IV.

Galileo’s Work in Physics

The key to Galileo’s new physics lay in mathematics. While registered as a medical student at the University of Pisa, he increasingly devoted his time to the study of mathematics, with the encouragement of court mathematician Ostilio Ricci. After leaving the university he tutored privately for a time and wrote on hydrostatics, but he did not publish anything. In 1589 he became professor of mathematics at Pisa.

A.

Falling Bodies

Before assembled university professors, Galileo reportedly refuted Aristotle’s belief that speed of fall is proportional to weight by simultaneously dropping two objects of the same material but different weights from the Leaning Tower of Pisa. This celebrated story of Galileo’s demonstration that Aristotle was fundamentally mistaken about motion comes from his last pupil and first biographer, Vincenzo Viviani. Though Viviani’s account is sometimes dismissed as legend, it is more probably an exaggerated version of an actual event. Galileo’s manuscript shows that he was still unclear about acceleration in free fall and that he thought more in terms of the characteristic speed of a body of a given material in a given medium.

Yet Galileo could already improve on Aristotle. Galileo considered himself a follower of the ancient Greek scientist Archimedes and abandoned Aristotelian notions of heaviness and lightness in favor of the more useful notion of density. Galileo made his first attempts at producing simple mathematical comparisons of how bodies of varying densities fall in various substances, and he was willing to ignore minor discrepancies, leaving them to be explained by further investigation. He even toyed with the idea of a body resting on a perfectly smooth surface being movable by the slightest of forces—a hint of his later work on inertial motion and a measure of how he was distancing himself from Aristotelian ideas of natural and forced motions.

Galileo’s contract at the University of Pisa was not renewed in 1592, probably because he contradicted Aristotelian professors. The same year, he was appointed to the chair of mathematics at the University of Padua, where he remained until 1610. Galileo’s mathematical work depended on his ability to discern simple mathematical patterns underlying familiar occurrences, such as the free fall of objects to the ground. He combined this with a knack for devising controlled observations in which the looked-for mathematical relationships presented themselves as obvious and as measurable with precision. His fundamental conviction was that the universe is an open book but, as he wrote later in The Assayer (1623), “One cannot understand it unless one first learns to understand the language and recognize the characters in which it is written. It is written in mathematical language.…” 

Galileo’s conviction led to important discoveries in the first decade of the 17th century. He not only recognized that the acceleration of any body in free fall was uniform but he expressed this in a simple law: The distance traveled in free fall is proportional to the square of the time elapsed; that is, in two seconds a body will fall four times as far as it will in one second; in three seconds it will fall nine times as far; and so on.

B.

Projectiles and Pendulums

Galileo’s law of falling bodies led to an understanding of the motion of projectiles. Galileo could look at the fall of an arrow or cannonball and see it as made up of two independent motions: The vertical component was uniformly accelerated and conformed to his law of falling bodies; the horizontal motion imparted to the body by the bowman or gunner was at constant speed. When the horizontal and vertical components were combined, the resultant path was a parabola. This seemingly abstract geometrical account had practical consequences for efficient gunnery.

In a similar vein Galileo investigated mechanics and the strength of materials. In his studies of pendulums he discovered that the swing of a given pendulum takes the same time no matter how large its arc. Others soon pointed out that this was true only if the swing did not become too large.

C.

Inertia

One of the greatest contrasts between Galileo’s ideas and Aristotle’s ideas is in their underlying models of motion. Galileo believed that an object moving uniformly on Earth’s surface without meeting any resistance would continue to move at the same speed without needing any force to keep it going. Aristotelians, on the other hand, would look for a force to cause the continuing motion. Galileo’s idea approximates Isaac Newton’s first law of motion, according to which a body will continue in its state of rest or uniform motion in a straight line unless interfered with. Although Galileo failed to define uniform motion as a straight line, he made the advance of not treating rest as a state more natural than motion.