Galileo's New Physics

Galileo is famous as an “astronomer,” from his association with the telescope and largely derived from his notorious troubles with the Church. However, mapping stars and constructing calculations was not the primary interest of this diversely talented scholar. We should think of his focus as creating a new physics, based on a unified theory of matter and motion, contradicting the traditional Aristotelian physics. He rejected distinction of terrestrial (the four elements) and celestial (the ætherial fifth element) realms, along with their distinct natural motions. He produced a way of using mathematical proportions and relations to describe the properties of motion, and matter acting in lawlike ways. He accomplished this by using simple machines, measurements, and experiments to explore those physical relationships. His campaign against the Scholastic categories and explanations was not accomplished simply, quickly, or consistently. That is, questions he opened in the 1580s-90s sometimes did not come to fruition until the 1630s, and even then, he could not resolve all of the problems he raised. Nonetheless, we can see him throughout his long career thinking deeply about the nature of matter and of motion, and attempting to find a new, unified theory. His goals do relate to astronomy – he was an early Copernican, and he knew that he needed physical principles to explain how things move on a moving earth. One way to view him is as using Copernican astronomy as a way to critique Aristotle, but also as an open problem that a new physics would solve.

The beginning was Galileo’s reading of Archimedes on density (the “Eureka” story of displacement), inspiring him in the 1580s as a student and then as a young professor of mathematics to use similar methods. He developed devices for make precise measurements, such as for weight in his La Bilancetta (“The Little Balance”) in 1586. He used Archimedean reasoning in applying mechanical principles to simplified problems, such as deriving an analytical method for the center of gravity of solids (a treatise in 1589). These applications and some mathematical publications impressed leading mathematicians, including the Jesuit scholars Clavius and Bellarmine.

In addition to being a professor of mathematics, Galileo became known as an inventor. His advice was to “Measure all things, and make measurable what is not.” To that end, he developed, among other things, surveying instruments, optical devices, balances, timekeepers, pumps, the “military compass” (a calculating device), thermoscopes (for temperature), and the refracting telescope. The goal was twofold – to attract patrons, with instruments and techniques for practical problems (such as the 1606 treatise on “The Operation of the Geometric and Military Compass”); and to pursue his new way of investigating physical phenomena.

Galileo wrote early treatises on “motion” (1590) and on mechanics (1600), disputing Scholastic explanations and attempting to build a system built on weight and balance (equilibrium). He was hampered by not being able to measure all the properties he needed, and by not yet seeing how to bring all phenomena into one system as “dynamics” (action over time) instead of static relationships. He did develop novel experiments with balances, specific gravities, inclined planes, falling bodies, acceleration, and pendulums. These led to articulation of some particular rules or relationships, such as the law of pendulums and ideas about acceleration (1603-1609). Not fully able to resolve these phenomena into a cohesive theory, Galileo left most of it unpublished until his summary work of 1638.

Galileo’s Discourses and Mathematical Demonstrations concerning Two New Sciences (1638) summed up his work on various laws of action and motion (the two new sciences of statics and dynamics). It included drawings to illustrate the problems and solutions to matters of motion and trajectory, providing his laws and applying them to practical problems. With his descriptions of experiments and mathematical treatment of falling objects, such as this investigation of a ball rolling down an incline, Galileo brought new techniques and research questions to the study of motion.