Section II, Chapter Two: Galileo's Tools
Abstracting away irrelevant details, experimentation as a means of ruling hypotheses out, mathematical analysis over qualitative description, and rejecting arguments from authority seeped in...
Note—this is a draft of Chapter Five of a book I’m writing. The book is going to cover humanity’s deepest ideas from philosophy, physics, epistemology, and economics. Each chapter is meant to be short and digestible. Most of the chapters will explain just one or two ideas. The first few chapters, though, set the stage with some history, too.
‘Chapter []’ indicates a future chapter that I’ve not yet written.
Section II: Classical Mechanics
Section II, Chapter Two: Galileo’s Tools
By the time Copernicus died in 1543, the intellectual winds were shifting: not only was the weight of Aristotle’s authority on a host of subjects coming under siege by novel modes of argumentation, but people’s worldviews themselves were improving (see Chapter Four). The scientific way of thinking had progressed from its embryonic stage—but it had not quite evolved into the robust set of principles and institutions that make up the contemporary scientific enterprise.
As I mentioned in Chapter Four, Galileo Galilei (1564 C.E. - 1642 C.E.) took the scientific baton from Copernicus and carried it to near-culmination, setting the stage for the climax of the Scientific Revolution with Isaac Newton. In both word and action, Galileo brought rigorous mathematics and experimentation into the prevailing scientific culture (thereby infusing it with the best of Plato and Aristotle–see Chapter Three). He criticized and improved upon both Aristotle’s theory of motion in the terrestrial realm and demonstrated flaws in the philosopher’s ideas about the celestial realm. If Copernicus had knocked some stones off of the Aristotelian fortress, then Galileo ran a battering ram right through it.
In describing Galileo’s scientific outlook, Herman writes, “Galileo’s science managed to fuse the Platonist’s faith in mathematics with the Aristotelian faith in experience as the basis of discovery. All his work on mechanics, optics, and astronomy was deeply rooted in experiment and empirical research. When experience proved ambiguous or unreliable, however, Galileo realized then that mathematics must take over.”
At the University of Padua in Italy, Galileo grew weary of his Aristotelian colleagues, who thought that science “consisted of observation and theorizing”, as Mlodinow writes. Galileo insisted that scientific progress also required experiment. Mlodinow writes, “Scholars had been performing experiments for centuries, but they were generally done to illustrate ideas that they already accepted” [emphasis mine]. Galileo, on the other hand, levied experiments to rule ideas out, rather than in (a crucial feature of experiments that we will revisit in Chapter []). Finally, “his experiments were quantitative, a revolutionary idea at the time.”
Aristotle held that objects fall at a rate dependent on intrinsic properties such as their weight, a doctrine that had held for nearly two-thousand years. Rather than take common sense and the philosopher’s authority on the matter, Galileo devised an ingenious experiment to test Aristotle’s idea. Limited by the technology of his day, Galileo decided to roll balls down inclined planes and time their descent. He reasoned that the relevant physical laws should be the same, regardless of the steepness of the incline. And if that were so, then free fall would be equivalent to rolling down a maximally steep incline (one tilted at ninety degrees relative to the surface of the earth). Thus was born the concept of a limiting case.
Galileo also conjectured that the real physics of falling objects was obscured by factors like friction. Aristotle thought that feathers fell more slowly than stones because the former were lighter than the latter, but Galileo was convinced that both objects would fall at the same rate in the absence of complicating forces such as air resistance (a kind of friction). Thus was born yet another crucial concept in science: abstracting away details of a phenomenon that are immaterial towards explaining it. So, not only did Galileo’s inclined plane experiment allow objects to roll slowly enough for him to measure their speeds, but its design also minimized any significant effects of friction. With the complicating force neutralized, Galileo expected the balls to roll down the inclined plane at the same rate, regardless of what they were made of and how much they weighed.
He found that, for a given angle of the inclined plane’s tilt, balls of all weights accelerated at a constant rate (see Chapter []). The greater the tilt, the greater the acceleration, but weight seemed to play no role in determining the ball’s acceleration from the height of the plane to the ground (Mathematically, constant acceleration implies that distance covered is proportional to the square of the time it takes for an object to traverse that distance.). In other words, Galileo showed via careful experiment, mathematics, and measurement that Aristotle was mistaken.
As Herman writes, Galileo “knew that his experiments had shown that Aristotle was wrong twice—not only about whether two balls of different weights would hit the ground at different speeds, but also about the reason why they don’t behave as Aristotle said they would.”
Understandably wary of the supposedly infallible word of Aristotle, Galileo then turned from the philosopher’s physics of the earth to those of the stars. Heavily influenced both by Copernicus’ On the Revolutions of the Heavenly Spheres (see Chapter Four) and Johannes Kepler’s further improvements, Galileo quickly recognized the superior purchasing power of the heliocentric model over Aristotle’s geocentrism in explaining physical phenomena. For instance, he saw that the tides made little sense if the Earth was stationary but were far better explained if our planet, in fact, moved.
Whereas Galileo took to experiments to tear down Aristotle’s physics of bodies near the Earth’s surface, he relied on observations to contradict the philosopher’s astronomical ideas. Aristotle and the ancient Greeks imbued heavenly objects with a kind of geometric mysticism (see Chapter Three)—for instance, they thought the skyward domain was both immutable and of perfect shape. Herman writes, “According to Aristotle, no change should ever occur in the heavens. Everything existing in the celestial spheres…was made from an immaculate and unalterable substance called the quintessence.”
In 1604, Galileo witnessed a faraway supernova, a sudden and singular change to a cosmic background that Aristotle had maintained was unchangeable. Between that and Galileo’s acceptance of the heliocentric model, he was confident that Aristotle’s word could not be trusted on much, if anything, pertaining to the cosmos. But as he well knew, suspicions did not a refutation make.
So Galileo turned to the telescope, where observations confirmed what his gut had told him. The moon, far from a perfect sphere, was riddled with craters and mountains alike. He discovered that Jupiter had moons revolving around it and found evidence that Venus revolved around the Sun, both observations in utter violation of the ancient notion that Earth held special status in the cosmic order. Although he’d already known it in theory, Aristotle’s pristine system crumbled under the weight of Galileo’s observations.
In 1610, Galileo published his telescopic adventures as a short book, The Starry Messenger. But the Aristotelians of his day chose the word of their forebear over Galileo’s findings. As Herman writes, “Aristotelians dismissed what Galileo had seen through his telescope as an optical illusion…Even when Galileo gave them his telescope and offered to let them see the moon’s craters for themselves, they refused to look. Aristotle had said that all celestial bodies were perfect. This meant they couldn’t have any flaws.”
But Galileo’s discoveries proved too persuasive to ignore for long. His elaborations as to why heliocentrism was a better explanation than geocentrism (as found in his 1632 book, The Dialogue Concerning the Two Chief World Systems), as well as pages of astronomical observations, would persuade thinkers not long after his death. And his insights into the physics of falling objects laid critical stepping stones on which Isaac Newton would walk towards the Holy Grail of classical mechanics (see Chapter []). It took many moons for Galileo’s knife to penetrate, but eventually it would cut through the heart of Aristotle’s physics, cosmology, and perceived scientific authority.
Galileo’s scientific tools, too, were too fruitful to give up. Abstracting away irrelevant details, experimentation as a means of ruling hypotheses out, mathematical analysis over qualitative description, and rejecting arguments from authority gradually seeped into Europe’s distributed network of thinkers and tinkerers in the decades following Galileo’s death.
With Aristotle waning and the dawn of the scientific mindset on the horizon, it would take another forty-five years for the Scientific Revolution to culminate in the first hard-to-vary (see Chapter []), universal theory of physics.
Thanks to Moritz Wallawitsch and Dennis Hackethal for early feedback.