The Clockwork Universe: Isaac Newton, the Royal Society, and the Birth of the Modern World - Edward Dolnick (2011)
Part II. Hope and Monsters
Chapter 31. Two Rocks and a Rope
Tradition has it that Galileo discovered how objects fall by dropping weights from the top of the Leaning Tower of Pisa. Unlike most legends—Archimedes and his bathtub, Columbus and the flat Earth, George Washington and the cherry tree—historians believe this one might possibly be true. A tower drop would have disproved Aristotle’s claim that heavy objects fall faster than light ones. But it took the ramp experiments, which Galileo indisputably carried out, to yield the quantitative law about distance and time.
Whether he really climbed a tower or not, Galileo did propose a thought experiment to test Aristotle’s claim. Imagine for a moment, said Galileo, that it was true that the heavier the object, the faster its fall. What would happen, he asked, if you tied a small rock and a big rock together, with some slack in the rope that joined them? On the one hand, the tied-together rocks would fall slower than the big rock alone, because the small rock would lag behind the big one and bog it down, just as a toddler tied to a sprinter would slow him down. (That was where the slack in the rope came into play.) On the other hand, the tied-together rocks would fall faster than the big rock alone, because they constituted a new, heavier “object.”
Which meant, Galileo concluded triumphantly, that Aristotle’s assumption led to an absurd conclusion and had to be abandoned. Regardless of what Aristotle had decreed, logic forced us to conclude that all objects fall at the same rate, regardless of their weight. This is a story with a curious twist. Galileo, the great pioneer of experimental science, may never have bothered to perform his most famous experiment. No one is sure. What we know with certainty is that, like the Aristotelians he scorned, Galileo sat in a chair and deduced the workings of the world with no tool but the power of logic.
Since Galileo’s day, countless tests have confirmed his Leaning Tower principle (including some at the Leaning Tower itself ). In ordinary circumstances, air resistance complicates the picture—feathers flutter to the ground and arrive long after cannonballs. Not until the invention of the air pump, which came after Galileo’s death, could you drop objects in a vacuum. A century after Galileo, the demonstration retained its power to surprise. King George III demanded that his instrument makers arrange a test for him, featuring a feather and a one-guinea coin falling in a vacuum. “In performing the experiment,” one observer wrote, “the young optician provided the feather, the King supplied the guinea and at the conclusion the King complimented the young man on his skill as an experimenter but frugally returned the guinea to his waistcoat pocket.”
Today we’ve all seen the experiment put to the test, at every Olympic games. When television shows a diver leaping from the ten-meter board, thirty feet above the pool, how does the camera stick with her as she plummets toward the water? Galileo could have solved the riddle—just as a small stone falls at exactly the same rate as a heavy one, a camera falls at exactly the same rate as a diver. The trick is to set up a camera near the diver, at exactly the same height above the water. Attach the camera to a vertical pole and release the camera at the instant the diver starts her fall poolward. Gravity will do the rest.
Galileo exulted in his discovery that “distance is proportional to time squared.” The point was not merely that nature could be described in numbers but that a single, simple law—in operation since the dawn of time but unnoticed until this moment (just as the Pythagorean theorem had been true but unknown before its discovery)—applied to the infinite variety of falling objects in the world. A geranium knocked off a windowsill, a painter tumbling off his ladder, a bird shot by a hunter, all fell according to the same mathematical law.
The difference between Galileo’s world and Aristotle’s leaps out, as we have seen. Galileo had stripped away the details that fascinated Aristotle—the color of the bird’s plumage, the motives behind the painter’s absentmindedness—and replaced the sensuous, everyday world with an abstract, geometric one in which both a bird and a painter were simply moving dots tracing a trajectory against the sky. Ever since, we have been torn between celebrating the bounty that science and technology provide and lamenting the cost of those innovations.