Galileo Galilei's parents were Vincenzo
Galilei and Guilia Ammannati. Vincenzo, who was born in Florence in
1520, was a teacher of music and a fine lute player. After studying
music in Venice he carried out experiments on strings to support his
musical theories. Guilia, who was born in Pescia, married Vincenzo in
1563 and they made their home in the countryside near Pisa. Galileo was
their first child and spent his early years with his family in Pisa.
In 1572, when Galileo was eight years old, his family returned to
Florence, his father's home town. However, Galileo remained in Pisa and
lived for two years with Muzio Tedaldi who was related to Galileo's
mother by marriage. When he reached the age of ten, Galileo left Pisa to
join his family in Florence and there he was tutored by Jacopo
Borghini. Once he was old enough to be educated in a monastery, his
parents sent him to the Camaldolese Monastery at Vallombrosa which is
situated on a magnificent forested hillside 33 km southeast of Florence.
The Camaldolese Order was independent of the Benedictine Order,
splitting from it in about 1012. The Order combined the solitary life of
the hermit with the strict life of the monk and soon the young Galileo
found this life an attractive one. He became a novice, intending to join
the Order, but this did not please his father who had already decided
that his eldest son should become a medical doctor.
Vincenzo had Galileo return from Vallombrosa to Florence and give up the
idea of joining the Camaldolese order. He did continue his schooling in
Florence, however, in a school run by the Camaldolese monks. In 1581
Vincenzo sent Galileo back to Pisa to live again with Muzio Tedaldi and
now to enrol for a medical degree at the University of Pisa. Although
the idea of a medical career never seems to have appealed to Galileo,
his father's wish was a fairly natural one since there had been a
distinguished physician in his family in the previous century. Galileo
never seems to have taken medical studies seriously, attending courses
on his real interests which were in mathematics and natural philosophy.
His mathematics teacher at Pisa was Filippo Fantoni, who held the chair
of mathematics. Galileo returned to Florence for the summer vacations
and there continued to study mathematics.
In the year 1582-83 Ostilio Ricci, who was the mathematician of the Tuscan Court and a former pupil of Tartaglia, taught a course on Euclid's Elements
at the University of Pisa which Galileo attended. During the summer of
1583 Galileo was back in Florence with his family and Vincenzo
encouraged him to read Galen to further his medical studies. However
Galileo, still reluctant to study medicine, invited Ricci (also in
Florence where the Tuscan court spent the summer and autumn) to his home
to meet his father. Ricci tried to persuade Vincenzo to allow his son
to study mathematics since this was where his interests lay. Certainly
Vincenzo did not like the idea and resisted strongly but eventually he
gave way a little and Galileo was able to study the works of Euclid and Archimedes from the Italian translations which Tartaglia
had made. Of course he was still officially enrolled as a medical
student at Pisa but eventually, by 1585, he gave up this course and left
without completing his degree.
Galileo began teaching mathematics, first privately in Florence and then
during 1585-86 at Siena where he held a public appointment. During the
summer of 1586 he taught at Vallombrosa, and in this year he wrote his
first scientific book The little balance [La Balancitta] which described Archimedes'
method of finding the specific gravities (that is the relative
densities) of substances using a balance. In the following year he
travelled to Rome to visit Clavius
who was professor of mathematics at the Jesuit Collegio Romano there. A
topic which was very popular with the Jesuit mathematicians at this
time was centres of gravity and Galileo brought with him some results
which he had discovered on this topic. Despite making a very favourable
impression on Clavius, Galileo failed to gain an appointment to teach mathematics at the University of Bologna.
After leaving Rome Galileo remained in contact with Clavius by correspondence and Guidobaldo del Monte
was also a regular correspondent. Certainly the theorems which Galileo
had proved on the centres of gravity of solids, and left in Rome, were
discussed in this correspondence. It is also likely that Galileo
received lecture notes from courses which had been given at the Collegio
Romano, for he made copies of such material which still survive today.
The correspondence began around 1588 and continued for many years. Also
in 1588 Galileo received a prestigious invitation to lecture on the
dimensions and location of hell in Dante's Inferno at the Academy in Florence.
Fantoni left the chair of mathematics at the University of Pisa in 1589
and Galileo was appointed to fill the post (although this was only a
nominal position to provide financial support for Galileo). Not only did
he receive strong recommendations from Clavius,
but he also had acquired an excellent reputation through his lectures
at the Florence Academy in the previous year. The young mathematician
had rapidly acquired the reputation that was necessary to gain such a
position, but there were still higher positions at which he might aim.
Galileo spent three years holding this post at the university of Pisa
and during this time he wrote De Motu a series of essays on the
theory of motion which he never published. It is likely that he never
published this material because he was less than satisfied with it, and
this is fair for despite containing some important steps forward, it
also contained some incorrect ideas. Perhaps the most important new
ideas which De Motu contains is that one can test theories by
conducting experiments. In particular the work contains his important
idea that one could test theories about falling bodies using an inclined
plane to slow down the rate of descent.
In 1591 Vincenzo Galilei, Galileo's father, died and since Galileo was
the eldest son he had to provide financial support for the rest of the
family and in particular have the necessary financial means to provide
dowries for his two younger sisters. Being professor of mathematics at
Pisa was not well paid, so Galileo looked for a more lucrative post.
With strong recommendations from Guidobaldo del Monte,
Galileo was appointed professor of mathematics at the University of
Padua (the university of the Republic of Venice) in 1592 at a salary of
three times what he had received at Pisa. On 7 December 1592 he gave his
inaugural lecture and began a period of eighteen years at the
university, years which he later described as the happiest of his life.
At Padua his duties were mainly to teach Euclid's
geometry and standard (geocentric) astronomy to medical students, who
would need to know some astronomy in order to make use of astrology in
their medical practice. However, Galileo argued against Aristotle's
view of astronomy and natural philosophy in three public lectures he
gave in connection with the appearance of a New Star (now known as 'Kepler's supernova') in 1604. The belief at this time was that of Aristotle,
namely that all changes in the heavens had to occur in the lunar region
close to the Earth, the realm of the fixed stars being permanent.
Galileo used parallax arguments to prove that the New Star could not be
close to the Earth. In a personal letter written to Johannes Kepler in 1598, Galileo had stated that he was a Copernican (believer in the theories of Copernicus). However, no public sign of this belief was to appear until many years later.
At Padua, Galileo began a long term relationship with Maria Gamba, who
was from Venice, but they did not marry perhaps because Galileo felt his
financial situation was not good enough. In 1600 their first child
Virginia was born, followed by a second daughter Livia in the following
year. In 1606 their son Vincenzo was born.
We mentioned above an error in Galileo's theory of motion as he set it out in De Motu
around 1590. He was quite mistaken in his belief that the force acting
on a body was the relative difference between its specific gravity and
that of the substance through which it moved. Galileo wrote to his
friend Paolo Sarpi, a fine mathematician who was consultor to the
Venetian government, in 1604 and it is clear from his letter that by
this time he had realised his mistake. In fact he had returned to work
on the theory of motion in 1602 and over the following two years,
through his study of inclined planes and the pendulum, he had formulated
the correct law of falling bodies and had worked out that a projectile
follows a parabolic path. However, these famous results would not be
published for another 35 years.
In May 1609, Galileo received a letter from Paolo Sarpi telling him
about a spyglass that a Dutchman had shown in Venice. Galileo wrote in
the Starry Messenger (Sidereus Nuncius) in April 1610:-
About ten months ago a report reached my ears that a certain Fleming had constructed a spyglass by means of which visible objects, though very distant from the eye of the observer, were distinctly seen as if nearby. Of this truly remarkable effect several experiences were related, to which some persons believed while other denied them. A few days later the report was confirmed by a letter I received from a Frenchman in Paris, Jacques Badovere, which caused me to apply myself wholeheartedly to investigate means by which I might arrive at the invention of a similar instrument. This I did soon afterwards, my basis being the doctrine of refraction.
From these reports, and using his own technical skills as a
mathematician and as a craftsman, Galileo began to make a series of
telescopes whose optical performance was much better than that of the
Dutch instrument. His first telescope was made from available lenses and
gave a magnification of about four times. To improve on this Galileo
learned how to grind and polish his own lenses and by August 1609 he had
an instrument with a magnification of around eight or nine. Galileo
immediately saw the commercial and military applications of his
telescope (which he called a perspicillum) for ships at sea. He
kept Sarpi informed of his progress and Sarpi arranged a demonstration
for the Venetian Senate. They were very impressed and, in return for a
large increase in his salary, Galileo gave the sole rights for the
manufacture of telescopes to the Venetian Senate. It seems a
particularly good move on his part since he must have known that such
rights were meaningless, particularly since he always acknowledged that
the telescope was not his invention!
By the end of 1609 Galileo had turned his telescope on the night sky and
began to make remarkable discoveries. Swerdlow writes (see [16]):-
In about two months, December and January, he made more discoveries that changed the world than anyone has ever made before or since.
The astronomical discoveries he made with his telescopes were described in a short book called the Starry Messenger
published in Venice in May 1610. This work caused a sensation. Galileo
claimed to have seen mountains on the Moon, to have proved the Milky Way
was made up of tiny stars, and to have seen four small bodies orbiting
Jupiter. These last, with an eye to getting a position in Florence, he
quickly named 'the Medicean stars'. He had also sent Cosimo de Medici,
the Grand Duke of Tuscany, an excellent telescope for himself.
The Venetian Senate, perhaps realising that the rights to manufacture
telescopes that Galileo had given them were worthless, froze his salary.
However he had succeeded in impressing Cosimo and, in June 1610, only a
month after his famous little book was published, Galileo resigned his
post at Padua and became Chief Mathematician at the University of Pisa
(without any teaching duties) and 'Mathematician and Philosopher' to the
Grand Duke of Tuscany. In 1611 he visited Rome where he was treated as a
leading celebrity; the Collegio Romano put on a grand dinner with
speeches to honour Galileo's remarkable discoveries. He was also made a
member of the Accademia dei Lincei
(in fact the sixth member) and this was an honour which was especially
important to Galileo who signed himself 'Galileo Galilei Linceo' from
this time on.
While in Rome, and after his return to Florence, Galileo continued to make observations with his telescope. Already in the Starry Messenger
he had given rough periods of the four moons of Jupiter, but more
precise calculations were certainly not easy since it was difficult to
identify from an observation which moon was I, which was II, which III,
and which IV. He made a long series of observations and was able to give
accurate periods by 1612. At one stage in the calculations he became
very puzzled since the data he had recorded seemed inconsistent, but he
had forgotten to take into account the motion of the Earth round the
sun.
Galileo first turned his telescope on Saturn on 25 July 1610 and it
appeared as three bodies (his telescope was not good enough to show the
rings but made them appear as lobes on either side of the planet).
Continued observations were puzzling indeed to Galileo as the bodies on
either side of Saturn vanished when the ring system was edge on. Also in
1610 he discovered that, when seen in the telescope, the planet Venus
showed phases like those of the Moon, and therefore must orbit the Sun
not the Earth. This did not enable one to decide between the Copernican
system, in which everything goes round the Sun, and that proposed by Tycho Brahe
in which everything but the Earth (and Moon) goes round the Sun which
in turn goes round the Earth. Most astronomers of the time in fact
favoured Brahe's
system and indeed distinguishing between the two by experiment was
beyond the instruments of the day. However, Galileo knew that all his
discoveries were evidence for Copernicanism, although not a proof. In
fact it was his theory of falling bodies which was the most significant
in this respect, for opponents of a moving Earth argued that if the
Earth rotated and a body was dropped from a tower it should fall behind
the tower as the Earth rotated while it fell. Since this was not
observed in practice this was taken as strong evidence that the Earth
was stationary. However Galileo already knew that a body would fall in
the observed manner on a rotating Earth.
Other observations made by Galileo included the observation of sunspots. He reported these in Discourse on floating bodies which he published in 1612 and more fully in Letters on the sunspots
which appeared in 1613. In the following year his two daughters entered
the Franciscan Convent of St Matthew outside Florence, Virginia taking
the name Sister Maria Celeste and Livia the name Sister Arcangela. Since
they had been born outside of marriage, Galileo believed that they
themselves should never marry. Although Galileo put forward many
revolutionary correct theories, he was not correct in all cases. In
particular when three comets appeared in 1618 he became involved in a
controversy regarding the nature of comets. He argued that they were
close to the Earth and caused by optical refraction. A serious
consequence of this unfortunate argument was that the Jesuits began to
see Galileo as a dangerous opponent.
Despite his private support for Copernicanism, Galileo tried to avoid
controversy by not making public statements on the issue. However he was
drawn into the controversy through Castelli who had been appointed to
the chair of mathematics in Pisa in 1613. Castelli had been a student of
Galileo's and he was also a supporter of Copernicus.
At a meeting in the Medici palace in Florence in December 1613 with the
Grand Duke Cosimo II and his mother the Grand Duchess Christina of
Lorraine, Castelli was asked to explain the apparent contradictions
between the Copernican theory and Holy Scripture. Castelli defended the
Copernican position vigorously and wrote to Galileo afterwards telling
him how successful he had been in putting the arguments. Galileo, less
convinced that Castelli had won the argument, wrote Letter to Castelli
to him arguing that the Bible had to be interpreted in the light of
what science had shown to be true. Galileo had several opponents in
Florence and they made sure that a copy of the Letter to Castelli was sent to the Inquisition in Rome. However, after examining its contents they found little to which they could object.
The Catholic Church's most important figure at this time in dealing with
interpretations of the Holy Scripture was Cardinal Robert Bellarmine.
He seems at this time to have seen little reason for the Church to be
concerned regarding the Copernican theory. The point at issue was
whether Copernicus
had simply put forward a mathematical theory which enabled the
calculation of the positions of the heavenly bodies to be made more
simply or whether he was proposing a physical reality. At this time
Bellarmine viewed the theory as an elegant mathematical one which did
not threaten the established Christian belief regarding the structure of
the universe.
In 1616 Galileo wrote the Letter to the Grand Duchess which vigorously attacked the followers of Aristotle.
In this work, which he addressed to the Grand Duchess Christina of
Lorraine, he argued strongly for a non-literal interpretation of Holy
Scripture when the literal interpretation would contradict facts about
the physical world proved by mathematical science. In this Galileo
stated quite clearly that for him the Copernican theory is not just a
mathematical calculating tool, but is a physical reality:-
I hold that the Sun is located at the centre of the revolutions of the heavenly orbs and does not change place, and that the Earth rotates on itself and moves around it. Moreover ... I confirm this view not only by refuting Ptolemy's and Aristotle's arguments, but also by producing many for the other side, especially some pertaining to physical effects whose causes perhaps cannot be determined in any other way, and other astronomical discoveries; these discoveries clearly confute the Ptolemaic system, and they agree admirably with this other position and confirm it.
Pope Paul V ordered Bellarmine to have the Sacred Congregation of the
Index decide on the Copernican theory. The cardinals of the Inquisition
met on 24 February 1616 and took evidence from theological experts. They
condemned the teachings of Copernicus,
and Bellarmine conveyed their decision to Galileo who had not been
personally involved in the trial. Galileo was forbidden to hold
Copernican views but later events made him less concerned about this
decision of the Inquisition. Most importantly Maffeo Barberini, who was
an admirer of Galileo, was elected as Pope Urban VIII. This happened
just as Galileo's book Il saggiatore (The Assayer) was about to be published by the Accademia dei Lincei
in 1623 and Galileo was quick to dedicate this work to the new Pope.
The work described Galileo's new scientific method and contains a famous
quote regarding mathematics:-
Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth.
Pope Urban VIII invited Galileo to papal audiences on six occasions and
led Galileo to believe that the Catholic Church would not make an issue
of the Copernican theory. Galileo, therefore, decided to publish his
views believing that he could do so without serious consequences from
the Church. However by this stage in his life Galileo's health was poor
with frequent bouts of severe illness and so even though he began to
write his famous Dialogue in 1624 it took him six years to complete the work.
Galileo attempted to obtain permission from Rome to publish the Dialogue
in 1630 but this did not prove easy. Eventually he received permission
from Florence, and not Rome. In February 1632 Galileo published Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican.
It takes the form of a dialogue between Salviati, who argues for the
Copernican system, and Simplicio who is an Aristotelian philosopher. The
climax of the book is an argument by Salviati that the Earth moves
which was based on Galileo's theory of the tides. Galileo's theory of
the tides was entirely false despite being postulated after Johannes Kepler had already put forward the correct explanation. It was unfortunate, given the remarkable truths the Dialogue supported, that the argument which Galileo thought to give the strongest proof of Copernicus's theory should be incorrect.
Shortly after publication of Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican
the Inquisition banned its sale and ordered Galileo to appear in Rome
before them. Illness prevented him from travelling to Rome until 1633.
Galileo's accusation at the trial which followed was that he had
breached the conditions laid down by the Inquisition in 1616. However a
different version of this decision was produced at the trial rather than
the one Galileo had been given at the time. The truth of the Copernican
theory was not an issue therefore; it was taken as a fact at the trial
that this theory was false. This was logical, of course, since the
judgement of 1616 had declared it totally false.
Found guilty, Galileo was condemned to lifelong imprisonment, but the
sentence was carried out somewhat sympathetically and it amounted to
house arrest rather than a prison sentence. He was able to live first
with the Archbishop of Siena, then later to return to his home in
Arcetri, near Florence, but had to spend the rest of his life watched
over by officers from the Inquisition. In 1634 he suffered a severe blow
when his daughter Virginia, Sister Maria Celeste, died. She had been a
great support to her father through his illnesses and Galileo was
shattered and could not work for many months. When he did manage to
restart work, he began to write Discourses and mathematical demonstrations concerning the two new sciences.
After Galileo had completed work on the Discourses it was
smuggled out of Italy, and taken to Leyden in Holland where it was
published. It was his most rigorous mathematical work which treated
problems on impetus, moments, and centres of gravity. Much of this work
went back to the unpublished ideas in De Motu from around 1590 and the improvements which he had worked out during 1602-1604. In the Discourses he developed his ideas of the inclined plane writing:-
I assume that the speed acquired by the same movable object over different inclinations of the plane are equal whenever the heights of those planes are equal.
He then described an experiment using a pendulum to verify his property
of inclined planes and used these ideas to give a theorem on
acceleration of bodies in free fall:-
The time in which a certain distance is traversed by an object moving under uniform acceleration from rest is equal to the time in which the same distance would be traversed by the same movable object moving at a uniform speed of one half the maximum and final speed of the previous uniformly accelerated motion.
After giving further results of this type he gives his famous result
that the distance that a body moves from rest under uniform acceleration
is proportional to the square of the time taken.
One would expect that Galileo's understanding of the pendulum, which he
had since he was a young man, would have led him to design a pendulum
clock. In fact he only seems to have thought of this possibility near
the end of his life and around 1640 he did design the first pendulum
clock. Galileo died in early 1642 but the significance of his clock
design was certainly realised by his son Vincenzo who tried to make a
clock to Galileo's plan, but failed.
It was a sad end for so great a man to die condemned of heresy. His will
indicated that he wished to be buried beside his father in the family
tomb in the Basilica of Santa Croce but his relatives feared, quite
rightly, that this would provoke opposition from the Church. His body
was concealed and only placed in a fine tomb in the church in 1737 by
the civil authorities against the wishes of many in the Church. On 31
October 1992, 350 years after Galileo's death, Pope John Paul II gave an
address on behalf of the Catholic Church in which he admitted that
errors had been made by the theological advisors in the case of Galileo.
He declared the Galileo case closed, but he did not admit that the
Church was wrong to convict Galileo on a charge of heresy because of his
belief that the Earth rotates round the sun.
