Let’s Do Math,
Acceleration Due to Gravity
The Truth of the Tower
The most famous example of Galileo’s ability to strip complications away from simplicity is the Leaning Tower of Pisa story. Many experts doubt that this fabled event ever took place. Stephen Hawking, for one, writes that the story is “almost certainly untrue.” Why, Hawking asks, would Galileo bother dropping weights from a tower with no accurate way of timing their descent when he already had his inclined plane to work with? Shades of the Greeks! Hawking, the theorist, is using Pure Reason here. That doesn’t cut it with a guy like Galileo, an experimenter’s experimenter.
Stillman Drake, the biographer of choice of Galileo, believes the Leaning Tower story is true for a number of sound historical reasons. But it also fits Galileo’s personality. The Tower experiment was not really an experiment at all but a demonstration, a media happening, the first great scientific publicity stunt. Galileo was showing off, and showing up his critics.
Galileo was an irascible sort of guy not really contentious, but quick of temper and a fierce competitor when challenged. He could be a pain in the ass when annoyed, and he was annoyed by foolishness in all its forms. An informal man, he ridiculed the doctoral gowns that were required attire at the University of Pisa and wrote a humorous poem called “Against the Toga” that was appreciated most by the younger and poorer lecturers, who could ill afford the robes. (Democritus, who loves togas, didn’t enjoy the poem at all.) The older professors were less than amused. Galileo also wrote attacks on his rivals using various pseudonyms. His style was distinct, and not too many people were fooled. No wonder he had enemies.
His worst intellectual rivals were the Aristotelians, who believed that a body moves only if driven by some force and that a heavy body falls faster than a light one because it has a greater pull towards the earth. The thought of testing these ideas never occurred to them. Aristotelian scholars pretty much ruled the University of Pisa and, for that matter, most universities in Italy. As you can imagine, Galileo wasn’t a big favorite of theirs.
The stunt at the Leaning Tower of Pisa was directed at this group. Hawking is right that it wouldn’t have been an ideal experiment. But it was an event. And as in any staged event, Galileo knew in advance how it was going to come out. I can see him climbing the tower in total darkness at three in the morning and tossing a couple of lead balls down at his postdoc assistants. “You should feel both balls hitting you in the head simultaneously,” he yells at this assistant. “Holler if the big one hits you first.” But he didn’t really have to do that, because he had already reasoned that both balls should strike the ground at the same instant.
Here’s how his mind worked: let us suppose, he said, that Aristotle was right. The heavy ball will land first, meaning that it will accelerate faster. Let us then tie the heavy ball to the light ball. IF the light ball is indeed slower, is will hold back the heavy ball, making it fall more slowly. However, by tying them both together, we have created an even heavier object, and this combination object should fall faster than each ball individually. How do we solve this dilemma? Only one solution satisfies all conditions: both balls must fall at the same rate of speed. That is the only conclusion that gets around the slower/faster conundrum.
According to the story, Galileo spent a good part of the morning dropping lead balls from the tower, proving his point to interested observers and scaring the heck out of everybody else. He was wise enough to not use a penny and a feather but instead unequal weights of very similar shapes (such as a wooden ball and a hollow lead sphere of the same radius) to roughly equalize the air resistance. The rest is history, or it should be. Galileo had demonstrated that free fall is utterly independent of mass (though he didn’t know why, and it would take Einstein, in 1915, to really understand it). The Aristotelians were taught a lesson they never forgot or forgave.
Is this science or show biz? A little of both. It’s not only experimenters who are so inclined. Richard Feynman, the great theorist (but one who always showed a passionate interest in experiment), thrust himself into the public eye when he was on the commission investigating the Challenger space shuttle disaster. As you may recall, there was a controversy over the ability of the shuttle’s O-rings to withstand low temperatures. Feynman ended the controversy with one simple act: when the TV cameras were on him , he tossed a bit of O-ring into a glass of ice water and let the audience view its loss of elasticity. Now, don’t you suspect that Feynman, like Galileo, knew in advance what was going to happen?
In fact, in the 1990s, Galileo’s Tower experiment has emerged with a brand-new intensity. The issue involves the possibility that there is a “fifth force,” a hypothetical addition to Newton’s law of gravitation that would produce an extremely small difference when a copper ball and, say, a lead ball are dropped. The difference in time of fall through, say, on hundred feet might be less than a billionth of a second, unthinkable in Galileo’s time but merely a respectable challenge with today’s technology. So far, evidence for the fifth force, which appeared in the late 1980s, has all but vanished, but keep watching your newspaper for updates.