One outstanding astronomer who contributed notably to mathematics in the early part of the seventeenth century is the Italian, Galileo Galilei.
Galileo, the son of an impoverished Florentine nobleman, was born in Pisa in 1564 on the day that Michelangelo died. At the age of seventeen, he was sent by his parents to the University of Pisa to study medicine. One day, while attending a service in the cathedral, his mind was distracted by the great bronze suspended from the high ceiling. The lamp had been drawn aside in order to light it more easily, and when released it oscillated to and fro with gradually decreasing amplitudes. Using the beat of his pulse to keep time, he was surprised to find that the period of an oscillation of the lamp was independent of the size of the arc of oscillation. Later, by experiments, he showed that the period of a swinging pendulum is also independent of the weight of the pendulum’s bob and thus depends solely on the length of the pendulum.
It is reported that Galileo’s interest in science and mathematics was roused by the above problem and then further stimulated by the chance attendance at a lecture on geometry at the university. The result was that he asked for, and secured, parental permission to abandon medicine and to devote himself to science and mathematics instead; fields in which he possessed here strong natural talent.
At the age of twenty-five, Galileo was appointed professor of mathematics at the University of Pisa, and while holding this appointment he is said to have performed public experiments with falling bodies. According to the story, before a crowd of students, faculty and priests, he dropped two pieces of metal, one ten times the weight of the other, from the top of leaning tower of Pisa. The two pieces of metal struck the ground practically at the same time, thus contradicting Aristotle, who said that a heavier body falls faster than a lighter one. Galileo arrived at the law that the distance a body falls is proportional to the square of the time of falling, in accordance with the familiar formula that distance is equal to gravitational acceleration multiplied by the square of the time taken and the result is then divided by two.
However even the visual evidence of Galileo’s experiments did not shake the faith of other professors at the university in the teaching of Aristotle. The authorities at the university were so shocked at Galileo’s sacrilegious insolence in contradicting Aristotle that they made life unpleasant for him there, with the result that in 1591 he resigned his professorship. The following year he accepted a professorship at the University of Padua, where the atmosphere was more friendly to scientific pursuits. Here, for nearly eighteen years, Galileo continued his experiments and his teachings and won widespread fame.
1607, an apprentice to the spectacle maker, Hans Lippershey of Holland,
while playing with some of his master’s spectacle lenses, discovered that
if he held two of the lenses at an appropriate distance apart, objects
seen through the pair of lenses became enlarged. The apprentice brought
his discovery to the attention of his master, who placed two lenses in
a tube and displayed the device as a toy in his window shop. The lens was
seen by a government official, who bought it and presented it to Prince
Maurice of Nassau. As commander of the armed forces of the United Netherlands,
Prince Maurice saw the possibilities of the toy as a spyglass for military
By 1609, the news of the invention of the spyglass reached Galileo, who soon made a spyglass which was greatly superior to the one made by Lippershey. Upon request, he demonstrated his instrument in Venice, where, from the top of the highest church in the city, Venetian senators were able to see the sails of an approaching ship a full two hours before they were visible by naked eye. Galileo presented his model to Doge of Venice, who, like Prince Maurice, who recognized the immense possibilities of the instruments in naval and military operations. Thus Galileo was given a sizably increased stipend.
Galileo went on and made four more telescopes, as his instruments were named (from the Greek tele, “far” , skopos, “watching”), each more powerful than the last. With the fifth telescope, which had a power of 30 diameters, Galileo noticed, on the night of January 7, 1610, two small stars to the east of the planet Jupiter and one to the west. The following night, to his surprise, all three stars were to the west of the planet. Three nights later, he found that there was still another small star revolving about Jupiter. He had discovered Jupiter’s four bright satellites and observed a striking confirmation of the Copernican theory of smaller bodies revolving about larger ones. With his telescope, Galileo observed sunspots, the mountains on the moon, the phases of Venus and Saturn’s rings. However these discoveries only aroused once more the bigoted opposition of many churchmen who accepted the authority of Aristotle; Aristotle had asserted that the sun is without blemish and that the earth, and hence men, is the center of the universe.
Finally in 1633, a year after his publication of a book that supported the Copernican theory, Galileo was summoned to appear before the Inquisition, and there, an ill and old man, forced, under the threat of torture, to recant his scientific findings. His book was placed on the Index of prohibited works, there to remain for two hundred years. Having perjured his conscience, the old scholar’s life was broken. He was permitted to continue innocuous scientific work, but became blind and died in January 1642, still under the supervision of the Inquisition and a virtual prisoner in his own home.
There is a legend that, as Galileo rose to his feet after his forced recantation and denial of the earth’s motion, he muttered softly under his breath to himself, “the earth does move all the same.” Whatever the basis of this story, it has come to be a sort of proverb to the effect that truth shall prevail despite all attempts at suppression. And so it came to pass, for the year 1642, which saw the death of Galileo in captivity, also saw the birth of Isaac Newton.
To Galileo we owe the modern spirit of science as a harmony between experiment and theory. He founded the mechanics of freely falling bodies and laid the foundation of dynamics in general, a foundation upon which Isaac Newton was able later to build the science. He was the first to realize the parabolic nature of the path of a projectile in a vacuum and speculated on laws involving momentum. He invented the first modern-type microscope and the once very popular sector compasses. Historically interesting are the statements made by Galileo showing that he grasped the idea of equivalence of infinite classes, a fundamental point in Cantor’s nineteenth- century theory of sets, which has been so influential in the development of modern analysis. These statements and the bulk of Galileo’s ideas in dynamics, can be found in his Discorsi e dimonstrazioni mathematiche intorno a due nuove scienze, published in Leyden in 1638. Galileo had been quoted as saying: “In questions of sciences, the authority of a thousand is not worth humble reasoning of a single individual.”
It would seem that Galileo was jealous of his famous contemporary, Johann Kepler, for although Kepler had announced all three of his important laws of planetary motion by 1619, these laws were completely ignored by Galileo.
All his life long, Galileo was a religious man and a devout Catholic. It accordingly distressed him to find the views to which he was irresistibly led by his observations and reasonings as a scientist condemned as contradicting the scriptures of the Church, of which he considered himself a loyal member. He therefore felt compelled to reason for himself the relation between science and scripture. Many scientists have, from time to time, found themselves in this position. It occurred, for example, in the middle of the nineteenth century when difficulties were felt in reconciling Darwin’s theory of evolution with the Biblical account of the creation of living things (Book of Genesis).
Galileo’s conclusion was that the Bible is not, and never was intended to be a textbook on astronomy, or biology, or any other science. In short, Galileo maintained it was not intended as a book to teach us scientific truths that we can discover for ourselves. Rather it was intended as a book to reveal spiritual truths that we could not have found out for ourselves. Now the conflict between science and scripture lies in the fact that these spiritual truths are expressed in the Bible in ways natural to the people to whom, and through whom, they were originally revealed (the Israelites). But this is clearly an accident of time and should therefore be overlooked. A scientist should not be upset to find the Bible picturing the world in a way natural to the early Hebrews, and a churchman should not be upset to find a scientist picturing the world in a way contrary to the description in the Bible. The way in which the world is described is entirely incidental to the real aim of the Bible and in no way is inconsistent with the spiritual teachings of the Bible.