To begin this section on Greek cosmology, let’s watch a short clip on the history of physics from the very popular television show “The Big Bang Theory.” Sheldon, a physicist at Caltech, tries to explain physics to Penny, a waitress/actress who lives next door.
The show has been criticized for its sexism, and this clip does indeed play on the familiar stereotypes of super-smart nerdy guy and super-pretty really dumb blonde girl. (For more extensive discussion, criticism and analysis of gender roles and relations in this show, see here and here and here. Or just do a Google search on “Big Bang Theory” and “sexism” or “women in STEM.”) While the portrayal of a woman who is incapable of understanding Newton’s laws of motion is something I find decidedly irritating, I am nonetheless amused by this clip. I think I identify quite heavily with Sheldon, who keeps trying to “begin at the beginning” by talking about the Greeks. Frequently, when I am teaching this course, I find myself returning again and again to the Greeks, and I fear that some of my students (although they are all sharper than poor Penny) mentally groan “oh balls!” when I start going on about Aristotle for the third, fourth or fifth time.
So I’d like us to first think about why Sheldon (and why we in this class) begin with the Greeks. What was so magical about that warm evening in Greece in the sixth century B.C.?
Let me begin by asking you to consider what YOU see when you look up at the night sky. If you are reading this at night, I encourage you to head outside and look up. In case you’re reading this during the day (or you’re not wearing pants), here’s a picture of the night sky to contemplate.
What do you see? Your first thought might be, “I see stars” or “I see the moon and stars.” But let’s investigate this response. What you see is points of light against a dark background. On some nights you might see a large (much larger than the points of light) illuminated disc. On other nights, you might see an illuminated crescent. If you watch the sky over the course of the night, you will see the points of light and the illuminated disc move slowly across the sky. Probably all of you can identify these points of light as stars and the illuminated disc as the moon. Those of you with some experience in astronomy can identify which of the (somewhat larger and brighter) points of light are planets. When you look at one of the points of light in the sky and say to yourself, “that’s a star,” you are saying , “that’s a massive, luminous sphere of plasma held together by its own gravity” (the definition of a star according to Wikipedia). You see a point of light but you interpret that observation to fit what you have learned – from school, science museums, independent reading, television or the internet – about the structure and nature of the universe. The same is true of your observations of the moon, sun and planets. Further, depending on your background and inclinations, you may “see” other things when you look at the night sky. Some of you may see the immense power and goodness of a Creator God. Some of you may see the vastness of the universe and the cosmic insignificance of human beings. Some of you may see the beauty that has inspired poets and writers and artists and lovers for millennia. Here’s just one example from Shakespeare’s Romeo and Juliet:
Give me my Romeo; and, when he shall die,
Take him and cut him out in little stars,
And he will make the face of heaven so fine
That all the world will be in love with night
And pay no worship to the garish sun.
Some of you may see the unsolved mysteries of the cosmos (Is there intelligent life out there? What is dark matter? Can we capture a black hole?), and be inspired to pursue a career in astrophysics. These are all valid responses to the night sky. But note that all of them, from the belief that a star is a ball of gas to lines of poetry, are particular to your time and place and your education and upbringing. The point is that what you “see” when you “look” at the night sky is profoundly shaped by your culture.
Let’s go back to that warm night in Greece in the 6th century B.C. What did a Greek observer “see” when he or she “looked” at the sky? Our hypothetical Greek saw a dazzlingly beautiful, perfect, regular, orderly and harmonious cosmos. Look again at the night sky or at the picture of the night sky above. Is the first thing that strikes you regularity and order? It might well strike you as beautiful, but it probably doesn’t strike you as having a clear pattern and order. To me, the stars appear to be scattered at random through the sky and to be at widely varying distances from the earth. Also, from time to time, one sees somewhat unusual events in the night sky: comets, meteor showers, shooting stars and eclipses. Earlier civilizations (like the Egyptians, Babylonians and Chinese) made detailed observations of the appearance of the night sky, and even recorded these observations. But they did not “see” regularity and order. Rather, they believed what they saw in the night sky was fundamentally irregular and arbitrary. Strange appearances in the sky were generally attributed to supernatural interference – the actions of a god or goddess. What makes the Greeks so special, and the reason Sheldon and I begin our histories of science with the Greeks, is that they were the first to see order and pattern and harmony when they looked at the night sky, and they were the first to completely reject supernatural explanations for what they saw in the heavens. It is more precise to say that Greek philosophers saw the cosmos as inherently regular and rejected supernatural explanations. The pantheon of gods and goddesses and belief in divine intervention remained important in Greek culture long after the birth of philosophy. But at least one small and highly influential group of Greek intellectuals adopted a radically new way of looking at the heavens (and other aspects of the natural world). And that is why the history of western science typically begins with the Greeks.
From around the 6th century B.C., Greek philosophers believed that the cosmos must, despite rather strong evidence to the contrary, be regular and orderly. There must be a pattern underlying the seeming chaos and randomness of celestial events. And they set out to find this pattern, to see the order underneath the appearance of the night sky. The early Greek philosopher Anaximander (611 – 546 B.C.), was the first to propose a structure for the cosmos that made sense of many observations of the heavens. He proposed that the universe was spherical, with the earth at its center. The earth was surrounded by a sphere of mist, and beyond the mist was a sphere of fire. The points of light in the night sky were holes in the sphere of mist through which the fire shone. Anaximander’s ideas were not widely accepted, and they were soon superseded by more accurate and sophisticated models of the cosmos, but they started Greek philosophers on a quest to understand the structure of the universe. Anaximander is one of a group of the earliest Greek philosophers, a group known as the Pre-Socratics. If you are interested in these philosophers, a good place to start is the essay in the Stanford Encyclopedia of Philosophy.
I turn now to the model of the cosmos that subsequent Greek philosophers developed. The two figures associated with the origins of this model are Plato and Aristotle (although their ideas had roots in the work of Anaximander and other pre-Socratic philosophers. (For anyone interested in biographical information on Plato and Aristotle and a fuller description of their philosophical projects, see the essays on each in the Stanford Encyclopedia of Philosophy.)
This model is easier to understand with a picture. To illustrate the following discussion, I have chosen an image from the history of Science Collections. This comes from the title page of Giuseppe Biancani’s Sphere of the World from 1620. I selected this both because it is relatively simple (many illustrations in astronomical texts are too complex for our purposes here) and also because it demonstrates the very long life of this ancient Greek model of the cosmos. It was still being actively discussed and taught in the 17th century!
The first thing to know about the Greek cosmos is that it was spherical. This idea predates Aristotle and Plato – Anaximander actually held that the universe was a sphere. Remember that I said the ancient Greek philosophers saw order and beauty and perfection when they looked at the heavens? Well, they believed the sphere was the most perfect and beautiful shape. In the Timaeus, Plato declared that the Divine Creator “made the world in the form of a globe, round as from a lathe, having its extremes in every direction equidistant from the center, the most perfect and the most like itself of all figures; for he considered that the like is infinitely fairer than the unlike.” Aristotle, although he denied that the world had a Creator, also held that the universe was a sphere. Rather more prolix on this point the Plato, he declared that:
“The shape of the heaven is of necessity spherical; for that is the shape most appropriate to its substance and also by nature primary. First, let us consider generally which shape is primary among planes and solids alike. Every plane figure must be either rectilinear or curvilinear. Now the rectilinear is bounded by more than one line, the curvilinear by one only. But since in any kind the one is naturally prior to the many and the simple to the complex, the circle will be the first of plane figures. Again, if by complete, as previously defined, we mean a thing outside which no part of itself can be found, and if addition is always possible to the straight line but never to the circular, clearly the line which embraces the circle is complete. If then the complete is prior to the incomplete, it follows on this ground also that the circle is primary among figures. And the sphere holds the same position among solids. For it alone is embraced by a single surface, while rectilinear solids have several. The sphere is among solids what the circle is among plane figures.” (On the Heavens, Book II, Part 4)
The universe is perfect, orderly and regular, therefore the shape of the universe must be a sphere. Note that the Greek universe is finite. There is nothing outside the outer boundary of the sphere. When we look at the night sky, we may see stars stretching on into infinite space, but that is not what the ancient Greeks saw. They believed that all of the stars they could see were fixed onto a colossal sphere that bounded the entire universe. This sphere was known as the celestial sphere or the starry vault.
The second thing to know about the Greek cosmos is that the earth is at the center and is stationary. All the motion in the heavens – the daily rising and setting of the sun, the moon and the stars, as well as the more complex motions of the planets – are the result of heavenly bodies moving around the stationary earth. Although we today know that the earth is in motion, it is important to note that all of the observations the Greeks made of the heavens were perfectly consistent with a stationary earth. Some Greek philosophers considered the possibility that the earth was in motion around the sun or that it rotated on its own axis, but Aristotle provided a series of highly compelling arguments why this could not be the case.
Let’s look at the image from Biancani’s Sphere. The earth is the point at the center of this diagram. The starry vault is the outer circle. The starry vault is a solid sphere in which all the stars are embedded. This starry vault rotates from east to west once every twenty-four hours. The axis of the starry vault’s rotation is a line that runs through the north and south poles of the earth. This is the line AB in the diagram. As the starry vault rotates, the stars, and the sun and the moon and the planets appear to move around the earth. Celestial bodies rise on the eastern horizon and set on the western horizon. This is why the sun rises in the east and sets in the west. This actually quite accurately accounts for the motions of the stars.
The motion of the sun is somewhat more complex. The sun rises and sets every twenty-four hours, but the sun also moves to different positions in the heavens over the course of a year. Another way of thinking about this is that the sun rises and sets on different parts of the horizon over the course of a year. To understand the two combined motions of the sun (the daily and the yearly), we need to look at two other parts of the diagram: the celestial equator and the zodiac. The celestial equator is the projection of the earth’s equator onto the starry vault. This is the line CD in the diagram. The zodiac is the band that stretches between points K and L. The zodiac is like a belt wrapped around the middle of the starry vault. The zodiac is divided into twelve parts or houses, each containing a different constellation (Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius and Pisces). The line that runs right through the exact middle of the zodiac is called the ecliptic. The ecliptic is the line traced by the sun on its yearly rotation from west to east around the earth. Imagine a line drawn between points E and F on the starry vault (this is not drawn in the diagram) – this is the axis of the sun’s yearly rotation. So the sun rotates around the earth from east to west once every twenty-four hours with the starry vault, but it also rotates around the earth from west to east one every 365¼ days. If you look closely at the diagram you can see symbols for six zodiacal signs (from L to K they are Capricorn, Aquarius, Pisces, Aries, Taurus and Gemini) and six months of the year (again from L to K they are January, February, March, April, May, June). The other six are on the other side of the starry vault. Each month is roughly but not exactly aligned with a sign of the zodiac.
The motion of the sun is thus the combination of rotation in opposite directions, on different axes and with widely varying speeds. In his book Theories of the World from Antiquity to the Copernican Revolution, Michael J. Crowe suggests visualizing this by imagining that you are spinning a basketball rapidly in one direction while an ant crawls slowly around the ball in the opposite direction.
As the sun moves on the ecliptic through the different houses of the zodiac, the seasons change and the days get longer and shorter. The Greeks (like you) were aware that the days (the hours of light) are longer in the summer and shorter in the winter. The longest and shortest days of the year are called the solstices. They occur when the sun is at the most northerly and most southerly points on its rotation around the earth.
In the diagram, point A is directly above the North Pole and point B is directly above the South Pole. Point K is the most northerly point in the sun’s annual rotation. When the sun is at point K, people on earth (in the northern hemisphere) experience the longest day of the year. This is called the summer solstice, and it occurs around June 22. Point L is the most southerly point in the sun’s rotation. When the sun is at point L, people on earth (in the northern hemisphere) experience the shortest day of the year. This is called the winter solstice, and it occurs around December 22. Further, there are two points at which the ecliptic crosses the celestial equator. At these points, the hours of day and night (light and darkness) are exactly equal. These points are called the equinoxes. There is a spring equinox around March 21 and a fall equinox around September 23. On the diagram, one of the equinoxes is at the center. The other would be on the other side of the sphere.
The next prominent celestial body is the moon. The motions of the moon are similar to those of the sun. The moon rotates around the earth every twenty-four hours, rising in the east and setting in the west. And the moon rotates around the earth from west to east about once a month (the moon’s period is 28 days). In its west to east rotation, the moon moves roughly along the ecliptic, but not quite. Whereas the sun is always on the ecliptic, the moon deviates from the ecliptic as it moves around the earth. Sometimes it is slightly below the ecliptic and sometimes slightly above. However, the moon is always to be found in the band of the zodiac. We will discuss the phases of the moon and eclipses next week. For now, it is enough to note that the motion of the moon is a combination of two motions, a daily rotation and a monthly rotation. As in the case of the sun, these rotations are in opposite directions, about different axes, and at different speeds. The added complexity in the case of the moon is that it “wobbles” around the ecliptic instead of always being on it.
Finally, let’s turn to the planets. There are five planets visible to the naked eye: Mercury, Venus, Mars, Jupiter and Saturn. These five bodies have motions that are considerably more complex than those of the stars, sun and moon. Planets look like stars – and in fact, and untrained observer may easily mistake the planets for stars. However, planets tend to be brighter than stars. Also, stars remain fixed in position and brightness relative to each other. Remember, they are all embedded in a giant, solid spherical shell that forms the boundary of the cosmos. Planets change position relative to the stars and vary in brightness. Sometimes the stars were referred to as the “fixed stars” and the planets as the “wandering stars.” Planets have motions similar to the sun and moon. They move around the earth once every twenty-four hours, rising in the east and setting in the west. They also rotate around the earth through the band of the zodiac in a west to east direction. Like the moon, the planets “wobble” above and below the ecliptic. Their periods of rotation vary greatly. Mercury and Venus each take about a year to travel around the earth. Mars takes two years, Jupiter twelve years, and Saturn thirty-three.
There are two more distinctive features of planetary motion that the stars, sun and moon do not share. First, Mercury and Venus are always close to the sun. Mercury is actually so close to the sun that it is very hard to see. It rises immediately before the sun rises or sets immediately after the sun sets. Any haze on the horizon (which is fairly common) makes Mercury impossible to see. Venus is also close to the sun but not as close as Mercury, so it is much more easily visible. It too rises a little before the sun rises or sets soon after the sun sets. Because of this, Venus is often referred to as the “morning star” or the “evening star.” The second feature of planetary motion is called “retrograde motion.” Planets usually move, like the sun and moon, from west to east around the zodiac. However, unlike the sun and moon, all five planets sometimes back up (i.e. move from east to west through the zodiac) for a time, and then continue moving forward (i.e. from west to east).
These are the main motions of the stars, sun, moon and planets. On a subsequent page I examine the various mathematical models devised by Greek astronomers and mathematicians to account for these motion.
Before Newton 