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VI:AN HISTORICAL CASE STUDY -- GALILEO AND THE COPERNICAN THEORY
is written in this grand book - I mean the
universe - which stands open to our gaze, but it cannot be understood
unless one first learns to comprehend the language and interpret
the characters in which it is
written.It is written in the language of mathematics,
and its characters are triangles, circles, and other
geometrical figures, without which it is humanly impossible to
understand a single word of
it; without these, one is wandering about in a dark labyrinth.
us now turn to an example of scientific reasoning in situ.
I have chosen certain episodes in Galileo's life for two reasons:
First, this story is one of the most famous and fascinating in
the history of science. Secondly, it provides excellent material
with which to illustrate the ways in which real life scientific
practice does and does not conform to thehypothetico deductive
controversy over the acceptability of the Copernican theory involved
at least four separable debates. As you study this case it will
be helpful to keep the following four topics in mind:
Astronomical Dispute: What were the competing models of the
universe? What was the evidence for and against each?
Dispute in 'Physics: What were the competing theories of
motion? What was the evidence for and against each?
The Religious Dispute : What were the competing theories
about the proper relationship between the Bible and science?
What were the arguments on each side?
Methodological Debate: Was Galileo introducing new scientific methods as
well as new scientific theories?
- Although the
story I tell below is intended to be roughly correct and certainly
not seriously misleading, at times I have oversimplified things
slightly. And since there is an ever-growing body of historical
information about this period, my story (and the secondary sources
on which I relied) may very well be out-of-date at some points.
- I.Life Begins
at Forty-Five 1
- Prior to his
famous telescopic observations, Galileo's scientific career had
not been anything extraordinary. After brief studies at a monastery,
Galileo studied medicine and then mathematics at the University
of Pisa. In 1589, he gained the chair of mathematics there. In
1591 he moved to the University of Padua.
- At that time
mathematics included not only Euclidean geometry but also quantitative
sciences such as astronomy. Most discussions of subjects which
we would include under physics took place within philosophy departments.
One concern of Galileo (and other anti- Aristotelians) was to
introduce mathematical methods into the study of motion. When
Galileo later moved to court at Florence in 1610 he insisted
that his title be "mathematician and philosopher to the
grand duke of Tuscany."
- During this period
Galileo gave lectures on Ptolemaic astronomy. He also knew about
the Copernican system and wrote a letter to Kepler in 1597 in
which he expressed his sympathy towards it. However, he did not
make his sentiments public, although Kepler urged him to.
- At this time
Galileo was much more interested in mechanics than in astronomy.
While at Pisa he wrote, but did not publish, a treatise on motion
(called De Motu) in which he criticized the Aristotelian
account of the motions of
1. Based on Stillman Drake's article on Galileo in The Dictionary
of 'Scientific Biography.
- falling bodies
and projectiles. Galileo's own positive account of motion in
this early work was a variant of the Medieval impetus theory.
It was only later that he arrived at a theory which resembles
the modern account.
- Galileo also
invented several useful practical instruments - a proportional
compass for surveyors, a pendulum device for timing pulses in
hospitals, and a clever little balance to be used for assaying
metals according to their density. In 1606 someone stole his
idea for the proportional compass and so Galileo pressed charges.
Following the custom of the times Galileo also wrote a pamphlet
denouncing the plagiarist: "Difesa . . . contro alle calunnie
& imposture di Baldessar Capra." At the time when Galileo
heard about the telescope (subsequently he sold the idea to the
Venetian government) this pamphlet was his only published work.
- II. Aristotelian
Cosmology and Physics
- Although the
Aristotelian world-view had been criticized and revised in important
ways during the Middle Ages, (Footnote 2) it was the traditional
Aristotelian cosmology and physics which Galileo always set up
as the chief opponent. And to a large extent, people in the Church
and University establishments were Aristotelians.
- According to
Aristotle, the universe is finite. It is convenient to divide
phenomena into two classes: sub lunar (or terrestrial) and celestial.
Below the moon everything is composed of four elements - earth,
air, fire, and water. Each element has associated with it a natural
propensity for motion. Fire and air have levity and tend to go
up (away from the center of the earth). Earth and water are heavy
and tend to go down. Thus the upward motion of smoke (composed
largely of the element air) and the downward motion of a cannon
ball (largely earth) are natural motions requiring no further
explanation. Cannon balls fall faster than cork balls because
they are heavier (they have a larger percentage of the element
earth in them). All objects move faster as they get closer to
their natural place. Th us smoke goes faster and faster as it
flees away from the earth and cannon balls go faster as they
near the center of the earth.
- (1) Aristotle
died in 322 B.C.
- (2 This section
is written with apologies to historians of Medieval Science.
- In addition to
these natural motions, there are also so-called "violent"
motions. All horizontal motions, such as the flight of an arrow,
are violent. Vertical motions are also violent if they are in
an unnatural direction (e.g., when we throw a ball straight up).
Whereas natural motions happen spontaneously, violent motions
have to be forced to occur. They always require a source of motive
power, such as the hand and arm of the person throwing the ball
or the "animal soul" of a wiggling worm.
- The speed of
violent motions increases with the strength of the motive force
and decreases with resistance. For example, a sledge will go
faster if it is pulled by two horses instead of one and slower
if it is pulled through mud instead of on beaten ground.
- One problem for
the Aristotelian was to explain why projectiles, such as an arrow
or ball, continued to move once they ceased to be in contact
with the source of motive power. One proposal was that air was
set in motion by the original action of the bowstring or arm
and somehow continued to
- propel the projectile.
Another more ingenious solution went roughly as follows. As the
projectile moved forward, there was a tendency for a vacuum to
form in its wake. However, since nature abhors a vacuum, air
would swarm in to fill the empty space, thus hitting the rear
of the projectile and propelling it onward.
- According to
Aristotle, things in the celestial domain behaved quite differently.
Heavenly bodies were made out of a fifth element (called the
and in this sphere there was no generation or corruption or change
of any kind. The natural motion for bodies made of the fifth
element was circular. The planets, stars, sun and moon were embedded
in transparent crystalline spheres all of which were inter-nested
like a graduated series of embroidery hoops. The outermost sphere
(called the primum mobile) provided the dominant 24 hour
circular motion shared by all bodies in the celestial system,
although each planet, etc., also had its own proper motion, too.
- A popular analogical
model which was used for pedagogical purposes in the Middle Ages
was the following: Imagine a round solid wheel rotating on its
axis. Suppose that there are also circular grooves on the wheel
populated by marching ants. Here the wheel corresponds to the
- which carries
the stars around every 24 hours and the ants correspond to the
sun, moon and planets. An ant's total motion is compounded of
two parts - the basic motion of the wheel (shared by all ants)
and its own proper motion as it walks along the wheel.
- III. Ptolemaic
(1) Astronomy (2)
- The simple concentric
sphere model of the universe described above gave a rough, qualitative
account of what we can observe in the sky, but it didn't get
the details right. In particular, it failed to explain the retrograde
motion of the planets - the fact that at certain times the planets
appear to move backwards.
- In order to obtain
a more accurate theoretical modelling of what we actually observe
in the sky, Ptolemy introduced various geometrical devices, the
most famous being the epicycle. If we were to develop our ants-on-
the wheel analogy, we would have to imagine the ants moving along
the groove on a little Tilt-a-whirl!
- The proper motion
of a planet moving on an epicycle can be diagrammed as follows:
[See Kuhn figure 19, p. 61]
- By a judicious
adjustment of the sizes and velocities of the big circle (called
the deferent) and the little circle (the epicycle) one could
hope to reproduce both the velocity and duration of the retrograde
motion. Note that on this model, the planet is closer to
the earth when it is in retrograde motion and hence we should
expect it to appear biggest and brightest
- (1)Ptolemy flourished
A.D. His book on
astronomy was called the Almagest.
- (2)For more details
see T. S. Kuhn The Copernican Revolution.
- at this time. This
effect is in fact observed, and is especially dramatic in the
case of Mars.
- Although the epicycle
was a useful geometrical device for "saving the phenomena"
it was difficult to make a realistic physical model of it. (Some
made the deferent into a hollow tube and had a solid epicycle
rolling around in it like a marble.
- Ptolemy himself sometimes
treated his theory simply as a useful calculating device or instrument
and did not claim that it was a true physical description.
- IV.The Medieval
Impetus Theory (1)
- During the Middle
Ages, there was much piece-meal criticism of Aristotle's natural
philosophy. We will mention only a few of the revisions in his
theory of motion. In order to handle the problem of projectile
motion, it was suggested that as they were hurled a certain degree
of motive force was impressed on them. This impressed force or
impetus kept them moving until it was used up in combatting the
resistance of the medium.
- Impetus was analogous
to heat - it takes effort to raise the temperature of a body,
but once it is heated up it will stay hot until the heat dissipates
into a cooler environment.
- The impetus theory
explained natural motion as the result of a constant tendency
(or conatus) of a body to move towards its natural place.
Falling bodies speed up because the conatus continues to act
as it falls thus giving the body more and more impetus.
- When we throw
a body upward it moves more and more slowly until its remaining
impetus upward just balances the conatus downward. At that moment
it is stationary; then the conatus takes over and it falls slower
and slower to the ground.
- One important
contributor was Nicole Oresme, 1323-82.
- Medieval philosophers
also proposed a quantitative account of the motion of falling
- Let y be
the velocity of a falling body and x be the time elapsed.
Since triangle ABC is equal in area to the rectangle 1/2 AB.AC,
we see that the distance traversed by a uniformly accelerated
body is the same as that covered by a body moving at the given
initial and final velocities.
- The "Mean
Speed Theorem", as it was called, provided a simple method
for integrating under a curve and as such was a quite legitimate
piece of mathematics. However, medieval philosophers had no way
of knowing whether their curve described motion ofany important
motions in nature such as bodies in free fall because they had
not checked in detail the behavior of falling bodies.
- Actually it is
rather difficult to do a direct experimental test of the Mean
Speed Theorem because bodies fall so rapidly. (A ball dropped
from the top of a ten-story building takes only about three seconds
to hit the ground.)
measured distances and times for balls rolling down
inclined planes and this provided an indirect test of the Mean
- In De revolutionibus
orbium caelestium, published just after his death
in 1543, Copernicus
put forward a detailed heliocentric system of the universe, Like
Ptolemy's system it was constructed out of circles (Kepler introduced
elliptical orbits in 1609-1619). It was superior to Ptolemy's
in two major respects. First, it gave more accurate predictions
as to exactly where the heavenly bodies would be seen at any
given time. This improved accuracy was not due to any intrinsic
superiority of the Copernican system, but arose simply because
he had used more up-to-date observations in fixing the various
orbital parameters. The second advantage of the new
- (1) For a charming
account of the personalities as well as the scientific achievements
of the characters in this story, see Arthur Koestler's The Sleepwalkers.
Koestler calls Copernicus (1473-1543) "the timid canon".
- system was the
fact that it was supposedly simpler. Although Copernicus used
at least as many circles as Ptolemy did (hence the overall simplicity
of the new system was hardly greater), his theory did have one
impressive feature: It was not necessary to introduce epicycles
to explain the existence of retrograde motion. The qualitative
aspects of the retrograde motions of both the superior and inferior
planets were a natural result of the basic geometry of the situation.
Since the earth was moving around the sun with all the other
planets, it was relatively easy to see that sometimes they might
appear to be moving backwards - for example, when the earth passed
the outer planets which were moving more slowly.
- There were some
other technical qualitative advantages to Copernicus' system
which appealed to astronomers. However, it presented real problems
for the physicists.
- In his introductory
chapter, Copernicus tried to suggest a modification of the Aristotelian
doctrine of natural motions. But his system required that the
earth have two "natural" motions. One, the yearly revolution
around the sun, wasn't so bad - at least the other planets also
moved this way. But the daily rotation around its axis caused
all sorts of problems. None of the other heavenly bodies were
observed to spin. And if the earth was whirling around like a
great wheel, why didn't things fly off like mud from the rim
of a spinning wheel? Why weren't there terrible winds?
- Copernicus hinted
at a couple of possible answers but he didn't work them out in
detail.Neither did he offer any arguments for either of them:
the contiguous air contains an admixture of earthy or watery
matter and so follows the same natural law as the Earth, or perhaps
the air acquires motion from the perpetually rotating Earth by
propinquity and absence of resistance[De revolutionibus, Section
- Even though the
Copernican system desperately needed the foundations which only
a new physics could provide, it might still have been taken as
a serious new cosmological conjecture had it not been for its
- The story of
the publication of De revolutionibus is a very complicated
one, full of unknowns and ironies. A few of the facts are these.
It is almost certain that Copernicus would never have gotten
around to publishing
anything had not Rheticus, a young enthusiastic Lutheran astronomer
and mathematician, heard about his heliocentric ideas and literally
seduced Copernicus into writing them up.
- Rheticus took
the finished manuscript from Copernicus' house in Frauenburg
up on the Baltic Sea down to Nuremberg and was intending to see
it through publication but had to leave town unexpectedly. (It
seems that he got into trouble because of his liking for what
the Germans call "the Italian perversion".)
- In any case,
another Lutheran, this one a theologian called Osiander, took
over responsibility for the printing. Although Osiander was sympathetic
to the Copernican system, he knew that Luther opposed it and
so he added a preface to the reader in which he proposed that
the heliocentric system not be construed as a realistic description
of the universe but merely as a useful device for making astronomical
- "For these
hypotheses need not be true or even probable ...as far as hypotheses
no one expect anything certain from astronomy, which cannot furnish
he accept as the truth ideas conceived for another purpose [i.e.,
as mere calculating aids], and depart from this study a greater
fool than when he entered it. Farewell."
- Osiander's Preface
accomplished what he intended it to. Copernicus' system
became popular as a basis for making calendars and star charts.
But for a long time it had little impact on pure science.
- VI.Galileo's Telescopic
- In 1609 Galileo heard about
the newly invented telescope and designed one which was good
enough for astronomical observations. By March, 1910, he had
already made a series of discoveries which refuted or at least
seriously undermined several features of Aristotle's cosmology.
- First of all, he "observed"
(we will return later to the question of the reliability of Galileo's
interpretations of what he saw) that the moon
- Footnote 1. For Galileo's
own account (including diagrams) , see his 1610 "Siderius
Nuncius," translated in S. Drake, Discoveries and Opinions
- had mountains. This was inconsistent
with Aristotle's claim that the heavenly bodies were perfect
and suggested that some of them might be made of stuff similar
to the earth.
- Secondly, he "observed"
(again there are some problems about interpretation) that Jupiter
had four moons (he called them "Medicean stars" in
order to gain points with the Venetian Duke). This discovery
argued against the claim that Jupiter was carried along by an
invisible crystalline sphere. (Tycho Brahe had reached a similar
conclusion in 1577 when he observed a comet move freely through
several places where spheres were supposed to be.)
- The moons revolving around
Jupiter also showed conclusively that there was more than one
center of motion in the universe. This was important because
Copernicus had the moon moving around the earth as the earth
in turn moved around the sun. The Jupiter-four moons system showed
that such a motion was possible. It did not of course
prove that the earth-moon system actually worked in a similar
- Galileo also determined the
composition of the Milky Way. This discovery had no direct relevance
to the debate over the Copernican system. However, it did indicate
that Aristotle didn't get everything right and also that the
Universe was bigger than had been previously suspected.
- In 1543 Copernicus had pointed
out two important areas in which his system and Ptolemy's made
different predictions. One concerned the phases of Venus. On
Copernicus' account, if Venus shone by reflected light, it should
appear to wax and wane. According to the Ptolemaic system it
should always appear crescent shaped. Since Venus always appears
round, some Ptolemains concluded that it must generate its own
light as do the stars and the sun.
- In 1610 (but not in time to
be reported in The Starry Messenger Galileo observed that
Venus did indeed have phases, the timing and apparent magnitudes
of which were just as predicted by the Copernican system.
- This discovery provided a
decisive refutation of the Ptolemaic system. Unfortunately, the
other major new prediction of the Copernican system, stellar
parallax, told against it and for a geocentric system. If the
earth is in motion, a line
between an observer on earth and a fixed star does not quite
stay parallel the year around. Therefore, each star should seem
to shift its position slightly with respect to the pole of the
- However, stellar parallax
could not be detected - even with the new telescope. (It was
eventually observed in 1838.) Defenders of Copernicus could explain
this away by postulating that the stars were much farther away
than had been thought, but this seemed like a rather ad-hoc move
since there was no reason to believe it except that it
would save the Copernican theory from refutation.
- The observations of the sunspots
around 1612 by Galileo and others showed that Aristotle was wrong
in claiming that the heavenly bodies were immutable. It was not
clear exactly what or where the sunspots were, but they surely
came and went in a most imperfect fashion!
- VII.Galileo's Dialogo
- In 1632 Galileo published
his Dialogo sopra i due Massimi Sistemi del Mondo; Tolemaico,
e Copernico. His strategy had two parts. First, he wished
to show that it was possible that the earth moved. To
do so he had to answer all the physical arguments against Copernicus,
e.g., that birds would get left behind, etc. essentially what
was required was a new physics of inertial motion.
- Secondly, he wanted to show
that the earth actually moved. His major argument here
was his theory of the tides (which, as we will see, many historians
of science find embarrassingly mistaken).
- Before looking at these arguments
in any detail, the significance of the title must be pointed
out. Galileo speaks of two world systems, but in so doing he
omits a third possibility, the very one which was most popular
in the early 17th century. Tycho Brahe, a very good Danish astronomer,
who invented many new instruments and had by far the most accurate
astronomical data available at that time, had proposed a third
alternative which seemed to many to be the ideal compromise.
It was geocentric - so there were no problems about birds getting
blown away and furthermore it explained the absence of stellar
- But in Tycho's system all
the planets revolved around the
sun - so, unlike the Ptolemaic system, it made the right predictions
about the phases of Venus.
- Galileo, unlike his contemporaries,
never took Tycho's system seriously. For one thing, he considered
it to be very inelegant - it seems rather clumsy to have all
the planets carried around the earth by the sun. But more importantly,
he recognized that if his theory of the tides was correct, it
would refute all geostatic systems, Ptolemaic, Tychonic, or what
have you. It all hinged on his theory of the tides.
- Galileo's Dialogo is
a masterpiece of both polemics and popular scientific writing.
There are three protagonists: Simplicio is a very likable but
fundamentally stupid Aristotelian. Salviati is the slick expert
who often refers in reverential tones to a learned Academician
(obviously Galileo). The moderator is Sagredo, a kind of Dick
Cavett character personable, alert and determined to keep both
sides honest. (Unfortunately, Sagredo does not know about the
Tychonic system.) Almost all of the discussion is non-technical.
Galileo's quantitative theory of motion came later in the Discorsi.
- From the beginning Galileo
attacks a naive reliance on observation and common sense reasoning.
He points out that as we walk along the street at night the moon
appears to run along behind us like a cat on the rooftops.
Likewise as a ship floats along a canal, the shore sometimes
appears to be moving instead. A tower in the distance
appears to be a continuous translucent streak.
- But all of these appearances
are deceiving. The observations suitable for science have to
be based on correct theories and good instruments. For example,
observations of size (such as in the case of the tower) have
to be corrected by the laws of perspective. Many observations
with the naked-eye can be improved by using the telescope. And
observations of relative motion alone can never tell us which
object is actually at rest.
- Galileo also extols the use
of what are sometimes misleadingly called "thought experiments."
For example, in criticizing the Aristotelian claim that heavier
bodies fall faster, he not only reports on experiments done by
dropping balls from towers, but also argues as follows: Suppose
were right. Now imagine two identical cannon balls with strings
attached falling side by side. Now suppose the strings become
knotted. We now have a composite body which weighs twice as much
as the separate parts. It follows on Aristotle's account that
they should immediately start falling faster. But that is absurd.
Therefore, Aristotle is wrong.
- (Because Galileo criticized
naive observation and relied on thought experiments, some historical
commentators have concluded that he was not an empiricist. However,
this may only show that he was a sophisticated empiricist. It
hinges in part on what is meant by "absurd" in the
above argument. Do we conclude that the cannon balls would not
speed up when tied together because of some a priori metaphysical
principle such as "no effect without a cause"? Or is
it because we have lots of experience which indicates that a
change in velocity requires some force to be applied?)
- Galileo argues that the birds
would not get left behind if the earth were moving in a variety
of ways. He points out that flies in the cabin of a ship share
the ship's motion and do not have to fly all the way from Venice
to Constantinople. Likewise, if a ball is dropped from the mast
of a moving ship it lands at the foot of the mast, not behind
- In the fourth and final section
of the book Galileo switches from merely arguing that it is possible
that the Copernican system is true and tries to prove that
it is true. Here the claims that the ebbing and flowing of the
tides is caused by a combination of the daily rotation and yearly
revolution of the earth. Roughly, the theory goes like this:
Consider a given point on the earth's surface. During the night
the two motions add up so that water accelerates. During the
day the daily and yearly motions partly cancel out so the water
- This theory, which Santillana
calls "Galileo's folly" and Koestler labels as an idée
fixe, is unsatisfactory for two reasons. First of all it
violates Galileo's own ideas about motion. Relative to the earth,
the water does not speed up or get left behind. It travels along
with the earth just as the air does. Galileo's theory of the
tides is inconsistent with his own physics.
- Secondly, it
predicts that there should be a high tide once a day. However,
tides are generally observed to occur about every twelve hours.
Galileo explained this discrepancy away by vague talk about the
major tide bouncing back and forth in the sea bed. It was not
a good concluding section for an otherwise brilliant book.