Galileo Galilei

Born: 15 Feb 1564 in Pisa (now in Italy)

Died: 8 Jan 1642 in Arcetri (near Florence) (now in Italy)

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 Sienna 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  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  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.

J J O'Connor and E F Robertson

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