it made the diurnal rotation, a tower from whose top a rock was let fall, being carried by the whirling of the earth, would travel many hundreds of yards to the east in the time the rock would consume in its fall, and the rock ought to strike the earth that distance away from the base of the tower. This effect [the Aristotelians] support with another experiment, which is to drop a lead ball from the top of the mast of a boat at rest, noting the place where it hits, which is close to the foot of the mast; but if the same ball is dropped from the same place when the boat is moving, it will strike at that distance from the foot of the mast which the boat will have run during the time of fall of the lead, and for no other reason than that the natural movement of the ball when set free is in a straight line toward the center of the earth21.
You say, then, that since when the ship stands still the rock falls to the foot of the mast, and when the ship is in motion it falls apart from there, then conversely, from the falling of the rock at the foot it is inferred that the ship stands still, and from its falling away it may be deduced that that ship is moving. And since what happens on the land, from the falling of the rock at the foot of the tower one necessarily infers the immobility of the terrestrial globe22.

  • 23 Galileo, Dialogue, 144.

In both thought experiments, the analogies between the moving boat and the ‘moving earth’ seem quite appropriate. Thus the only chance of refuting them lies in challenging the central assumption. After all, why should a projectile launched from a moving object ‘fall behind’? According to Aristotelian dynamics, it is ‘for no other reason than that the natural movement of the ball when set free is in a straight line toward the center of the earth’23.

53Oresme and Galileo disagree. Both challenge that assumption and propose an alternative framework – one in which a projectile launched from a moving object in some sense preserves the motion that was previously imparted to it.

54Oresme directly undermines the central assumption of where the body would fall by positing that if the earth were rotating, it would carry the atmosphere along with it. (This anticipates ‘aether drag’ assumptions that would be made in the late 19th century in order to account for unexpected results in optical experiments.) Hence, if an arrow were to be shot vertically up, the moving air would be responsible for keeping the arrow on track as it falls back towards its point of origin. Thus, just from seeing the stone return to its place of origin, we can conclude nothing about the motion of the earth.

  • 24 Oresme, Le Livre du ciel et du monde, Sambursky (trans.) 162.

Concerning the arrow or stone thrown upwards etc., one could say that the arrow fired up is moved very quickly towards the east with the air through which it passes, and with all the mass of the lower part of the world which is moved with a diurnal movement; and for this reason, the arrow falls back to the place on the earth from which it started24.

55The mere fact that a projectile launched vertically upwards returns to its place of origin confirms nothing. It could be the result of the earth standing still, or it could just as easily be explained in a Copernican model with atmospheric drag. The point is that Ptolemy’s thought experiment fails, because it does not take into account something like the principle of Galilean relativity. Oresme, however, clearly does possess at least an intuitive appreciation of relative motion, if not full-fledged inertial motion.

56The real issue here is the relativity of motion, not antiperistasis. Even conceding, for the sake of the argument that Aristotle is right in his dynamics, the problem of rotation of the Earth is still not settled. Galileo makes the same point. The Copernican model of the universe as such is not incompatible with the tenets of Aristotelian dynamics. All one has to do is posit a medium which is normally responsible for projectile motion that also rotates along with the earth. Hence, the moving air itself ensures that the stone ‘follows along’ with the tower’s horizontal motion.

  • 25 Galileo, Dialogue, 143.

SALVIATI: I might add at least that part of the air which is lower than the highest mountains must be swept along and carried around by the roughness of the earth’s surface, or must naturally follow the diurnal motion because of being a mixture of various terrestrial vapors and exhalations. That [object] which leaves the top of the tower finds itself in a medium which has the same motion as the entire terrestrial globe, so that far from being impeded by the air, it rather follows the general course of the earth with assistance from the air25.

57In order to render this thesis more credible, Galileo’s next thought experiment draws upon an analogy between a flying eagle and the moving earth. According to Galileo, if the wind imparts some horizontal motion to the eagle’s dropped payload, it can similarly be responsible for the ‘slanting’ parabolic trajectory of a stone dropped from a tower. Notice that Galileo speaks of using the ‘mind’s eye’ in order to envision this analogy – he is explicitly presenting this argument as a thought experiment.

  • 26 Galileo, Dialogue, 143.

SALVIATI: If you want to present a more suitable experiment, you ought to say what would be observed (if not with one’s actual eyes, at least with those of the mind) if an eagle, carried by the force of the wind, were to drop a rock from its talons. Since this rock was already flying equally with the wind, and thereafter entered into a medium moving with the same velocity, I am pretty sure that it would not be seen to fall perpendicularly, but, following the course of the wind and adding to this that of its own weight, would move in a slanting path26.

58It is important to point out that Galileo himself does not intend to rely too heavily on this last analogy. After all, as we shall see in a moment, he strongly opposes the view that the medium is responsible for projectile motion. Rather, Galileo merely wishes to point out that the trajectory is not always what it seems. Thus, even a committed Aristotelian must admit that, while from the point of view of the eagle, the dropped payload perhaps seems to fall in a straight vertical line downwards, an earthbound observer sees the rock trace out a parabolic path. If the Aristotelian wants, he can attribute this motion to the wind rushing behind the eagle.

59Oresme’s response to Ptolemy includes several short thought experiments which confirm his thesis by analogy.

  • 27 Oresme, Le Livre du ciel et du monde, Sambursky (trans.) 162-163.

And [the trajectory of the arrow] seems possible if one considers a similar case; suppose a man to be in a ship travelling very swiftly towards the east, without perceiving this motion, and suppose him to move his hand quickly down against the mast of the ship, it would seem to him that his hand was not moved except in a straight line; and thus, according to this opinion, the case of the arrow which rises or falls straight up or straight down seems to us similar27.

60Oresme identifies a fault in the central Ptolemaic and Aristotelian assumption: that only in a frame of reference ‘absolutely’ at rest could the laws of motion conform to our experience. The faulty premiss should be replaced, Oresme urges, with an understanding of motion as a purely relative phenomenon. Oresme thus leaves us in an agnostic state, unable to choose between the rival accounts – Ptolemaic or Copernican. He offers us a counter-thought experiment that has the effect of neutralizing the first without resolving the issue in favour of the alternative. When it comes to the rotation of the earth, the fault is not so much with the dynamic theory (including antiperistasis), rather it is a failure to recognize the need for something akin to the relativity of motion.

61Counter thought experiments have a rather complex structure. The experiential part is in the middle. Typically, there is a set up, followed by a claim of some phenomenon, followed by an explanation, which we tend to think of as the result of the thought experiment. What counter thought experiments really do is undermine some other thought experiment that has previously been found persuasive. Thus, first came Newton’s bucket thought experiment, which was used by him to argue for absolute space. 1We start with a bucket half-filled with water. It is connected to a twisted rope, released, and starts to spin. The surface of the water, initially flat and at rest with respect to the bucket, eventually becomes concave. What is causing this? Newton’s answer is that the water-bucket system (every part of which is at rest with respect to every other part), must be moving – rotating – with respect to space itself. And, so, space must be a thing in its own right.

62Mach later produced a counter thought experiment by asserting that the water in a bucket with extremely thick walls would not climb the walls, if the bucket were rotated. Of course, we have no reason to believe Mach’s assertion, but we see from his counter thought experiment that Newton’s claims about what would happen to the bucket in empty space are not so obvious and inevitable as we had previously thought. We need not accept Mach’s positive conclusion that all motion must be relative motion, but we do find that his counter thought experiment has undermined Newton’s. And that is precisely what Oresme’s thought experiment has done to Ptolomy’s. (For more on counter thought experiments see Brown 2007.)

63Let’s turn now to Galileo. We will see that although Galileo’s thought experiments proceed much in the same vein as Oresme’s, they provide a more rigorous justification for their assumptions. The first thought experiment does not introduce a new analogy, but, like Oresme’s first argument, instead challenges Aristotle’s underlying dynamical assumption (i.e. that if the earth were rotating, a projectile launched vertically up would ‘trail behind’ its point of origin). It, too, is a counter thought experiment.

  • 28 Galileo, Dialogue, 139-140.

SALVIATI: But if it happened that the earth rotated, and consequently carried along the tower, and if the falling stone were seen to graze the side of the tower just the same, what would its motion have to be?…The motion would be a compound of two motions; the one with which it measures the tower, and the other with which it follows it. From this compounding it would follow that the rock would no longer describe that simple straight perpendicular line, but a slanting one, and perhaps not straight…Hence just from seeing the falling stone graze the tower, you could not say for sure that it described a straight and perpendicular line, unless you first assumed the earth to stand still28.

64Galileo clearly explains that the mere observation of a falling rock on its own is inconclusive. He is obviously endorsing the relativity of motion. Motion can only be perceived relative to one’s own inertial reference frame. That is, no object moving at the same velocity as an observer can help that observer determine whether or not she is actually moving. No ‘strange’ kinematic effects occur within frames of reference moving with uniform velocity. To illustrate the relativity of motion, and, by analogy, the futility of using earth-bound experiments to determine whether or not the earth itself is rotating, Galileo presents the following thought experiment, one of his most effective:

  • 29 Galileo, Dialogue, 186.

SALVIATI: Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drop falls into the vessel beneath; and, in throwing something to your friend, you need throw no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully (though there is no doubt that when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still29.

65What a wonderful thought experiment it is. It generates that much sought after Aha! effect or Eureka moment when all seems crystal clear. This thought experiment, perhaps more than any other, yields the idea of the relativity of inertial frames of reference, what came to be called Galilean relativity.

66Armed with this principle of relativity, Galileo is now able to reverse the original analogy which the Aristotelian thought experiment drew upon in an attempt to establish the immobility of the earth.

  • 30 Galileo, Dialogue, 144.

SALVIATI: If the stone dropped from the top of the mast when the ship was sailing rapidly fell in exactly the same place on the ship to which it fell when the ship was standing still, what use could you make of this falling with regard to determining whether the vessel stood still or moved?30

67To his own question, he again offers an agnostic response:

  • 31 Galileo, Dialogue, 145.

SALVIATI: The same cause holding good on the earth as on the ship, nothing can be inferred about the earth’s motion or rest from the stone falling always perpendicularly to the foot of the tower31.

4. Impetus and inertia

68The crucial change in the post-Aristotelian outlook is the transfer of the source of motion from the medium to the object itself. Galileo argues in this next thought experiment that the moving ship itself imparts a horizontal motion to the rock as it sits on top of the mast. As the rock falls, it preserves this horizontal motion (since there is nothing to impede it) and therefore lands straight below its point of departure.

  • 32 Galileo, Dialogue, 148.

SALVIATI: As to that stone which is on top of the mast; does it not move, carried by the ship…? And consequently is there not in it an ineradicable motion, all external impediments being removed? And is not this motion as fast as that of the ship?
SIMPLICIO: By the final conclusion you mean that the stone, moving with an indelibly impressed motion, is not going to leave the ship, but will follow it, and finally will fall at the same place where it fell when the ship remained motionless32.

69What led up to this? We will begin with a selection of remarks from Buridan, amounting to his theory of impetus. According to Buridan, impetus is the motive force which is responsible for maintaining detached motion, whether projectile or circular.

If light wood and heavy iron of the same volume and of the same shape are moved equally fast by a projector, the iron will be moved farther because there is impressed in it a more intense impetus, which is not so quickly corrupted as the lesser impetus would be corrupted.

70This also is the reason why it is more difficult to bring to rest a large smith’s mill which is moving swiftly than a small one, evidently because in the large one, other things being equal, there is more impetus.

  • 33 Buridan, Questions on the Physics of Aristotle VIII.12.5, Clagett (trans.) 535.

And for this reason you could throw a stone of one-half or one pound weight farther than you could a thousandth part of it. For the impetus in that thousandth part is so small that it is overcome immediately by the resisting air33.

71We would stress the very thing that Buridan stresses, namely, the source of motion is in the object, not the surrounding medium. In fact, the medium offers some resistance, which depletes the impetus. Buridan goes so far as to say what would happen if all sources of resistance were to be removed from a spinning wheel.

  • 34 Buridan, Questions on Aristotle’s On the Heavens, Clagett (trans.) 561.

If you cause a large and very heavy smith’s mill [i.e., a wheel] to rotate and you then cease to move it, it will still move a while longer by this impetus it has acquired. Nay, you cannot immediately bring it to rest, but on account of the resistance from the gravity of the mill, the impetus would be continually diminished until the mill would cease to move. And if the mill would last forever without some diminution or alteration of it, and there were no resistance corrupting the impetus, perhaps the mill would be moved perpetually by that impetus34.

72Now Buridan can definitively conclude that Aristotelian dynamics are false. For recall that in Aristotle’s theory, motion without resistance is impossible, because then an object would move with infinite velocity. Buridan thus presents a logically plausible scenario which, he gives us reason to believe, would result in motion of eternal duration – indeed inconsistent with Aristotelian dynamics.

73Buridan develops a similar thought experiment in order to explain the motion of celestial bodies, which subsist in an utterly resistance-free environment. Again, the thought experiment consists of an inference to the best explanation: the reason why the motion of celestial bodies appears perpetual is because they encounter no resistance to ‘corrupt’ the impetus originally imparted on them.

  • 35 Buridan, Questions on the Metaphysics of Aristotle, XII.9, Maier (1982a) (trans.) 89.

You know that many maintain that a projectile, after leaving the thrower, is moved by impetus imparted by the thrower and moves as long as the impetus remains stronger than the resistance; and that the impetus would last forever if it were not diminished and destroyed by the opposing resistance or by the tendency to contrary motion. And in celestial motions there is no opposing resistance; therefore when God, at the Creation, moved each sphere of the heavens with just the velocity he wished, he [then] ceased to move them himself, and since then those motions have lasted forever due to the impetus impressed on those spheres35.

74In a particularly Ockham’s razor-like manouever, Buridan argues that the celestial bodies in and of themselves contain the reason for their continued motion. There is no need to posit additional causes or ‘intelligences’ in order to explain cosmological movement.

  • 36 Buridan, Questions on the Physics of Aristotle, VIII.12, Clagett (trans.) 524-525.

It does not appear necessary to posit intelligences of this kind, because it could be answered that God, when He created the world, moved each of the celestial orbs as He pleased, and in moving them impressed in them impetuses which moved them without His having to move them any more… And these impetuses which He impressed in the celestial bodies were not decreased or corrupted afterwards because there was not inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus36.

75Let’s turn to Oresme and a pair of thought experiments in the same spirit as Buridan’s, in support of the theory of impetus. A wheel that is set in motion:

  • 37 Oresme, Questiones super De cœlo, II.7, Grant (2002) (trans.) 155.

cannot be stopped immediately without great difficulty, but is moved by a certain impetus, though separated from the first moving agent and [is not moved] by the surrounding air37.

76Having progressively eliminated all possible sources of motion, Oresme concludes that the spinning wheel must have received an impetus which effectively ‘keeps it going’. For this is the best remaining possible explanation.

77Oresme’s second thought experiment is more complex, but also more successful because it sets up an idealized scenario in a resistance-free environment. It thus enables Oresme to scrutinize more thoroughly the consequences of the theory of impetus. Much like his predecessor, Buridan, Oresme infers that in the absence of resistance, the impetus imparted on an object will keep it moving forever. This passage appears in Oresme’s Le Livre du ciel et du monde, where he discusses incommensurable circular motion.

Now, I should like to show next that it is possible both in fact and in uncontradictable theory that some motion has a beginning and lasts forever. First, with regard to circular motion: I assume that a wheel of any kind of material is like the wheel of a clock [see Oresmeís figure below]; this we will designate as a and will call its center a.b. Let us next set in a another wheel smaller than the first, in the manner of an epicycle, with its center labeled b. Let us add a third wheel set on the second, having its center on the circumference of the second like the moon in its epicycle, and let us call this third wheel c. Now let us place a fourth wheel outside these three so fixed that c can touch it, and let its center be marked d. Then, I posit that a be moved around its center, that b be moved with the motion of a on which it is set, and, with this, that b be moved also with its proper motion around its center, while c has no proper motion but is moved with the motion of a and b

  • 38 Oresme, Le Livre du ciel et du monde, 1.29.46a-46d, Grant (1971) (trans.) 38. Our reproduction of h (...)

Now I posit that d be so adjusted or controlled by counterweights and otherwise that it is inclined to move but is not moved until touched by c; this contact removes the hindrance and d begins to move regularly. Something of this sort or similar to it could be performed artificially or by skilled craftsmanship. Next, I posit that the two motions of a and b should be incommensurable, regular, and perpetual…At this present moment, I posit that the wheel c touches wheel d, and I say that it is impossible that it should have touched it previously or should touch it again, for it can touch it only when the centers b, c, and d are in conjunction exactly in one line; and this cannot have happened before not again in future time…From this it follows necessarily that wheel d would now begin to move and would never stop; and, although such a series of events cannot occur in nature, nor be shown by material art or in destructible matter, nor endure so long [as forever], nevertheless, it contains or implies no contradiction whatever, nor is it within its own frame of reference incongruous to reason, but it is possible if we grant the nature of the motions. All the incongruity arises by reason of the material or from something outside the frame of reference38.

78Perhaps the most effective example of an inference to the best explanation occurs in a thought experiment Galileo uses to illustrate the law of inertia. Because the example is so abstract, Galileo is able to minimize and simplify the assumptions needed in order to infer the conclusion.

  • 39 Galileo, Dialogue, 145-147.

SALVIATI: Suppose you have a plane surface as smooth as a mirror and made of some hard material like steel. This is not parallel to the horizon, but somewhat inclined, and upon it you have placed a ball which is perfectly spherical and of some hard and heavy material like bronze. What do you believe this will do when released?
SIMPLICIO: [It rolls down.]
SALVIATI: Now how long would the ball continue to roll, and how fast?
SIMPLICIO: The ball would continue to move indefinitely, as far as the slope of the surface extended, and with a continually accelerated motion.
SALVIATI: If one wanted the ball to move upward on this same surface, do you think it would go?
SIMPLICIO: Not spontaneously, no; but drawn or thrown forcibly, it would.
SALVIATI: Now tell me what would happen to the same movable body placed upon a surface with no slope upward or downward.
SIMPLICIO: There being no downward slope, there can be no natural tendency toward motion; and there being no upward slope, there can be no resistance to being moved, so there would be an indifference between the propensity and the resistance to motion. Therefore it seems to me that it ought naturally to remain stable.
SALVIATI: But what would happen if it were given an impetus in any direction?
SIMPLICIO: It must follow that it would move in that direction.
SALVIATI: How far would you have the ball continue to move?
SIMPLICIO: As far as the extension of the surface continued without rising or falling.
SALVIATI: Then if such a space were unbounded, the motion on it would likewise be boundless? That is, perpetual?
SIMPLICIO: It seems so to me, if the movable body were of durable material39.

79In this Socratic-like dialogue, Salviati draws out of Simplicio the conclusion that, in the absence of resistance or indeed any externally-acting force, there is no need for an object to change its motion. In his thought experiment, Galileo uses a step-by-step method to progressively eliminate all the influences which the environment might realistically have on the ball. Fist of all, he asks us to imagine the ball and plane surface as perfectly smooth and without any impediment – so that all source of friction might be removed from the thought experiment. Next, Galileo has the surface held at such an angle so as to cancel any effect which gravity might have on the ball. Finally, we are told that the surface is unbounded and extends to an infinite distance in every direction. By abstracting from all resistances and dynamical influences on the ball, Galileo concludes that the speed of the ball will forever remain unchanged. This result is in clear opposition to Aristotelian dynamics, but thanks to Galileo’s clever manipulation of the dynamical variables on the ball, we cannot help but infer that it must be true. Notice that Galileo’s dynamical explanation of the phenomenon of inertial motion is just to say that the ball has neither a propensity nor a resistance to motion. Thus, Galileo turns the tables on the question which preoccupied both Aristotle and his mediaeval critics. Instead of assuming that the ball’s natural state is one of rest, and asking ‘what keeps the ball in uniform motion’, he assumes that the ball’s natural state is one of uniform motion, and asks ‘what prevents the ball from staying in uniform motion’.

80The inference to the best explanation seems in general to be a very effective style of thought experiment. Though it all comes as a package, strictly, the thought experiment establishes some phenomenon, then after that comes the explanation of it. The effectiveness of this form of reasoning is perhaps unsurprising, given how closely this kind of thought experiment resembles the style of scientific reasoning used in actual empirical experiments.

5. Conclusion

81The story of inertial motion does not end here, but all that remains must be left to another occasion. We will only give the briefest of outlines, starting with an example from Galileo.

  • 40 Galileo, Two New Sciences, 170.

I mentally conceive of some moveable projected on a horizontal plane, all impediments being put aside. Now it is evident from what has been said elsewhere at greater length that equable motion on this plane would be perpetual if the plane were of infinite extent40.

82By infinite extent, Galileo can mean no more than unbounded, that is, there is no impediment to the object’s continued motion. He does not intend an infinite straight line, since Galileo’s inertia is circular. Centres of gravity are all important in his conception of how and why things move. Imagining a body in horizontal motion, he declares,

  • 41 Galileo, Two New Sciences, 172.

it is impossible that a heavy body … should naturally move upward, departing from the common center toward which all heavy bodies mutually converge; and hence it is impossible that these be moved spontaneously except with that motion by which their own center of gravity approaches the said common center. Whence, on the horizontal, which here means a surface [everywhere] equidistant from the said [common] center, and therefore quite devoid of tilt, the impetus or momentum of the moveable will be null41.

83Descartes deserves the credit for the modern concept of inertia, namely, a state of motion that involves constant speed in a straight line.

  • 42 Descartes, Principles of Philosophy, II, 37.

The first law of nature: that each thing, as far as it is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move42.

  • 43 Descartes, Principles, II, 39.

The second law of nature: that all movement is, of itself, along straight lines; and consequently, bodies which are moving in a circle always tend to move away from the centre of the circle which they are describing43.

84Descartes, in these passages, has introduced two crucially important things. First, the idea of a state. Even though a body may be changing its location, it’s state could be constant. Second, the idea that inertial motion is along straight lines.

 

85By the time we get to Newton, inertial motion is well entrenched and shows up as the first law in Newton’s Principia. The remarkable thing, from our point of view, is that by the time Newton formulated his view, he was putting inertia to work in his thought experiments for absolute space. Why does the water climb the sides of the bucket? The parts of water are rotating, that is, they are accelerating with respect to space itself. Space is the cause of inertial motion of a body, that is, of constant speed in a straight line, when there is no force being applied. With Newton, we have come back to the idea that some aspects of motion are due to the medium, not the body. It is space itself that is the cause of constant velocities when no forces are acting.

86After Newton, the next big event is the re-affirmation of a principle of relativity in the special theory of relativity, after it had been seriously threatened by 19th century electrodynamics. Following that, the general theory of relativity introduced free fall, that is, motion along spacetime geodesics as inertial motion, the natural state for any body.

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Bibliografia

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Buridan, Jean, Questions on Aristotleís On the Heavens

Descartes, Principles of Philosophy

Galileo, Dialogue Concerning the Two Chief World Systems, transl. and ed. by S. Drake, Berkeley, The University of California Press, 1967

Galileo, Two New Sciences, transl. and ed. by S. Drake, Madison, University of Wisconsin Press, 1974

Oresme, Nicole, Le Livre du ciel et du monde, ed. by A.D. Menut and A.J. Denomy, detached from «Mediaeval studies», v. 3-5, 1941-1943, New York, 1943

Oresme, Nicole, Le Livre du ciel et du monde, transl. and ed. by B. Tolley, in Physical Thought from the Presocratics to the Quantum Physicists: An Anthology, ed. by S. Sambursky, London, Hutchinson of London, 1974: 161-163

Oresme, Nicole, Questiones super De celo

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Note

1 1 Aristotle, Metaphysics, A4, 985b4.

2 2 The distinction between actual and potential infinity is central to all so-called constructive accounts of mathematics. It remains a contentious issue to this day. Brouwer, for instance, will only accept the potential infinite. The majority of mathematicians, however, cheerfully accept the existence of actual infinities.

3 3 Aristotle, Physics, 212a20.

4 Aristotle, Physics VIII.10.266b,27-267a.20, Clagett (trans.) 506.

5 Aristotle, Physics VIII.10.266b,27-267a.20, Clagett (trans.) 507.

6 Aristotle, Physics VIII.10.266b,27-267a.20, Clagett (trans.) 506.

7 Aristotle, Physics VIII.10.266b,27-267a.20, Clagett (trans.) 507.

8 An Anonymous Treatment of Peripatetic Dynamics, 460, Clagett (trans.) 451.

9 Some go so far as to say, ‘It can scarcely be doubted that impetus is analogous to the later inertia, regardless of ontological differences.’ Clagett 524.

10 Buridan, Questions on the Physics of Aristotle, VIII.12.2, Clagett (trans.) 533.

11 Buridan, Questions on the Physics of Aristotle, VIII.12.2, Clagett (trans.) 533.

12 Buridan, Questions on the Physics of Aristotle, VIII.12.2, Clagett (trans.) 533.

13 Buridan, Questions on the Physics of Aristotle, VIII.12.2, Clagett (trans.) 533.

14 Buridan, Questions on the Physics of Aristotle, VIII.12.3, Clagett (trans.) 534.

15 Buridan, Questions on the Physics of Aristotle, VIII.12.2, Clagett (trans.) 533.

16 Buridan, Questions on the Physics of Aristotle, VIII.12.3, Clagett (trans.) 534.

17 Galileo, Dialogue, 153.

18 Galileo, Dialogue, 152.

19 Galileo, Dialogue, 154.

20 Oresme, Le Livre du ciel et du monde, Sambursky (trans.) 161.

21 Galileo, Dialogue, 126.

22 Galileo, Dialogue, 144.

23 Galileo, Dialogue, 144.

24 Oresme, Le Livre du ciel et du monde, Sambursky (trans.) 162.

25 Galileo, Dialogue, 143.

26 Galileo, Dialogue, 143.

27 Oresme, Le Livre du ciel et du monde, Sambursky (trans.) 162-163.

28 Galileo, Dialogue, 139-140.

29 Galileo, Dialogue, 186.

30 Galileo, Dialogue, 144.

31 Galileo, Dialogue, 145.

32 Galileo, Dialogue, 148.

33 Buridan, Questions on the Physics of Aristotle VIII.12.5, Clagett (trans.) 535.

34 Buridan, Questions on Aristotle’s On the Heavens, Clagett (trans.) 561.

35 Buridan, Questions on the Metaphysics of Aristotle, XII.9, Maier (1982a) (trans.) 89.

36 Buridan, Questions on the Physics of Aristotle, VIII.12, Clagett (trans.) 524-525.

37 Oresme, Questiones super De cœlo, II.7, Grant (2002) (trans.) 155.

38 Oresme, Le Livre du ciel et du monde, 1.29.46a-46d, Grant (1971) (trans.) 38. Our reproduction of his figure.

39 Galileo, Dialogue, 145-147.

40 Galileo, Two New Sciences, 170.

41 Galileo, Two New Sciences, 172.

42 Descartes, Principles of Philosophy, II, 37.

43 Descartes, Principles, II, 39.

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Mark Shumelda e James Robert Brown, «Thought Experiments and Inertial Motion: A Golden Thread in the Development of Mechanics»Rivista di estetica, 42 | 2009, 71-96.

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Mark Shumelda e James Robert Brown, «Thought Experiments and Inertial Motion: A Golden Thread in the Development of Mechanics»Rivista di estetica [Online], 42 | 2009, online dal 30 novembre 2015, consultato il 22 juin 2024. URL: http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/estetica/1838; DOI: https://0-doi-org.catalogue.libraries.london.ac.uk/10.4000/estetica.1838

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