The Greek context

• In contrast to Mesopotamia, which was a large, centrally-administrated empire, the city-states of the Greek world were largely independent of each other. 2. The Greek • Many were ports and had maritime trade with Egypt and other Mediterranean states and colonies. Invention of • As a result, while Mesopotamian society was essentially conservative and traditional, the Greeks were aware of many different cultural traditions and beliefs. Scientific Theory • The Greeks were therefore more intellectually adventurous and curious, and it is out of this context that Greek natural philosophy was born.

Classical Greece Greek natural philosophers

• Although they proposed many different ideas about the natural world, all were attempting to find underlying and unchanging principles responsible for the constantly- changing phenomena of the everyday natural world. • These earliest natural philosophers came from Ionia, on the western coast of Asia Minor (what is now Turkey). • Note that these thinkers adopted completely naturalistic explanations-no gods involved. • They invented the idea of a scientific theory: underlying principles which show why things happen in the natural world as they do.

Ionian natural philosophers Ionian natural philosophers

• Thales of Miletus was apparently the first of these, ca. 600 • The Pythagoreans were a Greek cult in southern Italy. BCE. • Among other things, they discovered the relationships between • Among other ideas, Thales said the Earth is floating on water. the lengths of different plucked strings and harmonious chords. • Anaximander was also from Miletus. • They are credited with discovery of the Pythagorean theorem for right triangles and other mathematical theorems. • He suggested that the earth was like a disc of thickness one- third its diameter. • They saw mathematical relationships as the unchanging principles. (Pythagoras is reputed to have said, ”Things are • There were wheels of fire in the heavens, and “breathing- numbers.”) holes” in these wheels accounted for the Sun, Moon, planets, and stars. • Pythagoreans said that there is fire at the center of the Universe, and the Earth rotates around this, making day and • Eclipses were due to stoppages in these holes, and partial night. stoppages accounted for the phases of the Moon. • The distances of the planets are related to the ratios for • Anaximander seems to have been the first to speculate on pleasant-sounding chords, producing the “music of the the relative distances of the heavenly objects. spheres.” Plato Interlude: Retrograde motion • Plato taught in Athens (427-347 BCE). of the planets • His school was called “The Academy.” Normally the planets move to the East (Right-Hand Rule) • Plato’s philosophy included the idea through the background pattern of stars. motion in the heavens is “perfect” and he saw the sphere as the most perfect Mars geometrical shape for celestial objects. January February • Plato produced a geometrical model of the heavens: a nest of 8 concentric spheres turning on a common axle, with Earth at the center, and the Sun, Moon, and planets each embedded in one of these spheres. • Plato is clearly influenced by the Pythagoreans, since he is assuming that mathematical principles govern the cosmos.

Retrograde motion of the planets Eudoxus’ model • Plato’s student Eudoxus improved the model to account for the retrograde motion of the planets. • He needed 27 spheres, each turning on its individual axle. • Example: Mars’ motion ! Sphere 1--diurnal (24-hr) motion ! Sphere 2--Mars’ orbital motion ! Spheres 3 & 4--turning opposite directions produced a figure- eight motion to approximate the retrograde motion of Mars.

Aristotle Aristotle’s cosmos

• Aristotle was a student of • Everything under the Plato. Moon was composed of four elements: Earth, • He taught in Athens (384-322 Water, Air, & Fire BCE). (Empedocles, ca. 450 • His school was called BCE). “The Lyceum.” • Each of these elements • He is one of the greatest had a natural place in a philosophers and thinkers of sphere around the all time, and he wrote about a Earth. vast range of topics. • Most objects were • He had a much more practical composite, i.e. made of point of view than did Plato. combinations of these elements. Aristotle’s theory of motion Natural motion in the heavens

• Aristotle agrees with Plato that all is perfect in the heavens. • Aristotle follows Plato in assuming that everything is perfect and eternal in the heavens, whereas on the Earth • The shapes of celestial objects must be perfect spheres, there is corruption and decay and all is transitory. since this is the most perfect shape. • Aristotle distinguishes natural motion, in which each • Natural motion in the heavens is circular and eternal, and element seeks its own natural place, and forced motion. objects move at constant speed. Example: the Sun, Moon, • Examples of forced motion would be shooting an arrow & planets. or throwing a spear. • Natural motion in the heavens is necessarily circular, since • Natural motion under the Moon is vertical--up or down, only circles come back on themselves and can be eternal. depending on the object’s composition. Examples: • But celestial objects can’t be composed of Earth, Air, Fire, smoke rising, water falling. or Water, for these elements have natural motion that is • Natural motion under the Moon is transitory, and stops vertical and toward or away from the Earth. when the object reaches its natural place. • Celestial objects must be composed of a fifth element, or quintessence, whose natural motion is circular and eternal.

Aristotle’s cosmology Later Greek cosmology

• Aristotle adopted Eudoxus’ scheme, but made • Alexander the Great (356-323 BCE) established the mechanical sense of it, so that the turning of each sphere largest empire of ancient times. on its axle was driven by the turning of the sphere its • He founded a city with his name, Alexandria, on the axle was embedded in, etc., etc. Nile delta in Egypt, and when he died one his generals, • To make it accurately follow observed planetary Ptolemy, became ruler of that area of his empire. motions, he needed 56 spheres, with the Earth stationary • His successor set up what became the famous at the center of it all. (Extra spheres were needed to “Museum” and “Library” in Alexandria ca. 280 BCE. cancel out motion of each outer planet for connection to the next inner one.) • This was a sort of Institute for Advanced Study. It became the center for study and research in the western Aristotle’s Universe was also eternal--what could make it • world, and it remained so until the 5th C CE. begin or end it. • N.B. that although Alexandria was in Egypt, it was a This model, with further refinements, remained the basic • Greek colony. description of the structure of the heavens, and how celestial objects moved, for nearly 2,000 years.

The Library in Alexandria Later Hellenistic refinements

Artists’ reconstructions of how the Great Hall and Scroll Room • Two major refinements of Aristotle’s model of the heavens of the Library in Alexandria might have looked. At one time were made by later Greek thinkers. the Library had 500,000 scrolls, all of which were lost when • Hipparchos (160-127 B.C.) added the deferent and the Library was destroyed in 415 A.D. epicycles to Aristotle’s model to account for the retrograde motion of the planets • The epicycle was a small circle in which the planet moved, while the center of this circle moved in a larger circle, the deferent, around the Earth. • He also added the eccentric, locating the Earth to one side of the center of the deferent, to account for the non- uniform speeds of planets. • N.B. the spheres turning on axles in which the planets were originally embedded have been replaced by a mathematical model. Hipparchos’ model Epicycles

The epicycle provided the observed retrograde motion.

This model was very accurate: Hipparchos’ values for the lunar month and mean solar year differ from modern values by <1 sec and <5 min respectively.

The Ptolemaic model The Ptolemaic model • Claudius Ptolemy (85-165) (in Alexandria) added the equant, a place from which the motion of the center of • This was all described in Ptolemy’s Mathematical the epicycle would appear to have uniform angular Syntaxis, or the Almagest, a massive and highly technical velocity as seen from the Earth. astronomy manual. • This produced a model with accuracies in the positions • This Ptolemaic construction was very complicated to use, of the planets of about 2 deg over several centuries. with more than 70 simultaneous motions to work out. • A different construction was required for each problem one wanted to solve, e.g. when the next lunar eclipse would be, or how the apparent size of the Moon changes, or where Mars would be in the sky in 30 years. • Note that Ptolemy has replaced a physical model for planetary motions with a mathematical model. • Ptolemy’s model remained the model of the heavens for another 1,500 years.

Summary The Greek achievement

• The Greek model of the heavens had the Earth fixed and • The Greeks invented the idea of a scientific theory. unmoving at the center of the Universe. • They used rational, mathematical models to describe the • Celestial objects, and the entire Universe, moved in perfect motions in the heavens. circles at constant speed round the Earth once a day. • They compared theoretical predictions with observations to • In addition, the spheres of the Sun, Moon, and planets modify and extend their mathematical theories. moved faster than the stars. • Note that cosmological ideas were thoroughly integrated • Retrograde motion of the planets was described by the with Aristotle’s larger understanding of Nature. epicyclic motion of additional small spheres whose centers Cosmological ideas were also integrated with Aristotle’s moved in uniform circles about the Earth. • more general philosophical system, so that cosmology--the • While this model was extremely complicated to calculate structure and movement in the heavens--was part of the with, it could predict positions of planets with amazing metaphysical and epistemological worldview Aristotle accuracies of < 2 degrees over several centuries. developed.