A historical interlude Galileo Galilei 15641642

Galileo was born in Pisa on February 15, 1564 (the same year as William Shakespeare). His family was of noble ancestry, but modest means. His father, Vincenzio, was a musician who made a number of discoveries about stringed instruments, which Galileo was later to incorporate into his own work. It was the wish of his father that he embark on a 'real' career as a doctor, rather than pursue his interest in mathematics, so the young Galileo enrolled in medical school at the University of Pisa. He never finished his medical studies, and left without obtaining a degree, reverting to teaching mathematics, privately in Florence.

Galileo was a determined and sometimes pugnacious character, red-haired and of stocky build. He was loyal to his friends, but was not known for suffering fools gladly. He was also known for writing verses about both his colleagues and his enemies. These verses were often funny, but sometimes also scurrilous.

At the age of 25 Galileo was appointed to a teaching post in mathematics in Pisa. It was badly paid and he did not enjoy the work. One of his duties was to teach Euclidean geometry to medical students, so that they could understand the then-standard geocentricmodel of the universe, in which the earth was stationary at the centre, with the sun and planets moving in complicated paths around it. Students of medicine were required to study astronomy so that they could apply this knowledge to astrology and use it in their medical practice.

One might safely assume that Galileo had no time for astrology, but what made the situation more ironic was that he did not believe in the geocentric model. Galileo followed the theories of Copernicus, at that time considered to be unsound and even heretical. In 1543, Copernicus had published De Revolutionibus Orbium Celaestium, a book in which he put forward a heliocentric theory of the universe, in which the earth and planets orbit a stationary sun.

In 1592, Galileo was appointed as Professor of Mathematics at Padua, where he spent the next 18 years of his life. Not only was he a mathematician, but he also had a great talent for practical inventions. Some of these (such as a high precision balance to measure the density of precious stones and what would now be called an analogue computer for military use, invented in 1597) have been preserved at the Accademia Cimento in Florence. He lived with his common law wife, Marina Gamba, and their son and two daughters. Those were the best years of his life and it is thought that the foundations of much of his work were laid at that time.

In 1610, Galileo moved to Florence, on foot, after receiving an invitation from Grand Duke Cosimo II, who had been one of his pupils, to become 'court mathematician and philosopher'. The duke had made him an offer he could not refuse. His salary was to be five times that at Padua and there would be very little teaching. Galileo abandoned Marina Gamba and placed his daughters in the care of a convent at Arcetri, some distance from Florence. Remarkably, his elder daughter, Virginia, was to become his greatest supporter during the troubled times in his old age.

Galileo pioneered the application of mathematical argument to observation and to experiment. Hitherto, the authority of Aristotle had been entrenched in philosophi- Galileo facing the Roman Inquistion, cal discussions on the painting by Cristiano Banti.

Courtesy of An Post, Irish Post Office.

cosmos. It was believed that the Ptolemaic system of a fixed earth at the centre of the universe was endorsed by the Bible with certain passages. One example is Joshua 10: 12-14: 'God caused the sun to stand still in response to Joshua's prayer'. The church authorities in Rome went so far as to condemn the works of Copernicus, stating that 'the doctrine that the earth moves around the sun and that the sun is at the centre of the universe, and does not move from east to west, is contrary to the Holy Scriptures, and cannot be defended or held'.

In 1616 Pope Paul V, Cardinal Bellarmine, called Galileo to his residence, warning him not to defend the Copernican theory and not to discuss it orally or in writing. However, in 1624, having met the at first seemingly more liberal Pope Urban VIII, a compromise was reached in which Galileo was allowed to write about the theory, as long as it was treated purely as a mathematical hypothesis, and did not represent 'the actual construction of the universe'.

In 1632, Galileo published his Dialogue Concerning the Two Chief World Systems. Written in his typical satirical manner, it depicted a discussion between three people regarding the relative merits of the models of Ptolemy and Copernicus. The case for Copernicus was argued most convincingly by Salviati, an intellectual who spoke for Galileo. Sagredo was a wealthy nobleman, an interested onlooker who was seeking the truth. Simplicio, an Aristotelian philosopher who defended the theories of Ptolemy, was portrayed as not being very bright and using arguments which were not only weak but also included word-for-word statements made by Pope Urban VIII. The Dialogue was not well received in Rome, and Galileo was summoned to appear before a tribunal of the Inquisition in 1633. Although the Inquisition did not have the power to force him to comply, Galileo voluntarily went to Rome to appear before the tribunal.

The tribunal concluded that the idea that the earth moves was absurd and erroneous, if not actually blasphemous, and Galileo was ordered not to discuss the theory in writing or in speech. He was confined to his villa in Arcetri under what we now call house arrest, ordered to recant his 'errors', and forbidden to publish any further writings. As he was by then 70 years of age, the inquisitors must have thought that he was unlikely to continue to give them further problems. They were underestimating the resolve of this man, who is said to have muttered as the verdict was announced 'Eppuor si muove'— 'All the same it moves'.

Galileo's sharp style and cynical wit come through clearly, even in English translation. His scant regard for some of his adversaries is echoed in his words: 'I have taken the Copernican side of the discourse against the arguments of the Peripateticsf. These men indeed deserve not even the name, for they do not walk about, they are content to adore the shadows, philosophising not with due circumspection, but merely from having memorised a few ill-understood principles'

The three debaters

'Many years ago I was to be found in the marvellous city of Venice, in discussions with Signore Giovanni Francesco Sagredo and Signore Filippo Salviati, in the presence of a certain Peripatetic philosopher whose greatest obstacle in apprehending the truth seemed to be the reputation he had acquired by his interpretations of Aristotle. I have resolved to make their fame live on these pages by introducing them as interlocutors in the present argument.'

The discussion centres on the question whether the earth moves, or stands still at the centre of the universe. The argument of Simplicio is that if the earth were moving, this would be noticeable because falling objects would not fall perpendicularly, because thier motion would be compounded of 'both transverse and perpendicular'. Salviati proposes a very interesting experiment:

T (1) One who walks from place to place, an itinerant; (2) a follower of Aristotle, who gave his instructions while walking about in the Lyceum in Athens.

'Shut yourself up with some friend in the largest room below decks of some large ship, and there procure gnats, flies, and such other, small winged creatures. Also get a great tub full of water and within it put certain fishes; let also a certain bottle be hung up, which drop by drop lets forth its water into another narrow-necked bottle placed directly. Having observed all these particulars as long as the vessel stands still, how the small winged animals fly with like velocity towards all parts of the room, how the fishes swim indifferently towards all sides, and how the distilling drops all fall into the bottle placed underneath, now make the ship move with what velocity you please, so as the motion is uniform and not fluctuating this way and that. You will not be able to discern the least alteration in all the above-mentioned effects, or gather by any of them whether the ship moves or stands still.'

Many of the passages are entertaining, and often amusing, showing the fascination of the mysterious action of gravity. Salvatio: 'If from the top of a tower you let fall a dead bird and also a live one, the dead bird shall do the same as the stone does, it shall first follow the general diurnal motion, and then the motion of descent, just like a stone. But if the bird be let fall alive, the difference is that the stone is moved by an external projector, and the birds by an internal principle.'

The controversy did not affect Galileo's religious beliefs. He felt that the Bible was intended to be understood by common people, and that it was pointless to try to read advanced physical theories out of its pages. A few months before the final trial he wrote to his friend Ella Deliati: 'Nobody will maintain that Nature has ever changed in order to make its works palatable to men. If this be the case, then I ask why it is that, in order to arrive at an understanding of the different parts of the world, we must begin with an investigation of the Words of God, rather than his Works. Is then the Work less venerable than the Word?'

During the final period of his life Galileo was nominally under house arrest, but this did not debar him from settling at a place of his choice. He remained at Alcetri to be near his daughter Virginia, who now proved to be a great support. Sadly she died in 1634, as he was becoming increasingly ill and feeble. Nevertheless, he still managed to write what turned out to be perhaps his greatest book, Two New Sciences Dialogue. Salvati, Sagredo and Simplicio remain as central characters, but they have changed. Simplicio is no longer the stubborn fool, but represents Galileo's own thinking when he was young, Sagredo his middle period and Salvati his mature reflections. They are discussing the motion of objects and the properties of matter; in fact many ideas form the starting points of what was to constitute Newtonian dynamics.

The two new sciences depicted by Galileo were the science of motion and the science of materials and construction. Galileo questioned the ideas of Aristotle, regarding objects falling to earth. Aristotle's 'explanation' was that this was the motion of things seeking their natural place in the centre of the earth. He also asserted that heavier objects fall faster as their attraction towards their natural habitat is more intense. In the course of the discussion, Salviati makes the following observation:

'I greatly doubt that Aristotle ever tested by experiment whether it be true that two stones, one weighing ten times as much as the other, if allowed to fall at the same instant, from a height of, say, 100 cubits, would so differ in speeds that when the heavier had reached the ground, the other would not have fallen more than 10 cubits.'

Since Galileo was not allowed to publish his writings in Italy, the manuscript was brought to Holland, and published in Leiden in 1638.

This was the beginning of a new era of science. The world is not constructed in the manner one might assert it should be constructed, even if that assertion is made by an authority, no matter how much that authority is revered. The laws of nature must be discovered and tested by experiment. Whether or not Galileo's experiments were carried out, as legend says, at the leaning Tower of Pisa, is not clear, but he did test the laws of gravity in many carefully controlled experiments with smooth polished spheres of different weights rolling down inclined planes and found no discrepancy in the results.

Galileo died in 1642, the same year that marked the birth of Isaac Newton, who was to make the well-known statement 'If I have seen further than most men, it is by standing on the shoulders of giants'. Galileo Galilei was undoubtedly one of those giants.

Appendix 4.1 Mathematics of the ellipse

The ellipse can be defined mathematically in a number of ways, so we will choose the definition which is most relevant physically:

An ellipse is the locus of a point that moves so that the sum of its distances from two fixed points is constant. The two fixed points are called the foci of the ellipse.

This property can be used as a simple method to draw the ellipse. Fix two pins at the foci, and place a loop of thin string over them. With a pencil point pull the string taut, forming a triangle. As the pencil is moved over the paper around the pins, keeping the string taut, it will trace out an ellipse.

The eccentricity describes the elongation of the ellipse. The smaller the eccentricity, the nearer the foci are to each other, and the more it resembles a circle. For e = 0 the foci coincide at the centre of the circle.

Figure 4.18 Properties of an ellipse.

minor axis p major axis minor axis p major axis e = eccentricity Figure 4.19 The eccentricity of an ellipse.

e = eccentricity Figure 4.19 The eccentricity of an ellipse.

From the definition of the ellipse (Figures 4.18 and 4.19),

F1P + PF2 = const = F1X + XF2 = (a + ae) + (a - ae) = 2a From symmetry,

In triangle OPF,

The ellipse is a closed conic section where the ratio semi-minor axis = ^ ^2" semi-major axis

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