Eureka! Page 6
Aristotle’s teleology differed from that of Plato. While Plato saw teleology as imposed on nature by the demiourgos, for Aristotle it was inherent in nature. Nature did not deliberate – that is, there was no conscious design or conscious designer – but many things (in particular, animals) could be seen to have the best possible form. Nature inherently produced what was best of its own nature. This difference in teleology is reflected in the two philosophers’ views on the origins of life and the cosmos. Plato believed the cosmos, and human beings, to have been ordered for the best, out of a chaos, by the demiourgos. Aristotle believed that both the cosmos and human beings had always existed.
There was another important aspect of explanation for Aristotle, and that was the ‘potential’ and the ‘actual’. Everything had a potential to be something or somewhere else, which it might actualise. An acorn, which is potentially an oak tree, would grow into one unless hindered from doing so, and a foal would become a horse. This looks quite handy for biology, but Aristotle also used it for physics. So earth had a potential to be at the centre of the universe, and it fell unless prevented from doing so. All objects had a natural place, and would undergo natural motion to that place unless stopped. The heavens were more actual than the terrestrial realm (where there may be unnatural motion), since they were always actualising their potential. The prime mover was entirely actual, since it had no motion.
Direction of Explanation: Clockwork Lives
This reveals a very important aspect of ancient, as opposed to modern, explanation. Let us ask a deceptively simple question. What is the physical world like? Is it like something mechanical (so that it works like a clock) or something organic (so that it works like an animal)? The scientific revolution of the seventeenth century very firmly opted for clockwork. The world was a giant mechanism, and even animals were to be thought of as very complex pieces of clockwork. The modern view is, of course, more sophisticated, but we retain the notion that ultimately the world is made up of inert pieces of matter (atoms, sub-atomic particles) which interact in a mechanical manner. Thus, we might explain a living thing in terms of its component parts, reducing qualities to matter and motion. Analysing a tree, we might move from botany to biology to biochemistry to chemistry, and ultimately to physics. We are happy when we can explain things (at least in principle) in terms of the physics of the ultimate particles.
Not all of the ancients shared this view either of the world or of mechanisms. The sorts of machines that they were acquainted with (wooden carts, etc.) were not paradigms of regularity and precision in the way that clocks are. Regularity, precision and order for the Greeks were the signs of intelligence, not mechanism. The ancients also struggled to explain the growth and behaviour of animals and plants in mechanical terms, and they tried to explain the origins of life and the cosmos as well. Aristotle and many other ancients rejected atomism.
So instead of mechanical explanations being used in biology, they tended to use organic explanations in physics. Where modern explanations tend to be analytical and reductive (we try to explain in terms of the ultimate component parts), many ancient explanations tended to be more holistic, especially among those who rejected atomism. In the case of Aristotle, we see some of the consequences of the lack of a proper conception of gravity and force. He needed the idea of natural place and natural motion, and the idea of the actualisation of potential – both rather organic ideas – to account for phenomena that we would explain by the force of gravity.
Aristotle’s legacy was an immensely broad, coherent and powerful system of the world. His views were those which the scientific revolution had to replace. In explanation, holism was replaced with reductionism, qualities with quantities, organic metaphors with mechanical ones – especially the favourite seventeenth-century metaphor of clockwork. Teleology was rejected, and mathematics, in the form of mathematically framed laws of nature which applied precisely and universally, found a new importance. Atoms with mathematically quantifiable properties replaced qualities, and heliocentrism replaced geocentrism. The distinction between the celestial and terrestrial realms was abandoned, since gravity could now explain both the motions of the planets and the falling of objects dropped on earth.
4 Heavenly Thoughts
But did thee feel the earth move?
Ernest Hemingway, For Whom the Bell Tolls (1940), chapter 13
We have already seen something of the beginnings of Greek cosmology, and the crucial change from myth to theory. The pre-Socratics overcame some significant conceptual hurdles to achieve a more sophisticated cosmology. There was the move from a hemispherical universe to a spherical one, and from an earth supported by water to one supported by air, and then to one which required no support. In the earlier Greek cosmologies, objects were thought to drop in parallel straight lines from the top of the cosmos to the bottom. This led to the problem of why the earth, which would seem to be heavy, does not fall to the bottom of the cosmos. In this sort of cosmology, something is required to support the earth. A different way of accounting for the effects of gravity was to have a ‘centrifocal’ theory. Aristotle placed the earth at the centre of the cosmos, and had heavy objects move towards it. There was now no question of the earth dropping, since, as a heavy object, it moved to the centre of the cosmos, which was itself.
The idea that the earth was central and stable dominated Greek astronomy and cosmology. The Greeks had some good reasons for their belief. We suppose the earth to have two main motions. It spins on its axis once a day and orbits the sun once a year. The Greeks were worried that if the earth was in motion, then there ought to be perceptible consequences. Their experience told them that if you were in rapid motion (and ‘rapid’ for the Greeks would be horse-riding or running), you certainly knew about it. So they asked: If the earth has a daily rotation (from west to east), why is there not a constant wind (east to west)? If the earth is in motion around the sun, why are objects such as ourselves not swept off the face of the earth? Today we have answers to these problems. We believe that the earth carries its atmosphere with it, and that space is a vacuum, so we see no problem in having the earth (with its atmosphere) spinning on its axis and orbiting the sun. Greek physics had no such answers. The Greeks did not believe space to be a vacuum, but to be full of matter, and so did not distinguish between the earth’s atmosphere and space. They did not observe the consequences that they thought should come from the earth being in motion, so they did not believe the earth to be in motion.
There were further problems which occurred to some of the Greeks, which would not occur to someone with a knowledge of gravity. They worried that if the earth was in rapid motion, why did it not disintegrate? For many of the Greeks after Aristotle, the reason why the earth held together, and why objects fell to its surface, was that pieces of earth had a natural motion towards the centre of the cosmos. Move the earth from the centre of the cosmos, and there was no longer any reason why it should hold together, or why objects should fall to its surface. And if the earth was in motion, why did the moon follow it around?
And there was something else. The earth takes up different positions around the sun during the year, and so has different positions relative to the stars. Observations taken six months apart (to maximise the difference) should reveal slight changes in the apparent positions of the stars from earth. This effect is called ‘stellar parallax’. However, the Greeks could observe no such parallax effects. This is no great surprise, since we know these effects to be very small, due to the distance of the stars. They were not detected until 1838, by an astronomer called Bessel. Without telescopes, and indeed very sophisticated and powerful telescopes at that, the Greeks had no hope of detecting stellar parallax. Those who believed the earth to be in motion, from Copernicus in 1543 onwards, said that the stars were too far away for stellar parallax to be detected by current means. However, the Greeks believed the cosmos to be relatively small. They believed that the stars were all equidistant, and were beyond the furthermost of the
planets visible to the naked eye, Saturn. The whole cosmos, for the Greeks, was no bigger than our solar system. They believed that stellar parallax should have been observable, if the earth orbited the sun. It was not, so they believed the earth to be immobile.
The Greeks, then, had several good reasons for believing the earth to be central and stable. Their physics, astronomy, philosophy and common sense all seemed to indicate an immobile earth. What is more, their astronomy seemed to be making great strides forward. There was no reason to suppose that the earth was in motion.
There was an important consequence from this. All of the motions of the heavens were real motions to the Greeks, not apparent ones due to the motion of the earth. If one looks at the stars over the course of a night, they appear to move in a circle. We know that this is due to the fact that the earth spins on its axis. It is the earth that is moving, not the stars. The motion of the stars is apparent, not real. The Greeks, with their faith in the immobility of the earth, believed that it was the stars that were moving in great circles, not the earth. For them, the motion of the stars was real, and not apparent.
At the outset, Greek observational astronomy was rather divorced from philosophical speculation about the nature of the cosmos. There were those who observed the heavens and took careful note of what they saw; and there were those who produced cosmological models based on general philosophical considerations. No one produced cosmological models that were anywhere near explaining, in a precise manner, the phenomena that had been recorded. This is no great surprise, since the phenomena are quite complex.
Figure 10: The problem of parallax (not to scale – the star would be very, very much further away!). If the earth orbits the sun in one year, then there is a significant difference in its positions at six-monthly intervals. This ought to be detectable relative to the fixed stars, which should appear to be in slightly different positions. In fact, this is difficult, since the amount that the earth moves is very small compared to the distance of the stars, and parallax was not detected until 1838. Parallax for alpha centauri (our nearest star) = 0.75 of 1” (one second of arc), where 60” = 1’ (one minute of arc) and 60’ = 1° (one degree). One needs to look at a very near star (4 light years away, not 400 or 4,000), or this effect is not seen at all. The Greeks believed all of the stars to be equidistant and relatively near, just beyond Saturn.
The first attempt was made by the Pythagoreans, though it was still somewhat vague and speculative. In the centre of the cosmos was a fire (not the sun), but this was shielded from the earth by a body known as the counter-earth. We never saw this central fire, but the other heavenly bodies revolved around it, outside the earth (see Figure 11).
A slightly better model of the heavens can be found in Plato’s The Republic. Here we have a central earth, with the moon, the sun, the five planets and the stars all orbiting it (Figure 12).
You will notice that in both of these models, all of the motions of the heavenly bodies are assumed to be regular and circular. This was a basic assumption of Greek astronomy and cosmology. Why? Simply because the Greeks considered this to be the best sort of motion. Circular motion could continue without change, and it had a simplicity and elegance which appealed to them. A well-ordered cosmos, such as the one that the Greeks believed themselves to live in, would see the heavens moving with regular circular motion.
Figure 11: The Pythagorean cosmos, showing the central fire, then the counter-earth, earth, moon, sun, five planets and stars.
Figure 12: Plato’s early view from The Republic. A central earth, then the moon, sun, five planets and stars.
Neither of these two models could account for two important phenomena relating to the point at which the sun sets. The sun does not always set due west. If one takes note of where on the horizon the sun sets during a year, this changes from a maximum of 23.5° north of west to a maximum of 23.5° south of west. Solstices (shortest day or night) occur at the maximum points, while equinoxes (equal day and night) occur when the sun sets due west. If one takes note of which stars first rise at the point on the horizon where the sun sets, these can be seen to change during the year as well. These phenomena were well known to the Greeks and many other ancient societies.
Figure 13: The sun’s motion against the background of the fixed stars, tracing out a line called the ‘ecliptic’. One observes where the sun sets and which stars then appear at that point.
The first model that could give a reasonable account of these phenomena, and which was perhaps the first serious attempt to unite the astronomical and cosmological traditions, came with Plato’s book The Timaeus. Here he introduced some very important ideas. The stars seemed to the Greeks to show good order. They moved in what appeared to be perfect circles. However, the five planets that can be seen with the naked eye – Mercury, Venus, Mars, Jupiter and Saturn – all have motions relative to the stars. These motions are quite complex, and initially did not seem orderly to the Greeks. Indeed, our word ‘planet’ comes from the Greek ‘planetes’, which means a wanderer or a vagabond. The Babylonian word for a planet was ‘bibbu’, meaning sheep. Plato insisted that the planets did not in fact wander, but moved in orderly but complex combinations of regular circular motions. This set the terms for astronomy for two millennia. Not until 1609, when Kepler recognised that planetary orbits are ellipses around the sun, was this to change.
The essence of Plato’s later model was that the sun, moon and planets have a combination of two regular circular motions. The stars are still carried around once a day in one motion, but the sun, moon and planets have a second motion in addition to the daily one, offset at an angle to it. So they had motion relative to the fixed stars, as well as moving with the stars (see Figure 14).
This model gave a reasonable approximation of the setting sun phenomena, but could not explain everything. If you watch the motions of the planets against the background of the fixed stars over a year or two, you will see something strange. Normally, the planets will progress against the background of the fixed stars. However, they will sometimes come to a halt, go in the other direction for a while, stop again and then go in their normal direction once more. This is called ‘retrogression’ or the ‘retrograde motion’ of the planets (Figure 15).
Figure 14: Plato’s later model, employing two spheres for moon, sun and planets. The earlier Greeks assumed the angle between these motions to be 24°, 1/15 of a circle.
The planets do not follow the ecliptic (the path of the sun against the background of the fixed stars) exactly. They deviate a few degrees either side of it. The band within which the planets move is called the zodiac. This band can be split into twelve parts to give the houses of the zodiac.
Plato’s model, though an advance in astronomy, was still qualitative and did not account for either retrograde motion or the deviation of planets from the line of the sun.
Figure 15: A planet undergoing retrograde motion. Planets do not actually stop and then move on again. They appear to do so to someone on earth, because the earth and planet have different sizes and speeds of orbit around the sun. Sometimes these combine in such a way that the planet appears to come to a halt, reverse its direction, and then move on as normal. Because the Greeks believed in an immobile earth, the planets for them had to have real retrograde motion.
Figure 16: The ecliptic and zodiac are often represented like this. The zodiac can be divided into twelve parts, as is familiar from astrology.
Eudoxus: Thinking Regressively
While Plato may have been important in formulating the ideas underpinning ancient astronomy, undoubtedly the greatest early theoretician was Eudoxus of Cnidus (fl. 365 BC), who was also a brilliant mathematician. Eudoxus was a pupil of Archytas the Pythagorean, and seems to have had a close relationship with Plato. He travelled widely, made astronomical observations and founded a school at Cyzicus. He took Plato’s model and made it more complex and much more accurate. The next part is a little tricky, but worth following to get a sense of Eudoxus’ genius
and the way in which the Greeks went about astronomy. While Plato’s model had two regular circular movements for each planet, Eudoxus used four (see Figure 17).
The first sphere generated a daily motion, and the second generated the motion of the planet along the ecliptic (so far, as with Plato). The other two spheres were so arranged that they produced a pattern like the figure 8 laid on its side. The Greeks called this pattern a ‘hippopede’, or horse fetter (see Figure 18).
When this hippopede is combined with the other two motions, you get a pattern that looks very like regressive motion (Figure 19).
Figure 17: Plato’s two-sphere model, and Eudoxus’ four-sphere model for a planet.
Figure 18: The shape generated by two of Eudoxus’ spheres, known as a hippopede (horse fetter).
Figure 19: The resultant motion of Eudoxus’ four spheres.
This allowed Eudoxus to cope with some of the main deficiencies of Plato’s model. In one of the most brilliant pieces of ancient science, Eudoxus did the mathematics required to make this system work as a real model of the cosmos. Eudoxus’ resources were some primitive writing materials and a record of the motions of the heavens. That is all. It is quite amazing that he was able to produce a complex and workable mathematical model of the heavens with nothing more than this.
But this system, known as the ‘concentric’ or ‘homocentric’ sphere system – since all of the spheres have a common centre, the centre of the cosmos – was far from perfect, and Eudoxus was well aware of this. One of Eudoxus’ pupils, Callippus of Cyzicus (fl. 330 BC), made further changes to his scheme of rotating spheres in order to make the model fit more closely with what actually happened in the heavens. He introduced even more rotating spheres to account for some quite subtle changes in the motions of the planets. Aristotle made no improvements to concentric sphere astronomy, but thought hard about the cosmology. He conceived of each of the spheres of Eudoxus and Callippus as being real and made out of the fifth element, aether. These spheres were considered to be next to each other with no space between, a conception of the heavens as being like a Russian doll, or the layers of an onion. Each of the spheres then contributed to the motion of its planet.