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13.7: Cosmos And Culture
Mon February 17, 2014
Galileo Lives On
This past weekend marked the 450th anniversary of Galileo's birth. In articles celebrating his contributions to science, Clara Moskowitz at Scientific American wonders what he'd make of contemporary science, while Dan Vergano at National Geographic credits him with nothing short of the invention of "our own modern world."
In fact, Galileo has been called the father of modern science for his systematic use of observations and experiments. But, ironically enough, one of his most important discoveries may have required nothing more than an experiment in thought.
Legend has it that Galileo orchestrated a critical experiment at the Leaning Tower of Pisa: two balls of different masses were dropped from the top of the tower at the very same time. Which would reach the ground first?
According to the prevalent Aristotelian theory, bodies fall at a speed proportional to their mass, so the heavier ball should have reached the bottom before the lighter ball. According to Galileo's theory, bodies fall at a rate that's independent of their mass, so the two balls should have reached the bottom at the very same time.
We now know that — controlling for effects of air resistance — Galileo's prediction was the right one. Yet most historians agree that the famous experiment never took place. So how did Galileo arrive at and support his alternative to Aristotelian dogma? How did he convince others that he was right?
Fortunately (or unfortunately, if you like a good tiramisu), there's no need to travel to Italy — or even to leave your armchair — to appreciate the virtues of Galileo's theory over Aristotle's. You need only follow Galileo in conducting the following clever thought experiment.
In his writings, Galileo asked us to imagine connecting a light body to a heavy body (with, say, a thin rod) and then dropping the resulting object from a great height. How quickly would the new object fall? Galileo demonstrated that the Aristotelian view led to two contradictory expectations.
On the one hand, you might imagine that the heavier object would accelerate the descent of the lighter object, resulting in a net speed for the new object somewhere between the speeds that the light body and the heavy body would each achieve on their own. On the other hand, the new object (that is, the light body plus the heavy body plus the connecting rod) would weigh more than the heavy body alone, and should thus fall at a speed even faster than the heavy body alone.
The resolution to this puzzle, Galileo suggested, was to recognize that the speed of a body's fall is not proportional to its mass, but constant. And you never even had to leave your armchair.
So while we celebrate Galileo this week, and rightly praise the value of rigorous empirical investigation, let's not forget one of the most powerful tools in our scientific arsenal: the human mind.
You can keep up with more of what Tania Lombrozo is thinking on Twitter: @TaniaLombrozo