Le Secret de l'Occident quoted in a paper on the role of astronomy
in the history of science, short-named "The consequence of cloud cover"
by Brian Davies of King's College in London, floated on line on July 2002.
Available on the PhilSci Archive,
an electronic archive for preprints in the philosophy of science.
Safety copy Aug 02. Original document.
THE ROLE OF ASTRONOMY
IN THE HISTORY OF SCIENCE
E B Davies
We discuss the extent to which the visibility of the heavens was a necessary condition for the development of science, with particular reference to the measurement of time. Our conclusion is that while astronomy had significant importance, the growth of most areas of science was more heavily influenced by the accuracy of scientific instruments, and hence by current technology.
It is undoubtedly the case that observations of the heavens were of great significance to early societies. Signs of the zodiac may be found in tombs of the Egyptian pharaohs, and many ancient monuments, from Stonehenge to the Egyptian pyramids, are thought to have been aligned with solar or other astronomical events. Astronomy occupies such a central place in the history of science that it might be thought that science would have developed much more slowly without it. In this paper we subject this intuition to a detailed examination, and come to the conclusion that the changes in the development of the physical sciences would have been surprisingly limited. We see no reason why the development of the biological sciences should have be affected one way or the other. Our main thesis is that, although the order of particular discoveries may depend upon external factors such as cloud cover, eventually the same scientific laws will be discovered. Social factors determine whether science will develop, but important scientific laws are supported by such a variety of evidence that the removal of any one form of support is, ultimately, irrelevant.
Astronomical observations have had such complex interactions with the other sciences that it seemed simplest to adopt a fictional device for this study. Following an idea of Poincaré, [Poincaré, 1902], we discuss the development of science on a world called Gaia, exactly like our own except for the fact that it is permanently covered by a thin layer of cloud at high altitude. This is supposed to make the Sun, Moon and stars invisible, but with no other effects. We impose stringent ground rules. On Gaia, scientists are supposed to have carried out those aspects of their research which did not depend directly upon astronomy. Unhistorical scientific discoveries are only allowed when evidence which was gathered in the historical record makes them inevitable, even in the absence of astronomical confirmation. These rules of procedure neglect the question of motivation: perhaps experiments which could have been done at some stage would not have been, in the absence of previous astronomical discoveries. I have tried to be sensitive to this issue, but such questions cannot ultimately be resolved. Spiritual and religious issues are discussed briefly in the final section, and, as in the rest of the article, we try to find historical evidence for our statements.
The regular failure of experts (futurologists and those in business) to predict how science and technology would develop indicates that one should not take our account below as a definitive description of how Gaia would have developed. In the language of mathematicians, we are presenting an existence proof, not a uniqueness proof. All we claim is that science on Gaia could have developed in the way we describe. We have attempted to present the most plausible scenario which we could. A secondary thesis is mentioned in our final section: that the progress of science depended more closely upon the growth of technology, particularly during the Industrial Revolution, than upon the brilliance of individuals such as Galileo, Newton and Einstein.
The difficulty of determining longitude at sea was an increasing problem on Earth in the sixteenth and seventeenth centuries as trade developed. Shipwrecks were responsible for great commercial losses, and led to many prizes being offered for a solution to the problem. On Gaia both latitude and longitude would have been impossible to determine accurately. Magnetic compasses would have provided vital help in keeping on course, in addition to mere reliance on the stability of the wind and ocean currents, but one would expect early sailors to have stayed within sight of land to a much greater extent than they did on Earth.
There is no reason why cloud cover should have hampered long land journeys within the Eurasian continent. A coast-hugging route around Africa to India could certainly have been followed by Vasco da Gama in 1497/98, opening up trade with the East. However, it is likely that the (re-)discovery of the Americas would have been long delayed, with the consequent losses of the trade which ensued on the Earth. Cloud cover might therefore have resulted in a less buoyant growth of European economies on Gaia after 1500. This might have had knock-on effects for science, because of its dependence on the patronage of the wealthy. This is impossible to quantify, because there could have been more active development of trade with the East in Gaia.
For particularly important trade routes (the Mediterranean, North Sea and English Channel) many different methods of providing guidance for mariners could have been developed if commercial needs justified them. Lighthouses would have been used, of course, just as they were on Earth. Rockets were developed in China before 1200AD and knowledge of them reached Italy by 1380. By the beginning of the nineteenth century they were used by many countries (as weapons), and could have been fired from major ports at regular intervals to show their location. Herschel used them to determine the difference between the local times at Greenwich and Paris, and stated that in clear weather they were visible for up to forty miles (sixty kilometres), [Herschel, 1826]. In the nineteenth century governments might have developed chains and eventually networks of anchored lightships far out to sea to guide mariners and cut the lengths of their journeys.
3. The Shape of the Earth
The classical Greeks (Plato, Euclid, Archimedes, Aristotle) had no serious interest in observational astronomy, as opposed to cosmology, and we assume that the development of Euclidean geometry would not have been affected by the presence of continuous cloud cover. (Hipparchus and Ptolemy's applications of geometry to astronomy, and of both of these subjects to the mapping of the known world, came considerably later.) Surprising as it may be to us, their interest in astronomy did not lead the Babylonians, Egyptians or Chinese to the belief that the world was round. It appears that the Pythagoreans were the first to speculate about this. The first serious estimate of its circumference was based upon the observation that the apparent angular height of the Sun varied from place to place (Eratosthenes in Egypt). All that would remain in Gaia would be the regular alternation between day and night, with a transition between the two which was rather gradual. It seems likely that the belief in a flat Gaia would have persisted for many centuries. The globe might not have been circumnavigated until the nineteenth century, because of the greatly heightened dangers of long voyages far from land.
As long as it was not possible to distinguish whether Gaia was flat or round, it could, by definition, not have been of practical importance. Direct evidence that the Earth was round was obtained by Galileo using his telescope in 1610. (He did not report it this way because every educated person already agreed about this fact.) His first use of this was to examine the world around him, and only later did he think of turning it towards the Moon. The ability to use telescopes to spy ships far out at sea was regarded as being of great military significance. They would also have shown ships disappearing below the horizon as they moved away, rather than simply shrinking to spots. The conclusion that the world was round would have been unavoidable. By systematically measuring this effect, Galileo could also have estimated its diameter to within a few percent. The distance between two observation stations at opposite ends of a large enough bay could have been determined by triangulation, using a nearby mountain. On a clear and calm day, the parts of these stations hidden by the curvature of the sea could have been observed with a telescope, and the diameter of Gaia estimated. The accuracy would be limited by the variation of the height of the sea caused by tides. If we abandon the fictional language, our claim is that, once the telescope had been invented, measurements of the diameter of the Earth became straightforward, if not very accurate, without reference to observations of the heavens.
The division of the world into two hemispheres would have been clear as soon trade around the Cape of Good Hope had become well established. Compasses provided a method of distinguishing north/south from east/west. The precise location of the Equator would have been unclear on Gaia, but the fact that summer in the southern hemisphere coincided with winter in the northern hemisphere could not have escaped attention. Nor could the great variation in the length of a winter day as one travelled north-south. But translating such observations into precise measurements of the latitude would not have been possible. Up to the seventeenth century magnetic inclination (dip) would have provided a useful, if rather crude, approximation to the latitude. We will discuss more precise methods of measuring latitude in the section on time.
The development of the telescope would have been rather different on Gaia. Apart from its military and leisure uses, its main application would have been to geodesy. Static telescopes with very large lenses or mirrors would not have been useful, and efforts would have concentrated on the production of portable telescopes with high quality optics and moderate magnification.
The systematic mapping of the world in the nineteenth century depended upon the development of highly accurate surveying instruments with telescopic sights to carry out the necessary triangulations. The Great Trigonometric Survey of India commenced in 1802, and the local deviations of gravity due to the Himalayas were measured in the 1850s. Gauss's heliotrope of 1822 achieved much greater accuracy than previous instruments by using the Sun's rays, but this was not an essential feature. Drummond described a modification which depended instead upon the very bright light produced by machined beads of incandescent lime, [Drummond, 1826]. Using this he was able to sight between stations in Ireland a hundred kilometres apart, if the air was clear enough. The differences between the direction of the local gravitational vertical at different places amounts to about 0.54 minutes of arc for every kilometre of horizontal displacement. It was possible to measure such angles to a hundredth of a second of arc between stations a hundred kilometres apart by 1856, [Pratt, 1856]. This should be contrasted with the situation at the end of the sixteenth century, when Tycho Brahe could only measure angles to slightly better than one minute of arc. We conclude that surveying instruments would have yielded an accurate value for the diameter of Gaia by 1800, and its deviations from sphericity by 1860, without the help of astronomical observations.
4. Mathematics and Mechanics
Arithmetic was used for many purposes by early societies, including the keeping of accurate records of time, weights, lengths and money. Only the first of these has any connection with the visibility of the Sun, and there seems no reason to suppose that the development of the Hindu-Arabic counting system would have been delayed in Gaia. The same applies to the algebra and calculus. From its earliest origins in Greek times, the latter was closely related to geometrical problems: the calculation of lengths of curves, areas and volumes. Newton's development of the subject may have been linked with his interest in astronomy, but Leibniz's version, first published in 1684, was in many ways more influential than that of Newton, because of its superior notation.
Trigonometry is quite a different case. The earliest surviving work is by Ptolemy in the second century AD, but there were substantial earlier contributions by Hipparchus and Menelaus, now lost. All developed the properties of the trigonometric functions for applications to astronomy, as did later Indian and Arab mathematicians. They put great effort into the production of tables of these functions. Historically trigonometry did not become independent of astronomy until the thirteenth century. Its obvious area of application on Gaia would have been in surveying, which combines geometry and computation in much the same way as astronomy does. We have to accept that trigonometry provides no support for our main thesis, unless one is willing to indulge in unsubstantiated speculation.
The originator of mechanics as an experimental science was Galileo. He spent a large part of his life investigating the behaviour of simple machines and falling bodies. One of the applications of this work was to ballistics. Another was to the basic theory underlying pendulum clocks. This aspect of his work was separated rather strongly from his observational astronomy. He never explained the motion of the planets using his mechanics; indeed his ideas about the naturalness of circular motion seem rather strange to us. His theory of the tides was wrong precisely because he refused to entertain any notion that the Moon might have some mysterious effect upon Earthly bodies.
In Newton's Principia, the laws of motion of moving bodies were taken as already known, and attributed to Galileo. This was uncharacteristic generosity on Newton's part, since his mathematical formulation of these laws was far superior to that of Galileo. I shall assume that Newton published a book containing his three laws of motion, and that the correctness of these was widely accepted. He could not have produced his universal law of gravitation, but would have noted that all bodies are affected by a gravitational force on Gaia. Principia Book 3 contains a terrestrial, experimental proof that (in our language) the inertial and gravitational masses of various different materials are equal to within one part in a thousand.
The extremely weak gravitational attraction between two metal balls was measured by Cavendish in 1797/98. His extremely delicate series of experiments were often referred to as weighing the Earth, but on Gaia they would have had greater significance. By varying the distances between the balls it would have been possible to deduce the inverse square law of gravitation from these experiments, had not this result been known; he did in fact state that he had found no deviations from the law which governed gravitational forces at much longer ranges, [Cavendish, 1798]. Cavendish would probably not have gained the fame for this discovery on Gaia which Newton had a century earlier on the Earth: the glamour of difficult mathematics, linked with people's fascination with the heavens, outweighed the fact that Newton's result was useless in practical terms. Whether Cavendish would have carried out his experiments if Newton's law of gravitation had not already been known is a moot point. The gravitational attraction of bodies to the Earth was obvious, and it is difficult to believe that there would not have been prolonged attempts to try to understand the nature of this force. In 1856 Airy reported using a pendulum to compare the strength of the Earth's gravity at the top and bottom of a deep mine; his measurements were accurate to better than one part per million, [Airy, 1856].
The belief that the world was governed by mathematical laws originated with Galileo, but was reinforced by the extraordinary astronomical accuracy of Newton's theory of universal gravitation. However, optics (Newton, Young), chemistry (Lavoisier, Dalton), electricity, magnetism and thermodynamics also provided contexts in which scientific investigations could be combined with precise measurements to produce universally applicable laws. The importance of Newton's three laws of motion became clear during the nineteenth century, when the Industrial Revolution led to the manufacture of machines such as steam engines, and eventually aircraft: reciprocating parts need to be balanced very carefully in order to prevent disastrous vibrations in a machine. Faraday's work relating electricity and magnetism led to Maxwell's creation of a highly sophisticated mathematical theory to explain the effects observed. Apart from the universal law of gravitation, all of the above developments should have occurred on Gaia.
5. The Measurement of Time
The passage of the seasons was of great importance for early agriculture. The earliest calendars were all based on observations of the Sun (and Moon in the case of China). However, methods based simply on counting would be only slightly more inconvenient. By keeping records of the flowering of a few plant species over several decades, it would have become apparent that the Gaian year was about 365 days long. More accurate estimates would have become possible once sealed liquid in glass thermometers had been developed in Florence in the second half of the seventeenth century. By analyzing temperature records in a region with well enough defined seasons over a long enough period, the length of the year could have been determined fairly accurately.
Gnomons, sundials and water clocks provided the earliest methods of measuring parts of a day. The Karnak clepsydra dates to the fourteenth century BC, and may have emptied over a period of about twelve hours, [Mills and Symons, 2000]. The earliest surviving Egyptian shadow clock dates to somewhere between the eight and tenth centuries BC. The early history of gnomons is difficult to trace, but a Babylonian text of about 700 BC refers to their use, as does a Chinese text dated 645BC [Cullen, 1996, p101; Ronan, 1981, p 128]. Probably all three methods of keeping time had been widely used many hundreds of years earlier. The lack of evidence prevents any conclusions about priorities being drawn. Sun-based systems had the obvious disadvantage that they would not work in cloudy weather. Mechanical water clocks were invented in China in the eighth century AD, and led to the marvellous 'cosmic engine' of Su Sung, built in 1088. The impetus for their development was not the investigation of astronomical phenomena, but the need to regulate activities around the Emperor. Mechanical weight-driven clocks first appeared in the Middle Ages, and by 1600 they were to be found in many European towns and villages. However, they were inaccurate and had to be corrected on a regular basis by reference to the Sun. As urban society and commerce developed there was a steadily increasing pressure to develop clocks which were accurate and portable, [Schechter, 2001].
The modern era of time measurement started with Galileo, who provided the theoretical basis for the invention of the pendulum clock. In 1659 Viviani produced a drawing of a simple pendulum clock which had been designed by Galileo shortly before his death. Huygens, however, actually designed and built such a clock in 1657, improving the accuracy of timekeeping dramatically. From this time onwards a huge variety of ingenious clock and watch mechanisms were invented. It is not clear why so much energy was put into this, but one reason would have been the simple joy of the technical challenge. The beauty of the mechanisms led to clocks and watches being highly prized; possession of one was a form of conspicuous consumption, used to prove the wealth of the owner. Pendulum clocks, however, also had serious scientific uses, and their design continued to improve until they were all rendered obsolete in the twentieth century by atomic clocks.
There would have been a fundamental difference between Earth and Gaia as far as the measurement of time was concerned: in the absence of the heavens, there would have been no external standard to calibrate clocks against on Gaia. Time might well have been measured using different units in different places, just as was the case for lengths and weights. Medieval clocks in different places would have got completely out of step over a period of a week or so, even if they were ostensibly using the same measure of time. Once this became sufficiently important commercially, clocks in different towns could have been reset daily by reference to a regional standard. On Gaia this could have involved optical signalling: flares, beacons or rockets. The need for accurate coordination of clocks should not be exaggerated: local time was used in everyday life well into the nineteenth century, and was only abandoned with the advent of the railways. By the middle of the nineteenth century the electric telegraph was being used to coordinate railway timetables in Britain [Cook, 2001].
After temperature-compensated pendulum clocks had been invented by Graham in 1721, it would have been discovered that identical clocks in different places did not keep exact time with each other, because of variations in the strength of gravity. The effect would be small in a single day, but over a period of time would have been quite obvious. This problem was avoided by the use of balance wheels regulated by spiral springs. On Earth this innovation was the responsibility of Huygens and Thuret, who designed and built the first such clock in 1675. The incentive for the development of this method of regulation on Earth was the measurement of longitude at sea, but accurate portable chronometers can only be used to determine longitude if there is an independent method of finding the local time. On Earth this was based upon the measurement of the positions of the Sun, Moon or stars, but on Gaia no such method existed. Nevertheless, there was a different and quite important reason to develop them. Namely they would have provided the best means of adjusting pendulum clocks in different towns to run at the same rate, in spite of the variations of gravity. It thus seems reasonable to assume that by about 1760 Harrison or someone else would have built a chronometer which was highly portable, independent of the force of gravity and accurate to within a few seconds per month.
Variations in the strength of gravity could have been used as a proxy for latitude measurements as follows. One needs to have two clocks, one using a pendulum and the other regulated by a spring balance wheel, both of which are accurate to a fraction of a second per day. These are adjusted so as to keep exact time with each other in one place, and then they are transported elsewhere, where the discrepancy between their records of the passage of time is measured. There is no need for the two clocks to keep going during the journey, so a crucial demand made on marine chronometers is unnecessary. The discrepancy between the two clocks depends on the variation in the local strength of gravity, which only affects the pendulum clock. The variation is caused by the fact that the Earth is a rotating oblate spheroid, and amounts to about 0.5% between the equator and poles. Using the International Gravity Formula we obtain a discrepancy of very roughly ten seconds per day per degree of latitude at Paris. Even without knowing its cause, the discrepancy itself could be observed and recorded for a wide variety of locations. It would be observed that places which were on a strict East-West line, as measured using a compass, would exhibit little discrepancy, and that the discrepancy varied steadily as one moved on a North-South line.
We mention in passing that in 1688 Flamsteed resolved a long-standing problem concerning the inconsistency between sidereal and Solar time, [Cook, 2001]. He had already argued that it was caused by the details of the Earth's passage around the Sun, and by 1688 pendulum clocks were sufficiently accurate that he could show that they were consistent with sidereal and not with solar time. From this time onwards sidereal time was regarded as the 'correct' standard for measuring time. This event could not have happened on Gaia, but it illustrates the dramatic improvement in time-keeping associated with the pendulum mechanism.
We conclude that the pressures for the development of accurate timepieces would have been greater on Gaia than on Earth, because of the lack of an external standard to which people could refer. In the absence of sundials, water clocks would have had a greater importance and would been refined. Once commercial needs made the accurate measurement of time important, mechanical clock technology might well have developed more rapidly on Gaia. However, the differences would not have been great, because the accuracy of clocks at any time depended ultimately upon the precision which technology could deliver.
The effect of constant cloud cover on the development of optics is not easy to assess. Newton's analysis of sunlight into its component colours would not have been so easy, because the source of daylight would be so diffuse, but he could have used other sources of light. In 1752 Melville discovered spectral lines by putting various substances into a flame and passing the resulting light through a prism. At the end of a paper on a different aspect of optics, Wollaston noted the existence of several sharp lines in the spectrum of daylight, candle light and electric light, [Wollaston, 1802]. He used daylight simply because it was convenient and bright. Herschel's investigation of radiant heat and of the infra-red spectrum in 1800 again used the Sun as just one of several sources of light. Fraunhofer's purpose in producing his first map of the solar spectrum in 1815 was to provide markers for definitive colours to aid opticians and glass manufacturers, [Jackson 2000, Hentschel 2002]. The detailed investigation of spectral lines occupied physicists and chemists throughout the nineteenth century, and was one of the important observations leading to the discovery of quantum mechanics early in the twentieth century.
Historically the detailed laboratory investigation of spectra is difficult to separate from the study of the solar spectrum. Fraunhofer's study of the solar spectrum could not possibly have led to any understanding of what he observed. In 1836 Talbot wrote that it was much to be desired that an extensive course of experiments should be made on the spectra of chemical flames, which would, he considered, throw some additional light on chemistry, [Talbot 1836]. However, he did not follow up this idea. The idea that each of the lines in the solar spectrum could be attributed to a particular element came to Kirchhoff in 1859. He and Bunsen made an exhaustive laboratory investigation of the spectra of many elements. From the beginning they perceived that this study would lead to the determination of the chemical composition of the Sun. However, their new spectrometer also proved of great importance for chemical analysis, and led very quickly to the discovery of several new elements.
The question for us is whether these developments would have taken place without the motivation provided by the solar spectrum. It might, in the other direction, also be argued that instead of Fraunhofer 'wasting his time' describing the extremely complicated solar spectra, on Gaia he might have got down to the more useful task of determining the spectra of individual substances. Such questions are unanswerable, and the terms of this study require us to assume that laboratory investigations which have important applications in the laboratory would also have taken place on Gaia. In defence of this we observe that people have a natural curiosity about any sufficiently surprising phenomenon, and that early spectral observations were not undertaken for astronomical purposes, but formed part of a general interest in all aspects of light.
The development of astronomy on Gaia would have been prevented by cloud cover. The only evidence for anything outside Gaia would have been the daily alternation between light and dark. However, a number of different discoveries would have started to raise suspicions that people's world view was incomplete. As clocks and maps of the world became more accurate during the nineteenth century, it would have been obvious that only a half of the world was illuminated at any one time, and that this half rotated at constant speed. This would be easy to explain on the hypothesis that Gaia was illuminated by an external source of light rotating around it. I will call this light source the Light rather than the Sun, so as not to suggest anything else about its nature. The fact that the proportion illuminated was always exactly a half would imply that the Light was at a great distance, with the conclusion that it must be extraordinarily bright. An estimate of the amount of energy being emitted by the Light would have resulted in such a huge figure that it would have been regarded as a major puzzle. The existence of the Arctic and Antarctic circles would have shown that the Light was not orbiting Gaia in the simplest and most perfect way possible, i.e. above the equator. This would have supported the view that the Light was caused by an object rather than being of a divine (i.e. inexplicable) nature.
The twice daily tides would have reminded scientists that their theories of the world were seriously inadequate, and the regular progression of neap and spring tides would also have been inexplicable. It is not likely that the existence of the Moon would have been deduced from these facts. The intellectual jump involved would be too large. The much less frequent eclipses would also have been a source of much puzzlement. The fact that they were confined to narrow strips of land demonstrated that they could not be caused by the Light being temporarily extinguished, and the most plausible other explanation would be that some moderately small object was coming in between the Light and parts of Gaia. The fact that eclipses always coincided with spring tides would have been noted, but probably regarded as just one more mystery. Once enough records of their paths and dates had accumulated, it would have been possible for a sufficiently able person to work out some of the basic orbital parameters of the Moon. Gauss and Poincar¾ spring to mind as suitable candidates. The problem with such calculations would be that they would not lead anywhere and could not be confirmed independently.
It might be argued that the difficulty of explaining such basic phenomena would have seriously retarded the development of science on Gaia. There are two counter- arguments. The key period for the establishment of the physical sciences was the first half of the seventeenth century, when most such questions remained unresolved. Galileo's astronomical work was not particularly mathematical, in contrast to his mechanics. He never referred to Kepler's observation that the planetary orbits were elliptical, which did not explain anything at all. Conversely the observation of the heavens did not lead to the development of modern science outside Western Europe. Most commentators explain the rise of science in this period on the basis of social factors; see the final section of this article.
During the nineteenth century several facts should have promoted suspicions that Gaia was rotating about its axis, and that the Light was stationary. One was the fact that explanations of the global circulation of the oceans and atmosphere required the inclusion of an ad hoc Coriolis force, discovered (or perhaps invented) in 1835. The fact that hurricanes always circulate anticlockwise in the Northern hemisphere and clockwise in the Southern hemisphere depends upon this Coriolis force. Foucault's pendulum experiment in 1851 would have provided the physical evidence for the rotation of the Earth which Galileo had sought in the 1620s, and wrongly believed he had found in the tides; the rate of precession of such a pendulum is proportional to the sine of the latitude, a fact which is best explained by the rotation of the Earth about its axis. Poincar¾ suggested that the rotation of the Earth might also be deduced from its oblateness, but this seems somewhat hopeful, [Poincar¾ , 1902]. Once gyroscopes housed in gimbals (invented by the Chinese for use in hanging lamps) had been designed by Foucault in 1852 the evidence for believing that Gaia rotated would have been much stronger. Of course ad hoc explanations might have been devised for all of these facts, as for the alternation between day and night, but the simpler, unifying explanation would surely have been considered at length. In the twentieth century high precision gyroscopes would have provided precise information about the latitude and the direction of true north anywhere on Gaia.
We will not discuss again the deep issue that Poincare raised in [Poincar¾ , 1902, Ch. 7], namely what would inhabitants of Gaia mean by the rotation of the Earth? In other words does it mean anything to talk about a body rotating when there is nothing for it to rotate relative to? We only mention that at the time when he was writing this book, he was also struggling with the notions of relativity theory, of which he was a co-inventor.
By the middle of the twentieth century it would have been possible to think about trying to penetrate the cloud layer to see what lay beyond. The seventeenth century investigations of Boyle and others into the gas laws would have been combined with the fact that the air became very thin at the tops of high mountains to deduce that at heights of about a hundred kilometers the atmosphere would have given place to a vacuum. The cloud barrier would therefore no longer be present. The construction of the X-15 rocket plane in the 1950s made it possible to conduct manned flights through the cloud layer to see what lay beyond it. This would have taken considerable courage, and might have been considered as worthless 'grey skies' research, but it would have been as scientifically justified as the current searches for new elementary particles. Once the first flight had taken place, the course of science would have started to converge back to that of the Earth.
8. Relativity Theory
It has long been evident that light travels in straight lines and does so extremely rapidly. Galileo attempted to measure its speed, but was only able to conclude that it was too high for his method to succeed. The first successful measurements by Roemer and then Bradley depended upon astronomical observations. Only in 1849 was Fizeau able to determine its speed accurately using ingenious Earth-based measurements. Once this had been achieved, Michelson and Morley attempted to measure the speed of movement of the Earth through the ether by finding the difference between the speed of light in different directions, with their famous and paradoxical null result (1887). On Gaia, there would also have been great interest in finding the speed of light, and the nineteenth century experiments would have provided the first actual values. If Michelson and Morley had carried out their experiment, the conclusion that Gaia was motionless might have been regarded as mere confirmation of what was obvious.
Popular accounts of Einstein's theory of relativity usually concentrate on the general theory. On Gaia this might well still be unknown, but the special theory would certainly have been discovered in the first half of the twentieth century, and perhaps by Einstein himself. In the opening paragraph of his paper 'On the Electrodynamics of Moving Bodies', Einstein described his main problem as being to reconcile Maxwell's electromagnetic theory and Newtonian mechanics, [Einstein, 1905]. At the start of the second paragraph there is a brief allusion to the Michelson-Morley result, followed by Einstein's assumption that the velocity of light would be independent of the motion of the emitting body. At no other point in the paper is there any mention of astronomical phenomena. It is not clear how important the Michelson-Morley result was for Einstein, since he was not entirely consistent in his answers to this question in later years; his claims that it had little significance for his own work cannot necessarily be taken at fact value. But even if Einstein (and Poincar¾ ) had not created the theory in 1905, the development of particle accelerators would have forced its discovery in the 1930s: the motion of elementary particles at the speeds obtained in these machines is not even approximately governed by Newton's laws.
We have seen that astronomy was not a prerequisite for the development of science in Europe. Nor did the Chinese develop modern science in our sense, in spite of their marvellous inventiveness and the systematic astronomical records which they kept during many centuries when Western civilization was at a low ebb. It is often suggested that the main cause for the sudden development of European science in the seventeenth century was the rise of detailed measurement and the search for mathematical laws governing phenomena. The idea that laws of Nature might have been laid down by an all-powerful God would indeed have been rejected as naïve by Taoists, as it now is by many Western scientists; but in seventeenth century Europe it was extremely important, [Ronan, 1978, p305]. However, after comparing the history of Europe and China, one must conclude that there were also many crucial social differences between the two regions, [Cosandey, 1997], [Ronan, 1978, 1981], [Pyenson, 2002]. European culture was less centralized and bureaucratic than that in China. There were many independent city states in Europe, some of whose leaders were enlightened and rich enough to grant patronage to sufficiently talented individuals. The movable type printing press provided wide communication of ideas, and the authoritarian tendencies of the Roman Church were increasingly thwarted by religious dissent after the Reformation. The long coastline of Europe facilitated the development of ship-born commerce.
It appears that the great delay in the development of astronomy on Gaia would not have had serious consequences for other areas of science, because most important scientific laws are supported by many independent forms of evidence. A variety of different phenomena, ranging from geodesy to the behaviour of gyroscopes, would eventually have led people towards a correct understanding of the world. In the twentieth century it would have become possible to make high altitude flights above the cloud cover, with the consequent discovery of the rest of the universe by 1960.
One of the interesting features of our study is that it indicates that the brilliance of particular individuals is not as important in the development of scientific knowledge as some accounts of the history of science suggest. On Gaia the order of discovery of scientific laws was different from that on Earth, but many discoveries became inevitable as soon as technology had advanced sufficiently far. Perhaps this explains why so many scientific advances have been made independently by different people. Outstanding individuals may discover certain laws substantially earlier than others would have, and their discoveries may speed up the advance of science. But most advances had to wait until the relevant technology, be this a clock, a telescope or a vacuum pump, was capable of being manufactured. This process was greatly accelerated by the improvements in machine tools which took place during the Industrial Revolution; indeed we identify this as a key influence on the development of modern science. On Gaia the development of astronomy had to wait for the appearance of rocket planes, just as on Earth the discovery of quarks had to wait for the appearance of high energy particle accelerators. Eventually, the same scientific laws would have been discovered as on Earth, but the convergence of the two sciences would not have been completed at the present time.
We have deliberately not discussed the spiritual influence of the heavens: the possible influence on people's minds of observing an aspect of reality which lies far beyond human interference. One reason is that this is difficult to quantify. The other is that one might have expected that its influence would be to make people realize the unimportance of their own conflicts in the great scheme of things. Unfortunately there is little evidence of this. If anything is drawing the world together it is environmental concerns rather than wonder about the heavens.
One can, however, explore the importance of the heavenly bodies in organized religion. Religious festivals were, and still are, often based on heavenly events, but this fact should not be over-interpreted. In ancient Egypt the Sun-god (Re or Aton) was of great religious importance. On the other hand Judaism, Christianity and Islam (in the order of their appearance) do not draw analogies between the Sun and God, being very much concerned with ethics and ritual behaviour. Early polytheistic religions have had Sun Gods, but only as one out of many, others being based upon animals, natural phenomena, ancestors, fertility, love, war, in fact almost anything of importance to people's lives. If there is any common theme binding together today's religions, it must surely be how to come to terms with human mortality. The conclusion which we draw from the huge energy devoted to such a variety of religions is that it would not have been quenched by the simple absence of the heavenly bodies. Particular religions might have been different, or might not even have developed on Gaia, but religion itself was unstoppable.
We should like to thank M Janssen, H Kalf, J D Norton, D C Robinson and R F Streater for penetrating comments.
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Department of Mathematics