“Galileo’s Big Idea” or, maybe, “The most important idea in the history of science?”

In 1592 Galileo was hanging out in the Armory of Venice, watching the craftsmen build ships and trying to figure out how to help the soldiers shoot their cannonballs more accurately. He knew that he would need to use mathematics to describe the paths of these projectiles, but the ancient natural philosophers had insisted that rigorous mathematics could only be applied to perfectly regular motions like those of the sun, stars, and planets.

But Galileo had an idea (and it might just be most important idea in the history of science!): If you can clear away in your imagination all the “external and accidental” factors affecting the motions of earthly objects then you will be left with purified motions that are as regular and orderly as the motions of the heavenly bodies. For example, instead of studying an actual ball rolling on an actual surface, Galileo imagined a perfectly round ball, on a perfectly flat and level plane, with no friction or air resistance to impede its motion. This imagined ball, unlike any actual ball, will keep rolling with the same uniform motion forever, and uniform motion is easy to describe using mathematics!

Galileo’s idea became the basis for his new mathematical science of motion and later inspired Newton’s Laws of Motion. Today we find not just physicists but even biologists, psychologists, and economists employing the tools of mathematical analysis in their study of earthly objects as complex as ecosystems, brains, and global trade relations. How are they able to create mathematical descriptions of such complex phenomena? By using the same strategy of imaginatively clearing away, simplifying, and purifying that Galileo invented in 1592.

This is all well and good, but shouldn’t we be concerned about what is going on here? Do the equations of modern sciences like physics, chemistry, biology ever describe anything real, or are they only about idealizations and abstractions? And, if the latter is true, how does it turn out that these equations are often so useful to us? Finally, even if we can see how they might be useful, how do equations like these help us know and understand the objects they are supposed to be about?

— Phil Bartok, Faculty Member