Shoulders of giants
Course 3 followed humanity from myth to Aristotle’s cosmos, and watched that cosmos break under better measurements. People kept asking why, and new instruments kept giving new answers. Now comes the thrilling part: the physics of Isaac Newton, and the picture of the universe as a machine.
Newton himself put it modestly. In a 1676 letter to his fellow scientist Robert Hooke, he wrote: “If I have seen further, it is by standing on the shoulders of giants.” This wasn’t false modesty, this course argues. It was simply true, and two of the giants stand out: Galileo and Kepler. This lesson is about the first.
How things fall
Drop a stone and it falls. You see it every day. Aristotle’s explanation was that the stone is made of the element earth, and earth by its nature moves toward the center of the universe. Heavier things, he held, fall faster, in proportion to their weight.
But by Galileo’s time the earth was no longer the center of the universe. So why does a stone fall at all, and how? Galileo’s answer came from a method worth noticing: experiment combined with imagination.
A falling stone is too fast to time. So Galileo slowed the fall down by rolling a ball down a gentle ramp. For a clock, he let water run steadily from a container and weighed how much collected. He couldn’t measure seconds, but he could compare times: twice as much water meant twice as long. Modern reconstructions sometimes add small bells along the ramp that ring as the ball passes. The result, which you tried yourself in Course 2, was simple. The distance the ball rolls grows with the square of the time.
Then Galileo changed the slope. On a steeper ramp the ball ran faster, but the rule stayed the same: distance still grew with the square of the time. Only the constant changed. Balls of different materials and weights on the same ramp kept pace with each other.
Now the crucial step. Imagine the ramp getting steeper and steeper, until it stands straight up. That limiting case is free fall. If the rule holds on every ramp, it must hold for a falling stone too, and a heavy ball and a light one must fall together. That contradicts Aristotle, and this time the reasoning rests on measured facts, not on ideas about perfection or natural places.
The famous story that Galileo dropped two balls from the Leaning Tower of Pisa comes from a biography written by his student years later, and historians doubt it happened. Either way, it doesn’t matter. The ramp was the real experiment, and the limit was the real idea.
Motion needs no push
Galileo’s second discovery went to the heart of Aristotle’s physics. Remember Aristotle’s rule from Course 3: rest is natural, and motion needs a push to keep it going.
Galileo set up two ramps facing each other. A ball rolls down one, speeds up, and climbs the other. Everyday experience says it won’t quite reach its starting height, but Galileo noticed that the smoother he made the ball and the track, the closer it came. Friction, he realized, was what made the difference.
Then he lowered the second ramp. The ball still climbed to almost the same height, but it had to roll farther to get there. Lower the ramp more, and it rolls farther still. Now take the limit again: lower the second ramp all the way to flat. The ball can never reach its starting height, so, without friction, it would roll on forever.
Galileo’s two ramps
Release the ball from the left ramp. Make the second ramp gentler, and turn the friction down, to see where Galileo’s reasoning leads.
This is the law of inertia. In Newton’s later wording, every body stays at rest, or keeps moving at a steady speed in a straight line, unless a force changes its state. Rest is no longer special. Steady motion is just as natural, and the two can’t even be told apart from inside. On a smooth train running at a steady speed, a ball on the table sits still, exactly as it would at home. Whether something is moving or at rest depends on what you compare it with.
The discovery and use of scientific reasoning by Galileo was one of the most important achievements in the history of human thought, and marks the real beginning of physics.
Albert Einstein and Leopold Infeld, The Evolution of Physics, 1938
Until Galileo, in this reading, humanity had been crawling toward scientific thinking, like a baby learning to walk. With Galileo it took its first real step.
A model in your head
What exactly was Galileo’s method? Here it is in terms anyone can use. To understand anything, you build a model of it in your head. When you meet someone new, you don’t record every detail about them. You note a few things that matter: a face, a name, a little background. The world sends us far more information than we can handle, so we pull out the core of it, set a boundary around what we will consider, and reason inside that boundary.
Think of the hero of the American TV series Prison Break, Michael Scofield, who looks at a desk lamp and sees every screw. Most of us can’t, and we shouldn’t try. An engineer’s drawing with every layer switched on is a flood of data. Galileo’s genius was knowing what to leave out, like friction and air, and what to keep.
Then you reason about the model from your most basic knowledge, your first principles. The first principles themselves change over time. For Aristotle they were the natural places of the elements. For Newton’s successors they were his laws of motion. Today, when physicists calculate the properties of a new material, they start from quantum mechanics: arrange the atoms and compute. Whoever has the more accurate first principles has the edge in solving problems.
What did Galileo conclude from lowering his second ramp?
Closer to home
On August 2, 1971, the Apollo 15 astronaut David Scott stood on the Moon, where there is no air, and dropped a geologist’s hammer and a falcon feather at the same moment. They hit the ground together. “How about that,” he said. “Mr. Galileo was correct in his findings.”
The idea of first principles has a Silicon Valley echo. Entrepreneurs like to talk about “first-principles thinking”: strip a problem down to the basic facts instead of copying what others do. It is Galileo’s method, applied to business. Remember, though, that the method works only as well as the first principles you start from.
Another view
Galileo had predecessors. In the sixth century, the Greek scholar John Philoponus argued, against Aristotle, that heavy and light bodies fall at nearly the same speed. In the 1300s, scholars at Oxford and Paris worked out the mathematics of uniformly accelerated motion, and the French philosopher Jean Buridan proposed that a thrown object carries an “impetus” that keeps it moving. Historians still debate how much Galileo owed them.
Some have found an echo even in ancient China. A line in the Mohist Canon, from around the fourth century BCE, reads 止，以久也. Joseph Needham translated it as a statement close to inertia: motion stops only because of an opposing force. Other scholars read the line differently, and it never grew into a physics of motion. Galileo’s achievement was to make the idea precise, test it, and build on it.
What to keep
- Galileo slowed falling down on a ramp, timed it with water, and found that distance grows with the square of time on any slope.
- By reasoning toward limiting cases, he concluded that heavy and light bodies fall together, and that without friction motion continues forever: the law of inertia.
- Rest and steady motion are equivalent and relative, which overturned Aristotle’s physics.
- The lesson for everyone: understanding means building a simplified model and reasoning about it from first principles.
Think it over
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Sources and further reading
- Galileo Galilei, Two New Sciences, 1638; trans. Stillman Drake, University of Wisconsin Press, 1974.
- Albert Einstein and Leopold Infeld, The Evolution of Physics, Simon & Schuster, 1938.
- Stillman Drake, Galileo at Work: His Scientific Biography, University of Chicago Press, 1978.
- David C. Lindberg, The Beginnings of Western Science, 2nd ed., University of Chicago Press, 2007.