Monthly blog archive

About PDX OPERAbeat




PDX OPERAbeat | A Company Blog is the blog for all things Portland Opera, featuring a variety of guest contributors who will provide insider's tidbits on all we do to celebrate the beauty and breadth of opera.

Galieo Galilei: Scenes 5 & 6, Galileo's Experiments

Scenes 5 and 6 are both explorations of Galileo's scientific experiments and findings, so I'm going to talk about them together.

But first: SCIENCE!


Scene 6 is full of SCIENCE! Just so you know, I have been yelling SCIENCE! intermittently, at random, in the middle of the production office backstage. I encourage you to do the same. Except not in the production office, because it's already pretty crowded in there.


Scene 6: Incline Plane There is no singing in this scene; instead, Galileo, in spoken language, expounds on his findings on the inclined plane.

I can't tell you what Philip Glass or Mary Zimmerman intended to happen during the long musical interlude here (because, as I've mentioned previously, all stage directions have been accidentally excluded from the score). What I can tell you is what's happening on our stage, which is, basically, six minutes of gleeful wonder at the process of scientific discovery. IT'S AWESOME!

Using a ladder and a beautiful replica of Galileo's inclined plane, our cast of characters explore three of Galileo's most important scientific experiments.


Falling Bodies
Okay, first, let's just clear this up. Bodies = cannonballs/large weighted objects. Bodies =/= corpses.

[the cast rehearses a section of Scene 6]

Early in his career as mathematician at the University of Pisa, Galileo allegedly climbed, along with his students, the eight stories of the Leaning Tower with a collection of differently sized cannonballs. Reaching the top, he dropped balls of differing weights from the tower to see whether the weight of the falling body affected the speed of its fall -- which, he proved, it did not.


Let's backtrack for a second. Prior to Galileo's experiments from the Leaning Tower, Aristotelian physics asserted that objects of different weights fall at different speeds, completely dependent on their weight. So, according to Aristotle, a 10-pound cannonball would fall exactly 10 times faster than a 1 pound cannonball. Galileo knew, even without experimentation, that this idea was patently absurd: imagine dropping a one pound and a ten pound weight simultaneously, and having the one pound ball travel a distance of only ten meters, while the ten pound weight travels one hundred.


Of course, Galileo's findings were that, regardless of weight, objects fall at the same speed. However, when he demonstrated this for some of his colleagues, they found that the hundred-pound cannonball Galileo used landed just before the one-pound ball, and thus declared his findings inaccurate.


"Aristotle," wrote a frustrated Galileo, "says that a hundred-pound ball falling from a height of a hundred braccia (arm lengths) hits the ground before a one-pound ball has fallen one braccio. I say they arrive at the same time. You find, on making the test, that the larger ball beats the smaller one by two inches. Now, behind those two inches you want to hide Aristotle's ninety-nine braccia and, speaking only of my tiny error, remain silent about his enormous mistake."


On a slight alteration of the above experiment, Galileo dropped one cannonball, while the other he pushed away from the tower (or threw it, essentially), making sure to keep the toss parallel to the ground (rather than arcing it in an upward motion).


Which one would drop first? The one falling straight, or the one traveling both horizontally and vertically? The experiment concluded -- again, as Galileo presumed it would -- that despite one ball's horizontal travel, the two landed at the same time. This is because the vertical distance traveled by the two projectiles is the same; therefore, the force of gravity exerted on the two is equal.


As an aside: NOVA has an absolutely excellent website on this experiment, which you can play with here. The demonstration there includes a ball dropped from the mast of a moving ship, which is observed both from the mast itself and from the shore. From the mast, the dropped ball appears to travel in a straight line from mast to deck; from the shore, the ball appears to travel in a curved line as, while falling, it follows the motion of the ship. In one motion, the ball represents both the dropped projectile and the thrown one (depending on the observer); the experiment proves that the two balls will hit the ground simultaneously. So elegant!

Inclined Plane
Galileo's experiments with the inclined plane were prompted by his experiments on falling bodies; he wanted to study acceleration in greater detail. The inclined plane allowed the observer to study the behavior of falling objects essentially in "slow motion," as it allowed the ball to be affected by gravity (just as it would be in free fall) while impeding its motion enough for more detailed observation.

inclined plane
[André Chiang, as Galileo, rehearses the spoken dialogue in Scene 6]


At, for example, a 60% grade, a ball rolled down the plane would essentially be traveling almost at the same speed as it would in freefall; but at a 30% grade, the ball would be slowed enough for its motion to be observed. Galileo saw that a ball rolled down the plane traveled faster and faster, until at the bottom it rolled on the horizontal plane. At this point, Galileo reasoned, gravity is no longer accelerating the motion of the ball; instead, the effect of gravity is now uniform, meaning that the ball, unimpeded, will roll forever. Thus, Galileo discovered one of the laws of inertia.


One of the ways that Galileo timed this -- since, of course, stopwatches didn't exist -- was to use bells, positioned at precise lengths along the inclined plane, which the ball, rollng downward, would ring. Galileo discovered that in the first second, the ball would cover the distance of one unit (say, a meter); in the next second the ball covered three times this distance (three meters), in the next; five. It did not matter how steep he made the incline; the bells, set at these increments, tolled in precise rhythm as the ball descended. In this way, Galileo discovered that acceleration acting uniformly on a falling object does so in such a way that the distance covered is directly proportional to the square of time. D = T^2. If a ball takes 4 seconds to fall, it's traveled 16 units.




So, that's Scene 6 -- lots of experiments at work. Plus the music is really rocking.


Scene 5: Dialogue Concerning the Two Chief Systems of the World

the gondola

The title of Scene 5 is a reference to Galileo's seminal publication of the same title, published, after many years of work, in 1632. The Dialogue compares the Copernican system of the universe (heliocentric) with the Ptolemaic and Aristotelian view of the universe (geocentric).

The form of the work was, as the title suggests, that of a dialogue, an ancient Greek form where two speakers debate an argument. In Galileo's work, a third voice was added, an independent observer who serves as a sort of master of ceremonies.


The three characters of the Dialogue are as follows:

Sagredo: Named for Giovanni Francesco Sagredo, a wealthy nobleman nine years younger than Galileo, and a close friend, who often lent money to the astronomer. In the Dialogue, Sagredo serves as the independent observer.


Salviati: Named for Filippo Salviati, another close friend, whom Galileo met in Tuscany upon being appointed Court Mathematician. A wealthy nobleman twenty years Galileo's junior, Salviati was interested in science, and loved good food and fine wine. Galileo occasionally visited his home to convalesce during his many illnesses. The voice of Salviati in the Dialogue is essentially that of Galileo himself.

Simplicio: The name was a reference to an ancient Greek who'd written a commentary on Aristotle's work, although readers at the time could not fail to notice the implication that this character was to be considered a "simpleton." In the text, Simplicio is a believer in the systems of Ptolemy and Aristotle, and presents the traditional arguments against the Copernican system; in part, he is modeled loosely after two acquaintances of Galileo's, including a colleague of his at Padua who had steadfastly refused to look through the telescope

. gondola rehearsal

In this scene, Sagredo, Salviati, and Simplicio are aboard a gondola in Venice, where they begin to converse about the movement of the earth. Sagredo greets the other two, and suggests that Simplicio may need some convincing about the things they have previously been speaking about: sunspots, planets, and tides.

"The sunspots you spoke of imply the sun, which is perfect, is not," Simplicio says. "And this motion of the earth you imply would mean that our earth might be altered, might be base, uncertain, and lost."

Salviati counters that of course the earth might be altered: if change were the rare thing, he says, then princes would be trading diamonds and gold -- those unchanging elements -- for a tiny bit of changeable soil.

But if the earth moves, argues Simplicio, then how do the birds keep up? And why isn't there a tremendous wind all the time?

"Because the earth, dear Simplicio," answers Salviati, "carries with it part of the air. Think of a boat on the ocean -- think of yourself below deck. You find a bowl of water with fish, and the air full of butterflies and birds. The ship might be sailing from Venice to Cairo and back, but the fish in the bowl swim where they will, and the butterflies fly where they please."

"I cannot imagine this earth moves," says Simplicio, stubbornly. "I know I would feel it move."

Salviati explains: "A person born in a forest, and passing his life there, could never imagine a world other than maples and elms; could never imagine the heaving ocean and its creatures who move without wings or legs. The quickest mind in its quickest way cannot know what it does not know -- and the coward's mind, like a horse, starts back from its own shadow."

Ouch, Salviati. Ouch.

The two men momentarily reach an impasse, but with Sagredo's gentle urging, they finally agree that the human mind is the most beautiful of all of God's instruments, and that the mind was made for asking questions of all things.

gondola rehearsal

This segment of a recent episode of Radiolab begins with a really interesting discussion of how Galileo's discoveries on projectiles led Isaac Newton to accidentally discover how bodies orbit.

NOVA lets you play with inclined planes and falling bodies.

My explanations on other scenes of the opera:
Scene 7

Scene 8
Scene 9

Scene 10