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The Ancient Greeks


The religious traditions of Judaism and Christianity have provided one foundation of Western civilization, while the philosophy of the ancient Greeks has provided another.

The ancient era is dominated by the Greeks, some of whom were influenced by ideas developed much earlier in Egypt and Mesopotamia. During the ancient era Greek philosophy was the most creative. The Romans derived most of their thought from it and built upon it, but they did not add much that was new. During the time of Aristotle, there was a flowering of mathematics and natural philosophy, spurred by the conquests of Alexander the Great, Aristotle's most famous pupil. Alexander accumulated one of the largest empires the world had ever seen, stretching from Egypt to the Punjab and covering most of what is now known as Asia Minor. The information acquired by the engineers and surveyors whom Alexander took on his military campaigns initiated a shift away from theoretical speculation and towards more empirical investigation. This development was aided by the conquering of Mesopotamia by the Greeks, which gave them access to Babylonian mathematics and science.

The period of Greek philosophy may conveniently be divided into three parts: the pre-Socratics; the work of Socrates, Plato, and Aristotle; and the schools that followed these three giants.

We will concentrate on two of the fields of enquiry that concerned the natural philosophers of the ancient world. The first, cosmology, attempts to understand the nature of the universe, of the sun, the moon, the planets and the stars. The second, mechanics, investigates the motion of terrestrial bodies and the action of forces upon them. Having virtually no experimental apparatus and a philosophy that often discouraged experimentation, the conclusions of the ancient Greeks are sometimes wildly inaccurate. Yet so influential was their thought that it was not called into question for more than 1500 years later, when the methods of true scientific enquiry were developed. Only then, with the work of Galileo and Newton, did it became clear that cosmology and mechanics were subject to the same universal laws of motion.

The ideas of the Greek philosophers are worth investigating, if only because they give a context to the extraordinary accomplishments of later scientific understanding. In addition, the progression of scientific thought from the ideas of the Greek philosophers to the theories of Galileo and Newton often seems to mirror our own development in understanding as we grow from childhood to maturity. However, since this is a course in Physics rather than Philosophy, I will concentrate only on those philosophers whose ideas can be directly traced to the later developments we will be studying.

In order to understand the views of the Greek philosophers it is important to appreciate the background to their thought. It was believed that gods ruled the universe and often interfered in human affairs. While we tend to explain the movement of animals by mechanical models, the Greeks rather attempted to explain the movements of the heavenly bodies by analogy to that of the animals. Early Greek religion, for example, demanded that the sun and moon were alive. Even when this view was no longer widely accepted, the regular movements of the stars and planets in contrast to the irregular movements of earth-bound animals were seen as a manifestation of divine control. The nature of terrestrial objects was base, while that of the planets, moving under the control of a divine mover, was perfect and indestructible.

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The Miletian School. (7th and early 6th centuries BC)

It was in Miletus in Ionia that the seeds of Greek philosophy were planted. The destruction of Miletus by the Persians in the middle of the 6th century BC encouraged the emergence of Athens as the intellectual and commercial centre of the Western world. Thales was a well-known Miletian mathematician who was interested in natural phenomena and attempted to explain the world without the contemporary appeal to the deities. His discovery of sea fossils found far from the Mediterranean Sea led him to suggest that water is the basic building block of the world. He believed that the earth is a cylinder or a disc that floats in water, inside the sphere of the heavens. Slightly later, Anaximander explained the sun, moon and stars as holes in fiery rings which were left over from a primeval conflict between the basic elements, water and hot. Anaximenes has the distinction of having made the first known formulation of what is now close to as the conservation of energy, in his statement that nothing can be created from nothing. One of Anaximenes pupils, Anaxagoras, had a surprisingly modern view of the universe. He believed that the sun was a small red-hot stone, around which the (inhabited) moon and earth orbited. He discovered that the moon shines by light reflected from the sun, and gave an explanation for the eclipses of the sun and moon that were correct in essence. Unlike many of his contemporaries and intellectual descendants, he believed that earth and the heavens were made of similar material; for this revolutionary view he was prosecuted for impiety.

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Pythagoras (6th century BC)

Pythagoras probably could lay claim to be called the very the First Mathematician, although his interests were much wider than pure mathematics. His influence in founding the rational intellectual tradition of the West is enormous and his name lives on in every mathematics school book. He was the first to indicate the intimate connection between physics and mathematics. For example, he discovered that musical notes produced by vibrating strings are associated with the lengths of the strings. He was thus led to conclude that real numbers are the true essence of the universe, and that material objects are but pale copies. This view was called into question by his discovery of irrational numbers (a discovery his disciples attempted to hide!). Pythagoras was probably the first to suggest that the earth was spherical, although his reasons were more probably mystical than scientific. He is rumoured to have had a poor view of sex.

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Socrates (470?-399 BC)

Socrates was certainly one of the most interesting and enormously influential philosophers of ancient Greece. His ideas were passed on through his famous pupil, Plato, who in turn passed them on to Aristotle. His contributions to scientific development were small; his importance lay in his non-materialist philosophy and his method of teaching which carries his name. Socratic dialogue aims to force the questioner to think for himself. His probing questions, his impatience with faulty arguments, and his disdain of power or fame did not endear him to the politicians of his time, who finally forced him to commit suicide.

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Plato (428?-348? BC)

The influence of Plato on the development of our understanding of the natural world has been immense. He believed that the world was fixed and immutable, but that this world was not available to our senses. "True" reality lies in a transcendental world of unchanging Forms, at whose pinnacle is the Good, an immutable and eternal being. Our senses contact this world only imperfectly through the mediation of the Demiurge, which is locked within the world of senses. Our impressions are the results of the Demiurge's attempts to fashion the world using the Forms as a blueprint. Imagine being imprisoned within a cave, your back to the entrance, outside of which is a source of light. Objects passing in front of the cave will have their shadows projected on to the back wall of the cave; this shadow world is all we can ever see. This metaphor has had immense influence throughout the ages on the way in which we in the West view ourselves and our place in the universe.

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Aristotle (384-322 BC)

The separation of cosmology from physics which continued until the time of Newton started with Aristotle. His ideas about astronomy are laid out in his book De Caelo. He was one of the earliest philosophers to construct a systematic formulation of physical phenomena, and possible the first true experimentalist. He is Plato's most famous student and had a huge influence, not always benign, on the development of science well into the 17th century. Indeed there is considerable research evidence that over half of all first year university students hold Aristotelian ideas about motion!

Aristotle believed that everything on Earth, which is composed of a mixture of the four elements, earth, fire, air and water, is subject to decay; the heavens are perfect and eternal, as are the heavenly bodies, which are composed of a fifth element (from this theory comes our word "quintessence"). Bodies on Earth move naturally in straight lines, but the natural movement of the heavenly bodies, which are attached to perfect spheres, is circular. The base Earth, which is spherical, is stationary and sits at the centre of the Universe.

Aristotle believed that the world is infused with purpose, moving toward a fixed goal. Terrestrial objects, both animate and inanimate, possess souls that determine the "nature" of the objects. The "natural state" of terrestrial material is one of rest, and since there exists a tendency for every body to reach its natural state every motion must have a cause (in modern terms, a force). There are two kinds of cause (or force): (a) those inherent in the body ("levity" for air or fire, "gravity" for material bodies) : (b) contact forces exerted by an external agent. Thus motion is only possible when forces are applied to them. Since the latter type of force requires physical contact with the object, it is difficult to explain how an arrow can continue to move after it leaves the bow. Aristotle's explanation was that the arrow is propelled by air which rushes in behind it to fill the void that would otherwise form as it moved forward; motion in a vacuum is thus impossible. Since the natural motion of earth-bound objects is rectilinear, the arrow moves horizontally for a while, until it begins to fall vertically. Motion is seen as a balance between propulsion (a pushing force) and a resistance to motion, occasioned by the natural tendency of the body to attain a state of rest. The speed of a falling body is considered to be proportional to weight, inversely proportional to the resistance. Heavier bodies fall faster than lighter ones.

Aristotle also believed that matter is continuous, in disagreement with the Atomists , of whom Democritus is the most famous example; they believed that matter consisted of indivisible particles called atoms. However, Aristotle's influence was so great that any enthusiasm for atomism was dampened for many centuries, until the physical evidence became compelling at the end of the 19th century.

Aristotle's most famous pupil was Alexander the Great, who accumulated one of the largest empires the world had ever seen, stretching from Egypt to the Punjab. During this period there was a flowering of mathematics and natural philosophy, and the information acquired by the engineers and surveyors whom Alexander took on his military campaigns initiated a shift away from theoretical speculation and towards more empirical investigation. This development was aided by the conquering of Mesopotamia by the Greeks, which gave them access to Babylonian mathematics and science.

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Aristarchus of Samos (3rd/4th century BC)

Aristarchus is interesting since he was one of the few early natural philosophers who hypothesized that the Earth, and all the planets, revolves around the sun and rotates on its own axis once a day; this is essentially the complete Copernican view. This hypothesis was so contrary to the Greek view of the entirely different natures of the Earth and the heavens that one of Aristarchus' contemporaries suggested that he be indicted for impiety. So great was the authority of Aristotle, backed up by Hipparchus, that the heliocentric view of Aristarchus had virtually no influence in the development of cosmology although it is probable that Copernicus knew of his hypothesis, and was presumable somewhat encouraged. Aristarchus was an observational astronomer of great talent, who made the first realistic measurement of the distances from the earth to the sun, and to the moon and the magnitude of the earth's diameter.

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Archimedes of Syracuse (387-212 BC)

If Pythagoras can lay claim to be the first mathematician and Aristotle the first Natural Philosopher, Archimedes may be called the first engineer. As a result he contributed greatly to our understanding of the mechanical world, but only marginally to the developing philosophy of that understanding. An inventor of considerable talent, he invented the water screw for raising water, which is still used in Egypt today, and constructed a mechanical model of the solar system which reproduced the apparent movement of the planets. According to legend the enunciation of the famous principle which bears his name arose from his successful attempt to determine if King Herod's crown was made of pure gold or had been debased with a less dense, baser metal. He was also a geometer of no mean ability, originating a method of estimating the ratio of the circumference of a circle to its radius (pi) to any required accuracy.

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Euclid (3rd/4th century BC).

A discussion of the scientific and mathematical development of the ancient Greeks would not be complete without a mention of the Elements of Geometry by Euclid that, for the first time, presented in a systematic fashion the principles and proofs of geometry. This work had enormous influence, and continues to form the basis of high school geometry. Euclid was a younger contemporary of Aristarchus

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Hipparchus of Nicaea (2nd century BC).

Sometimes described as the greatest astronomer of antiquity, Hipparchus agreed with the Aristotelian view that the stars, the sun and the planets revolve in circular orbits around the stationary Earth, which lies at the centre of the Universe. The difficulty with this view is that it fails to explain the observations. Certainly the stars move in perfect spheres across the heavens. However, the planets, though their orbits repeat themselves, move much more erratically, even reversing direction for a few months. Further, the observed variation in brightness of such planets as Mars and Venus indicates that the distances of these planets from Earth is not constant as would be required by a circular orbit centred on the Earth. In order to explain this behaviour a geometrical construction was invented. If a planet moves in a circle whose centre moves around the Earth on a larger one, both of these observations could be explained. The smaller circle is called an epicycle.

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Claudius Ptolemy (85-165 AD)

Ptolemy was the last important astronomer of antiquity. He was also a mathematician, a physicist and a geographer. He published data on the rising and setting of stars, he studied optical phenomena, and produced a wildly inaccurate set of maps, but his main work was his compilation of Greek astronomy, which included a catalogue of over 1,000 stars. He believed that the planets and fixed stars moved inside crystalline spheres which revolved around the earth. The "motive force" for these spheres was a "prime mover". Although his observations were less accurate than those of Hipparchus who preceded him by two centuries, he developed and extended the system of epicycles thereby giving his name to the geocentric view of the Universe. With the large number of reasonably accurate observations now available, the Ptolemaic universe required an epicycle system containing no less than eighty epicycles. This view of the universe dominated the ideas of Christian Europe until the 16th century.

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