The life and achievements of Galileo form a subject of enduring interest. He is certainly one of the greatest scientists of all time and indeed has been called the founder of modern science. He showed that natural phenomena obey mathematical laws and thus laid the foundations of quantitative dynamics and used it to give the first accurate account of the motions of falling bodies and of projectiles. He improved the telescope and used it to discover the moons of Jupiter, the mountains on the moon, the phases of Venus and the spots on the sun. All this combined to throw doubt on Aristotelian cosmology, and to support the heliocentric theory of Copernicus. More than any scientist, he was responsible for initiating the transition from the Aristotelian science of the Middle Ages to the mathematical science of the following centuries.
This is more than enough to secure his fame, but he is more widely known because of his clashes with the authority of the Church. These are frequently presented as an archetypal struggle between reactionary theologians and a brave lone scientist, showing the irreconcilability of faith and science.
Like all scientists, Galileo learned from his teachers a way of looking at the world, the meaning of scientific explanation and the criteria of truth. These continued to exert their influence even as he was pioneering a new approach. He made many mistakes, sometimes holding on to his vision in the teeth of the evidence, as in his writings on the comets and his explanation of the tides. His assessment of his achievements is not always ours, and we must beware of interpreting him according to our own ideas and criteria.
Galileo lived at a critical moment in the development of science. According to the popular account, the first steps towards a scientific understanding of the world were made by the ancient Greeks. Their writings were inherited by the Muslim civilisation, and were transmitted to the new universities in the Middle Ages through translations made mainly in Spain. Thereafter the intellectual development of Western Europe was controlled by an authoritarian Church which prevented any independent thought or scientific development. It was only in Renaissance times that the authority of the Church was challenged by men like Galileo who insisted on the priority of experiment and observations over ancient texts. This is dramatised by the story that he dropped two balls of different masses from the leaning tower of Pisa and showed that, contrary to Aristotle, they reached the ground simultaneously. Thereafter science developed as a free and independent search for truth.
The reality is, of course, very different and highly instructive. The familiar story, still heard today, that there was no science worth speaking about in the long period from the time of the ancient Greeks to the flowering of genius in the Renaissance has long been disproved by modern scholarship. Galileo himself was not only a highly original scientist but remained throughout his life a devout Catholic (Pedersen, 1985). He had a sound grasp of theology and saw very clearly that the new knowledge of the world gained by the scientific method is in no way inconsistent with the teaching of the Church, since both come from God. He also saw that some of the new knowledge raised important problems of Scriptural interpretation that could be resolved within the context of traditional Catholic theology. It is now recognised that Galileo's views on the interpretation of Scripture are basically correct, and he was particularly anxious to prevent the tragedy that actually happened, namely the condemnation by the Church of a genuine scientific breakthrough. He was, however, over-confident concerning his scientific arguments which were still at that time inconclusive, at least to non-scientists. In view of the delicate theological questions raised by the heliocentric theory it was not unreasonable for the Church authorities to ask him to moderate his claims until a definite proof was forthcoming. The main protagonists were all motivated to defend the truth but they were strongly influenced by their intellectual backgrounds and did not lack personal character traits that exacerbated their misunderstandings.
To show how this drama developed it is desirable to consider briefly the principal influences on Galileo's thought, in particular the work of Archimedes and the natural philosophies of Plato and Aristotle. It should be mentioned that practically everything concerning the life and work of Galileo is the subject of controversy among professional historians, and so it is not easy to present an accurate and balanced account.
Before considering the struggles and achievements of Galileo it is useful to sketch briefly the understanding of the physical world that existed before his time. The youthful Galileo was attracted to mathematics and avidly studied the works of Archimedes. His interest in hydrostatics was stimulated by Archimedes' solution of the problem of King Hiero's crown, which led to his first publication The Little Balance (1586). Nature, he realised, is written in the language of mathematics. Further stimulus came from his further experiments on the relation between musical tones and the length, weight and tension of strings. Galileo's work on the centres of gravity of solids led to his appointment to the chair of mathematics at Pisa. This emphasis on mathematics shows the influence of Plato, who was widely influential in the early Middle Ages, largely due to the writings of Augustine. Plato held that terrestrial phenomena are imperfect copies of abstract mathematical forms existing in the mind of God. Thus mathematical relations are only approximately realised in nature. It was Galileo's greatest achievement to show how nature follows mathematical laws, but he went beyond Plato in requiring exact correspondence, with the limits of experimental uncertainties.
In later medieval times, thinking about the natural world was dominated by the cosmology of Aristotle. Initially, his philosophy encountered some resistance, but it soon became generally accepted. Aristotle was a universal genius who made important contributions to physics, chemistry, astronomy, biology and medicine, as well as to philosophy, logic, metaphysics, politics and literary criticism, and organised this knowledge into a unified view of man and nature. His writings were immensely influential, and through the work of Aquinas and others were integrated with Christian theology. Over the centuries Aristotle's views were developed by numerous commentators, and so the Aristotelianism of the Middle Ages is not always the same as Aristotle's own views. Since Galileo had to contend with contemporary Aristotelians it is their views that are described here.
It is important to distinguish between the professional Aristotelians in the universities who infuriated Galileo by insisting on the literal text of Aristotle and refusing to listen to Galileo's arguments, and the open-minded Jesuits at the Collegio Romano who so strongly influenced the young Galileo in his formative years. These Jesuits followed Aristotle in many respects and taught 'a somewhat eclectic Thomism containing elements deriving from Scotist, Averroist and nominalist thought' (Wallace, 1984) that may be described as scholastic Aristotelianism. Thus Galileo, although he bitterly attacked the professional Aristotelians, particularly their views on mechanics and cosmology, retained throughout his life a basic adherence to Aristotelian natural philosophy.
Aristotle thought of nature as a process, an organism, and held that the main object of science is to see how it is related to man. The aim of science is to obtain certain knowledge by understanding the causes of natural phenomena. His cosmology was based on direct commonsense experience, and this is why it has such a strong appeal, even today. He emphasised the primacy of the senses, which takes precedence over any theory. Who can doubt that the earth is solid and immoveable, with the sun, the stars and planets moving around it? Do we not see the sun rising in the morning, moving across the sky and setting in the evening? The heavens seem perfect and unchangeable, in contrast to the earth, where all is changeable and corruptible. It is thus very reasonable to conclude that there are two kinds of matter, and correspondingly two kinds of natural motion: circular in the heavens and the linear motion of free fall or rise on the earth. In addition there is unnatural motion such as that of projectiles, which cannot be combined with natural motion.
The motions of the stars and the planets were studied by the astronomers and Ptolemy was able to describe them quite accurately by compounding circular motions in the form of cycles and epicycles. This was a purely mathematical description, and it was not maintained that the cycles and epicycles corresponded to anything real. In contrast, Aristotle sought a more physical cosmology in terms of real entities. The two approaches were finally unified by Kepler (Russell, 1975).
At the centre of Aristotle's cosmology is the immovable earth, and surrounding it a number of concentric crystalline spheres bearing the moon, the inner planets Mercury and Venus, then the sun and finally the outer planets Mars, Jupiter and Saturn. Enclosing all is the sphere of the fixed stars, and outside this nothing at all. There were differing views about the reality of the crystalline spheres; Aristotle believed that there are fifty-five in all, made of a pure, unalterable, transparent, weightless crystalline solid. The whole set of spheres rotates once a day, thus accounting for the diurnal motion of the sun and the stars. Seen against the background of the stars, the paths of the planets sometimes show a retrograde or looped motion, and this was accounted for by fixing the planets to secondary spheres linked to the main ones. The Aristotelian cosmology was thus able to give an account of all observable celestial motions, including the prediction of eclipses.
Guided by direct experience, Aristotle made a sharp distinction between terrestrial and celestial matter. Terrestrial matter is changeable whereas celestial matter is unchangeable. There are four types of terrestrial matter, earth, air, fire and water, and each seeks its natural place. Celestial matter is the quintessence (or fifth essence), pure and unchangeable, and naturally moves on the most perfect curve, the circle. On the earth, natural motion is linear: the falling of earth and water and the rising of air and fire. These motions accelerate because their cause becomes stronger as the body approaches its natural place. Unnatural motion, such as the flight of an arrow, requires the continuing action of a mover. Thus Aristotle's physics was based on direct observation and accounted for many natural phenomena in a reasonable and coherent way. As a result, it was widely accepted for two thousand years.
One of the weakest parts of Aristotle's physics is his theory of projectile motion. He had no concept of force and denied the notion of inertia. He rejected the theory of antiperistasis, attributed to Plato, that explained the continuing motion of a projectile after it has left the hand of the thrower by assuming that the medium in which the motion takes place is moved by the front of the projectile and comes round to the back and pushes it along. This is obviously false, as it implies that it is impossible to throw things against the wind. It also cannot account for the continuing rotary motion of a smooth sphere, or the flight of an arrow. Aristotle believed that since the motion is unnatural it requires the continued action of a mover, and this must be the medium. He therefore suggested that the thrower communicates motion to the medium and also the power to move.
Buridan, a fourteenth century philosopher, rejected this theory because it cannot explain the continuing motion of a spinning wheel and also because it is common experience that the medium resists the motion of the projectile. Instead, Buridan proposed that the thrower gives the projectile some impetus that carries it along after it has left the hand of the thrower. This is related to one of the arguments against the motion of the earth. According to Aristotle, a projectile thrown vertically upwards from a moving earth will fall behind and hit the ground west of its starting point, contrary to experience. The impetus theory, however, predicts that it retains an eastward impetus throughout its motion, and so returns to the same point as observed.
It was widely believed that the ancient Greeks had achieved the summit of knowledge; they knew essentially all that could be known, and so the answer to any problem could be found by scrutinising ancient texts, particularly those of Aristotle. The duty of a scholar is simply to understand, defend and teach Aristotle's ideas. Within this mindset the Aristotelians simply could not understand what Galileo was trying to do. To them, the world is a living organism that can be understood by experience and reason. For this, direct perception is all that is needed. They interpreted the world in terms of a close-knit system of purposeful behaviour, using organic categories and concepts like matter and form, act and potency, essence and existence. Thus the qualitative properties of things suffice to reveal their essences.
Galileo, in sharp contrast, said that it is an illusion to think that we can understand the essences of things; what we can and should do is to describe their behaviour as accurately as we can using mathematics, and then make experiments to test the validity of our ideas. Quantitative relations are the real clues to the unique, orderly, immutable reality. By establishing them we can find out how things behave, but not what they are. This seemed quite useless to the Aristotelians, who had a low view of mathematics: indeed, Aristotle 'left to mechanics and other low artisans the investigation of the ratios and other secondary features of acceleration' (Shea, 1977, p.142). To them, number, weight and measure have no philosophical significance; motion is interpreted in terms of purpose, and to this mathematics is irrelevant. They had no interest in accurate descriptions of the motions of projectiles, or in the mathematical description of levers and pulleys. Mathematics, they allowed, is an interesting game, but it can tell us nothing about the real world. Galileo, on the other hand, thought that their elaborate structure of abstractions in fact leads nowhere.
Since Galileo occupied a chair of mathematics his duty was to expound the works of Euclid and Archimedes. Thus he could be much freer in his criticisms of Aristotle than if he had been a member of the philosophical establishment whose main duty was to master and teach the works of Aristotle.
It is important to distinguish between Aristotle's general ideas concerning scientific method, his natural philosophy, and the way it was applied to particular problems. Aristotelian physics is an attempt to find the real structure of the world, deduced rationally from general principles, and this always remained Galileo's goal, though he went further than Aristotle by requiring a precise mathematical description of reality. Aristotle's cosmology included many statements about the heavenly bodies and detailed theories of familiar physical processes that have subsequently been found to be incorrect, but this does not necessarily falsify his natural philosophy. Thus although Galileo showed that many of Aristotle's views are incorrect, he did this within the framework of Aristotelian natural philosophy, and himself remained essentially an Aristotelian. Aristotle aimed to provide a rational account of the world, deduced from general principles. In the end, Aristotle's attempt was a heroic failure, largely because he greatly underestimated the difficulty of obtaining these principles, and also the value of precise measurement and detailed mathematical analysis.
Christian beliefs can easily be interpreted within the framework of Aristotelian cosmology. Hell is in the centre of the earth, and volcanoes provide evidence of its fires. Beyond the outermost sphere is the abode of God and the saints. Thus we can speak of the descent into hell and the Ascension into heaven. This imagery is lost in the heliocentric system. In addition, if the earth is just one of the planets, then is it not possible that people are to be found on other planets, and if so how can they be redeemed by Christ? The Aristotelian universe thus accommodated all that was known in a unified logical structure, and this accounts for its great power over the human imagination. To throw doubt on any part of it would be to threaten the whole and upset the well-established order of the universe.
Modern science, by which we mean the detailed quantitative understanding of the material world expressed in the form of differential equations, is unique to our European civilisation. Nothing like it is found in the great civilisations of antiquity despite their impressive achievements in many other fields. It is commonly believed that modern science began in the Renaissance. Leonardo da Vinci, the great polymath, filled thousands of pages with accounts of dynamical principles, sketches of mechanical contrivances and other ingenious devices. But did this all spring from his own mind, or did he learn it from others?
Pierre Duhem was the first to study this question, and he found that all the results recorded by Leonardo were common knowledge in the High Middle Ages, and originated in studies by the Mertonian school of William Heytesbury, Richard Swineshead and John of Dumbleton in Oxford between 1328 and 1350 and the contemporary school of John Buridan and Nicholas Oresme in Paris. Many of their ideas are also found in the writings of John Philoponos in the sixth century.
The Mertonian school formulated the mean speed theorem, namely that in a given time a uniformly accelerated body traverses the same distance as a body moving with a constant velocity equal to that of the accelerated body at the mid-point of its motion. They had to express this verbally as the appropriate mathematical notation had not then been invented.
Duhem showed that science achieved its first viable birth in the High Middle Ages, when Christian theology provided for the first time in human history the essential beliefs about the material world that form the basis of modern science: that matter is good, orderly, rational, contingent and open to the human mind. The philosophers of the Middle Ages were independent thinkers who did not hesitate to differ from Aristotle if Christian beliefs, or reason or experiment required it. In particular, the Christian doctrine of the creation of the world out of nothing by God provided the stimulus to the Parisian philosophers like John Buridan to break with Aristotle and to formulate in a qualitative way the law of inertia, later to become Newton's first law of motion (Clagett, 1961). The writings of Buridan and his pupil Nicholas Oresme were widely diffused throughout Europe and provided the basis of our understanding of motion, the most fundamental problem of physics and hence of all science.
Oresme subjected many of Aristotle's arguments, including those against the motion of the earth, to a critical analysis, and showed that they are invalid. His purpose was simply to show that the earth could move; later on Galileo used the same arguments to show that the earth does move.
The impetus theory was also applied to celestial bodies, and Buridan supposed that when God created them he gave them the impetuses necessary for them to continue in motion. Thus, contrary to Aristotle, there is no distinction in this respect between celestial and terrestrial bodies. The breaking of Aristotle's distinction is necessary if the earth is to be considered one of the planets, making it possible for them all to follow the same dynamics.
The work of Buridan affected only the Aristotelian description of motion, and even in that area it was still possible to maintain the Aristotelian view by saying that now the mover is internal to the body but extrinsic. In other areas the vast system of Aristotle still dominated the intellectual scene. Furthermore, his philosophical concepts had been used by Aquinas and other theologians to express in a more precise way the whole of Christian theology. Dante's Divine Comedy describes his journey through the Aristotelian universe beginning on the earth and descending through the nine circles of hell that mirror the celestial spheres, then passing through purgatory and earth, through the celestial spheres to the throne of God in the highest sphere. This integration of Aristotelian cosmology and Christian theology is of great imaginative power and exerted a strong hold on the medieval mind. Since the whole conception is destroyed if the earth is allowed to move, we can appreciate the strong psychological opposition to such a suggestion. Anyone who challenged any part of the Aristotelian system could be sure to encounter strong opposition. The very idea that an upstart scientist with a leaden tube with lenses at either end could upset a vast philosophical system that had stood for two thousand years was just too preposterous to merit serious attention.
Since ancient times, there had been a few isolated astronomers who proposed a heliocentric cosmology, but the arguments against this view appeared to be overwhelming. If the earth rotates, the strong winds would blow everything off it. If the earth is moving around the sun, then the relative apparent positions of the stars must change, contrary to experience. Copernicus realised that these arguments are not conclusive, and that the heliocentric system had several advantages for computational purposes. These were gradually appreciated by astronomers, but to most people the heliocentric theory seemed just absurd. Some astronomers however, including Copernicus, became convinced of the correctness of the heliocentric theory, although they had no conclusive arguments in its favour.
Central to the whole debate is the question of why we believe, what are the criteria that we apply to judge whether a scientific theory is true or not. More fundamentally, how do we justify the criteria themselves? In Galileo's time, a theory was judged by the Aristotelian criterion: whether it gave an explanation in terms of causes. It was also required to 'save the appearances', that is to give predictions in numerical agreement with the experimental measurements. Finally, it had to be in accord with Scripture.
A related question is why a theory is accepted by some people and not by others. There could be a fundamental disagreement on the criteria to be applied, but there may also be inability to apply them due to lack of knowledge. Much scientific work depends on the correct interpretation of signs. Thus an elementary particle physicist can look at a bubble chamber or emulsion photograph and immediately identify the particles and processes responsible for them. It is possible for a sceptic to say that the whole photograph could be due to the chance alignment of unconnected bubbles or grains, but this suggestion would be derisively rejected by the scientist. The important point is that the photographs can only be interpreted by those with adequate knowledge. The same applies to medical X-ray photographs and radiographs. In addition to our technical knowledge we bring a whole range of beliefs about what is important and what is peripheral together with the experience gained by a wide range of observations. At that time science was considered a very minor activity, hardly worthy of attention, and certainly not comparable in importance with philosophy and religion. Thus the theologians who were not convinced by the arguments for heliocentrism were not necessarily obtuse or stupid, though the same cannot be said about those who refused even to look through Galileo's telescope.
Many of Galileo's actions, even those concerning his research, can only be understood in the context of the situation of scientists of his time. For those without private means, the only possibilities were employment by a university or by a rich patron. University positions were rather more secure, but they were poorly paid and it was necessary to give many lectures and to undertake long hours of private tuition. It was far more lucrative to hold a position in the entourage of a great prince, but this was continually dependent on the prince's favour. Moreover, most princes were more interested in their horoscopes and in practical matters such as the design of fortifications and the dredging of harbours. Sometimes they were interested in the scientific discoveries made by their scientists, but even then it was more as something that enhanced their prestige than for its intrinsic value. The scientists would often share the prince's table, and be expected to make entertaining and instructive discourse to impress the prince's guests. The scientist thus had to keep up a stream of interesting discoveries, and if he made a mistake this would tarnish the reputation of his prince and lead to his speedy dismissal. The favour of a powerful prince could be most prestigious and lucrative, but it was exceedingly precarious and could easily be lost.
In this situation, scientists were continually scheming to obtain the favour of a prince or, failing that, a university chair. It was normal to write fawning letters extolling their skills as an astrologer and as a designer of fortifications, and if they were successful they were likely to spend much of their time on such pursuits. They were inevitably the object of intense envy among other scientists, who would do their best to undermine and ridicule their work so that they fell out of the favour of the prince.
As an ambitious scientist, Galileo had to spend much time trying to find a position that would support his work, and his need was exacerbated by the demands of an impecunious family. His brother Michelangeiolo was an irresponsible spendthrift with a large family who was continually demanding money, and he was also expected to provide dowries for his two sisters Livia and Virginia, not to mention his own three children. These pressing needs go a long way to explain his pushy, aggressive and pugnacious behaviour. He had to fight to survive and he was not slow to round on his detractors with withering sarcasm. He did not scruple to advance his ambitions by political intrigue, and his enemies repaid him in kind. He used to the full his great powers as a writer in the vernacular to propagate his views, and indeed was the first scientific populariser.
Galileo was born in Pisa in 1564 and ten years later moved to Florence. He entered the university of Pisa in 1581 and decided to devote his life to physics. He developed a hydrostatic balance and worked on the centre of gravity of solids and this led to his appointment to the Chair of Mathematics at Pisa in 1589. There he wrote a book on motion (De Motu, 1592) summarising Aristotle's ideas, with critical comments and corrections. In 1592 he moved to a similar Chair at the university of Padua in the Venetian Republic. He wanted to return to his native Tuscany and to enjoy the extra freedom of a post in the entourage of the Grand Duke, and largely as a result of his astronomical discoveries succeeded in being appointed Chief Mathematician and Philosopher to Cosimo II, Grand Duke of Tuscany, in 1610. He remained in Florence for the remainder of his life, making several visits to Rome to publicise his work. His astronomical discoveries convinced him of the correctness of the Copernican system. His enemies criticised his Copernican views as contrary to Scripture, and he defended himself by writing an essay on the interpretation of Scripture. In 1616 the belief in a central sun was denounced as heretical, and the idea of a moving earth as erroneous in faith. These views were not to be taught or published. In 1632 he published his Dialogue on the Two Chief World Systems presenting arguments for and against the Copernican theory. In 1633 it was judged that by this work he has disobeyed the injunction of 1616 and so he was forced to recant and sentenced to spend the rest of his life confined to his villa in Florence. There he continued his scientific work until his death in 1642.
Galileo was acutely conscious of the importance of speedy publication to claim priority for his discoveries. In order to ensure this without prematurely revealing what he had found he sometimes resorted to the device of publishing an anagram. Then, when he had established the new result without doubt, he could reveal the meaning of the anagram. He wrote many books describing his work, some in reply to attacks on his ideas, or wrote formal letters to persons of distinction with a view to eventual publication. Finally there are longer, carefully-considered treatises that deal with a much wider range of material. It may be useful to list his principal writings in order of publication, together with references to available translations.
1. De Motu (On Motion) 1592. Considers the application of Archimedes' principle to motion in a medium. Summarises Aristotle's ideas on motion, with some critical comments. Translated with introduction and notes by I.E. Drabkin in Galileo Galilei on Motion and Mechanics. University of Wisconsin Press, 1960.
2. Le Meccaniche (On Mechanics) 1600. Summary of the statics of simple machines. Translated with introduction and notes by Stillman Drake in Galileo Galilei on Motion and Dynamics. University of Wisconsin Press, 1960.
3. Sidereus Nuncius (The Starry Messenger) 1610. An account of his discovery of the satellites of Jupiter and other astronomical discoveries. Translated with introduction and notes by Stillman Drake in Discoveries and Opinions of Galileo. Doubleday, Anchor Books, 1957.
4. Discorso . . . (Discourse on Bodies in Water) 1612. Describes experiments on floating bodies, with additional remarks on natural philosophy.
5. Letters on Sunspots, 1612. Critique of the views of Christopher Scheiner and a dispute over priority. Partly translated by Stillman Drake (see item 3).
6. Lettero alla Granduchessa di Toscana, Crestina di Lorena 1615. Summary of his view on the relation of theology to science. Translated by Stillman Drake. (see item 3). Finocchiaro, 1989, p. 87.
7. Discourse on the Tides, 1616. Finocchiaro, 1989, p. 119.
8. Il Saggiatore (The Assayer) 1623. Discussion of the nature of comets, and a general defence of scientific investigation. Partly translated by Stillman Drake (see item 3).
9. Dialogo . . . sopra i due Massimi Sistemi del Mondo, Tolemaico e Copernicano. (The Two Chief World Systems) 1632. Full discussion of the arguments for and against the Copernican system. Abridged translation and guide, Finocchiaro, 1997.
10. Discorsi a dimonstrazioni . . . (The Two New Sciences) 1638. Comprehensive discussion of the properties of materials and of terrestrial motions.
11. Dialogues concerning Two New Sciences. By Galileo Galilei. Translated by Henry Crew and Alfonso de Savio. Northwestern University Press, 1968.
12. Many letters and other documents are published by Finocchiaro, 1989.
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