To Explain the World: The Discovery of Modern Science (27 page)

In February 1616 Galileo was summoned to the Inquisition and received two confidential orders. A signed document ordered him not to hold or defend Copernicanism. An unsigned document went further, ordering him not to hold, defend, or teach Copernicanism in any way. In March 1616 the Inquisition issued a public formal order, not mentioning Galileo but banning Foscarini’s book, and calling for the writings of Copernicus to be expurgated.
De Revolutionibus
was put on the Index of books forbidden to Catholics. Instead of returning to Ptolemy or Aristotle, some Catholic astronomers, such as the Jesuit Giovanni Battista Riccioli in his 1651
Almagestum Novum,
argued for Tycho’s system, which could not then be refuted by observation.
De Revolutionibus
remained on the Index until 1835, blighting the teaching of science in some Catholic countries, such as Spain.

Galileo hoped for better things after 1624, when Maffeo Barberini became Pope Urban VIII. Barberini was a Florentine and an admirer of Galileo. He welcomed Galileo to Rome and granted him half a dozen audiences. In these conversations Galileo explained his theory of the tides, on which he had been working since before 1616.

Galileo’s theory depended crucially on the motion of the Earth. In effect, the idea was that the waters of the oceans slosh back and forth as the Earth rotates while it goes around the Sun, during which movement the net speed of a spot on the Earth’s surface along the direction of the Earth’s motion in its orbit is continually increasing and decreasing. This sets up a periodic ocean wave with a one-day period, and as with any other oscillation, there are overtones, with periods of half a day, a third of a day, and so on. So far, this leaves out any influence of the Moon, but it had been known since antiquity that the higher “spring”
tides occur at full and new moon, while the lower “neap” tides are at the times of half-moon. Galileo tried to explain the influence of the Moon by supposing that for some reason the Earth’s orbital speed is increased at new moon, when the Moon is between the Earth and the Sun, and decreased at full moon, when the Moon is on the other side of the Earth from the Sun.

This was not Galileo at his best. It’s not so much that his theory was wrong. Without a theory of gravitation there was no way that Galileo could have correctly understood the tides. But Galileo should have known that a speculative theory of tides that had no significant empirical support could not be counted as a verification of the Earth’s motion.

The pope said that he would permit publication of this theory of tides if Galileo would treat the motion of the Earth as a mathematical hypothesis, not as something likely to be true. Urban explained that he did not approve of the Inquisition’s public order of 1616, but he was not ready to rescind it. In these conversations Galileo did not mention to the pope the Inquisition’s private orders to him.

In 1632 Galileo was ready to publish his theory of the tides, which had grown into a comprehensive defense of Copernicanism. As yet, the church had made no public criticism of Galileo, so when he applied to the local bishop for permission to publish a new book it was granted. This was his
Dialogo
(
Dialogue Concerning the Two Chief Systems of the World—Ptolemaic and Copernican
).

The title of Galileo’s book is peculiar. There were at the time not two but
four
chief systems of the world: not just the Ptolemaic and Copernican, but also the Aristotelian, based on homocentric spheres revolving around the Earth, and the Tychonic, with the Sun and Moon going around a stationary Earth but all other planets going around the Sun. Why did Galileo not consider the Aristotelian and Tychonic systems?

About the Aristotelian system, one can say that it did not agree with observation, but it had been known to disagree with observation for two thousand years without losing all its
adherents. Just look back at the argument made by Fracastoro at the beginning of the sixteenth century, quoted in
Chapter 10
. Galileo a century later evidently thought such arguments not worth answering, but it is not clear how that came about.

On the other hand, the Tychonic system worked too well for it to be justly dismissed. Galileo certainly knew about Tycho’s system. Galileo may have thought his own theory of the tides showed that the Earth does move, but this theory was not supported by any quantitative successes. Or perhaps Galileo just did not want to expose Copernicus to competition with the formidable Tycho.

The
Dialogo
took the form of a conversation among three characters: Salviati, a stand-in for Galileo named for Galileo’s friend the Florentine nobleman Filippo Salviati; Simplicio, an Aristotelian, perhaps named for Simplicius (and perhaps intended to represent a simpleton); and Sagredo, named for Galileo’s Venetian friend the mathematician Giovanni Francesco Sagredo, to judge wisely between them. The first three days of the conversation showed Salviati demolishing Simplicio, with the tides brought in only on the fourth day. This certainly violated the Inquisition’s unsigned order to Galileo, and arguably the less stringent signed order (not to hold or defend Copernicanism) as well. To make matters worse, the
Dialogo
was in Italian rather than Latin, so that it could be read by any literate Italian, not just by scholars.

At this point, Pope Urban was shown the unsigned 1616 order of the Inquisition to Galileo, perhaps by enemies that Galileo had made in the earlier arguments over sunspots and comets. Urban’s anger may have been amplified by a suspicion that he was the model for Simplicio. It didn’t help that some of the pope’s words when he was Cardinal Barberini showed up in the mouth of Simplicio. The Inquisition ordered sales of the
Dialogo
to be banned, but it was too late—the book was already sold out.

Galileo was put on trial in April 1633. The case against him hinged on his violation of the Inquisition’s orders of 1616. Galileo was shown the instruments of torture and tried a plea bargain,
admitting that personal vanity had led him to go too far. But he was nevertheless declared under “vehement suspicion of heresy,” condemned to eternal imprisonment, and forced to abjure his view that the Earth moves around the Sun. (An apocryphal story has it that as Galileo left the court, he muttered under his breath, “Eppur si muove,” that is, “But it does move.”)

Fortunately Galileo was not treated as roughly as he might have been. He was allowed to begin his imprisonment as a guest of the archbishop of Siena, and then to continue it in his own villa at Arcetri, near Florence, and near the convent residence of his daughters, Sister Maria Celeste and Sister Arcangela.
²⁷
As we will see in
Chapter 12
, Galileo was able during these years to return to his work on the problem of motion, begun a half century earlier at Pisa.

Galileo died in 1642 while still under house arrest in Arcetri. It was not until 1835 that books like Galileo’s that advocated the Copernican system were removed from the Index of books banned by the Catholic church, though long before that Copernican astronomy had become widely accepted in most Catholic as well as Protestant countries. Galileo was rehabilitated by the church in the twentieth century.
²⁸
In 1979 Pope John Paul II referred to Galileo’s
Letter to Christina
as having “formulated important norms of an epistemological character, which are indispensable to reconcile Holy Scripture and science.”
²⁹
A commission was convened to look into the case of Galileo, and reported that the church in Galileo’s time had been mistaken. The pope responded, “The error of the theologians of the time, when they maintained the centrality of the Earth, was to think that our understanding of the physical world’s structure was, in some way, imposed by the literal sense of the Sacred Scripture.”
³⁰

My own view is that this is quite inadequate. The church of course cannot avoid the knowledge, now shared by everyone, that it had been wrong about the motion of the Earth. But suppose the church had been correct and Galileo mistaken about astronomy. The church would still have been wrong to sentence Galileo to imprisonment and to deny his right to publish, just as
it had been wrong to burn Giordano Bruno, heretic as he was.
³¹
Fortunately, although I don’t know if this has been explicitly acknowledged by the church, it would not today dream of such actions. With the exception of those Islamic countries that punish blasphemy or apostasy, the world has generally learned the lesson that governments and religious authorities have no business imposing criminal penalties on religious opinions, whether true or false.

From the calculations and observations of Copernicus, Tycho Brahe, Kepler, and Galileo there had emerged a correct description of the solar system, encoded in Kepler’s three laws. An
explanation
of
why
the planets obey these laws had to wait a generation, until the advent of Newton.

12

Experiments Begun

No one can manipulate heavenly bodies, so the great achievements in astronomy described in
Chapter 11
were necessarily based on passive observation. Fortunately the motions of planets in the solar system are simple enough so that after many centuries of observation with increasingly sophisticated instruments these motions could at last be correctly described. For the solution of other problems it was necessary to go beyond observation and measurement and perform experiments, in which general theories are tested or suggested by the artificial manipulation of physical phenomena.

In a sense people have always experimented, using trial and error in order to discover ways to get things done, from smelting ores to baking cakes. In speaking here of the beginnings of experiment, I am concerned only with experiments carried out to discover or test general theories about nature.

It is not possible to be precise about the beginning of experimentation in this sense.
¹
Archimedes may have tested his theory of hydrostatics experimentally, but his treatise
On Floating Bodies
followed the purely deductive style of mathematics, and gave no hint of the use of experiment. Hero and Ptolemy did experiments to test their theories of reflection and refraction, but their example was not followed until centuries later.

One new thing about experimentation in the seventeenth
century was eagerness to make public use of its results in judging the validity of physical theories. This appears early in the century in work on hydrostatics, as is shown in Galileo’s
Discourse on Bodies in Water
of 1612. More important was the quantitative study of the motion of falling bodies, an essential prerequisite to the work of Newton. It was work on this problem, and also on the nature of air pressure, that marked the real beginning of modern experimental physics.

Like much else, the experimental study of motion begins with Galileo. His conclusions about motion appeared in
Dialogues Concerning Two New Sciences
, finished in 1635, when he was under house arrest at Arcetri. Publication was forbidden by the church’s Congregation of the Index, but copies were smuggled out of Italy. In 1638 the book was published in the Protestant university town of Leiden by the firm of Louis Elzevir. The cast of
Two New Sciences
again consists of Salviati, Simplicio, and Sagredo, playing the same roles as before.

Among much else, the “First Day” of
Two New Sciences
contains an argument that heavy and light bodies fall at the same rate, contradicting Aristotle’s doctrine that heavy bodies fall faster than light ones. Of course, because of air resistance, light bodies do fall a little more slowly than heavy ones. In dealing with this, Galileo demonstrates his understanding of the need for scientists to live with approximations, running counter to the Greek emphasis on precise statements based on rigorous mathematics. As Salviati explains to Simplicio:
²

Aristotle says, “A hundred pound iron ball falling from the height of a hundred braccia hits the ground before one of just one pound has descended a single braccio.” I say that they arrive at the same time. You find, on making the experiment, that the larger anticipates the smaller by two inches; that is, when the larger one strikes the ground, the other is two inches behind it. And now you want to hide, behind those two inches, the ninety-nine braccia of Aristotle, and speaking only of my tiny error, remain silent about his enormous one.

Galileo also shows that air has positive weight; estimates its density; discusses motion through resisting media; explains musical harmony; and reports on the fact that a pendulum will take the same time for each swing, whatever the amplitude of the swings.
*
This is the principle that decades later was to lead to the invention of pendulum clocks and to the accurate measurement of the rate of acceleration of falling bodies.

The “Second Day” of
Two New Sciences
deals with the strengths of bodies of various shapes. It is on the “Third Day” that Galileo returns to the problem of motion, and makes his most interesting contribution. He begins the Third Day by reviewing some trivial properties of uniform motion, and then goes on to define uniform acceleration along the same lines as the fourteenth-century Merton College definition: the speed increases by equal amounts in each equal interval of time. Galileo also gives a proof of the mean speed theorem, along the same lines as Oresme’s proof, but he makes no reference to Oresme or to the Merton dons. Unlike his medieval predecessors, Galileo goes beyond this mathematical theorem and argues that freely falling bodies undergo uniform acceleration, but he declines to investigate the cause of this acceleration.