The most serious objection to Copernicus’ heliocentric model of the cosmos was that there was no satisfactory physics for such a system. The Ptolemaic system lasted as long as it did in part because it was very accurate, and in part because it was undergirded by Aristotelian physics. Aristotelian physics provided coherent and persuasive explanations for the behavior of falling bodies and the rotation of the planets. In this page, I’m going to take a more in depth look at Aristotle’s physics of the terrestrial realm, and examine a major challenge to this physics in the Middle Ages. In subsequent pages (on Galileo’s physics, Descartes’ physics and Newton’s physics) I will examine the gradual construction of a new physics that could make sense of motion in a heliocentric cosmos.
First, let’s review briefly what I’ve already written about Aristotelian physics as it pertains to the terrestrial realm. Everything below the sphere of the moon is made of four elements: earth, water, air and fire. The natural motion of these elements is in rectilinear and radial. That is, the heavy elements naturally move down toward the center of the cosmos (which is the earth), and the lighter elements naturally move up. Further, each element has a natural place. The natural place of the element earth is at the center of the cosmos. The natural place of water is just above the element earth. The natural place of fire is at the periphery of the terrestrial realm. The natural place of air is just below fire. All natural motion in the terrestrial realm is a result of elements seeking to reach their natural places. Terrestrial object can be compelled to move in unnatural ways as well. For example, you can make a rock move up instead of down if you toss it upwards. Such motion is called unnatural or forced or violent motion (these are all synonyms).
FOUR POINTS ABOUT ARISTOTELIAN PHYSICS
I. MOTION IS A TYPE OF CHANGE.
The first thing to understand about Aristotle’s understanding of motion in the terrestrial realm is that motion is a type of CHANGE. Specifically, motion is a change of place. However, Aristotle subsumed motion under the larger category of change. And the larger category of change included generation, corruption and alteration in quality. Generation and corruption are biological processes. Organisms are born, they grow, they get old, they decay and eventually they die.
Alteration in quality could be an organic, such as when the leaves of a tree turn from green to orange in the fall, or inorganic, such as when tea changes from hot to cold if it’s left on the counter. In the twenty-first century, the birth of a kitten and the falling of a rock are not regarded as the same type of phenomena. Birth (of kittens and other animals) is a subject we learn about in biology classes. And the behavior of falling bodies is something we learn in physics classes. But understanding that Aristotle subsumed motion into the broader category of change, and that his model or paradigm of change was biological change, may go some way to clarifying his thought. When I ask, “how would Aristotle explain why a rock falls?” most students can memorize the answer, “because the rock is trying to reach its natural place at the center of the cosmos,” but they find it deeply unsatisfying And they have good reason to find this answer unsatisfactory. It’s not just that students are so familiar with the Newtonian concept of gravity that they believe it is natural or intuitive (although it’s not!). It’s also that the answer seems fundamentally tautological (or circular). Why does a rock fall? Because it’s in the nature of the rock to fall. But if I asked, “how would Aristotle explain why a kitten grows up to be a cat?” you would find the answer, “because it’s in the nature of a kitten to become a cat,” considerably more satisfying. In fact, substitute “DNA” for “nature” and Aristotle’s answer in exactly the same as our modern answer. (If you want to know more about Aristotle’s understanding of motion as change, see the essay by Joe Sachs in the Internet Encyclopedia of Philosophy.)
II. CHANGE IS NOT MATHEMATICAL
Aristotle’s understanding of motion is not mathematical. He does not attempt to describe any kind of change, including motion, mathematically. Nor does he ever suggest that such a mathematical description would be desirable. This flies in the face of our modern understanding of physics as a fundamentally mathematical science. Again, it may help to reflect that most of the types of change that Aristotle sought to describe are not ones that modern scientists would attempt to describe mathematically either. Who thinks the process of a kitten turning into a cat can be described mathematically?
III. AN OBJECT CAN HAVE ONLY ONE KIND OF MOTION.
An object, like a rock, can only have one motion at a time. If you throw a rock upward, you force it to make an unnatural motion. Eventually, this unnatural motion will end and its natural motion, straight down, will begin. But at not point does the rock have two motions, the natural and the unnatural.
IV. LOCAL MOTION IS A WEAK AREA OF ARISTOTLE’S PHILOSOPHY
The final thing to understand about Aristotle’s terrestrial physics is that his explanation of local motion has some definite weak points. This is not really Aristotle’s fault. He was simply considerably more interested in biological change, and he devoted far more time and attention to it than he did to the subject of motion. However, these weak points would be ones that medieval scholars in the thirteenth and fourteenth centuries would attempt to figure out for themselves. Two serious problem areas were 1) how to explain why falling bodies fell faster the farther they fell, and 2) how to explain projectile motion. There was no really good explanation in Aristotle’s works for why a heavy body like a rock should fall faster the farther it falls, and yet it doesn’t take a whole lot of observation to convince yourself that this is the case. Some speculated that the earthy object moved more “joyfully” the closer it got to its natural place, but this was not really satisfactory. The problem of projectile motion was even worse. If I throw a rock in the air, why does it continue to travel upwards even when I’m no longer touching it? If I shoot an arrow from a bow, why does it travel forward before falling to the ground? Aristotle said, the mover (my hand or the bow) pushes the medium (generally air) as well as projectile. After the projectile leaves my hand or my bow, air displaced by the object rushes around behind the object so a vacuum does not form. Hence the projectile is pushed forward. At some point, the resistance of the medium will cause the projectile to stop moving upward or forward. At this point its natural motion, down to the center of the earth, takes over. So the medium both pushes the object upward or forward, and stops it from moving upward or forward. The technical term for this was antiperistasis. Note that for Aristotle projectile motion was a very small part of his general theory of change; he didn’t devote much attention to it. Medieval scholars found Aristotle’s description of projectile motion particularly unsatisfactory. I turn now to one of the most powerful responses to Aristotle’s theory of motion in the Middle Ages.
JOHN BURIDAN AND IMPETUS THEORY
John Buridan (ca. 1300 – ca. 1358) taught at the University of Paris in the fourteenth century. He taught students about Aristotle’s ideas, and he wrote numerous commentaries on the ancient Greek philosopher’s books. One of these commentaries was on Aristotle’s Physics, and in this commentary, Buridan critiqued Aristotle’s explanation of projectile motion. He gives several examples of forced motion that cannot be explained with antiperistasis.
His first example is a top. If you set a top in motion, it will spin for some time before it falls over. Now spinning is not a natural motion. The natural motion of the top (presuming it is made of some earthy substance) is straight down. You can force it to spin on its own axis for a little while, but then its natural motion takes over. But what is making the top spin when you take your hand away? This is an unnatural motion, but it can’t be caused by air rushing in to push the top around, because the top is not changing place.
His second example is a lance that is sharp at both ends. “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 sharpness.”
His third example is a ship being pulled down a river by men on the shore. “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 him.”
Aristotle’s explanation of violent motion – that the mover displaces the air as well as the object and the air in front of the object rushes around to fill in behind the object, thereby pushing it along – just doesn’t work in the case of the top, the two-tipped lance and the ship being dragged against the current. And it’s not a very satisfactory explanation of projectile motion either! Buridan’s solution is concept of impetus. Here it is in his own words:
Therefore, it seems to me that it ought to be said that the motor in moving a moving body impresses in it a certain impetus or a certain motive force of the moving body, which impetus acts in the direction toward which the mover was moving the moving body, either up or down, or laterally, or circularly. And by the amount the motor moves that moving body more swiftly, by the same amount it will impress in it a stronger impetus. It is by that impetus that the stone is moved after the projector ceases to move. But that impetus is continually decreased by the resisting air and by the gravity of the stone, which inclines it in a direction contrary to that in which the impetus was naturally disposed to move it. Thus the movement of the stone continually becomes slower, and finally that impetus is so diminished or corrupted that the gravity of the stone wins out over it and moves the stone down to its natural place.
When you throw a stone up in the air, you impart impetus to the stone. This impetus has direction. If you throw the rock straight up, the impetus continues to move the rock straight up. If you throw it to the side, it continues sideways. The impetus is proportional to the mass of the stone and the speed with which you throw it. This is why it is possible to throw a rock considerably farther than a feather. The feather may be much lighter, but this means the amount of impetus you can impart to it is very limited. The impetus is degraded by the resistance of the medium – that’s why projectiles eventually fall to earth. This image, from Niccola Tartaglia’s Nova Scientia (New science) of 1606, shows the paths of projectiles using impetus theory. Note that each path is straight to begin with, then curved, then straight again. The first straight part represents the motion of the object due to the impetus, the curved part represents the impetus being degraded by the object’s weight, and the last straight part represents the natural motion straight down.
Impetus is a cause of motion. It is not the same thing as our modern notion of inertia or momentum. Buridan is still working within an Aristotelian framework in which motion needs a cause. A moved object needs a mover. This is not the same as the Newtonian notion that a body in motion continues in motion unless acted on by some force, and a body at rest continues at rest unless acted on by some force. For Newton, continued motion or continued rest does not need to be explained; only a change in state from motion to rest or from rest to motion needs to be explained. For Buridan, motion always needs to be explained; rest does not.
Buridan also used impetus theory to explain why falling bodies move faster and faster as they get closer to earth. As the body falls its gravity (note: not gravity in modern sense, but the body’s own weightiness) generates additional impetus in the body. As the impetus increases, the body moves faster.
Buridan also suggested that impetus might explain the continual motions of the heavenly bodies:
It could be said . . . that God, when he created the world, moved each of the celestial orbs as He pleased, and in moving them He impressed in them impetuses which moved them without his having to move them. . . . And these impetuses which He impressed in the celestial bodies were not decreased nor corrupted afterwards, because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus.
Although he marks this as a suggestion, not an argument about the divine creation, this passage is quite remarkable, and foreshadows the later work of Galileo and Descartes. Buridan uses the same theory of motion to account for BOTH celestial AND terrestrial motion. This was a small but significant step toward breaking down the distinction between celestial and terrestrial physics.
Buridan, “The Impetus Theory of Projectile Motion,” trans. Marshall Clagett, in Sourcebook, pp. 275-280.