galileo vs aristotle--4/9/25

09 Apr 2025

galileo vs aristotle--4/9/25

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Today's selection-- from Beautiful Experiments by Philip Ball. The conventional wisdom through the centuries had been that heavier objects fall faster than lighter object, an assertion that had been made by none other than Aristotle. Since it was almost impossible to judge by eye, and the measurement tools of the 1600s were not sufficiently precise, it would take a great creativity to even design an experiment to measure any difference in the rate of fall. The genius who designed that experiment was the endlessly curious Galileo himself.

“It was one thing to know that all objects take an equal time to fall in gravity (if they are not significantly perturbed by air resistance). But how exactly did they fall? Seemingly based on observations of bodies falling through water, Aristotle asserted that they fall at a steady speed that depends on their weight. But the descent in air was too rapid to judge that by eye. If only there was some way to slow it down.

“In the early 1600s, Galileo saw how that might be simply done. A smooth ball placed on a slightly sloping tabletop begins to roll. If the slope is steeper, the ball gathers speed more quickly. Increasing the slope until it is vertical brings the motion steadily closer to perfect free fall. So Galileo reasoned that a ball rolling down such an ‘inclined plane’ is a slowed-down version of free fall that would enable him to make measurements.

“The question was how the distance traveled (call it s) depends on the time elapsed (t). If the ball rolls at constant velocity, the two are proportional: the speed is then just the ratio of distance to time. Galileo began experimenting with inclined planes in 1602, and two years later he had improved the method enough to deduce the mathematical relationship between and t. He describes the apparatus in the 1638 Two New Sciences. In a wooden beam about 28 feet long, a groove was cut in the edge and covered in smooth vellum, down which a bronze ball rolled when the beam was tilted at an angle. To measure the time taken to reach the bottom after being released from various points along the beam, Galileo used a water clock in which water flowed at a constant rate through a pipe. If the pipe could be opened and closed accurately enough, the amount of water accumulated was proportional to the time passed. Acknowledging the potential for error in this technique. Galileo repeated each experimental run many times — ‘a full hundred.’ he claimed.

“By this means, he deduced that the ball did not roll at constant speed after all, as Aristotle claimed, but gradually picked up speed: it accelerated. So the relationship between s and t was not one of simple proportionality; instead, s increased in proportion to the square of the time elapsed. As students learn to write it today; s = ½at2, where a is the acceleration. Thus, motion and mechanics were best described not in qualitative language but in mathematics. which Galileo famously declared to be the true language of nature.

“Galileo was the first to identify acceleration as a quantity in the theory of mechanics. A body accelerates if a force acts on it—in this case the force of gravity (and also the smaller retarding force of friction as the ball rolls). Galileo deduced that a body on which no forces act does not change speed: if it is already moving. it continues to do so at the same speed, but if it is at rest (a speed of zero), then it remains so. Isaac Newton was later to express this as his first law of motion, and added to it a second law relating acceleration to the force producing it: the force is equal to the mass of the body multiplied by its acceleration a.

“Galileo's inclined plane is one of the first instruments designed solely for quantitative experimental science. Previously, natural philosophers tended to use the resources they had to hand — sticks and rods, darkened rooms, prisms and jars—to investigate how nature works. But Galileo's was a genuine scientific instrument constructed with a specific aim in mind. The experiment marked the beginning of a century in which specialized ( often costly) scientific instruments became commonplace. Their use increasingly distinguished the ‘expert’ (later sometimes called the virtuoso) from the mere amateur dabbler.

“Still we should not suppose that Galileo was doing science in the same sense as scientists today. His method was poised between the older practice of starting with axioms and making logical deductions, and the modern way of formulating and testing hypotheses. As historian of science Domenico Bertoloni Meli says, ‘he formulated the science of motion as a mathematical construction and then used the experiment only at a later stage to show that the science he had formulated corresponded to nature's behaviour.’ Even if it did not, Galileo would argue that the science remained valid as a mathematical exercise.

Portrait c. 1640

“Because of its importance in the history of experimental science, the inclined-plane experiment has received intense scrutiny. One concern was whether Galileo could really have achieved reliable results with the rather crude methods at his disposal for measuring time. It takes only seconds for the ball to descend, so there is scope for significant error in determining exactly when it starts and ends. With this in mind, French philosopher of science Alexander Koyre was bitingly dismissive of the whole story, saying in 1953 ‘it is obvious that the Galilean experiments are completely worthless: the very perfection of their results is a rigorous proof of their incorrection.’ But Koyre's doubts were themselves questioned in 1961 when Thomas Settle, a student of the history of science at Cornell University, showed using cheap homemade equipment that with practice he could obtain data perfectly good enough to verify Galileo's law of acceleration. Koyre's argument from personal incredulity was not enough; it is now common for historians of science to make historical reconstructions of experiments with resources available at the time to see if the findings were plausible. Settle's work also showed the importance of getting a feel for one's apparatus before it could be used with confidence.

‘What is more, in 1972 historian Stillman Drake concluded from a close inspection of Galileo's scrappy ‘lab book’ jottings that Galileo might have also used another timing method, which involved inserting moveable gut frets into the inclined plane so that the rolling ball would create an audible click as it passed over. By relying on the good sense of a steady beat that his musical training would have instilled, Galileo might then have moved the frets until the ball's passage produced a regular series of clicks, and deduced the acceleration law from the distances between the frets as the ball rolled for an equal time. Drake suggested that Galileo had not recorded this timing method, perhaps for fear that it might sound foolish—requiring that he establish a regular rhythm by, say, singing a song.”