The Unnatural Nature of Science Page 6
The stage for science had been set, and for the first time there were named actors, with strong views and personalities. This was a radical departure, for Egyptian and Babylonian medicine, mathematics and astrology can, apparently, be combed in vain for examples of a text where an individual author explicitly distances himself from and criticizes the received tradition in order to claim originality for himself; whereas in Greece this became a normal procedure. Perhaps this arose from the similar requirement for recognition by the Greek poets, but, whether this is so or not, scientists and philosophers typically appear in the first person. This may also be related to the fact that many Greek citizens acquired experience in the evaluation of evidence and argument in the context of politics and law. So a critical tradition of crucial importance was established and, one after the other, pre-Socratic philosophers implied that no one else had got the answers right. Authority was challenged, and the ideas of individuals about the nature of the world became dominant. The admiration of one’s peers is one of the major rewards in science, and this became possible only when science became the work of individuals who adopted the crucial first-person singular.
Aristotle’s science, which became dominant, can make difficult reading. For example, he distinguishes four kinds of causes, only two of which relate easily to a modern reader: cause in the sense of one thing’s influence on another, and cause in the sense of the function that something serves. Nevertheless, his science accords with a reasonably commonsense picture of the world. He consciously applied a maxim that in the search for explanations it is necessary to start from what is familiar and that deductions in science can proceed from principles intelligible in themselves. One should view Aristotle’s situation with sympathy, for how was he to know that the world is constituted in a way that bears no relation to common sense? Aristotle’s world is made up of four basic elements – earth, fire, air and water – and each of them has two of the four primary qualities – wetness, dryness, coldness and hotness. All these are drawn from everyday experience. Movement of objects now finds a natural explanation. Fire moves upwards and earth downwards to their natural places. The earth is at the centre of the universe, and the heavenly bodies are embedded in a series of concentric spheres around it. Circular motion is regarded as perfect, and this describes the movement of the sun and the heavens. Aristotle’s contribution to biology was to open up many areas – comparative anatomy, embryology and animal behaviour – and to make an enormous number of observations. His teleological explanations also made sense, since they implied that natural phenomena had an end in view. Why do ducks have webbed feet? In order to swim. Aristotle never arrived at the fundamental requirement of doing experiments in relation to theories; however, he came close by providing the basis for thought experiments, such as thinking about what direction the earth would move in if the heavens stood still.
Aristotle also clearly recognized one of the key features of early science: it offered no reward other than intellectual gratification. ‘Thus, since men turned to philosophy in order to escape from a state of ignorance, their aim was evidently knowledge, rather than any sort of practical gain. The evidence of history confirms this: for, when the necessities of life were mostly provided, men turned their minds to this study as a leisure-time reaction.’
Most of Greek science turned out to be wrong – misconceptions about motion, embryological development and the place of the earth in the heavens. That is no disgrace, for being wrong is a constant feature of scientific method. However, at least two giants stand out. Their achievements are almost as great as Thales’s great leap. Euclid’s geometry and Archimedes’s mechanics were fundamental to further scientific advance, and one may speculate, with some concern, how the scientists of the Renaissance would have fared without them.
Euclid, who lived around 300 BC, was not the inventor of geometry, for many propositions had been known for a long time before him. His achievement was to follow through Aristotle’s demand for a logically derived science based on a minimum number of postulates, which had to be taken as given; his five postulates are undemonstrable but taken to be true. Most of Euclid’s postulates evoke little surprise and seem quite sensible – for example, that all right angles are equal, and that a circle can be constructed when its centre and a point on it are given. However, the fifth postulate is rather different: ‘If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.’
Another way of stating this postulate is to say that parallel lines never meet, and either formulation may seem to be obvious. But what is not at all obvious is that, given the other postulates, it cannot be proved. Euclid’s genius recognized that proof was impossible and that this needed to be included among the postulates. Of course, another postulate could be formulated to replace it, but some equivalent postulate is necessary. Now, given the five postulates, the richness of Euclidean geometry could be deduced. Also, a model for a hypothetico-deductive science as proposed by Aristotle was established; that is, given a number of laws and basic assumptions, a large and varied number of conclusions could be drawn. (It is worth noting that, given Euclid’s postulates, common sense would not alone be sufficient to derive the theorems of geometry.)
Archimedes studied under the disciples of Euclid in Alexandria in the third century BC and was the first applied mathematician: he applied mathematics to understanding how the world works. He laid the foundations not only for statics – that is, the study of non-moving forces in equilibrium, such as the forces exerted by levers and weights, which is the basis of all structural engineering – but also for hydraulics – the study of forces acting on bodies in water. Archimedes invented machines such as the compound pulley and a hydraulic screw for raising water, but he himself, in the Greek tradition, did not value such achievements: according to Plutarch, he regarded as ‘ignoble and sordid the business of mechanics and every sort of art which is directed to use and profit; he placed his whole ambition in those speculations the beauty and subtlety of which are untainted by any admixture of the common needs of life.’ This is an early and crucial example of the differing attitudes to pure and applied science. Apparent uselessness is one of early science’s pecularities, for what use was it to Thales that all the world was made of water, or to Archimedes that he understood why some bodies floated, or to Aristotle that the heart was the first organ in the embryo to develop?
While Archimedes made important contributions to mathematics – he defined the Archimedean spiral and made a good approximation for π, the ratio of the circumference to the diameter of a circle – it is his mechanics and hydrostatics that are so impressive. In these he achieved for the first time, for physics, what Euclid had done for geometry. He, like Euclid, begins with definitions and postulates and then proves certain propositions. This approach was applied to mechanics, where he determined the centre of gravity of simple figures like triangles and discovered the relationship between weights and distances in relation to levers. ‘Give me a point of support and I shall move the world,’ he proclaimed, for he had shown that, provided the lever was long enough, any weight could be supported. With hydraulics he started with postulates such as ‘Let it be granted that bodies which are forced upwards in a fluid are forced upwards along the perpendicular [to the surface] which passes through their centre of gravity.’ From such postulates he proves that the loss of weight which a body experiences in water is equal to the weight of water displaced. Such principles explained why bodies float and enabled him to determine the specific gravity of gold and silver. No wonder he shouted ‘Eureka!’ and leaped from the bath – it was a wonderful and totally surprising discovery. The application of mathematics to physical problems is in itself surprising, for it is far from obvious why the abstract language of mathematics should be able to provide so satisfying a description of the world.
Archimede
s’ work is a monumental achievement. Do most of us, lying in our baths, understand that our loss of weight is equal to the weight of water we displace? And that if this weight is greater than our own we will float? Could we tell whether a crown was made of gold or silver?
Cosmology is another area that demonstrates the triumph of Greek science. Every civilization and culture has provided its own answer to the question: what is the structure of the universe? Only Western civilizations, starting with the Greeks, have used studies of the heavens to provide an answer: other cultures have shaped their cosmologies on terrestrial events, the heavens merely providing an enclosure. For example, in one form of Egyptian cosmology the earth is depicted in some detail as an elongated platter – involving water, earth and air – an image probably taken from the Nile. The sun was the god Ra, who had two boats for his journeys across the skies – one during the day, one at night. Such cosmologies, it has been suggested, were not really meant as explanations but rather reflected the social structure of the society in which the people lived, and helped stabilize it. There is thus nothing in the Egyptian cosmology which even tries to account for Ra’s journeys or their seasonal variations.
Ancient astronomers, such as the Babylonians and Egyptians, made many observations on the movements of the sun and stars, but these did not form part of an explanation. The Egyptians were primarily concerned with their use in establishing a calendar, while the Babylonians were interested in the accurate prediction of events in the heavens, such as the appearance of the new moon. The attempt to provide an explanation was first made by Anaximander, Thales’s contemporary in Miletos, who assigned sizes to some heavenly bodies and likened the moon and its eclipses to the turnings of a wheel. With time, over two centuries, the Greeks developed a ‘two-sphere’ universe – the earth being a tiny sphere suspended at the geometric centre of a much larger sphere that carried the stars. This model has considerable conceptual elegance and provides, for the first time, an economical way of linking observations into a coherent whole. It is still convenient to use this model when learning navigation today.
Even in Greek times there were competitors to the two-sphere model. In the third century BC, for example, Aristarchus proposed that the sun was at the centre and the earth revolved about it. But that clearly contradicted common sense, and Aristotle gave cogent arguments as to why the earth is the centre of the universe. For example, if the earth were moving in space we would surely sense it, and why would we not fall off? For Aristotle there was perfection in the heavens, and they contained the power on which terrestrial life depends. The authority of Aristotle’s ideas derived in large part from his ability to express in an abstract and consistent manner a perception of the universe that embodied a spontaneous conception of the universe which had existed for centuries. They embody the ideas of many primitive tribes and children.
The concept of circular motion of the heavenly bodies about the earth created great problems when it came to understanding the movement of the planets. Because they, like the earth, in fact rotate around the sun, their motion did not fit in with simple circular motion. In AD 150, Ptolemy provided the most comprehensive explanation of their complex motion in terms of epicycles, which had been proposed earlier – that a planet rotates about a small circle which in turn rotates about the earth. But the problem was that, while considerable accuracy in predicting planetary motion was achieved, this accuracy was at the price of complexity – more and more epicycles had to be added to fit planetary observations.
Given the apparent progress of Greek science, we are faced with a problem. Why did progress in astronomy and other sciences stop, effectively, until the arrival of Copernicus, Kepler and Galileo? Copernicus’s ideas were, in principle, accessible to the Greeks, in the sense that they required no new observations. They were inaccessible, perhaps, because of the ideas themselves, which required a major conceptual advance. It was a barrier that is hard to explain. It was only with respect to the relative motion of the earth and planets with respect to the sun that Copernicus broke with tradition: all the rest of his work was in the Ptolemaic mould. Copernicus attacked Ptolemaic astronomy primarily because Ptolemy had not strictly adhered to the Aristotelian precept that all heavenly motions must be explained by uniform circular motions alone. While Copernicus’s view of the heavens, with the sun at the centre, was crucial for further advances, it was not a simplification, for he made no real attempt to explain the motion of the planets. That was left to Kepler, who more than fifty years later made use of Tycho Brahe’s observations and set out to provide a physical cause for those movements. Kepler had the intellectual courage to abandon motion in a circle for motion along an elliptical path.
As with mechanics and motion, these new ideas rarely relied on new observations but relied instead on a change in thinking. In part the pervasive influence of Aristotle had to be rejected, and this was much more difficult than it might appear. Nothing illustrates this more clearly than Galileo’s analysis of falling bodies.
In Aristotle’s view, the motion of an object up or down was related to the object’s natural place, and this in turn was governed by its constituents – steam went up because it contained fire; stones fell to earth because it was their natural place, and the bigger the stone the faster it fell. Hence, according to Aristotle, the rate of fall of a body is proportional to its weight. But, as Galileo says in the words of one of his characters, Salviati, ‘I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall, at the same instant, from a height of say, 100 cubits [the height of Pisa’s tower], would so differ in speed that when the heavier reached the ground, the other would not have fallen more than 10 cubits.’
Sagredo, Galileo’s interested layman, reports that he has done the experiment and it is not true, and Salviati continues, ‘even without further experiment, it is possible to prove clearly, by means of a short and conclusive argument, that a heavier body does not move faster than a lighter one provided the bodies are of the same material.’ If, he goes on, we take two bodies whose natural speeds of fall are different, it is clear that, on uniting the two, the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter. But if this is true, and if a large stone moves with a speed of, say, eight, while a smaller moves with a speed of four, then the system will move with a speed of less than eight when the stones are joined. But the two stones when tied together make a stone larger than that which before moved with a speed of eight; hence the heavier body moves with less speed than the lighter – an effect which is contrary to the original supposition. Aristotle’s ideas are wrong, since, if the rate of fall is proportional to weight, a logical contradiction can be demonstrated.
This delicious argument is an example of the kind of scientific thinking that was essential to the revival of science in the sixteenth and seventeenth centuries when Galileo was one of the giants. It also shows that one doesn’t always need to do experiments to falsify a theory, though Galileo was a master of experimental method, and that internal consistency is one of the fundamental requirements of a scientific theory. The puzzle – unsolved – is why even though there were critics of Aristotle’s ideas on motion, such as the Christian Stoic Philoponus in the sixth century, it took some 1,800 years for someone to point out the inconsistency or do the experiment. It requires a particular interest and mode of thought to deal with scientific problems.
It is particularly puzzling since Archimedes’s method of reasoning compares very favourably with that of Galileo. It should come as no surprise that one of Galileo’s first studies was in fact Archimedes. ‘Those who read his works,’ wrote Galileo, ‘realize only too clearly how inferior are all other minds compared with Archimedes’s, and what small hope is left over of their discovering things similar to the ones he discovered.’ This, in my view, was not merely a fashionable enthusiasm for the past but a just assessment. What is remarkabl
e is the maintenance over all those years of the Archimedean tradition. For this we must thank later Greek and Islamic scholars of the Middle Ages. A Flemish Dominican, Willem Moerbecke, in the thirteenth century translated every Archimedean treatise from the Greek into Latin, the language of scholarship at that time; and the Venetian editions of the sixteenth century were crucial in enabling Galileo to learn about Archimedes. Praise, too, to these noble scribes.
Why was it, then, that progress in science occurred in the West so many years after the Greeks? After all, each of the three inventions that Francis Bacon had identified as bringing about great changes in Renaissance Europe – printing, gunpowder and the magnetic compass – was a product of China, not Europe. The Chinese were brilliant engineers, but, though accurate observers of celestial phenomena, their contributions to science were minimal. They could build great bridges, and cast iron many years before it was done in Europe, but they never developed a mechanical view of the world. (Egypt provides us with another example of a highly sophisticated civilization which flourished for many centuries without making a single contribution to the development of the exact sciences.) The Chinese were fundamentally practical, but they had a mystical view of the world, a view which contained no concept of laws of nature but which was more directed to a social ethic whereby people could live together in happiness and harmony. Attitudes of this kind, in contrast to the passion for rationality that characterizes Christianity, perhaps partly account for science’s flowering in the West and its failure in the East even to begin.