2. The Greek Invention of

Scientific Theory

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.

• Many were ports and had maritime trade with Egypt and other Mediterranean states and colonies.

• As a result, while Mesopotamian society was essentially conservative and traditional, the Greeks were aware of many different cultural traditions and beliefs.

• 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

• Thales of Miletus was apparently the first of these, ca. 600 BCE.

• Among other ideas, Thales said the Earth is floating on water.

• Anaximander was also from Miletus.

• He suggested that the earth was like a disc of thickness one-third its diameter.

• There were wheels of fire in the heavens, and “breathing-holes” in these wheels accounted for the Sun, Moon, planets, and stars.

• Eclipses were due to stoppages in these holes, and partial stoppages accounted for the phases of the Moon.

• Anaximander seems to have been the first to speculate on the relative distances of the heavenly objects.

Ionian natural philosophers• The Pythagoreans were a Greek cult in southern Italy.

• Among other things, they discovered the relationships between the lengths of different plucked strings and harmonious chords.

• They are credited with discovery of the Pythagorean theorem for right triangles and other mathematical theorems.

• They saw mathematical relationships as the unchanging principles. (Pythagoras is reputed to have said, ”Things are numbers.”)

• Pythagoreans said that there is fire at the center of the Universe, and the Earth rotates around this, making day and night.

• The distances of the planets are related to the ratios for pleasant-sounding chords, producing the “music of the spheres.”

Plato• Plato taught in Athens (427-347 BCE).

• His school was called “The Academy.”

• Plato’s philosophy included the idea motion in the heavens is “perfect” and he saw the sphere as the most perfect geometrical shape for celestial objects.

• 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.

Interlude: Retrograde motion of the planets

Normally the planets move to the East (Right-Hand Rule) through the background pattern of stars.

JanuaryMars

February

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 was a student of Plato.

• He taught in Athens (384-322 BCE).

• His school was called “The Lyceum.”

• He is one of the greatest philosophers and thinkers of all time, and he wrote about a vast range of topics.

• He had a much more practical point of view than did Plato.

Aristotle’s cosmos

• Everything under the Moon was composed of four elements: Earth, Water, Air, & Fire (Empedocles, ca. 450 BCE).

• Each of these elements had a natural place in a sphere around the Earth.

• Most objects were composite, i.e. made of combinations of these elements.

Aristotle’s theory of motion

• Aristotle follows Plato in assuming that everything is perfect and eternal in the heavens, whereas on the Earth there is corruption and decay and all is transitory.

• Aristotle distinguishes natural motion, in which each element seeks its own natural place, and forced motion.

• Examples of forced motion would be shooting an arrow or throwing a spear.

• Natural motion under the Moon is vertical--up or down, depending on the object’s composition. Examples: smoke rising, water falling.

• Natural motion under the Moon is transitory, and stops when the object reaches its natural place.

Natural motion in the heavens• Aristotle agrees with Plato that all is perfect in the heavens.

• The shapes of celestial objects must be perfect spheres, since this is the most perfect shape.

• Natural motion in the heavens is circular and eternal, and objects move at constant speed. Example: the Sun, Moon, & planets.

• Natural motion in the heavens is necessarily circular, since only circles come back on themselves and can be eternal.

• But celestial objects can’t be composed of Earth, Air, Fire, or Water, for these elements have natural motion that is vertical and toward or away from the Earth.

• Celestial objects must be composed of a fifth element, or quintessence, whose natural motion is circular and eternal.

Aristotle’s cosmology

• Aristotle adopted Eudoxus’ scheme, but made mechanical sense of it, so that the turning of each sphere on its axle was driven by the turning of the sphere its axle was embedded in, etc., etc.

• To make it accurately follow observed planetary motions, he needed 56 spheres, with the Earth stationary at the center of it all. (Extra spheres were needed to cancel out motion of each outer planet for connection to the next inner one.)

• Aristotle’s Universe was also eternal--what could make it begin or end it.

• This model, with further refinements, remained the basic description of the structure of the heavens, and how celestial objects moved, for nearly 2,000 years.

Later Greek cosmology

• Alexander the Great (356-323 BCE) established the largest empire of ancient times.

• He founded a city with his name, Alexandria, on the Nile delta in Egypt, and when he died one his generals, Ptolemy, became ruler of that area of his empire.

• His successor set up what became the famous “Museum” and “Library” in Alexandria ca. 280 BCE.

• This was a sort of Institute for Advanced Study. It became the center for study and research in the western world, and it remained so until the 5th C CE.

• N.B. that although Alexandria was in Egypt, it was a Greek colony.

The Library in AlexandriaArtists’ reconstructions of how the Great Hall and Scroll Room of the Library in Alexandria might have looked. At one time the Library had 500,000 scrolls, all of which were lost when the Library was destroyed in 415 A.D.

Later Hellenistic refinements

• Two major refinements of Aristotle’s model of the heavens were made by later Greek thinkers.

• Hipparchos (160-127 B.C.) added the deferent and 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

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.

EpicyclesThe epicycle provided the observed retrograde motion.

The Ptolemaic model• Claudius Ptolemy (85-165) (in Alexandria) added the

equant, a place from which the motion of the center of the epicycle would appear to have uniform angular velocity as seen from the Earth.

• This produced a model with accuracies in the positions of the planets of about 2 deg over several centuries.

The Ptolemaic model

• This was all described in Ptolemy’s Mathematical Syntaxis, or the Almagest, a massive and highly technical astronomy manual.

• This Ptolemaic construction was very complicated to use, 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 model of the heavens had the Earth fixed and unmoving at the center of the Universe.

• Celestial objects, and the entire Universe, moved in perfect circles at constant speed round the Earth once a day.

• In addition, the spheres of the Sun, Moon, and planets moved faster than the stars.

• Retrograde motion of the planets was described by the epicyclic motion of additional small spheres whose centers moved in uniform circles about the Earth.

• While this model was extremely complicated to calculate with, it could predict positions of planets with amazing accuracies of < 2 degrees over several centuries.

The Greek achievement

• The Greeks invented the idea of a scientific theory.

• They used rational, mathematical models to describe the motions in the heavens.

• They compared theoretical predictions with observations to modify and extend their mathematical theories.

• Note that cosmological ideas were thoroughly integrated with Aristotle’s larger understanding of Nature.

• Cosmological ideas were also integrated with Aristotle’s more general philosophical system, so that cosmology--the structure and movement in the heavens--was part of the metaphysical and epistemological worldview Aristotle developed.