Hofstra Horizons Research

Galileo’s Muse: A Tale of Creativity and Insight

Benjamin Wolff
Adjunct Assistant Professor of Music

How the Brain Helps Control Our Behavior.

The year is 1604. A young Italian scientist sits alone in his workshop surrounded by the apparatus of his experiments – pendulums, bronze balls, wooden boards, and planes of various lengths. For months on end he has been trying to fi gure out how objects move. But now, in frustration, he realizes that his eye is just not quick enough, and his clocks not precise enough for the measurements that he desperately needs. Troubled by his failure he walks to the corner of his workshop and picks up his beloved lute. He tunes its strings and begins to play. Then, as music fi lls the space around him, he has an idea …

Narration from Galileo’s Muse, 2009

The great conductor, composer, and teacher Leonard Bernstein once made a statement about learning that I have remembered and treasured ever since I heard it. “The very best way to know a thing,” he said, “is in the context of another discipline.” Extolling this kind of exploration can seem out of fashion today, when our students are often encouraged to specialize and narrow their focus as the best way to get ahead. Without interdisciplinary exposure, however, our ability to be imaginative in developing new ideas and creative in solving problems is invariably diminished. I believe that it is only when we engage in wide-ranging and continued discovery in areas outside our own fi elds that we invite the kind of observations that spark new ideas and that make it possible for us to think in fresh ways about the things that are most familiar.

For the past few years I’ve been working on a performance project that offers a unique perspective on the value of thinking across disciplines. Galileo’s Muse tells the story of a remarkable kind of insight from one of history’s most innovative minds. Through music and words, it reveals how a breakthrough idea can come from where we least expect it, demonstrating one of the most powerful techniques of truly creative people — how they use their knowledge and expertise in one area to solve problems in another.

Background

Like the lesson it communicates, this project had its beginnings in chance and simple curiosity. Several years ago I happened across a fascinating and delightful book by Stony Brook Professor of Philosophy Robert Crease, titled The Prism and the Pendulum: The Ten Most Beautiful Experiments in Science. In the chapter on Galileo’s experiment of the inclined plane (one of the foundation experiments of modern science), Crease relates that, according to the late Galileo expert and science historian Stillman Drake, music held the key to one of Galileo’s most important scientifi c accomplishments – the formulation of his “Law of Falling Bodies.” Few people are aware of this (I certainly wasn’t at the time), but Galileo came from a family of respected professional musicians. His father, Vincenzo Galilei, was a well-known lute player, composer, and musical theorist in late 16th-century Florence. His younger brother Michelagnolo, also a lute player and composer, worked and performed at royal courts throughout Europe. And Galileo was an accomplished lute player himself – his music a constant companion throughout his life.

As a musician, and having recently performed the early Italian baroque music of Galileo’s time, I perked up on reading this – not at all expecting a reference to music in a book on science. It seems that, in addition to Galileo’s brilliance as a theorist, Stillman Drake was arguing for a greater appreciation of Galileo’s exceptional skill and creativity as an experimental scientist. After carefully examining a particular page in Galileo’s laboratory notebooks (folio 107v) that documents his work with inclined planes, Drake concluded that Galileo turned to his thorough musical training to help him equalize short intervals of time, leading him to the revolutionary conclusion that for an object falling freely, the distance from fall is always proportional to the square of the elapsed time.

Of course, this is Drake’s personal interpretation of 400-year-old laboratory data, but, as related in Crease’s book (and in Drake’s original research), I found it absolutely compelling and, being a musician, began immediately thinking of a way to bring this wonderfully elegant intersection of art and science off the page and onto the stage. With the right kind of presentation, it seemed to me that an audience from either discipline might learn from an important historical example that imagination shouldn’t have boundaries and that insight often comes from the most unexpected places. Actually creating that presentation took several years, but the fi nished piece has convinced me that my motivations were correct.

Galileo’s Muse – a combination of theater, music, and science demonstration – employs the combined forces of two baroque violins, baroque cello, lute and theorbo (bass lute), as well as a modern re-creation of Galileo’s inclined plane. With material from Drake’s writings, Galileo’s notebooks, contemporary accounts, rarely heard pieces by Galileo’s composer father and brother, and other music of Galileo’s time (composers such as Andrea Falconiero, Giovanni Legrenzi, and Tarquinio Merula), along with a liberal dollop of my own imagination to fi ll gaps in the story, the complete show is about an hour long. During the course of a performance, I wear many hats (though not literally). I narrate Galileo’s thoughts and discoveries, I demonstrate his experiment of the inclined plane, and I play baroque cello in the musical interludes, moving back and forth between all three roles. It keeps me quite busy! Unfortunately, a musical and theatrical performance doesn’t naturally translate onto the page, but, in a considerably shortened form, here is a description of the sights, sounds and some of the narration that you’d experience at a performance of Galileo’s Muse.

Synopsis of the Performance

Imagine a stage – violins, lutes, and cello in a shallow semicircle – an inclined plane at the front and to the left. The lights dim. A grainy video fi lls a screen that hangs across the back of the stage. Astronaut David Scott of the 1971 Apollo 15 mission stands in his spacesuit on the surface of the moon. He holds a feather in one hand and a hammer in the other. “One of the reasons we got here today,” he says, “is because of a gentleman named Galileo a long time ago who made a rather signifi cant discovery about falling objects in gravity fi elds. And we thought, where would be a better place to confi rm his fi ndings than on the moon? So I’ll drop the two of them here and, hopefully, they’ll hit the ground at the same time. [They do] How about that! Mr. Galileo was correct in his fi ndings.” As the video fades and the lights come up, a pair of lutes perform a ricercar composed by Vincenzo Galilei. And then the story begins …

The year is 1583. It is August – a hot summer’s day in the northern Italian city of Florence. A young university student, home for summer vacation, is taking a walk through his favorite city. All morning he has been playing lute duets with his father Vincenzo, a noted lute player and composer. But now in the mid-afternoon heat he is more than happy to be outside. He strolls along the river Arno, crosses it at the Ponte Alle Grazie, and heads towards the center of the city. When he reaches the Piazza della Signoria though, he fi nds himself surprised by an afternoon thunderstorm. Sheltering beneath a covered gallery of a nearby palazzo he waits there for the storm to pass. As the storm rages our student sees something he has never noticed before. The hailstones falling in the piazza are not all the same size. Some are small. Others are large. But since the storm began, both small and large hailstones have been falling together, and hitting the ground simultaneously. He’s puzzled by this, because all year long his professors at the university have been teaching that the speed of a falling object depends solely on its weight – that heavy objects fall faster than lighter ones. But now, watching the hailstones he wonders. If this is true shouldn’t he be seeing all the large hailstones falling fi rst, and then all the small ones? His professors at the University seem comfortable with things as they are. But he is no longer quite so sure …

It is now 1604. Twenty one years have passed since that afternoon storm, but in all this time Galileo has not forgotten what he saw in the Piazza della Signoria. Now chair of the mathematics department at the University of Padua, he is still consumed by the desire to understand the motion of falling bodies. As he sees it, there is nothing more essential and more profound in all of nature than how objects move. This is what he desperately wants to know: How an arrow fl ies from the bowstring. How a hailstone falls from the sky. Even how the planets in the heavens make their celestial rounds. But most importantly, he wants to be able to describe that motion precisely – with mathematics.

But how will he get there? How will he do this? Correctly reasoning that rolling is a form of falling, and that with a slowed descent he will be able to observe the acceleration of a descending object, Galileo constructs a gently inclined plane. On this plane his chosen object, a metal ball, will be able to “ fall” more slowly towards the ground. Galileo is thrilled with his ingenuity but quickly realizes that he has only partially solved his problem. Why? Because he still has no way to accurately measure the increasing speed at which the ball descends. He can see the acceleration but he can’t yet measure it.

As he mulls over this problem he again goes to his lute – now it is his inspiration, his favorite muse. He gazes at its fi ngerboard. He admires the wonderful patterns of horizontal strings and vertical frets. And then, bit by bit, the solution begins to come to him. He will treat his inclined plane just like the fi ngerboard of a lute and attach a similar series of moveable frets. As the rolling ball passes over each fret it will hop ever so slightly, and then make an audible “click” as it falls back to the surface of the plane. However, instead of placing the frets on his plane an equal distance from one another, he will move the frets further and further apart – just like the frets on a lute. How far apart will he move them? Well, his musician’s ear will guide him. He will roll ball after ball and, listening carefully, adjust the spacing of the frets after each roll so that the clicks made by the accelerating ball will be even and steady as the ball accelerates down the plane.

An accomplished lute player and trained musician, Galileo knows that he can keep a steady beat. He has been cultivating this rhythmic skill since he was a child taking music lessons from his father. Back then, of course, he never would have imagined it, but that skill, that ability to keep a steady beat will now make it possible for him to determine precisely the properties of acceleration.

Previously he could only see that the ball speeds up, but now, thanks to his frets, he can tell that it gets faster gradually and continuously. By adding frets to his inclined plane Galileo has found an ingenious way to divide continuous time into distinct units. And this is what he finds:

From the time the ball is released until it passes over the fi rst fret it travels a certain distance. When it reaches the second fret he fi nds that it has traveled four times as far. By the time he hears it passing the third fret it has gone nine times the distance. At the fourth fret it has traveled sixteen times as far. When it reaches the fifth fret it has gone 25 times as far. And at the sixth fret he finds that it has gone exactly 36 times the distance.

Galileo no longer has any doubt about it. The acceleration of an object falling freely is continuous and the rate of that acceleration is constant. The distance from fall is always proportional to the square of the elapsed time.

He smiles. So this is the sound of success. These even clicks of a metal ball rolling over thin gut frets. It is truly music to his ears …

Narration from Galileo’s Muse, 2009

Audience Response and Future Plans

Galileo’s Muse was first performed in summer 2007. In 2008 it was presented at CUNY’s Science and the Arts series, at Salisbury University, and at Hofstra’s Institute for the Development of Education in the Advanced Sciences (IDEAS). Most recently, I’ve performed it at the Association for Manufacturing Excellence (AME) 2009 National Conference, and at Rice University’s Shepherd School of Music in a special collaboration with Dr. Don Pettit, NASA astronaut and a wonderfully Galileo-like inventor himself. Initially, I anticipated that interest in and support for this interdisciplinary project would come, naturally, from two primary groups – arts organizations, presenting this performance as a way to reach new audiences; and the scientifi c community, as a model for how other disciplines can communicate basic scientific principles in an engaging manner. But reaction and responses from audiences have also provided me with unexpected ideas for future applications:

  • As an elegant and historical example of “Gemba,” a Japanese term used in Lean manufacturing (originally from the Toyota Production System) to describe the process of using all of one’s senses to investigate problems. It was practitioners at the AME who inspired me to make the connection between this important Lean principle and Galileo’s observing that his lute and a sense of rhythm could solve a problem of measurement.
  • As a way for students and teachers to experience the pathways of innovative thinking.Galileo’s Muse demonstrates creativity in real time – inviting an audience to enter Galileo’s mind, to join his creative process, to see what he saw, to hear what he heard, even to feel what he felt. At an October 2008 performance at Hofstra’s IDEAS Institute, it was tremendously rewarding to observe the many science teachers who joined the performers on the stage after the show. They handled the lutes, felt the frets under their fingers, and even rolled a few balls down the inclined plane, perhaps imagining themselves in Galileo’s workshop 400 years ago.

Reflections

Galileo observed hailstones falling in the piazza and wondered how they fell. He looked with fresh eyes at the familiar gut frets tied to the fi ngerboard of his lute and thought of putting them to a completely new purpose. He trusted his internal sense of rhythm when confronted by the limitations of the machines of his day. The genius of Galileo, I believe, was the way he lived his life with a truly open mind.

And that is an attitude, an approach to living that all of us can emulate. Whether we are students or teachers, scientists, artists, or pursuing our dreams in other areas – the ability to look for, and find insight in, the most common things is our creative birthright. All we need to do is open our eyes, open our ears and, most importantly, open our minds.

References:

Crease, R. (2004). The Prism and The Pendulum: The Ten Most Beautiful Experiments in Science. New York: Random House, Inc.

Drake, S. (1975). The Role of Music in Galileo’s Experiments. Scientifi c American (232: June 1975).

Drake, S. (1978). Galileo at Work: His Scientific Biography. New York: Dover Publications.

Drake, S. (1989). History of Free Fall: Aristotle to Galileo. Toronto, Canada: Wall & Thompson.

Hawking, S. (2002). Dialogues Concerning Two New Sciences [Galileo Galilei. Edited, with Commentary, by Stephen Hawking]. Philadelphia: Running Press Books.

Isacoff, S. (2003) Temperament: How Music Became a Battleground for the Great Minds of Western Civilization. New York: Random House, Inc.

Palisca, C. (1980) Vincenzo Galilei, in The New Grove Dictionary of Music and Musicians. Volume 7, 96-98, London, UK: MacMillan.

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