Eureka! Page 3

  The Greeks also began to have theories of cosmogony, and of the origins of life. Early mythical cosmogonies were often of a sexual nature – typically, the earth might come about due to the sexual coupling of two gods, perhaps of sky and sea. According to Anaximenes:

  The stars came about from earth, through the moisture rising from it, which when rarefied becomes fire, and the stars are composed of fire which has been raised high.

  He went on to say that:

  Living things were generated by water being evaporated by the sun. Humans, in the beginning, were similar to another animal, namely to fish.

  For the first time, we see an account of the origins of the cosmos and of life in entirely natural terms. Crucially, mankind was located firmly in nature. Once the Greeks began to have theories about the nature of the heavens and the earth, rather than myths and poems, the sophistication of their cosmologies rapidly increased. We do not see anything like this in ancient societies which had a dependence on mythopoeic thought. A civilisation as technologically advanced as the Egyptians, the architects of the great pyramids, believed that the goddess of the heavens, Nut, formed a hemisphere over the god of the earth, Qub (see Figure 1).

  In addition to this, the Greeks began to develop the first theories of matter. This began with Thales, whose theory was that everything was, at root, water. Whether he meant that everything was now water in some form or another, or that everything to begin with had been water (and that some had transformed into something else), is unclear. What is clear, though, is that Thales had a conception of matter as entirely natural. His fellow Milesians Anaximander and Anaximenes agreed that there was only one substance. Anaximander opted for ‘the unlimited’, and Anaximenes for air. The problem with Thales’ theory, as far as the Greeks were concerned, was this: how could water become fire? The point of Anaximander’s ‘unlimited’ may have been that the unlimited could become anything, while Anaximenes was keen to argue that air could change by condensation, becoming first water and then earth, or could become fire by rarefaction, and that all these processes could be reversed. Later, Heraclitus, who believed that all things were in a process of permanent change governed by a logos (hence his famous assertion that ‘you cannot step in ‘the unlimited’, and Anaximenes for air. The problem with Thales’ theory, as far as the Greeks were concerned, was this: how could water become fire? The point of Anaximander’s ‘unlimited’ may have been that the unlimited could become anything, while Anaximenes was keen to argue that air could change by condensation, becoming first water and then earth, or could become fire by rarefaction, and that all these processes could be reversed. Later, Heraclitus, who believed that all things were in a process of permanent change governed by a logos (hence his famous assertion that ‘you cannot step in the same river twice’), suggested that the one substance was fire.

  Figure 1: From the Egyptian Book of the Dead, c. 1000 BC.

  (Source: British Museum)

  The philosopher Empedocles of Acragas (492–432 BC) introduced the four elements of earth, water, air and fire, which were to become standard in Greek thought. These should not be understood as literally earth, water, and so on, but in a slightly more abstract manner as solid, liquid, gas and fire, or as principles of solidity, fluidity, gaseousness and fieriness. Earth, water, air and fire had always been a Greek classification of matter, but it was Empedocles who took the bold step of insisting that these were the four basic elements. He also insisted that physical objects were fixed proportions of these elements. For example, metals would be fixed proportions of earth and water (the Greeks considered metals to be made partly of water, since they became fluid when heated). As with cosmology, once the Greeks began to theorise, there was a rapid increase in the sophistication of their theories of matter.

  Despite the almost universal acceptance of the four elements after Empedocles, there were wide variations on exactly what constituted them, as we will see with Aristotle and Plato. It was not until the chemical revolution of the eighteenth century that air was shown to be composed of several different gases and that water could be made from, and dissociated into, hydrogen and oxygen, thus showing that air and water were not elements. It was not until the nineteenth century that the idea that fire, or heat, was some form of substance was abandoned.

  The Fathers of Medicine

  There is no doubting that the Babylonians, and indeed the Egyptians, had some effective healing practices and a reasonable knowledge of the human body. However good their healing techniques, though, the Babylonians did not consider health and disease to have physical causes. Rather, they saw disease as a punishment from the gods for some sin committed. Thus the first task of the doctor was to diagnose the sin, and then to work out a means of purification to absolve it. The Babylonian approach was in very sharp contrast to that of the Hippocratics. We know relatively little of the life of Hippocrates of Cos (c. 460–370 BC), but we do have an extensive set of writings known as the ‘Hippocratic corpus’, composed by Hippocrates and his followers between 430 and 330 BC. They believed that every disease had a physical cause, and that no disease was caused by the intervention of the gods. The Hippocratics were very forthright about this, to the extent of setting out their views on the most difficult sort of disease for them – epilepsy, known to the Greeks as the ‘sacred disease’. It was commonly thought that epileptic fits were due to possession by the gods, to some divine intervention, and hence ‘sacred’. Yet the Hippocratics put their point bluntly and forcefully in the opening passage of On the Sacred Disease:

  In my opinion, the so-called ‘sacred disease’ is no more divine or sacred than any other disease, but has a natural cause, and men consider it divine because of inexperience and wonder, it being unlike other diseases.

  In The Science of Medicine, their view is crystal clear:

  Every disease has a natural cause, and no event occurs without a natural cause.

  On the Sacred Disease goes on to say:

  The so-called ‘sacred disease’ comes from the same causes as the rest … each disease has a nature and power of its own, and none is unintelligible or untreatable … whoever knows how to bring about moistness, dryness, hotness or coldness in men can cure this disease as well, if he can diagnose how to bring these together properly, and he has no need of purifications and magic.

  Again, all diseases have a cause. This is a quite remarkable piece of optimism, typical of the early Greek thinkers. There is nothing in any disease which is ‘unintelligible or untreatable’. There is also an attack on magic in general. Prior to this, there had been criticism of individual magicians for being incompetent at their art, but with the early Greeks we find something quite new – the first recorded attack on magic as such. Magic and the supernatural simply did not exist. The world was a purely natural place, to be explained by natural means. There were not competent and incompetent magicians – there was simply no such thing as magic, and so all magicians were charlatans. The Hippocratics attempted to back up their views on the sacred disease through the use of experiments and reasoning. They opened the heads of goats, which suffer from a similar disease, and in On the Sacred Disease we are told that:

  If you cut open the head you will discover the brain to be moist, full of fluid and rank, showing that it is not a god who is harming the body, but the disease.

  Here was the physical basis of the disease. They criticised the ‘purifications’ which involved diet (because of the similarity of the disease in goats, people were advised not to eat goat meat or use goat skins). If one could avoid epilepsy by diet, then the disease could not be supernatural, said the Hippocratics. This insistence on the physical nature of all diseases, and the assault on magic and the supernatural, was a typical aspect of early Greek thought, and crucial in separating Greek science from that which preceded it.

  Eleatics and Atomists: Achilles and the Tortoise

  The Greeks also began to consider some more abstract scientific questions. The Eleatic philosophers (from Elea, a
Greek colony in southern Italy), Parmenides (fl. 480 BC) and Zeno (fl. 445 BC), investigated certain problems concerning motion and change at a highly abstract and theoretical level. The problems that they discovered were influential in the development of Greek science and philosophy. Zeno is most famous for creating a series of paradoxes, one of which has come down to us in the form of ‘the tortoise and the hare’. If a tortoise has a head start in a race, can the hare ever catch him up? Each time the hare runs half the distance to the tortoise, the tortoise will have moved on a small amount – so can the hare ever catch him? A different version of this paradox seems to show that it is impossible to move at all. All motion takes a certain amount of time, however small, you will agree. But if I try to walk to the door, first I must go half way, then half of what is left, then half of what is left again, ad infinitum. If each of these motions takes an amount of time, however small, and there are an infinite number of them, then it will take an infinite amount of time to complete my journey. So I can never reach the door! What is worse, I cannot even start, since the first part of my journey is infinitely divisible in the same manner.

  Zeno had a whole bag full of arguments such as these. While his paradoxes may seem frivolous, they played on important questions of divisibility and infinity. The central issues of concern for him were whether space, time and matter were continuous, and so infinitely divisible, or whether they were discrete – that is, occurring in small indivisible packages.

  Parmenides, too, was worried about the nature of change. His worry was deceptively simple, and can be put into two seemingly innocuous statements: what is, is; nothing comes from nothing. But if that is so, how can anything ever change? What is, cannot change, nor can what is not; nor can anything come to be from what is not. Yet this seems highly paradoxical, as do Zeno’s ideas, for there seems to be change all around us. Why did Parmenides and Zeno produce these paradoxes? At least part of the reason must be the Greek attitude to logos, which we saw in the last chapter. The Greeks were willing to follow an argument to the end, no matter what the consequences.

  Both Parmenides and Zeno produced paradoxical conclusions which stimulated others to delve much further into these matters. If the cosmos was comprehensible, then Parmenides and Zeno had to be wrong. The most important solution to the problems of change posed by the Eleatics came from the first Atomists, Leucippus of Miletus (fl. 435 BC) and Democritus of Abdera (fl. 410 BC). It is likely that Leucippus invented atomism and that Democritus refined it, but the sources tend not to distinguish between their opinions or their roles. Their view was that there was a void or vacuum in which there were discrete particles of matter. These particles were atoms, from the Greek atomos, meaning ‘uncuttable’. Unlike modern atoms, these particles were indivisible and did not undergo any change in themselves. However, these particles did move around in the void, becoming arranged in different patterns. These altered configurations of the atoms were perceived by humans as change. Ancient atomism is important for two reasons. Firstly, it is the ancestor of modern atomism. Though the modern theory of the elements is far more sophisticated, ultimately its roots are with Leucippus and Democritus. Secondly, ancient atomism was also the first properly thought out two-level theory of the world. It distinguished between what human beings perceive and how the world actually is at the atomic level. It introduced the idea that the reality behind appearances might be radically different from those appearances. Democritus said that what we perceive is:

  By convention sweet, by convention bitter, by convention hot, by convention cold, by convention colour, but in reality atoms and the void.

  Why did the problems posed by Parmenides and Zeno worry the Greeks so much? We come back to the idea of theories, and Greek assumptions about the cosmos. The Greeks assumed the cosmos to be comprehensible, to be understandable by humans. If so, then they required a coherent theory of change, and the paradoxes raised by Parmenides and Zeno had to be resolved. If Parmenides and Zeno were correct, then everyone else was wrong. Their views were not compatible with other theories, and had to be overcome. This requirement drove the Greeks to new heights of sophistication in their conceptions of matter and change.

  The Pythagoreans: the Secret Magic of Numbers

  Also of considerable importance were the philosopher and guru Pythagoras of Samos (fl. 525 BC) and his followers. The Pythagorean brotherhood was both secretive and religious, and held odd views about reincarnation and the transmigration of souls. Pythagoras is said to have stopped a man beating a dog, saying that he heard the voice of a reincarnated friend in the bark of the dog. Pythagoras himself may well have travelled in Egypt and learnt Egyptian geometry; certainly, some of his religious practices (such as not eating beans) show Egyptian influences. Pythagoras founded a school of religion and philosophy at Croton, in southern Italy, and his students devoted themselves to mathematics and spiritual purity, renouncing personal possessions and following a vegetarian diet.

  The Pythagoreans made some important contributions to mathematics and science. They took mathematics and geometry beyond the practical stage and developed them theoretically. It may seem odd to talk of practical geometry, but it is due to the Greeks that we have geometry in its current form. An example of practical geometry would be as follows. How can you measure the height of a tree? Cut a stick to your own height. When your shadow is as long as this stick, measure the length of the tree’s shadow. Geometry literally meant ‘land measuring’ (ge, earth, and metreo, to measure), and many pieces of practical geometry were based on measuring land in agriculture. It was typical of the Greeks that they sought to convert these practical procedures into a precise and abstract science. They converted the technology of practical geometry into the science that we know today. Pythagoras’ theorem about right-angled triangles was known well before this time, but was now proven. Another Pythagorean called Archytas of Tarentum (fl. 385 BC) solved the theoretical problem of how to construct a cube of twice the volume of the original.

  Figure 2: Pythagoras’ theorem. For all right-angled triangles, the square of the length of the longest side equals the squares of the lengths of the other two sides added together, so A2 = B2 + C2, or A = (B2 + C2)

  The Pythagoreans were also the first to think about the relationship between mathematics and nature, investigating numerical relationships in acoustics and musical theory. They discovered that if you halve the length of a string, then you obtain a note an octave higher. They also discovered that other notes could be expressed in terms of mathematical ratios, such as a fifth and a fourth being 1:2 and 3:4 respectively. The discovery that numbers could describe the world so well fascinated the Pythagoreans, and is their most important legacy. At the outset of the scientific revolution of the seventeenth century, Galileo declared that:

  Philosophy is written in a huge book, which stands open before our eyes, that is the universe. It cannot be read until we have learnt the language and become accustomed to the symbols in which it is written. It is in a mathematical language, and the letters are triangles, circles and other geometrical figures, without which it is not possible to understand a word.

  Nowadays, physicists do indeed believe that the world has a deep mathematical structure, best expressed in terms of mathematically framed laws of nature such as f = ma or e = mc2. The Pythagoreans, as pioneers of the idea that numbers are important in science, were understandably a little more naïve about the relation between numbers, nature and science. In fact, they went rather overboard, seeing numbers and harmony everywhere. Most famously, the Pythagoreans believed in a harmony of the heavens. The motions of the stars and planets were so related mathematically that a harmony was produced, though it was inaudible because we had heard it from birth and it was now background noise. They also believed in many seemingly arbitrary relationships, such as the male number being 3, the female 2 and the number of marriage 5. They even believed that the world was in some way constructed from numbers, rather than matter.

  We should not be too harsh o
n the Pythagoreans. It was not until the scientific revolution of the seventeenth century that something like the modern notion of mathematical laws of nature was worked out, and they did introduce the important idea that the cosmos could be captured in numbers as well as words, and that it was amenable to precise mathematical description. The Pythagoreans had one very nasty shock, though. They discovered that is not a rational number. That is, the square root of 2 cannot be expressed as the ratio of two whole numbers, as a:b. This was deeply disturbing to the Pythagoreans, who believed numbers to be part of the fabric of the world, and that all numbers were rational. Later legend has it that the Pythagorean who revealed this secret was drowned by divine retribution.

  Come the Time of Proof

  We have seen that once the Greeks began to formulate theories, their ideas developed rapidly. They also began to investigate some more abstract questions about the nature of the world they lived in. Along with this came the development of ideas about the nature of argument. This is in many ways characteristic of early Greek thinkers, who loved such abstraction. The problem they faced was this. Once you have theories which are not compatible with one another, then you need a procedure to decide between those theories. Certainly, the Greeks loved their philosophical debates, and theories were put to the test in discussions between philosophers. The quality of the theory and the evidence for it were examined minutely. However, some of the Greeks came to realise that there was another factor in these debates apart from the strength of the theory, which was the ability of the debater. It worried the ancient Greeks that the weaker theory could be made to defeat the stronger, in the hands of a good debater. There also emerged a group known as the Sophists, who were professional arguers. They would take either side of a debate, depending on who paid them and what the audience wanted to hear. Plato in particular was savage about the Sophists, insisting that the goal of philosophical argument should be truth, and not just defeating your opponent. Plato was keen to distinguish rhetoric – devices for winning over a crowd – from good philosophical argument.