Ideas

by Peter Watson

  For scientists, we are now living our lives surrounded by the second scientific revolution. This began just over a hundred years ago at the turn of the twentieth century with the simultaneous discovery of the quantum, the gene and the unconscious. The first scientific revolution stemmed from a similar set of simultaneous and equally momentous events. These were the discovery of the heliocentric view of the heavens, the identification of universal gravitation, important advances in the understanding of light, of the vacuum, of gases, of the body and of microscopic life.3 It is still not entirely clear why these advances all came together at much the same time. Protestantism, itself a revolutionary cause, with an emphasis on private conscience, surely had something to do with it. One of the other effects of the Reformation was to persuade reflective people that if there were so many, on all sides, who were convinced of their divine inspiration, they couldn’t all be right. Therefore, divine inspiration must be, by definition, often wrong. Capitalism was a factor too, with its emphasis on materialism, money and interest, and its focus on calculation. The growing capacity in the world for precision in all walks of life also played a role. The discovery of the New World, with its very different geography, botany and humanity, contributed much. A final general background factor may have been the fall of Constantinople in 1453, which removed the last living link with ancient Greek culture, and what it had to offer. Not long before the city fell, the Sicilian manuscript dealer and collector Giovanni Aurispa brought back, after just one visit, no fewer than 238 Greek manuscripts, introducing Westerners to Aeschylus, Sophocles and Plato.4

  Toby Huff has also drawn attention to the ways in which non-European sciences dropped behind. As late as the eleventh century there had been ‘hundreds’ of libraries in the Muslim Middle East, with one, in Shiraz, said to contain 360 rooms.5 But under Islam astronomers and mathematicians usually had other roles, as muwaqqit, time-keepers and calendar-makers in mosques–they were thus hardly motivated to come up with new ideas that might have been threatening to the faith. Huff makes the point that Arab astronomers knew all the astronomy that Kepler knew but never thought it through to the heliocentric system.6 The Chinese and Arabs never developed the ‘equals’ sign (=) and in fact the Chinese never believed that empirical investigation could ever completely explain physical phenomenon. In the thirteenth century there were, Huff says, the same number of scholars in Europe as in the Muslim world, or in China, but the latter two civilisations, because scholarship was validated centrally, either by the state or by masters, never developed organised or corporate scepticism and, ultimately, this is what counted. This is a question also addressed by the twentieth-century philosopher Ernst Cassirer, in his book The Philosophy of Symbolic Forms. He notes, for example, that in some African tribes the word for ‘five’ actually means ‘completes the hand’, whereas ‘six’ means literally ‘jump’–i.e., to the other hand. Elsewhere number is not divorced from the object it is qualifying: ‘two canoes’ for instance is different from ‘two coconuts’, and with others the counting is simply organised as ‘one’, ‘two’, ‘many’. With such a system, Cassirer says, the breakthrough to advanced mathematics is highly unlikely.7

  In the sixteenth century, understanding the heavens was regarded as the most important aim of science, by which people chiefly meant physics. In a religious society, ‘The whole fate of life and everything else was tied up with the movement of the heavens: the heavens ruled the earth. Therefore, whoever understood how the heavens worked, would understand everything on earth.’8 One of the chief effects of the scientific revolution–and it was clear by the time Newton’s work had been assimilated–was that the heavens do not rule the earth. As J. D. Bernal says, the scientists of the day came to realise that the problem was actually not very important and this of course downgraded the standing of the heavens. In the process, however, the new science of dynamics had been discovered, with its own mathematics, the mathematics of differential equations. This has been the bedrock for theoretical physics ever since.

  Nicholas Copernicus, a Pole, was fortunate in having an uncle who was a bishop, who took a great interest in his nephew and paid for his education in Italy. Copernicus was what we probably would call over-educated: he studied law, medicine, philosophy and belles lettres, and was also knowledgeable about astronomy and navigation.9 He was fascinated by Columbus’ discoveries but he would not have made a good navigator himself on Columbus’ fleet, because Copernicus was in fact a weak astronomer–his observations were notoriously inaccurate. But these drawbacks were more than offset by his one simple observation: that the traditional way to explain the heavens was in disarray. Copernicus became convinced that Ptolemy had to be wrong because he sensed that nature would never have organised herself into a complex set of ‘epicycles’ and ‘eccentrics’ as the Greek maintained. Copernicus applied himself to this disarray, with a view to simplifying the explanation. He described his approach as follows: ‘After I had addressed myself to this very difficult and almost insoluble problem, the suggestion at length came to me how it could be solved with fewer and much simpler constructions than were formerly used, if some assumptions (which are called axioms) were granted me. They follow in this order. 1. There is no one centre of all the celestial circles. 2. The centre of the earth is not the centre of the universe, but only of gravity and of the lunar sphere. 3. All the spheres revolve about the sun as their mid-point, and therefore the sun is the centre of the Universe. 4. The ratio of the earth’s distance from the sun to the height of the firmament [in other words, the fixed stars] is so much smaller than the ratio of the earth’s radius to its distance from the sun that the distance from the earth to the sun is imperceptible in comparison with the height of the firmament.’10

  Everyone remembers that Copernicus displaced the earth as the centre of the universe but, as can be seen from his words above, two other things stand out. The first is that he was only saying what Archimedes had said two thousand years before. Second, and no less important theologically than his displacement of the earth as the centre of the universe, was his claim that the heavens–the realm of the stars–were much, much further away than anyone thought. This was shocking and disconcerting but, unlike Archimedes, Copernicus was–before too long–believed. One reason for his high credibility was a further set of arguments that fitted well with people’s observations, namely that the earth has three different motions. In the first place, the planet revolves every year in a great circle around the sun. Second, it spins on its own axis. And third, there is a variation in the attitude of the earth to the sun. All of this, Copernicus said, meant that the apparent motion of the sun is not uniform. In some ways, this was his cleverest piece of reasoning: people had been puzzled for centuries as to why summer on earth does not last the same length of time as winter, and why the equinoxes do not occur half-way through the year, or half-way between solstices. The real answer of course was that the planets, including the earth, orbited not in circles but in ellipses. But that crucial insight–which we shall come to–would not have been possible without Copernicus’ observation about the relative movements of the earth and sun.

  Copernicus’ new ideas, systematised in his On the Revolution of the Celestial Orbs, commonly referred to by its Latin title as De revolutionibus, had some holes in it. For example, he still believed the medieval idea that the planets were fixed on the surfaces of a set of gigantic hollow concentric crystal balls. That apart, however, Copernicus had succeeded in his aim, of dispensing with the disarray and replacing Ptolemy’s complicated epicycles.11

  Though De revolutionibus was revolutionary, it was not immediately seen as incendiary. When Copernicus finally put pen to paper and sent it to the pope, the pontiff circulated the manuscript among fellow scholars, who recommended that it be printed. And although it was published by a Protestant printer, Copernicus’ new ideas were regarded as ‘perfectly respectable’ all the way through the sixteenth century. It was not until 1615 that anyone complained that it contravened co
nventional theology.12

  By then Copernicus’ work was already being built on by the Danish nobleman Tycho Brahe. The Brahe family fortune came from a share in the toll which the Danes imposed on every ship going in or out of the Baltic through the Oresund, the straits between Denmark and Sweden. Tycho was an argumentative soul who, once, in a duel, had the end of his nose snipped off, and thereafter always had to appear in public with a neat silver tip glinting in the light. But the Danish Crown realised that Brahe was a talented scientist and granted him an island of his own in the Oresund where there were few opportunities for argument and where he was allowed to set up ‘the first scientific institution of modern times’, called Uraniborg, or Heaven’s Gate.13 The laboratory included an observatory.

  Brahe may not have had as original a mind as Copernicus but he was a much better astronomer and, from his Oresund lab, he made many accurate astronomical measurements. These observations were left behind when, in 1599, Brahe quit Denmark and transferred to Prague, where he was appointed chief mathematician to the Holy Roman Emperor, Rudolf II, a highly eccentric man who was fascinated by alchemy and astrology. Back in Denmark, Brahe’s measurements were held by his no less talented assistant Johann Kepler. He set about the task of trying to marry Brahe’s measurements and Copernicus’ theories.

  Kepler was dogged and diligent and a keen observer. Like Copernicus he started with the belief that the stars were arranged, as traditionally thought, on a series of concentric crystal balls. Gradually, however, he was forced to dispense with this theory, when he found that Brahe’s observations could not be reconciled with the crystal ball theory. His breakthrough came when, instead of trying to fit all the planets into a system, he concentrated on Mars.14 Mars is particularly useful for astronomers because it can be observed almost all the time, and using Brahe’s measurements, Kepler came to realise that, in its journey around the sun, Mars described not a circle but an ellipse. Once this breakthrough had been made, Kepler soon showed that all planets that orbit the sun do so elliptically and that even the moon’s orbit of the earth is an ellipse. There were two immediate implications of this, one physical and mathematical, the other theological. In terms of science, an ellipse, though a relatively simple shape, is nowhere near as straightforward as a circle and would take a great deal more explaining–how and why should an orbiting planet be further away from the sun at some points than others? Thus the discovery of elliptical orbits stimulated the study of gravity and dynamics. At the same time, what did the existence of ellipses do to the idea that the heavens consisted of a series of hollow concentric crystal balls? It made such an idea untenable.

  Yet an elliptical orbit did explain why the seasons were of unequal length. An ellipse implied that the earth did not move around the sun at constant speed, but travelled faster when the planet was nearer the sun and slower when it was further away. There was, however, a constancy in the system, as Kepler found. The velocity multiplied by the radius vector (broadly the planet’s distance from the sun) remained the same.15 After his work with Mars, and Earth, and still using Brahe’s calculations, Kepler was able to calculate the orbits, speeds and distances of the other planets, all in relation to the sun. He found that there was a constancy here too: the period of rotation and the distance from the sun was in the ratio of the square to the cube. There was thus a new and definite harmony to the heavens and, as Thomas Kuhn says, whether or not it pointed to God, ‘it certainly pointed to gravity’.

  The fourth of the great heroes of the scientific revolution, after Copernicus, Brahe and Kepler, was Galileo. Professor of mathematics and military engineering at Pisa University, Galileo somehow got his hands on a Dutch discovery that, because of the Dutch wars with Spain, was regarded as a military secret. This was the telescope. Though he was well aware of the military applications of the device (in helping one side count the enemy before they could themselves be counted), his own interest lay in an exploration of the heavens. And when he pointed his telescope at the night sky, he received one of the greatest shocks in all history. It was immediately clear that the heavens comprised far more stars than anyone had seen previously. There are, roughly speaking, two thousand stars in the sky at night that are visible to the naked eye. Galileo saw that, via the telescope, there are myriads more. Again, this had profound implications for the size of the universe and was therefore theologically challenging. But that wasn’t all. With his telescope, Galileo also noticed three and then four ‘stars’ or ‘moons’ moving about Jupiter, just as the planets moved around the sun. This confirmed the Copernican theory of the heavens but at the same time provided Galileo with an example of what was in effect a celestial clock. The movement of these bodies was so far away as to be unaffected by the movement of the earth, thus providing a sense of absolute time. It offered navigators a way of finding longitudes at sea.16

  As a professor of military engineering, another interest of Galileo’s, naturally enough, was weapons–in particular what we call ballistics. At that point, as with much else, the basic understanding of dynamics (of which ballistics was a part) was essentially Aristotelian. Aristotle’s theory of spear-throwing, for example, was that a spear, when thrown, moved through the air, and the air which was displaced from the tip of the spear somehow went round to the back of the shaft and pushed it along. But a spear did not shoot through the air for ever, because it got ‘tired’ and dropped to the ground. This was clearly unsatisfactory as an explanation of movement but, for two thousand years, no one had been able to come up with a better one. That began to change after observations on another relatively new weapon–the cannon ball.17 Part of the point of a cannon was that its angle of attack could be varied. As the gun barrel was raised from parallel with the ground, the range increased and went on increasing until 45°, after which it began to fall off again. It was this behaviour of cannon balls which provoked Galileo’s interest in the laws of moving bodies, though another factor was the storms which periodically rocked Pisa and Florence, during which he noticed that the chandeliers and hanging lamps would sway and swing. Using his own pulse as measuring device, he timed the swaying of the lamps and found that there was a relation between the length of a pendulum and its swing. This became his square-root law.18

  Galileo produced two famous treatises, The Two Chief Systems (1632) and The Two New Sciences (1638). Both were written in Italian (rather than Latin) and were in the form of dialogues–plays almost–designed to introduce his ideas to a wider audience. In the first, the relative merits of the Ptolemaic and Copernican systems were discussed between three men: Salviati (a scientist and scholar), Sagredo (an intelligent layman) and Simplicio (an obtuse Aristotelian). In the dialogue Galileo left little doubt as to where his sympathies lay but he also (and indirectly) satirised the pope. This led to his famous trial before the Inquisition, and to his imprisonment. During his year in jail, however, he prepared The Two New Sciences, a dialogue between the same three men, concerning dynamics. It was in this second book that he set out his views on projectiles and was able to show that the path of a projectile, disregarding air resistance, is a parabola.19 A parabola is a function of a cone, as is an ellipse. For two thousand years, conics had been studied in the abstract: now, all of a sudden, two applications in the real world had emerged virtually simultaneously. Yet more harmony of the heavens had been revealed.

  It was ironic that The Two New Sciences was written in jail. Galileo’s imprisonment had been designed to keep the lid on the Copernican revolution. In fact, it provided Galileo with the opportunity to reflect and write the work which led to Newton and struck the greatest blow against religion.

  According to a list of the most influential people in history, published in 1993, Isaac Newton ranked as number 2, after Muhammad and ahead of Jesus Christ.20 Born in the same year that Galileo died, 1642, Newton grew up in an atmosphere where science was regarded as a quite normal occupation or interest. This is already very different from the world inhabited by Copernicus, Kepler or Galileo, wher
e religion and metaphysics mattered most.21 At the same time, Newton shared with them certain heroic qualities, in particular an ability to work almost entirely on his own. This was just as well because much of his ground-breaking labour was carried out in forced isolation in 1665 when London was devastated by the plague and he sought refuge in the village where he was born, Woolsthorpe in Lincolnshire. This was, in the words of Carl Boyer, in his history of mathematics, ‘the most productive period of mathematical discovery ever reported’, and was reflected later in Wordsworth’s lines: ‘a mind forever / voyaging through strange seas of thought alone.’22