Eureka! Page 7

  The two defining features of Greek astronomy were an immobile earth and a belief in circular motion. They treated all of the motions of the heavens as real motions, and as combinations of regular circular motions. Greek astronomy became even more complex as it tried to reproduce the motions of the heavens with ever greater accuracy. The other important feature of ancient astronomy was that it was naked-eye astronomy. The Greeks did have some devices to help them observe the heavens more accurately, but no means of image intensification. The first telescopes were not invented until 1609, leading to the discovery of a great amount of new information simply unknown to the Greeks.

  Ptolemaic Astronomy

  The system devised by Eudoxus and Callippus was an excellent model for that time, but there were some inherent difficulties. Planetary orbits are in fact elliptical around the sun, and not circular around the earth. This means that planets get nearer and then further away from the earth, such that their apparent size varies. The concentric sphere model has the planets at a constant distance. As a planet goes around its real orbit, its apparent speed varies – faster when it is nearer the sun, slower when further away. The concentric sphere model has great difficulties in coping with this. The planets have different shapes of retrogressive motion, while the hippopede can give only one shape.

  Building on the work of Apollonius of Perga (262–190 BC) and Hipparchus of Nichaea (fl. 135 BC), Ptolemy of Alexandria (c. 100–170 AD) produced a whole new system which was to last for nearly 1,500 years. Ptolemy observed the heavens from Alexandria in Egypt. He produced a book called the Suntaxis in Greek (meaning ‘great collection’) and the Almagest in Arabic (‘the greatest’). It was, quite simply, the peak of ancient astronomy. Ptolemy observed, invented new theories and synthesised his own work with what was already known. He was also an excellent geographer, and produced an atlas of maps of the known world.

  Ptolemy’s system was still based on combinations of regular circular motions. He gave up the concentric sphere and hippopede model in favour of a system based on a device known as the ‘epicycle’ (Figure 20).

  The epicycle is a combination of two regular circular motions, but not around the same centre. The centre of the smaller circle moves around the larger circle. The actual motion of the planet will depend on the size and speed of rotation of both of the circles, and some quite complex patterns can be produced (see Figure 21).

  Figure 20: The epicycle, the basic unit of Ptolemaic astronomy. The planet moves around the small circle, whose centre moves around the large circle, giving a combination of regular circular motion.

  With this, allied with two more complex devices based on the epicycle, known as the ‘eccentric’ and the ‘equant’, Ptolemy was able to account for most of the problems that beset the concentric sphere model. Planets could have varying distances from the earth with this system, so variation in apparent size and brightness could be accounted for. It was also easier to explain variations in the apparent velocity of the planets. In addition, Ptolemy’s system could provide several shapes for retrograde motion, and so was able to account for this phenomenon more accurately. This system was mathematically very powerful, and could in principle have explained virtually every astronomical phenomenon. The downside of this power was complexity – greater accuracy demanded more and more epicycles. Ptolemy’s astronomy and cosmology lasted throughout the Roman empire, the dark ages, middle ages and Renaissance, only to be displaced during the scientific revolution, when Copernicus proposed that the earth orbited the sun.

  Figure 21: One possible pattern produced by an epicycle. By varying the size and speed of the circles, many others are possible.

  The Four Seasons

  Ptolemy’s model took into account some quite subtle effects. The four seasons of the year were defined as the period between solstice and equinox. One might expect that these periods would be equal, but in fact they are not, and the Greeks Euctemon and Meton (both of Athens, both fl. 430 BC) recognised this quite early on. Hipparchus produced a way of accounting for the inequality of the seasons, as ever using regular circular motion (Figure 22).

  Figure 22: Hipparchus’ scheme for the inequality of the seasons. The earth is offset from the centre of the sun’s orbit. If the sun orbits with regular circular motion, the seasons will have slightly different lengths. In fact, this effect is due to the earth’s elliptical orbit around the sun.

  A more subtle effect is known as the ‘precession of the equinoxes’. The earth, in fact, has more than two motions. It orbits the sun and it spins on its axis, but there is also a change in the angle of that axis (imagine a spinning top which does not spin perfectly upright – the axis of spin moves around). This cycle of change takes 26,000 years to complete, and the effects on the night sky due to this phenomenon are therefore slow (the position of the stars at equinox appears to change slightly), but over time the Greeks gradually picked them up and were able to build them into their model.

  Revolutionary Thinking

  There was one ancient astronomer who believed that the earth orbited the sun, and that was Aristarchus of Samos (c. 310–230 BC). Aristarchus was a pupil of Strato of Lampascus, a follower of Aristotle. However, no one in the ancient world was convinced by him, since the Greeks had good arguments for a central and immobile earth. We do not know how Aristarchus would have answered the question about there being no constant east–west wind, nor how he would have accounted for gravitational effects with a moving earth, nor why he thought that the moon followed the earth around. Nor do we know how he would have accounted for the inequality of the seasons, the precession of the equinoxes and the lack of stellar parallax.

  In some ways, the reception of Aristarchus mirrored that of Copernicus – the first modern astronomer to argue for a mobile earth – nearly two millennia later. Copernicus published his theory that the earth orbited the sun in 1543. There were, however, many problems with his theory, since he lacked the physics to cope successfully with a moving earth. His theory was not significantly simpler than Ptolemy’s. He also lacked any hard observational evidence to back up his claim. It was not until after the work of Kepler (who discovered that planetary orbits are ellipses about the sun) and Galileo (who solved some of the physical problems and used the newly-invented telescope to produce excellent evidence in favour of Copernicus) that the Copernican theory became really plausible.

  Modelling the Heavens

  One question which worried the Greeks was why the planets should move as they do. For us today, the answer is simple. The planets move in elliptical orbits around the sun, and it is gravity that determines those orbits.

  The Greeks had the earth at the centre of their solar system, and had no conception of gravity. Equally, they believed that what we would call the ‘apparent motion’ of the planets was real. It was virtually impossible for them to conceive of a force, emanating from the earth or anywhere else, that would produce these complex motions. They had two sorts of explanation for these phenomena. Plato believed that the planets were intelligent, to the extent that they would always choose the best motion; Aristotle believed that the spheres which moved the planets were made of aether, and the natural motion of aether was in a circle. The result of both explanations was that the planets always moved in an orderly manner with combinations of regular circular motion.

  Figure 23: In 1609, Kepler discovered that planetary orbits are elliptical around the sun. Following on from this, one can think in terms of a force emanating from the sun controlling the planetary orbits. Why did the Greeks not think of ellipses? To do this, one must first of all have the sun at the centre. Planets do not have elliptical orbits around the earth.

  The Greeks are sometimes said to have an ‘organic’ picture of the cosmos. That is, instead of believing the cosmos to be inanimate and to work in the manner of a machine, they thought of it as more like a living entity. Why did they take this view? To them, the cosmos had certain properties. It was a finite, enclosed, unitary thing. It was well-ordered. T
he motions of the heavenly bodies were orderly and regular, and the Greeks associated such changes with intelligence. The cosmos appeared to be able to sustain itself in this well-ordered state. So if you had asked the Greeks what the cosmos was like, many would have said that it was like a living thing in these respects. This was no primitive anthropomorphism, but an attempt to understand the orderliness of the cosmos in the absence of modern ideas about gravity, force and the laws of nature. Other Greeks suggested that the cosmos was like a political entity, since they were keen to emphasise the orderliness and sophistication of the city in contrast to the chaos and crudeness of the countryside. Others considered the cosmos to be an artefact, something showing the marks of a craftsmanlike creator. If you find these ideas odd, remember that with ‘big bang’ cosmology, we believe ourselves to live in the aftermath of an explosion. What the universe is like is a very tricky question to answer.

  What was the picture of the cosmos at the end of antiquity? It was largely Aristotelian. The earth was at the centre, surrounded by the moon, sun, planets and stars moving in a circular manner.

  Astronomy was slightly more complex, since Ptolemy’s epicycles had proved more fruitful than the concentric sphere system. The size of the epicycles was used to produce a spacing for the planets. The radii of the epicycles of two adjoining planets gave the gap between their main circles. The principle here was that god, who did nothing in vain, would not create empty space.

  Figure 24: The picture of the cosmos at the end of antiquity. Note that the order of the planets is slightly different from that of Aristotle, who had the sun directly after the moon.

  Figure 25: How the ancients spaced orbits. The epicycles touch, but do not overlap, thus giving the spacing. This is very much simplified, but shows the general principle. The key philosophical idea behind this was that there should be no empty, disused space.

  The Greek study of the heavens was certainly remarkable in its accuracy and ingenuity. The system that they had in place at the end of antiquity was mathematically very sophisticated and powerful, and capable of extremely accurate predictions. The great problem, of course, was that they never got away from the idea of an immobile earth and regular circular motion. Another millennium and a half was to pass before the first serious suggestion was made that the earth was mobile, and it took another seventy years for the problems with this idea to be solved, and for it to become accepted.

  5 The Origins of the Cosmos and of Life: Consider your Origins

  Except the blind forces of Nature, nothing moves in this world which is not Greek in its origin.

  Sir Henry Maine, Village Communities, 3rd edition (1876), p. 238

  A question which divided the ancient Greeks was how the cosmos acquired its order, and how it was maintained. They effectively split into two camps on this issue. There were those who believed that something directed the cosmos such that there was a good, well-ordered result. Most influential here were Plato and Aristotle. In the opposing camp were those who believed that order came about by chance, the key thinkers here being the atomists Leucippus and Democritus. Along with this question of order was the question of whether there was one cosmos or many ‘cosmoi’. Plato and Aristotle firmly believed that there was one unique cosmos that was in some way structured for the best. The atomists, on the other hand, believed that there were many cosmoi, separate from one another, in which everything happened by chance. Their view was that:

  There are innumerable cosmoi, which differ in size. In some of these there is no sun or moon, in some they are larger than ours and in some more numerous. The spaces between cosmoi are not equal, in places there are more and in others less, some are growing, some are in their prime, some declining, some are coming to be and others failing. They are destroyed by falling into each other. There are cosmoi bereft of animals and vegetation and all moisture.

  The atomists’ explanation of the order of our cosmos was that among the infinite number of different cosmoi, there would be all of the possible arrangements of a cosmos, including the one that we live in and call a ‘good’ arrangement.

  To see how the atomists’ view works, we need to look at what they thought about the origins of the cosmos. Plato, as we have seen, believed that his craftsman god had ordered the cosmos out of a primordial chaos, while Aristotle believed that the cosmos had always been ordered as it is now, and would always be so ordered. The atomists Leucippus and Democritus believed that matter formed a vortex, in which it was whirled around. In this vortex, matter was sorted according to the like-to-like principle. Some types of atoms linked together to form a membrane around a cosmos, and when that happened a new cosmos was formed. The atomist account of such linking was crude. Since atoms had all sorts of shapes and sizes, some had hooks and some had eyes, and so they linked together. Gradually, cosmoi separated out from the vortex. There was no limit to this process, and it happened continually, so there were an infinite number of cosmoi. Much here depended on the precise effect of the like-to-like principle. A later philosopher, Sextus Empiricus (fl. 200 AD), tells us that:

  Democritus has confirmed this opinion, and Plato has mentioned it in his Timaeus. Democritus bases his argument on both living and inanimate things. Animals, he says, gather together with others of like species, as doves with doves and cranes with cranes, and so with other irrational animals. It is the same with inanimate things, as can be seen in the case of seeds which are being winnowed and pebbles on the sea-shore. The whirling of the sieve separates lentils with lentils, barley with barley and wheat with wheat, and due to the motion of the waves, oblong pebbles are moved into the same place as other oblong pebbles, and round with round, as though the similarity possessed by things leads to them being gathered together.

  According to the atomists, the actions of this principle produced our world, as one possibility among many others. As long as there were enough cosmoi, chance and the like-to-like principle would bring our cosmos into being. Plato agreed that this principle operated, but disagreed on what the result of its actions would be. He emphasised that the cosmos consisted of unlike things brought together in due harmony and proportion, and did not see how a like-to-like principle could achieve that.

  A question that one might ask here is this: Did no one believe that there was just one cosmos that did not require any teleological ordering? In fact, this view is very rare in the history of science. No one in the ancient world believed it. Virtually no one believed it in the era when cosmogony and cosmology were dominated by Christian thought, since the cosmos, in this system of thought, came ready formed by a good God in the six days of creation, as indeed did human beings in the shape of Adam and Eve.

  Some alternative early Greek views were those of Empedocles and Anaxagoras. Empedocles believed that there were the four elements of earth, water, air and fire, and that their ordering was governed by love and strife. Love brought things together and strife drew them apart again, and the cosmos underwent a continuous cycle of the dominance of love giving way to the dominance of strife and then vice versa. Two problems with many cosmogonies were pointed out by Plato and Aristotle. Aristotle questioned why motion began, while Plato questioned why, when motion began, it was assumed to have a specific form, such as the vortex of the atomists, rather than just be chaotic. Anaxagoras of Clazomenae (c. 500–428 BC) tried to get around these difficulties by suggesting that a cosmic intelligence initiated motion but then took no further part in the running of the cosmos.

  Anaxagoras’ position has some interesting similarities with those adopted by certain mechanical philosophers in the seventeenth century. For them, a Christian God created the world in a ready ordered state (in line with the book of Genesis), and then took no further part in the running of the universe. For Anaxagoras, cosmic intelligence (‘nous’) provided the initial impetus and order before withdrawing. It is interesting to note that, like a Christian God, nous knows all and is all-powerful. The critical difference is that in the seventeenth-century conception, God also
created a framework of physical law and forces to which matter is subject. Given the initial ordering, as in the book of Genesis, these forces and laws were supposed to be sufficient to explain the ongoing order of the world. As in the ancient world, there was a religious debate around this idea. Newton and his supporters argued that removing God from any part in the running of the world would lead to atheism. Leibniz, on the other hand, argued that to suggest that God was an incompetent craftsman who would produce a mechanism that needed ‘winding up and cleaning’ was derogatory of the power of God, and would also lead to atheism.

  The Greeks struggled to give a ‘one cosmos with no teleology’ account of the universe. Some went in for many cosmoi, while others opted for teleology to explain one cosmos. A similar question arose concerning the origins of life. There were those who believed that human beings originated to some extent by chance. They believed that there were many different combinations of the available parts of animals before self-sustaining human beings were produced. There needed to be many of these mutations, just as there needed to be many cosmoi, to explain how anything so apparently well-ordered as humans had come about by chance. Plato and Aristotle believed that human beings were the result of teleology. Equally, they believed that there was a sense in which humans – and indeed other animals – were unique. There was not a whole spectrum of close relatives which had not quite worked: teleological ordering had created the best arrangement straight away. Aristotle says this about living things: