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Natural Science - Year I

Unit 9: Early Greek Theories of Motion

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History Weblecture for Unit 9

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History Lecture for Unit 9: Greek Views of Motion

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Putting the unit in context

 Period Major events in Greece
600 - 450 B. C. Thales and Ionian philosophers speculate about the nature of matter; primarily monist philosophers
430 - 400 B. C. Leucippus and Democritus propose atomic theories and materialist view.
circa 450 B. C. Great age of Greek drama; Socrates begins teaching.
431 - 404 B. C. Peloponnesian War
399 B. C. Death of Socrates
 387 B. C. Plato establishes the Academy at Athens
 335 B. C. Aristotle establishes the Lyceum at Athens
332 B. C. Aristotle dies; Theophrastus takes over Lyceum
300-200 B. C. Development of Hellenistic mathematics: Euclid, Archimedes, Aristarchus, Eratosthenes.
200-100 B. C. Hipparchus catalogs star systems.
100 B. C. - 100 A. D. Roman Republic becomes Roman Empire. Jesus Christ lives; early Christian Church established.
100-200 A. D. Ptolemy writes the Almagest.

Explaining How Things Move

We've already seen how, in contrast to the widespread, stable empires of Egypt and Mesopotamia, the city-states of Greece never managed to form a unified or long-lived government. As cities at the crossroads of Europe and Asia, and with an economies that were primarily based on sea trade, they were exposed to many conflicting ideas and views of the universe, and developed their own views on the nature of matter. They realized that matter changes form: ice can melt to liquid water, and when heated, becomes steam. Hillsides erode, and wood burns, and leavened dough becomes bread when it is baked. They were not united on whether these changes in form meant that the essence of the matter changed. The monists, who believed in only one type of matter, of course saw change in form as something affecting only appearance and not the essential matterness of matterness. The atomists such as Leucippus and Democritus believed in different types of matter, and thought changes in form were the result of recombinations of types of matter.

Another type of change the Greeks had to consider was change of position. Is this an essential change in the nature of a material object? Or is it a different kind of change altogether? Or no change in the matter at all, but only in the accident of its location? If there is only one kind of matter, can there be only one kind of motion? How exactly do we pinpoint location? What do we refer to? How do we measure change or the rate of change in either matter or position?

These questions may seem strange to us, looking backward through the lens of Newtonian definitions of motion and nineteenth century concepts of matter, and several centuries of maps using grids and frames of reference, but the Greeks didn't have the benefit of Newton's summation of the laws of motion, or a way to separate movement from energy and force, or even a common way of making maps. They had to define these concepts from their own experience. As you work through the historical material, and look at the study of movement in the science chapter, you'll see how hard it is to really define what, exactly, we mean when we say "it moves!"

Presocratic Ideas of Motion

Anaxagoras (ca. 500-428 bce)
And whatever things were to be, and whatever things were, as many as are now, and whatever things shall be, all these mind arranged in order; and it arranged that rotation, according to which now rotate stars and sun and moon and air and aether, now that they are separated. Rotation itself caused the separation, and the dense is separated from the rare, the warm from the cold, the bright from the dark, the dry from the moist.

— Anaxagoras, On Nature

The transition from the monist theories of the Ionians and the classical philosophies of matter begins with Anaxagoras. Anaxagoras was the last of the Ionian philosophers, greatly influenced by Parmenides and Anaximenes. He moved from Asia Minor to Athens, where, as a close friend of Pericles, he was able influence the Athenians to study philosophy. As would later happen to Socrates, he was accused of teaching impiety and, although acquitted, went into self-imposed exile.

We have only some fragments of Anaxagoras' work On Nature. In this text, he proposes the division of matter into parts or seeds called spermata of different types. Like the atoms of Democritus (who was a contemporary of Anaximander), these seeds come in many types, but unlike atoms, the seeds can be divided into smaller parts forever. Each individual part, no matter how small or how many times it is divided, contains all the characteristics and attributes of its type and cannot be changed. (This is one of the earliest definitions of the concept of an "element", and we still use it in defining elements and substances.)

Anaxagoras envisioned a single principle, the nous or "mind", as the organizing principle behind the stuff of the universe, bringing together and arranging the different types of seeds. The nous enters into some matter, and animates it, makes it alive. Other matter it simply moves into place. For example, the nous causes heavenly bodies to revolve around the earth, and all subsequent motions of things on earth have their origin in this heavenly motion. The stars and planets and sun are made of "fire" seeds, but — and here Anaxagoras breaks with earlier philosophers — the moon as well as the earth is gross and solid matter. This important distinction leads to the realization that the moon makes no light of its own, so all the lunar phenomena, which include phases and eclipses, are the result of the moon's position and its ability to reflect sunlight back towards earth.

Empedocles (ca. 490-430 bce)
For it is by earth that we see earth, and by water water, and by air glorious air; so, too, by fire we see destroying fire, and love by love, and strife by baneful strife. For out of these (elements) all things are fitted together and their form is fixed, and by these men think and feel both pleasure and pain.

— Empedocles, On Nature

At almost exactly the same time that Anaxagoras was teaching in Athens, Empedocles was teaching in Acragas (Agrigentum) in Sicily. The biographer Diogenes Laertius describes him as a popular politician, a self-proclaimed physician, and widely known and admired for his poetry and eloquent defense of democracy and equality. For centuries, we had only reports of his work by authors who lived several centuries after his death, but in 1990, several papyrus fragments were discovered in the archives of the University of Strasbourg. These included both known and new sections of his works On Nature (sometimes called the Physics), and On Purifications, which often seem to present different and even opposing views of nature. This makes it difficult to reconstruct Empedocles' philosophy, although we can recognize some of its claims as a reaction to the Eleatic monism of Parmenides.

Four Elements

In On Nature, Empedocles proposed that all matter consists of four "root" elements, lifeless types of matter with opposing characteristics of dryness and heat: earth, fire, water, and air. None of these elements is found in a pure state, but only as mixtures that are in constant turmoil, motivated and driven by forces he called Love, an attractive force leading to combinations of the elements, and Strife, a repulsive forces leading to separation of substances into distinct elements. These forces were not part of matter itself. In On Purification, Empedocles is concerned with the motivations of men and women. He often identifies the force Love with the goddess Aphrodite, as though he now believed the gods and goddesses of Greek religion were actual physical forces in the universe.

This map of the elements and characteristics is based on a number of medieval diagrams, the elements earth, fire, water, and air are drawn together by shared qualities of dryness, coldness, heat, and wetness. So earth is attracted to fire by shared dryness, and to water by shared cold. Empedocles' proposal further fueled debates about the nature of matter: later philosophers asked whether the materials of the elements were real, and exhibited the qualities, or whether the qualities were real, and "manifested" themselves as elements.

Hippocrates of Cos (ca. 450-370 bce) and Medicine
I will use my power to help the sick to the best of my ability and judgement; I will abstain from harming or wronging any man by it.

— Hippocrates, Text of the Oath

Hippocrates is another Ionian. Famous in his own lifetime for writing over 50 works on medicine, he influenced many others, including the physician Galen who also wrote treatises on medicine that were used throughout the western world until the Renaissance. Many doctors today still swear the Hippocratic oath in receiving their degrees.

Hippocrates adapted Empedocles' theories on matter and movement to create a coherent view of living organisms so that he could describe physical health in terms of the ratio of elements in the body. Living matter was made of forms of these elements called humors. Earth took the form of the humor black bile, fire blood, water was phlegm, and air yellow bile. Changes in the amounts of each humor cause growth, corruption, and eventually death. It was the physician's job to identify imbalances in these humors and restore them to their healthy and harmonious state through sleep, rest, exercise, and proper nutrition.

The Roman physician Galen (129-200 ce) later extended Hippocrates' humors to explain differences in personality and changes to the emotional health of his patients. A person with too much black bile was dour, heavy, and slow, able to hold anger for a long time. We still use these images when we talk of someone in a "black humor". Imbalances of humors led to disease; both mental and physical health were the result of the presence of the humors proper proportions.

Socrates and Plato

The Life of Socrates

During the second half of the fifth century, the philosopher Socrates challenged the citizens of Athens to search themselves and the universe for meaning and true understanding. He believed that sense perception was often misleading and that only logic could distinguish between appearance and reality. Socrates questioned the established views about many things, including the nature of the gods. Unfortunately for him, the Athenians had just undergone the disastrous Peloponnesian War with Sparta and had suffered through a major plague (which we think was an incident of bubonic plague like the Black Death which struck Europe in 1348), and they were looking for someone to blame for their troubles. Socrates was accused of impiety and offered the choice of exile or death; he chose death, since he felt that to leave Athens was a kind of living death anyway.

Plato and His School

Socrates' ideas were preserved in the works of his student Plato, who established in Athens a school called the Academy sometime around 390 bce, after he had traveled through Italy and Egypt, where he was influenced by the some of the mathematical theories of the Pythagoreans.

Ideas and Reality

According to the many dialogues of Socrates, which Plato claims to have recorded (but for which we have no other documentation, so Plato could have made some of them up), the enduring truth of a thing rests in the Idea of that thing. To go back to our chair, a Real Chair is the Idea of the Chair which has all the appropriate essential attributes of chairness. If you have the Idea of the Chair firmly in mind, you can make many and varied chairs, but without the idea, you could not make even one. A physical chair (on which you might actually sit) is only manifestation or example of this Idea, but is an imitation at best. It can be manipulated, damaged, or even destroyed. A painting of a physical chair is as much (or as little) like the physical chair as the physical chair is like the Ideal chair.

Of course, Socrates (and Plato) were more interested in the reality of Beauty, Goodness, Justice, and in Matter itself, than in Chairness. Behind any solid material object, were the ideas of solidity and matter and shape. The simplest and most fundamental shapes were the five geometric regular solids. With three edges and three vertices (corner) to each face (making a triangle), and four faces, the simplest shape is the tetrahedron. Each edge is the same length, each vertice is the same angle. The cube, octahedron, dodecahedron, and icosahedron also share these characteristics.

 Element Earth Water Air Fire Ether
Shape Cube Icosahedron Octahedron Tetrahedron Dodecahedron
Body fluid Black bile Phlegm Blood Yellow Bile --
Body part Spleen Brain Heart Liver --
Season Autumn Winter Spring Summer --
The Timaeus

Plato's assertion in the dialogue with Timaeus that the solids could be mapped to the four elements preserved the concept that natural phenomena could be described mathematically throughout late antiquity and the medieval period, when a more strict division between physical and abstract sciences was dominant. It was a simple, elegant way to connect mathematical ideas to physical reality. Nevertheless, we are limited by our inability to completely realize the Ideas as they are imperfectly manifested in things. The best we can accomplish is "a likely story" that "saves the appearances", that is, a theory which logically and rationally accounts for all observed phenomena, without contradicting itself or our experience.

In the Timaeus, Plato describes the motivating force of the universe as a divine Demiurge whose actions create order out of the chaos of the elements, which is similar to the activity that Anaxagoras attributed to the nous. While he used his idea of this prime motivator to explain the motions of the planets (as we shall see in the next unit), Plato could not adequately explain simple motions. That exercise he left to his student, Aristotle.


We are going to spend the next four units, as well as this one, discussing Aristotle's theories of motion, the planets, and biology, so we will defer a longer description of his life for another time. For now, we want to concentrate on his own interpretation of Empedocles' four elements, and set some basics for our discussion of the motion of the planets in the next unit.

Aristotelian Motion and the Elements

Unlike Anaxagoras, who believed the nous moved things, and Empedocles who thought opposing forces he called Love and Strife moved matter, or even Plato's Demiurge, Aristotle made the direction of movement a characteristic of the type of matter involved. In his work The Physics, Aristotle explains that it is part of the nature of the elements earth and water to move downward, where down is always toward the center of the earth, while fire and air move upward, away from the center. Since earth's downward tendency is stronger than water's downward tendency, earth sinks through water. Only vertical motion to or away from the center of the earth is natural to these elements.

Earth Fire Water Air

Aristotle still had to explain horizontal motion, and for this, he used a theory called antiperistasis. Any horizontal or sideways motion is thus the result of forces acting on the object. For example, for an arrow to fly forward, the bow must push on the arrow. But the arrow can continue forward only so long as there is something pushing it. So what pushes the arrow after it leaves the bow?


Aristotle imagined that the arrow split the air as it traveled forward, and left a partial vacuum behind. The air rushing in to fill this vacuum created a forward push on the tail of the arrow, so that it continued forward. Eventually, though, this push weakens, and the natural motion of the earth-type elements in the arrow take over, bringing the arrow back to earth. Notice that the arrow doesn't follow an arc, but moves horizontally forward, then simply falls at the point where the air's push fails.

This definition of motion caused Aristotle some serious difficulty. If only straight line vertical motion was natural, what accounted for the motion of the planets, sun, moon, and stars, which apparently moved steadily and endlessly in circles around the earth? In order to resolve his problem, Aristotle postulated a fifth element, the quintessence (quinto = five), which was different from the other four. The moon, sun, planets, and stars were all composed of this quintessence, which could not be found below the moon's orbit. Objects made of the quintessences were not subject to corruption, growth, or any kind of change, and their movements were perfect, unending circles around the earth.

It is an elegant theory, but it had a number of problems. In the next unit, we'll see how Aristotle's theory applied to the motion of the planets.

Study/Discussion Questions:

Further Study/On Your Own