Galileo Galilei

Galileo Galilei was the founder of modern physics. To assess such a claim requires that we make a giant leap of the imagination to transport us to a state of ignorance about even the most elementary principles of physics. Today, the simple laws of motion as defined by Isaac Newton, for example, are known to the most modest students, yet Galileo spent his life unravelling these mysteries.

His many discoveries include the law of inertia later used by Isaac Newton as the first law of motion, the parabola as the path of a projectile, the relationships between distance and velocity and between distance and time and at the continuity of acceleration. He struggled towards an understanding of continuity, though the work had to wait for Newton and Gottfried Leibnitz to produce an infinitesimal calculus to master this difficulty.

Galileo and the Renaissance

Galileo lived at a time when the centuries-old Almagest of the Egyptian scholar Claudius Ptolemy, written in 139AD, was still being used by the Church as “evidence” and “confirmation” for the Aristotelian idea that the Earth was at the centre of the Universe. Galileo was part of the Renaissance, the centuries-long ferment accelerated and intensified by the invention of printing in the middle of the 15th century. He was not alone. More or less contemporary with him were physicists and mathematicians Willebrord Snell (the Dutchman who conceived the law of light refraction), the Belgian Simon Stevin and the four Frenchmen Marin Mersenne, Pierre de Fermat, Rene Descartes and Blaise Pascale. Yet it is Galileo’s name that survives as the “founder” of physics.

We must understand, however briefly, the sociological, political and religious climates of Galileo’s time. Italy, for instance, was no longer the great Roman Empire. It was divided into small states often warring with one another. The one in which Galileo was born was an autocracy, the Grand Duchy of Tuscany, with its capital at Florence and the second city at Pisa, his birthplace. The de Medici family ruled. Next to Tuscany was the state led by Venice – the Venetian Republic – as near as anyone came to a democracy in the 16th century. It refused to give in to the authority of Rome and the Church. It expelled the Jesuits and defied the Pope. It had its famous university at Padua (from which, it may be remembered, the learned doctor Bellario was to come to defend Antonio against Shylock in The Merchant of Venice, which William Shakespeare wrote in 1594, when Galileo was at Padua).

Early life

As a young student at Pisa, Galileo was highly intelligent, observant and questioning, a joy to the first-class teacher and a pest to the second rate, who as usual formed the majority. He wrote poetry and was a skilled musician and painter. He was highly cultured and came of a family of minor nobility. Vincenzio Galilei, his father, was also a musician, with original views, as well as being something of a mathematician. Galileo was to read medicine and so be able to earn a living. However, the biting winter winds of Florence at that time forced the court to relocate to Pisa. The court mathematician, Matteo Ricci, went with it. Galileo came upon Ricci teaching the young pages about Euclid and was at once entranced. Meeting Ricci later, Galileo also learned about Archimedes, a Latin version of whose work had been published in 1543. That was that. Archimedes became “that divine man” and Galileo saw in Euclid the wonder of geometry, especially in the work on ratios, which Galileo was to expand and use to its limit later.

His mind was alerted to the excitement and importance of mathematics applied to practical problems, that is in effect, physics. He timed the swinging of chandeliers in the cathedral and at once abstracted the essence of the problem, so that he made pendulums of string and small weights and established the relationship between length and time of swing, using his own pulse for measurement, for there existed no device for fine accurate timing. Later on Galileo utilised the phenomenon to make his pulsilogium, a device timing the human pulse, and on his deathbed 70 years later he designed a pendulum-regulated escapement for a proposed clock.

Leaving the university, he kept himself by teaching privately and lecturing, and then produced his first scientific paper at the age of 22. It was concerned with the story that Archimedes had found a way of discovering if a crown made for King Hiero of Syracuse was in fact of pure gold, as it was supposed to be, or had been adulterated with a cheaper metal. This he had done, according to the story, by finding the weight of water displaced from a full bowl. Galileo could not believe that a genius such as Archimedes would have used such a crude method. So Galileo set out to devise a method of considerable precision.

The Bilancetta

He made for himself a special balance with which he could measure the exact proportions of two metals in a mixture or alloy. He realised that fine-enough markings would be too difficult to read so he wound along a part of one arm of the balance a tight spiral of very fine brass wire, extending from where the suspended weight would balance metal A (suspended in water) to where it would balance metal B (suspended in water). He then balanced the immersed mixture by sliding the weight along. He measured the number of turns along his spiral by passing along it a fine stiletto knife, each winding making an audible “ping”. Thus, with his fine musical ear, he could count the number of turns, and therefore the distance. So he was able to state the proportion of A to B in the mixture. This tiny essay, which he called La Bilancetta, is enchanting.

In this little original work there is much of what we need to know about Galileo’s methods. There is first of all his outstanding and delicate manual skill. More important, there is always his insistence on accurate measurements and also repeatable measurements. And there is the use of mathematics, in this case the principle of the lever, which he was to use many a time in later work. Moreover his mathematical basis was Euclid and Archimedes.

Across his work Galileo was original in dynamics, hydrostatics, mechanics and the strength of materials, optics and astronomy. He continued to develop, correcting earlier errors, admitting his ignorance on “mysteries” and abhorring abstract notions. He was interested only in what he could see or hear or touch and, above everything, measure.

The spy-glass and Galileo’s telescopes

In 1609 came the most sensational discovery of his life. He heard of a Fleming who made a “spy-glass” and he rushed to experiment, not wishing to be outdone. And he succeeded in making a telescope of the sort familiar to everyone today who has seen an elementary book on optics. It astonished and delighted everyone, and when he succeeded in making one of eight magnifications and then even of 20 (grinding his own lenses!) he made celestial observations that shook the world of astronomy as well as the most learned of the Peripatetics (Aristotelian philosophers). He saw mountains on the Moon (very anti-Aristotle this), then satellites orbiting Jupiter, which he mapped with such accuracy that his orbital times are hardly different from those calculated today. That he saw sunspots and described their variations. Finally he observed that Venus showed phases very like those of the Moon, an observation that clinched the Copernican argument. In 1610 he published The Starry Messenger. He presented telescopes to the Doge of Venice (and had ageing councillors climbing bell towers to see merchant ships out at sea) and to his former pupil and friend Cosimo II, Grand Duke of Tuscany. He became famous all over Europe. He was the equivalent in science of a Nobel prize winner today.

When he left Padua and Venice, he returned to his home near Florence and completed his book on hydrostatics, in which it is interesting to see that he was nonplussed by the fact that a thin flake of ebony, though denser than water would nonetheless float. This pleased his Peripatetic opponents who asserted with Aristotle that sinking or floating was merely a matter of shape. Galileo did have the insight to perceive that the effect was probably the same as that when a drop of water would remain on a cabbage leaf. Of course surface tension was an unknown phenomenon.

The Galileo affair

A year later he published his three letters on sunspots. He was by now a very powerful man and had created jealousy and resentment. He had so many appreciative friends in high places, including former pupils, that he probably considered himself safe. Most of his enemies worked quietly like rats in a cellar, but some did not. There was, for example, the hateful person Christopher Scheiner, a Jesuit, who claimed priority in seeing sunspots and of course gave an Aristotelian explanation of them. His book challenged Galileo in the most spiteful way.

It looks like there was an opinion on high to leave Galileo alone, but then he made a mistake. He wrote a letter to his friend and former pupil Benedetto Castelli in which he discussed the Bible, especially the passage that stated that Joshua had commanded the Sun to stand still, a fact that would have proved that the Sun must previously have been moving, as Aristotle and Ptolemy had said. Galileo’s comment was that though the Bible was the word of God it must not be taken too literally, word for word, being written not for intellectuals but for common people. The spies were about and a Dominican in some way unknown secured a copy and sent it to the Inquisition at Rome.

Almost at the same time a loud-voiced and unpopular Dominican priest made an outspoken attack against all mathematicians and Galileo supporters. Galileo saw the danger and hurried to Rome. There, Cardinal Bellarmine after some talk persuaded Galileo to agree not to teach the Copernican theory as truth. In fact nobody knows exactly what Galileo did promise at this meeting in 1616, but his enemies, by a gangster-like trick, did much later produce an unsigned document (long after Bellarmine was dead) claiming that Galileo had promised not to teach or publicise the Copernican doctrine. He did not enter controversy again until 1623 when he produced a now-famous polemic book called The Assayer, acclaimed as the height of controversial writing. It was against a Jesuit who had written about comets and was a manifesto for intellectual freedom in science.

In 1623 his friend in Florence, Maffeo Barberini, was elected Pope and Galileo could not wait to get to Rome to see him, and the reception was cordial. Everything seemed to be going well, and it must have looked as if the weight of Galileo and the rest of the scientific world might succeed and get a thorough revision of orthodox science. Galileo produced his famous book called in brief A Dialogue etc. between a Peripatetic aptly called Simplicio, a Venetian gentleman Sagredo (actually Galileo’s close friend of the old days) and a scientifically informed Florentine, Salvatio, who was really voicing the opinions of Galileo himself. The subject of the dialogue was the two world systems, that of Ptolemy and that of Copernicus.

The imprimatur, the official licence to print the book, was obtained from the Papal censor and the book was published in 1632. Galileo had written a pious preface in which he ridiculed the Copernican theory as wild and fantastic and contrary to Holy Scripture. In this form the censor permitted the book to pass. The censor lost his job when the pious preface brought laughter down on the Church that had been duped by such an obvious pretence. All over Europe people read Galileo while the Pope and cardinals fumed.

It is said that Scheiner, on hearing this in a Rome bookshop, turned purple and shook violently. But he and his fellow haters and intriguers were not beaten. In fact they succeeded. It seems likely that the Inquisition would have liked to do nothing but was forced to do so by the detailed and documented evidence claiming that Galileo was in fact a heretic. There was another fact working against Galileo as well. It was that the Pope grew angry and anti-Galileo when he learned of the events of 1616, of which he had never been informed. He thought himself tricked by Galileo’s artfulness. Galileo was ordered to appear before the Inquisition.

Galileo’s recantation

Though ill, old and partially blind, he went, having been offered a horse-drawn “litter” by the Duke of Tuscany, though Venice had offered sanctuary. In Rome he was housed comfortably and on 13 April at the first hearing he pleaded ignorance of the unsigned document and promised to produce that signed by Bellarmine in 1616. He almost won the day. There followed considerable activity behind the scenes — the Cardinals probably detested the Scheiners — and Francesco Barberini, the Pope’s brother, who remained a loyal and admiring friend to Galileo throughout, was very active. He appeared once more and was then kept in suspense for months. The Pope eventually decided on life imprisonment. Of the 10 cardinals, three had refused to sign the verdict, Francesco had demanded a pardon and when it was refused he persuaded his brother to make life “imprisonment” that of house arrest in the home of a sympathetic bishop. To pay for this, Galileo was made to kneel and admit to being vain and ambitious and to renounce the Copernican doctrine as being wrong.

“I Galileo Galilei, being in my seventieth year having before my eyes the Holy Gospel, which I touch with my hands, abjure [renounce], curse and detest the error and heresy of the movement of the Earth.”

“And yet it moves”

The churchmen published Galileo’s recantation throughout Europe to demonstrate their power to make men recant. It was an enormous humiliation and Galileo was left a broken man, almost mentally deranged by the months of pressure. But the kindly bishop Ascanio Piccolomini nursed him back to mental health and at length the authorities in Rome allowed him to go home, though still under house arrest. It was possibly on this occasion that Galileo defiantly made his famous outburst: “Eppur si muove” (And yet it moves).

Why did Galileo make this adjuration at the trial, admitting what he knew to be a lie? Was he a coward? Did he think it more important to get back to his life work? Who are we to judge?

It was at his home that Galileo renewed his life work, that on mechanics and motion. The book Two New Sciences etc. published in 1638 can be considered his memorial. He died on 8 January 1642. Less than a year later Isaac Newton was born.

This article by C L Boltz was originally published in New Scientist on 7 April 1983