A few years later, as concerns mounted, Galileo was officially advised by Cardinal Bellarmino

on the Pope's behalf to proceed cautiously and speak only hypothetically about the Copernican theory, but not as if it were actually real.

Galileo returned to Florence and continued work on his book, but now he gave more emphasis to mathematical arguments rather than to esperimental or physical arguments. -- as the Pope wished. But when the book finally appeared in 1632,

it raised an immediate storm of protest leading immediately to Galileo's arrest and famous trial by the Inquisition in Rome.

which found him guilty of having published a heretical book. In the end, Galileo had no choice but to repent and confess that he had gone to far.

He was sentenced to life imprisonment, which he spent, for the most part at his own villa at Arcetri near Florence, under the surveillance of the Inquisition.

Even so, Galileo, in his last years,

now undertook his last and perhaps greatest work, his Discourses on the Two New Sciences, which has been described as "the cornerstone of modern physics." It was smuggled out of Italy to France, and published in Leyden in 1638.

In this book, Galileo presented the true laws of accelerated motion and falling bodies, as well as the fundamental theory of projectile motion and important applications of mathematics to a host of physical problems.

When Galileo died in 1642, totally blind and almost 78 years old, Pope Urban VIII refused to forget his feud with Galileo, and refused to permit his burial with a suitable monument -- instead, Galileo was buried unceremoniously in the Church of Santo Croce, in Florence. Only a few hundred years later were his remains moved to their present magnificent tomb, opposite that of Michelangelo near the entrance to the church.

By now it is possible to appreciate several basic and fundamental aspects of Galileo's scientific genius. Above all, his early work seems to have concentrated upon arguments against Aristotle, arguments involving a sustained pattern of observation and demonstration requiring little in the way of mathematics and concentrating instead on physical experience. His most revolutionary observational discoveries came with the telescope, and these provided, for the first time, about 1610, a number of good physical arguments in favor of the Copernican theory.

Later, however, Galileo had two additional concerns -- the problem of defending that theory against attacks from the Church without recourse to physical examples as the Pope had insisted -- but primarily with mathematical arguments. Secondly, his impressive discovery of the parabolic nature of projectile motion -- elaborated fully in 1638

-- seemed in a very profound way to display the essentially mathematical character of physical phenomena.

As we shall see in a more careful examination of the mathematical arguments arguments Galileo developed for accelerated motions (especially the parabolic trajectories of projectile motions) Galileo believed that nature was inherently mathematical, that mathematics was the language of nature, and that mathematics was the key to understanding the reality behind the appearance of natural phenomena -- for example, accelerated and parabolic motions.

What Galileo achieved in revolutionizing physics was to show how observation, careful measurement, and attention to the structure of a given event -- all led to an appreciation of hidden causes that ultimately expressed the pervasive mathematical unity of all nature.

But Galileo was not the first to have done this, although in terms of astronomy and physics he was clearly a pioneer. But Renaissance artists -- painters, sculptors and architects -- had been observing nature with a special interest in depicting it faithfully, realistically, from the early 15th century on. In fact, by turning to the problem of art and science in the Renaissance, it is possible to find what I believe are important roots for Galileo's own peculiarly realistic -- and idealistic -- approach to nature. For the values and attitudes Galileo held were ones he shared with Italian humanists -- including philosophers, artisans, even musicians. The question, now, is to determine what those values were, the important ones for Galileo's science -- and to decide what role they played in Galileo's experimental -- and mathematical -- revolution.

Go to the next section: Renaissance Art and Mathematical Perspective

Return to the Table of Contents