Greek Science

The Milesians

The first important contributions to Greek science came from the city of Miletus, near the coast of what is now Turkey, beginning with Thales in about 585 BC, followed by Anaximander in about 555 BC, then Anaximenes in 535 BC.  These Milesians were probably the first people to do real science, immediately recognizable as such to a modern scientist, as opposed to developing new technologies.

The crucial contribution of Thales to scientific thought was the idea that natural phenomena are explicable in terms of matter interacting by natural laws, and are not the results of arbitrary acts by gods.  An example is Thales' theory of earthquakes.  He thought that the (presumed flat) Earth is actually floating on a vast ocean, and that disturbances in the ocean occasionally caused the Earth to shake or even crack, just as they would a large boat.  The common Greek belief at the time was that earthquakes were caused by the anger of Poseidon, god of the sea.  Lightning was similarly thought to be the anger of Zeus.  Anaximander more rationally suggested that lightning is caused by clouds being split up by the wind.

An essential part of the Milesians' success in developing a picture of nature was that they engaged in open, rational, critical debate about each other's ideas.  It was tacitly assumed that all the theories and explanations were directly competitive with one another, and all should be open to public scrutiny, so that they could be debated and judged.  This is still the way scientists work.  Each contribution, even that of an Einstein, depends heavily on what has gone before.

The theories of the Milesians fall into two groups:

  • (1)  theories regarding particular phenomena or problems, of the type discussed above
  • (2)  doctrines of general cosmological import

A spectacular example of the second type of theory was Anaximander's suggestion that the Earth was actually a cylinder, and the Sun, Moon and stars were located on concentric rotating cylinders.  This is the first recorded attempt at a mechanical model of the Universe.  He postulated that the stars themselves were rings of fire.  Again, this was a revolutionary suggestion, as all heavenly bodies had previously been regarded as living gods.

He also considered the problem of the origin of life, which becomes more difficult to explain if you don't believe in gods.  He suggested that the lower forms of life might be generated by the action of sunlight on moist earth.  He also realized that a human baby is not self-sufficient for quite a long time, so he postulated that the first humans were born from a certain type of fish known at that time.  (Evolutionary theory in 550 B.C.!!)

All three of these Milesians struggled with the puzzle of the origin of the Universe, what was here at the beginning, and what things are made of.  Thales suggested that in the beginning there was only water, so somehow everything was made of it.  Anaximander supposed that initially there was a boundless chaos, and the Universe grew from this as from a seed.  Anaximenes had a more sophisticated approach, to modern eyes.  His suggestion was that originally there was only air (really meaning a gas) and the liquids and solids we see around us were formed by condensation.  Notice that this means a simple initial state develops into our world, using physical processes which are already familiar to us.  Of course this leaves a lot to explain, but it's on the right track.

Early Geometry

One of the most important contributions of the Greeks was their development of geometry, culminating in Euclid's Elements, a giant textbook containing all the known geometric theorems at that time (about 300 BC), presented in an elegant logical fashion.  The first account we have of the beginnings of geometry is from the Greek historian Herodotus, writing (in 440 BC or so) about the Egyptian king Sesotris (1300 BC):

"This king moreover (so they said) divided the country among all the Egyptians by giving each an equal square parcel of land, and made this the source of his revenue, appointing the payment of a yearly tax.  And any man who was robbed by the river of a part of his land would come to Sesotris and declare what had befallen him; then the king would send men to look into it and measure the space by which the land was diminished, so that thereafter it should pay the appointed tax in proportion to the loss.  From this, to my thinking, the Greeks learnt the art of measuring land..."

The Pythagoreans:  a Cult with a Theorem

Pythagoras was born about 570 BC on the island of Samos, less than a hundred miles from Miletus, and was thus a contemporary of Anaximenes.  However, the island of Samos was ruled by a tyrant named Polycrates, and to escape an unpleasant regime, Pythagoras moved to Croton, a Greek town in southern Italy, about 530 BC.

Pythagoras founded what we would nowadays call a cult, a religious group with strict rules about behavior, including diet (no beans), and a belief in the immortality of the soul and reincarnation in different creatures.  This noticably contrasts with the Milesians' approach to life.

The Pythagoreans believed strongly that numbers, by which they meant the positive integers 1,2,3,..., had a fundamental, mystical significance.  The numbers were a kind of eternal truth, perceived by the soul, and were not subject to the uncertainties of perception by the ordinary senses.  In fact, they thought that the numbers had a physical existence, and that the Universe was somehow constructed from them.  In support of this, they pointed out that different musical notes differing by an octave or a fifth, could be produced by pipes (like a flute), whose lengths were in the ratios of whole numbers, 1:2 and 2:3 respectively.  (Note that this is an experimental verification of a hypothesis.)  They felt that the motion of the heavenly bodies must somehow be a perfect harmony, giving out a music we could not hear since it had been with us since birth.  (The so-called "Music of the Spheres".)  Interestingly, they did not consider the Earth to be at rest at the center of the Universe.  They thought it rotated about a central point daily, to account for the motion of the stars.  Much was wrong with their picture of the Universe, but it was not geocentric.  For religious reasons, they felt the Earth was not noble enough to be the center of everything, where they supposed there was a central fire.

To return to their preoccupation with numbers, they coined the term "square" number, for 4,9, etc., drawing square patterns of evenly spaced dots to illustrate this idea.  The first square number, 4, they equated with justice.  5 represented marriage, of man (3) and woman (2).  7 was a mystical number.  Later Greeks, like Aristotle, made fun of all this.

The Square on the Hypotenuse

Pythagoras is most famous for the theorem about right triangles, that the sum of the squares of the two sides of a right triangle is equal to the square of the long side, called the hypotenuse.  Actually, it seems very probable that this result was known to the Babylonians a thousand years earlier, and to the Egyptians, who, for example, used lengths of rope 3, 4, and 5 units long to set up a large right-angle for building and surveying purposes.  It is possible, however, that Pythagoras and his followers were the first to rigorously prove that the theorem is true.

The point is, the reason the Pythagoreans worked on this problem (and others like it) is because they thought they were investigating the fundamental structure of the Universe.  Abstract arguments of this type, and the beautiful geometric arguments the Greeks constructed during this period and slightly later, seemed at the time to be merely mental games, valuable for developing the mind.  In fact, these arguments have turned out, rather surprisingly, to be on the right track to modern science.

Change and Constancy in the Physical World

Over the next century or so, 500 BC to 400 BC, the main preoccupation of philosophers in the Greek world was that when we look around us, we see things changing all the time, and how is this to be reconciled with the feeling that the Universe must have some constant, eternal qualities?  Heraclitus, from Ephesus, claimed that "everything flows", and even objects which appear static have some inner tension or dynamism.  Parminedes, an Italian Greek, came to the opposite conclusion, that nothing ever changes, and apparent change is just an illusion, a result of our poor perception of the world.  This may not sound like a very promising debate, but in fact it is, because trying to analyze what is changing and what isn't in the physical world led eventually to the idea of elements, atoms, and conservation laws, such as the conservation of energy.

The first physicist to give a clear formulation of a possible resolution of the problem of change was Empedocles around 450 BC, who stated that everything was made up of four elements, earth, water, air and fire, the elements themselves being eternal and unchanging, and different substances being made up of the elements in different proportions, just as all colors can be created by mixing three primary colors in appropriate proportions.  Forces of attraction and repulsion (referred to as love and strife) between these elements cause coming together and separation, and thus apparent change in substances.  Another physicist, Anaxogoras, argued that no natural substance can be more elementary than any other, so there were an infinite number of elements, and everything had a little bit of everything else in it.  He was particularly interested in nutrition, and argued that food contained small amounts of hair, teeth, etc., which our bodies are able to extract and use.

The most famous and influential of the fifth century BC physicists, though, were the atomists, Leucippus of Miletus and Democritus of Abdera.  They claimed that the physical world consisted of atoms in constant motion in a void, rebounding or cohering as they collide with each other.  Change of all sorts is thus accounted for on a basic level by the atoms separating and recombining to form different materials.  The atoms themselves do not change.  This sounds amazingly like our modern picture, but it was all conjecture, and when they got down to relating the atoms to physical properties, Democritus suggested, for example, that things made of sharp, pointed atoms tasted acidic, and those of large round atoms tasted sweet.  There was also some confusion between the idea of physical indivisibility and that of mathematical indivisibility, meaning something that only exists at a point.  The atoms of Democritus had shapes, but it is not clear if he realized this implied they could, at least conceptually, be divided.  This caused real problems later on, especially since at that time there was no experimental backing for an atomic theory, and it was rejected by Aristotle and others.

Hippocrates and his Followers

It is also worth mentioning that at this same time, on the island of Cos just a few miles from Miletus, lived the first great doctor, Hippocrates.  He and his followers adopted the Milesian point of view.  Applied to disease, this meant that illness was not caused by the gods, not even epilepsy, which was called the sacred disease, but instead there was some rational explanation, such as infection, which could perhaps be treated.

Here's a quote from one of Hippocrates' followers, writing about epilepsy in about 400 B.C.:

It seems to me that the disease called sacred … has a natural cause, just as other diseases have.  Men think it divine merely because they do not understand it.  But if they called everything divine that they did not understand, there would be no end of divine things! … If you watch these fellows treating the disease, you see them use all kinds of incantations and magic -- but they are also very careful in regulating diet.  Now if food makes the disease better or worse, how can they say it is the gods who do this? … It does not really matter whether you call such things divine or not.  In Nature, all things are alike in this, in that they can be traced to preceding causes.

The Hippocratic doctors criticized the philosophers for being too ready with postulates and hypotheses, and not putting enough effort into careful observation.  These doctors insisted on careful, systematic observation in diagnosing disease, and a careful sorting out of what was relevant and what was merely coincidental.  Of course, this approach is the right one in all the sciences.


In the fourth century B.C., Greek intellectual life centered increasingly in Athens, where first Plato and then Aristotle established schools, the Academy and the Lyceum respectively, which were really the first universities.  They attracted philosophers and scientists from all over Greece.

Actually, this had all began somewhat earlier with Socrates, Plato's teacher, who, however, was not a scientist, and so not central to our discussion here.  One of Socrates' main concerns was how to get the best people to run the state, and what were the ideal qualities to be looked for in such leaders.  He believed in free and open discussion of this and other political questions, and managed to make very clear to everybody that he thought the current leaders of Athens were a poor lot.  In fact, he managed to make an enemy of almost everyone in a position of power, and he was eventually brought to trial for corrupting the young with his teachings.  He was found guilty, and put to death.

This had a profound effect on his pupil Plato, a Greek aristocrat, who had originally intended to involve himself in politics.  Instead, he became an academic -- in fact, he invented the term!  He, too, pondered the question of what is the ideal society, and his famous book "The Republic" is his suggested answer.  He was disillusioned with Athenian democracy after what had happened to Socrates, and impressed with Sparta, an authoritarian state which won a war, the Peloponnesian war, against Athens.  Hence his Republic has rather a right wing, antidemocratic flavor.  However, he wanted to ensure that the very best people in each generation are running the state, and he thought (of course, being a philosopher) that the best possible training for these future leaders was a strong grounding in logic, ethics, and exercise with abstract ideas.

Plato, then, had a rather abstract view of science, reminiscent of the Pythagoreans.  In particular, he felt that the world we apprehend with our senses is less important than the underlying world of pure eternal forms we perceive with our reason or intellect, as opposed to our physical senses.  This naturally led him to downgrade the importance of careful observation, for instance in astronomy, and to emphasize the analytical, mathematical approach.

Plato's concentration on perfect underlying forms did in fact lead to a major contribution to astronomy, despite his own lack of interest in observation.  He stated that the main problem in astronomy was to account for the observed rather irregular motion of the planets by some combination of perfect motions, that is, circular motions.  This turned out to be a very fruitful way of formulating the problem.

Plato's theory of matter was based on Empedocles' four elements, fire, air, water and earth.  However, he did not stop there.  He identified each of these elements with a perfect form, one of the regular solids, fire with the tetrahedron, air with the octahedron, water with the icosahedron and earth with the cube.  He divided each face of these solids into elementary triangles (45-45-90 and 30-60-90) which he regarded as the basic units of matter.  He suggested that water could be decomposed into fire and air by the icosahedron breaking down to two octahedra and a tetrahedron.  This looks like a kind of atomic or molecular theory, but his strong conviction that all properties of matter could eventually be deduced by pure thought, without resort to experiment, proved counterproductive to the further development of scientific understanding for centuries.

Crystal Spheres:  Plato, Eudoxus, Aristotle

Plato, with his belief that the world was constructed with geometric simplicity and elegance, felt certain that the Sun, Moon and planets would have a natural circular motion, since that is the simplest uniform motion that repeats itself endlessly.  However, although the "fixed stars" did in fact move in simple circles about the North star, the Sun, Moon and planets traced out much more complicated paths across the sky.  These paths had been followed closely and recorded since early Babylonian civilization, so were very well known.  Plato suggested that perhaps these complicated paths were actually combinations of simple circular motions, and challenged his Athenian colleagues to prove it.

The first real progress on the problem was made by Eudoxus.  Eudoxus placed all the fixed stars on a huge sphere, the Earth itself being a much smaller sphere fixed at the center.  The huge sphere rotated about the Earth once every twenty-four hours.  So far, this is the standard "starry vault" picture.  Then Eudoxus assumed the Sun to be attached to another sphere, concentric with the fixed stars' sphere, that is, it was also centered on the Earth.  This new sphere, lying entirely inside the sphere carrying the fixed stars, had to be transparent, since the fixed stars are very visible.  The new sphere was attached to the fixed stars' sphere so that it, too, went around every twenty-four hours, but *in addition* it rotated slowly about the two axis points where it was attached to the big sphere, and this extra rotation took one year.  This meant that the Sun, viewed against the backdrop of the fixed stars, traced out a circular path which it covered in a year.  This path is called the ecliptic.  To get it all right, the ecliptic has to be tilted at 23 degrees to the "equator" line of the fixed stars, taking the North star as the celestial north pole.

This gives a pretty accurate representation of the Sun's motion, but it didn't quite account for all the known observations at that time.  For one thing, if the Sun goes around the ecliptic at an exactly uniform rate, the time intervals between the solstices and the equinoxes will all be equal.  In fact, they're not -- the Sun moves a little faster through some parts of its yearly journey along the ecliptic than others.  This, and other considerations, led to the introduction of three more spheres to describe the Sun's motion.  Of course, to actually show that the combination of these motions gives an accurate representation of the Sun's observed motion required considerable geometric skill!  Aristotle eventually wrote a summary of the "state of the art" in accounting for all the observed planetary motions, and also those of the Sun and the Moon.  This required the introduction of fifty-five concentric transparent spheres.  Still, it did account for everything observed in terms of simple circular motion, the only kind of motion thought to be allowed for objects made of aether.  Aristotle himself believed the crystal spheres existed as physical entities, although Eudoxus may have viewed them as simply a computational device.

It is interesting to note that, despite our earlier claim that the Greeks "discovered nature", Plato believed the planets to be animate beings.  He argued that it was not possible that they should accurately describe their orbits year after year if they didn't "know" what they were doing -- that is , if they had no soul attached.

Measuring the Earth, the Moon and the Sun:  Eratosthenes and Aristarchus

A little later, Eratosthenes and Aristarchus between them got some idea of the size of the Earth-Sun-Moon system.  To quote from Archimedes:

"...Aristarchus of Samos brought out a book consisting of certain hypotheses, in which the premises lead to the conclusion that the universe is many times greater than it is presently thought to be.  His hypotheses are that the fixed stars and the sun remain motionless, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same center as the sun, is so great that the circular orbit of the earth is as small as a point compared with that sphere..."

Aristarchus' model was not accepted, nor even the suggestion that the earth rotates about its axis every twenty-four hours.  However, work on the fifty-five crystal spheres model continued.  It had some obvious defects.  For example, in the model, the Sun, Moon and planets necessarily keep a constant distance from the Earth, since each is attached to a sphere centered on the earth.  Yet it was well-known that the apparent size of the moon varied about ten per cent or so, and the obvious explanation was that its distance from the earth must be varying.  So how could it be attached to a sphere centered on the earth?  The planets, too, especially Mars, varied considerably in brightness compared with the fixed stars, and again this suggested that the distance from the earth to Mars must vary in time.

Cycles and Epicycles:  Hipparchus and Ptolemy

A new way of combining circular motions to account for the movements of the Sun, Moon and planets was introduced by Hipparchus (second century BC) and realized fully by Ptolemy (around AD 150).  Hipparchus was aware the seasons weren't quite the same length, so he suggested that the Sun went around a circular path at uniform speed, but that the Earth wasn't in the center of the circle.  The solstices and equinoxes are determined by how the tilt of the Earth's axis lines up with the Sun.  But if the Earth's circle is off center, then some of the seasons will be shorter than others.  (The shortest season is the fall, in our hemisphere).

Another way of using circular motions was provided by Hipparchus' theory of the Moon.  This introduced the idea of the "epicycle", a small circular motion riding around a big circular motion.  (See the Ptolemaic reference at the Galileo project for an explanation of epicycles.)  The Moon's position in the sky could be well represented by such a model.  In fact, so could all the planets.  One problem he faced was that to figure out the planet's position in the sky -- that is, the line of sight from the Earth given its position on the cycle and on the epicycle -- one needs trigonometry.  Hipparchus developed trigonometry to make these calculations possible.

Ptolemy wrote the "bible" of Greek (and other ancient) astronomical observations in his immense book, the Almagest.  This did for astronomy what Euclid's Elements did for geometry.  It contained large numbers of tables by which the positions of the planets, Sun and Moon could be accurately calculated for centuries to come.  Let me mention one or two significant points:

The main idea was that each planet (and also, of course, the Sun and Moon) went around the Earth on a large circle centered on the Earth, but at the same time the planets were moving on smaller circles, or epicycles, about a point that was on the main circle.  Mercury and Venus had epicycles centered on the line from the Earth to the Sun.  This picture does indeed fairly accurately reproduce their apparent motion in the sky -- i.e., that they always appear fairly close to the Sun, and are not visible in the middle of the night.

The planets Mars, Jupiter and Saturn, on the other hand, can be seen through the night in some years.  Their motion is analyzed in terms of circles larger than the Sun's, but with epicycles such that they appear to undergo retrograde motion whenever they are on the opposite side of the Earth from the Sun.

This system of cycles and epicycles was built up to give an accurate account of the observed motion of the planets.  Actually, we have significantly simplified Ptolemy's picture:  he caused some of the epicycles to be not quite centered on the main circle.  These were termed eccentrics.  This departure from apparent perfection was necessary for full agreement with observations, and we shall return to it later.  Ptolemy's book received its name "Almagest" in the Middle Ages, by taking the Arabic prefix "al" with the Greek prefix for "the greatest'; the same as our prefix "mega".

Ptolemy's View of the Earth

It should perhaps be added that Ptolemy, centuries after Aristarchus, certainly did not think the Earth rotated.  He felt that the aether was lighter than any of the earthly elements, even fire, so it would be easy for it to move rapidly, whereas such motion would be difficult and unnatural for earth, the heaviest material.  And if the Earth did rotate, Athens would be moving at several hundred miles per hour.  How could the air keep up?  And even if somehow it did, since it was light, what about heavy objects falling through the air?  If somehow the air was carrying them along, they must be very firmly attached to the air, making it difficult to see how they could ever be moved relative to the air at all!  Yet they can't be attached, since they can fall, so the whole idea must be wrong.

Ptolemy did, however, know that the Earth was spherical.  He pointed out that people living to the east saw the Sun rise earlier, and how much earlier was proportional to how far east they were located.  He also noted that, though all must see a lunar eclipse simultaneously, those to the east will see it as later, at 1:00 am, say, rather than at midnight, as in Rome.  He also observed that on traveling to the north, Polaris rises in the sky, so this suggests the Earth is curved in that direction too.  Finally, on approaching a hilly island from far away on a calm sea, he noted that the island seemed to rise out of the sea.  He attributed this phenomenon (correctly) to the curvature of the earth.

This page is adapted from Michael Fowler's lectures and Web page at the University of Virginia.

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