Cosmology is the study of the Universe and its components, how it formed, how its has evolved and what is its future. Modern cosmology grew from ideas before recorded history. Ancient man asked questions such as “What’s going on around me?” which then developed into “How does the Universe work?”, the key question that cosmology asks.
Our exploration of cosmology begins with a brief history of the human desire to understand the cosmos. Mythology, humanity’s first attempt to grapple with cosmological questions, consists of narrative tales that describe the universe in understandable terms. Some of the earliest myths and religious stories picture the Universe as alive with many different spirits being the explination of everything early man witness in nature.
Cosmology is as old as humankind. Once primitive socal groups developed language, it was a short step to making their first attempts to understand the world around them. Very early cosmology, from Neolithic times of 20,000 to 100,000 years ago, was extremely local. The Universe was what you immediately interacted with. Cosmological things were weather, earthquakes, sharp changes in your environment, etc. Things outside your daily experience appeared supernatural, and so we call this the time of Magic Cosmology.
Early people projected their own inner thoughts and feelings into an outer animistic world, a world where everything was alive. Through prayers, sacrifices and gifts to the spirits, human beings gained control of the phenomena of their world. This is an anthropomorphic (magic) worldview, of the living earth, water, wind and fire, into which men and women projected their own emotions and motives as the guiding forces, the kind of world one finds in fantasy and fairy tales.
Later in history, 5,000 to 20,000 years ago, humankind begins to organize themselves and develop what we now call culture. A greater sense of permanence in your daily existences leads to the development of myths, particularly creation myths to explain the origin of the Universe.
Many of the myths still maintained supernatural themes, but there was an internal logical consistence to many of the stories. The myths often attempt a rational explanation of the everyday world. Even if we consider some of the stories to be silly, they were, in some sense, our first scientific theories. We call this the time of Mythical Cosmology.
The development of cosmology in ancient Egypt followed practical lines. Early man’s impressions of the night sky formulated into various myths which then later became the core of Egyptian religion. Since its principal deities were heavenly bodies, a great deal of effort was made by the priesthood to calculate and predict the time and place of their god’s appearances. These skills led to the division of the day and night into twelve sections each, the development of a lunar calendar and the development of a solar calendar of 12 30-day months with a special 5-day unit to bring the total to 365 days.
Because the sun god, Ra, was the pre-eminent god, the annual solar motion along the horizon was a key astronomical observation for the Egyptians. The timing and position of the northernmost and southernmost turning points, the solstices, ultimately fixed the mythology of Egyptian cosmology. Egyptian legend declares that the sky goddess Nut gives birth to Ra once a year, catalysing both calendar development and the concept of divine royalty plus the matrilineal inheritance of the throne.
Nut is often portrayed as a naked female stretched across the sky. The Sun (Ra) is shown entering her mouth, passing through her star speckled body and emerging from her birth canal nine months later (from the spring equinox to the winter solstice). Thus, Ra becomes a self-creating god, i.e. the Universe is self-creating and eternal.
By the Old Kingdom, the astronomical/religious zeal of the pharaohs is reflected in the construction of massive pyramids at Giza. Their shape reflects the manner in which clouds and dust scatter sunlight into broad swaths forming stairways to heaven. These were stone pathways to the gods and were oriented to reach the immortal ones, i.e. the northern circumpolar stars.
Cosmology in Mesopotamia was much more sophisticated. Babylonians believed in a six-level universe with three heavens and three earths: two heavens above the sky, the heaven of the stars, the earth, the underground of the Apsu, and the underworld of the dead. The Earth was created by the god Marduk as a raft floating on the Apsu. The gods were divided into two pantheons, one occupying the heavens and the other in the underworld.
Babylonian astronomy is noted for their detailed, and continuous, records of astronomical phenomenon such as eclipses, positions of the planets and rise and setting of the Moon. These records date back to 800 B.C. and are the oldest scientific documents in existence. The purpose of this activity was clearly astrological with the aim of forecasting the fortunes of the country as well as of the king. In addition to records, Babylonian astronomers also developed several arithmetic tools to aid in the prediction of eclipses and planetary motion. However, while their record keeping was a novel technology for the time, and their system of stellar names and measurement system was passed onto later civilizations, the Babylonians never developed a cosmological model in which to interpret their observations. Greek astronomers will achieve this goal using the Babylonian data.
The third stage, what makes up the core of modern cosmology, grew out of ancient Greek, later adopted by the Church. The underlying theme in Greek science is the use of observation and experimentation to search for simple, universal laws. We call this the time of Geometric Cosmology.
The struggle to formulation a Geometric Cosmology led to the development of the biggest philosophical achievement of humankind, the philosophy of science. Indirectly, through an examination of our myths and creation stories, we developed the ideas and techniques that later would become the core ideas to this thing we call science.
Central to Greek cosmology is the belief that the underlying order of the Universe can be expressed in mathematical form lies at the heart of science and is rarely questioned. But is mathematics a human invention or does it have an independent existence?
Idealization of physical phenomenon led Plato to hypothesize that there were two Universes, the physical world and an immaterial world of `forms’, perfect aspects of everyday things such as a table, bird, and ideas/emotions, joy, action, etc.
Thus, there came into existence two schools of thought. One that mathematical concepts are mere idealizations of our physical world. The world of absolutes, what is called the Platonic world, has existence only through the physical world. In this case, the mathematical world is the same as the Platonic world and would be thought of as emerging from the world of physical objects.
The other school is attributed to Plato, and finds that Nature is a structure that is precisely governed by timeless mathematical laws. According to Platonists we do not invent mathematical truths, we discover them. The Platonic world exists and physical world is a shadow of the truths in the Platonic world. This reasoning comes about when we realize (through thought and experimentation) how the behavior of Nature follows mathematics to an extremely high degree of accuracy. The deeper we probe the laws of Nature, the more the physical world disappears and becomes a world of pure math.
Four thousand years ago the Babylonians were skilled astronomers who were able to predict the apparent motions of the moon and the stars and the planets and the Sun upon the sky, and could even predict eclipses. But it was the Ancient Greeks who were the first to build a cosmological model within which to interpret these motions. In the fourth century BC, they developed the idea that the stars were fixed on a celestial sphere which rotated about the spherical Earth every 24 hours, and the planets, the Sun and the Moon, moved in the ether between the Earth and the stars.
This model was further developed in the following centuries, culminating in the second century AD with Ptolemy’s great system. One of the most influential Greek astronomers and geographers of his time, Ptolemy propounded the geocentric theory in a form that prevailed for 1400 years. However, of all the ancient Greek mathematicians, it is fair to say that his work has generated more discussion and argument than any other.
We know very little of Ptolemy’s life. He made astronomical observations from Alexandria in Egypt during the years AD 127-41. In fact the first observation which we can date exactly was made by Ptolemy on 26 March 127 while the last was made on 2 February 141. It was claimed by Theodore Meliteniotes in around 1360 that Ptolemy was born in Hermiou (which is in Upper Egypt rather than Lower Egypt where Alexandria is situated) but since this claim first appears more than one thousand years after Ptolemy lived, it must be treated as relatively unlikely to be true. In fact there is no evidence that Ptolemy was ever anywhere other than Alexandria.
His name, Claudius Ptolemy, is of course a mixture of the Greek Egyptian ‘Ptolemy’ and the Roman ‘Claudius’. This would indicate that he was descended from a Greek family living in Egypt and that he was a citizen of Rome, which would be as a result of a Roman emperor giving that ‘reward’ to one of Ptolemy’s ancestors.
We do know that Ptolemy used observations made by ‘Theon the mathematician’, and this was almost certainly Theon of Smyrna who almost certainly was his teacher. Certainly this would make sense since Theon of Smyrna was both an observer and a mathematician who had written on astronomical topics such as conjunctions, eclipses, occultations and transits. Most of Ptolemy’s early works are dedicated to Syrus who may have also been one of his teachers in Alexandria, but nothing is known of Syrus.
The most important of Ptolemy’s major works to have survived is the Almagest which is a treatise in thirteen books. Its original Greek title translates as The Mathematical Compilation but this title was soon replaced by another Greek title which means The Greatest Compilation. This was translated into Arabic as “al-majisti” and from this the title Almagest was given to the work when it was translated from Arabic to Latin.
The Almagest is the earliest of Ptolemy’s works and gives in detail the mathematical theory of the motions of the Sun, Moon, and planets. Ptolemy made his most original contribution by presenting details for the motions of each of the planets. The Almagest was not superseded until a century after Copernicus presented his heliocentric theory in the De revolutionibus of 1543.
Copernicus proposed a heliocentric system, he could not match the accuracy of Ptolemy’s Earth-centred system. Copernicus constructed a model where the Earth rotated and, together with the other planets, moved in a circular orbit about the Sun. But the observational evidence of the time favoured the Ptolemaic system as did the religious dogma of the time from Christian faith.
Nicolaus Copernicus is the Latin version of the famous astronomer’s name which chose later in his life. The original form of his name was Mikolaj Kopernik or Nicolaus Koppernigk but we shall use Copernicus throughout this article. His father, also called Nicolaus Koppernigk, had lived in Krakow before moving to Torun where he set up a business trading in copper. He was also interested in local politics and became a civic leader in Torun and a magistrate. Nicolaus Koppernigk married Barbara Waczenrode, who came from a well off family from Torun, in about 1463. They moved into a house in St Anne’s Street in Torun, but they also had a summer residence with vineyards out of town. Nicolaus and Barbara Koppernigk had four children, two sons and two daughters, of whom Nicolaus Copernicus was the youngest.
University education at Krakow was, Copernicus later wrote, a vital factor in everything that he went on to achieve. There he studied Latin, mathematics, astronomy, geography and philosophy. He learnt his astronomy from Tractatus de Sphaera by Johannes de Sacrobosco written in 1220. One should not think, however, that the astronomy courses which Copernicus studied were scientific courses in the modern sense. Rather they were mathematics courses which introduced Aristotle and Ptolemy’s view of the universe so that students could understand the calendar, calculate the dates of holy days, and also have skills that would enable those who would follow a more practical profession to navigate at sea. Also taught as a major part of astronomy was what today we would call astrology, teaching students to calculate horoscopes of people from the exact time of their birth.
While a student in Kraków, Copernicus purchased a copy of the Latin translation of Euclid’s Elements published in Venice in 1482, a copy of the second edition of the Alfonsine Tables (which gives planetary theory and eclipses) printed in Venice in 1492, and Regiomontanus’s Tables of Directions (a work on spherical astronomy) published in Augsburg in 1490. Remarkably Copernicus’s copies of these works, signed by him, are still preserved.
It was while he was a student at Krakow that Copernicus began to use this Latin version of his name rather than Kopernik or Koppernigk. He returned to Torun after four years of study at Krakow but, as was common at the time, did not formally graduate with a degree. His uncle Lucas Waczenrode was still determined that Copernicus should have a career in the Church and indeed this was a profession which would allow security for someone wanting to pursue leaning. So that he might have the necessary qualifications Copernicus decided to go to the University of Bologna to take a degree in canon law. In the autumn of 1496 he travelled to Italy, entering the University of Bologna on 19 October 1496, to start three years of study. As a native German speaker he joined the “German Nation of Bologna University”. Each student contributed to the “German Nation” an amount they could afford and the small contribution that Copernicus made indicates his poor financial position at that time.
While he was there his uncle put his name forward for the position of canon at Frauenburg Cathedral. On 20 October 1497, while in Bologna, Copernicus received official notification of his appointment as a canon and of the comfortable income he would receive without having to return to carry out any duties. At Bologna University Copernicus studied Greek, mathematics and astronomy in addition to his official course of canon law. He rented rooms at the house of the astronomy professor Domenico Maria de Novara and began to undertake research with him, assisting him in making observations. On 9 March 1497 he observed the Moon eclipse the star Aldebaran.
In 1500 Copernicus visited Rome, as all Christians were strongly encouraged to do to celebrate the great jubilee, and he stayed there for a year lecturing to scholars on mathematics and astronomy. While in Rome he observed an eclipse of the Moon which took place on 6 November 1500. He returned to Frauenburg (also known as Frombork) in the spring of 1501 and was officially installed as a canon of the Ermland Chapter on 27 July. He had not completed his degree in canon law at Bologna so he requested his uncle that he be allowed to return to Italy both to take a law degree and to study medicine. Copernicus was granted leave on 27 July 1501.
In 1509 Copernicus published a work, which was properly printed, giving Latin translations of Greek poetry by the obscure poet Theophylactus Simocattes. While accompanying his uncle on a visit to Krakow, he gave a manuscript of the poetry book to a publisher friend there. Lucas Waczenrode died in 1512 and following this Copernicus resumed his duties as canon in the Ermland Chapter at Frauenburg. He now had more time than before to devote to his study of astronomy, having an observatory in the rooms in which he lived in one of the towers in the town’s fortifications.
Around 1514 he distributed a little book, not printed but hand written, to a few of his friends who knew that he was the author even though no author is named on the title page. This book, usually called the Little Commentary, set out Copernicus’s theory of a universe with the sun at its centre. The Little Commentary is a fascinating document. It contains seven axioms which Copernicus gives, not in the sense that they are self evident, but in the sense that he will base his conclusions on these axioms and nothing else;
The axioms are:
There is no one centre in the universe.
The Earth’s centre is not the centre of the universe.
The centre of the universe is near the sun.
The distance from the Earth to the sun is imperceptible compared with the distance to the stars.
The rotation of the Earth accounts for the apparent daily rotation of the stars.
The apparent annual cycle of movements of the sun is caused by the Earth revolving round it.
The apparent retrograde motion of the planets is caused by the motion of the Earth from which one observes.
Some have noted that 2, 4, 5, and 7 can be deduced from 3 and 6 but it was never Copernicus’s aim to give a minimal set of axioms. The most remarkable of the axioms is 7, for although earlier scholars had claimed that the Earth moved, some claiming that it revolved round the sun, nobody before Copernicus appears to have correctly explained the retrograde motion of the outer planets.
It is clear that his fame as an astronomer was well known for when the Fifth Lateran Council decided to improve the calendar, which was known to be out of phase with the seasons, the Pope appealed to experts for advice in 1514, one of these experts was Copernicus.
The notable defenders of His views included Kepler and Galileo while theoretical evidence for the Copernican theory was provided by Newton’s theory of universal gravitation around 150 years later.
Copernicus is said to have received a copy of the printed book, consisting of about 200 pages written in Latin, for the first time on his deathbed. He died of a cerebral haemorrhage.
It was only with the aid of the newly-invented telescope in the early seventeenth century that Galileo could deal a fatal blow to the notion that the Earth was at the centre of the Universe. He discovered moons orbiting the planet Jupiter.
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. ). 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.
In May 1609, Galileo received a letter from Paolo Sarpi telling him about a spyglass that a Dutchman had shown in Venice. 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. 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.
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.
At the same time, Tycho Brahe’s assistant Kepler discovered the key to building a heliocentric model. The planets moved in ellipses, not perfect circles, about the Sun. Newton later showed that elliptical motion could be explained by his inverse-square law for the gravitational force.
But the absence of any observable parallax in the apparent positions of the stars as the Earth rotated the Sun, then implied that the stars must be at a huge distance from the Sun. The cosmos seemed to be a vast sea of stars. With the aid of his telescope, Galileo could resolve thousands of new stars which were invisible to the naked eye. Newton concluded that the Universe must be an infinite and eternal sea of stars, each much like our own Sun.
Isaac Newton was born in the manor house of Woolsthorpe, near Grantham in Lincolnshire. Although by the calendar in use at the time of his birth he was born on Christmas Day 1642, we give the date of 4 January 1643 in this biography which is the “corrected” Gregorian calendar date bringing it into line with our present calendar. (The Gregorian calendar was not adopted in England until 1752.) Isaac Newton came from a family of farmers but never knew his father, also named Isaac Newton, who died in October 1642, three months before his son was born. Although Isaac’s father owned property and animals which made him quite a wealthy man, he was completely uneducated and could not sign his own name.< His childhood years were known to have been unhappy times which later probably contributed to his nearly monk like stoic character.
An uncle, William Ayscough, decided that Isaac should prepare for entering university and, having persuaded his mother that this was the right thing to do, Isaac was allowed to return to the Free Grammar School in Grantham in 1660 to complete his school education. This time he lodged with Stokes, who was the headmaster of the school, and it would appear that, despite suggestions that he had previously shown no academic promise, Isaac must have convinced some of those around him that he had academic promise. Some evidence points to Stokes also persuading Isaac’s mother to let him enter university, so it is likely that Isaac had shown more promise in his first spell at the school than the school reports suggest.
We know nothing about what Isaac learnt in preparation for university, but Stokes was an able man and almost certainly gave Isaac private coaching and a good grounding. There is no evidence that he learnt any mathematics, but we cannot rule out Stokes introducing him to Euclid’s Elements which he was well capable of teaching.
Newton entered his uncle’s old College, Trinity College Cambridge, on 5 June 1661. He was older than most of his fellow students but, despite the fact that his mother was financially well off, he entered as a sizar. A sizar at Cambridge was a student who received an allowance toward college expenses in exchange for acting as a servant to other students. There is certainly some ambiguity in his position as a sizar, for he seems to have associated with “better class” students rather than other sizars.
Newton’s aim at Cambridge was a law degree. Instruction at Cambridge was dominated by the philosophy of Aristotle but some freedom of study was allowed in the third year of the course. Newton studied the philosophy of Descartes, Gassendi, Hobbes, and in particular Boyle. The mechanics of the Copernican astronomy of Galileo attracted him and he also studied Kepler’s Optics. He recorded his thoughts in a book which he entitled Quaestiones Quaedam Philosophicae (Certain Philosophical Questions). It is a fascinating account of how Newton’s ideas were already forming around 1664. He headed the text with a Latin statement meaning “Plato is my friend, Aristotle is my friend, but my best friend is truth” showing himself a free thinker from an early stage.
How Newton was introduced to the most advanced mathematical texts of his day is slightly less clear. According to de Moivre, Newton’s interest in mathematics began in the autumn of 1663 when he bought an astrology book at a fair in Cambridge and found that he could not understand the mathematics in it. Attempting to read a trigonometry book, he found that he lacked knowledge of geometry and so decided to read Barrow’s edition of Euclid’s Elements.
Returning to the beginning, Newton read the whole book with a new respect. He then turned to Oughtred’s Clavis Mathematica and Descartes’ La Géométrie. The new algebra and analytical geometry of Viète was read by Newton from Frans van Schooten’s edition of Viète’s collected works published in 1646. Other major works of mathematics which he studied around this time was the newly published major work by van Schooten Geometria a Renato Des Cartes which appeared in two volumes in 1659-1661. The book contained important appendices by three of van Schooten disciples, Jan de Witt, Johan Hudde, and Hendrick van Heuraet. Newton also studied Wallis’s Algebra and it appears that his first original mathematical work came from his study of this text. He read Wallis’s method for finding a square of equal area to a parabola and a hyperbola which used indivisibles. Newton made notes on Wallis’s treatment of series but also devised his own proofs of the theorems writing.
Despite some evidence that his progress had not been particularly good, Newton was elected a scholar on 28 April 1664 and received his bachelor’s degree in April 1665. It would appear that his scientific genius had still not emerged, but it did so suddenly when the plague closed the University in the summer of 1665 and he had to return to Lincolnshire. There, in a period of less than two years, while Newton was still under 25 years old, he began revolutionary advances in mathematics, optics, physics, and astronomy.
While Newton remained at home he laid the foundations for differential and integral calculus, several years before its independent discovery by Leibniz. The ‘method of fluxions’, as he termed it, was based on his crucial insight that the integration of a function is merely the inverse procedure to differentiating it. Taking differentiation as the basic operation, Newton produced simple analytical methods that unified many separate techniques previously developed to solve apparently unrelated problems such as finding areas, tangents, the lengths of curves and the maxima and minima of functions. Newton’s De Methodis Serierum et Fluxionum was written in 1671 but Newton failed to get it published and it did not appear in print until John Colson produced an English translation in 1736.
Newton’s first work as Lucasian Professor was on optics and this was the topic of his first lecture course begun in January 1670. He had reached the conclusion during the two plague years that white light is not a simple entity. Every scientist since Aristotle had believed that white light was a basic single entity, but the chromatic aberration in a telescope lens convinced Newton otherwise. When he passed a thin beam of sunlight through a glass prism Newton noted the spectrum of colours that was formed.
He argued that white light is really a mixture of many different types of rays which are refracted at slightly different angles, and that each different type of ray produces a different spectral colour. Newton was led by this reasoning to the erroneous conclusion that telescopes using refracting lenses would always suffer chromatic aberration. He therefore proposed and constructed a reflecting telescope.
In 1672 Newton was elected a fellow of the Royal Society after donating a reflecting telescope. Also in 1672 Newton published his first scientific paper on light and colour in the Philosophical Transactions of the Royal Society. The paper was generally well received but Hooke and Huygens objected to Newton’s attempt to prove, by experiment alone, that light consists of the motion of small particles rather than waves. The reception that his publication received did nothing to improve Newton’s attitude to making his results known to the world. He was always pulled in two directions, there was something in his nature which wanted fame and recognition yet another side of him feared criticism and the easiest way to avoid being criticised was to publish nothing. Certainly one could say that his reaction to criticism was irrational, and certainly his aim to humiliate Hooke in public because of his opinions was abnormal. However, perhaps because of Newton’s already high reputation, his corpuscular theory reigned until the wave theory was revived in the 19th century.
Newton’s relations with Hooke deteriorated further when, in 1675, Hooke claimed that Newton had stolen some of his optical results. Although the two men made their peace with an exchange of polite letters, Newton turned in on himself and away from the Royal Society which he associated with Hooke as one of its leaders. He delayed the publication of a full account of his optical researches until after the death of Hooke in 1703. Newton’s Opticks appeared in 1704. It dealt with the theory of light and colour and with investigations of the colours of thin sheets ‘Newton’s rings’ and diffraction of light. To explain some of his observations he had to use a wave theory of light in conjunction with his corpuscular theory.
Another argument, this time with the English Jesuits in Liège over his theory of colour, led to a violent exchange of letters, then in 1678 Newton appears to have suffered a nervous breakdown. His mother died in the following year and he withdrew further into his shell, mixing as little as possible with people for a number of years.
Newton’s greatest achievement was his work in physics and celestial mechanics, which culminated in the theory of universal gravitation. By 1666 Newton had early versions of his three laws of motion. He had also discovered the law giving the centrifugal force on a body moving uniformly in a circular path. However he did not have a correct understanding of the mechanics of circular motion.
Newton’s novel idea of 1666 was to imagine that the Earth’s gravity influenced the Moon, counter- balancing its centrifugal force. From his law of centrifugal force and Kepler’s third law of planetary motion, Newton deduced the inverse-square law.
The Principia is recognised as the greatest scientific book ever written. Newton analysed the motion of bodies in resisting and non-resisting media under the action of centripetal forces. The results were applied to orbiting bodies, projectiles, pendulums, and free-fall near the Earth. He further demonstrated that the planets were attracted toward the Sun by a force varying as the inverse square of the distance and generalised that all heavenly bodies mutually attract one another. He also went on to write all of his own theory of gravity which even to this day is found accurate for all non-relativistic objects.
The Modern period of 1900 and on has been marked by many great men of science. But none other has made the impact that Albert Einstein did.
Around 1886 Albert Einstein began his school career in Munich. As well as his violin lessons, which he had from age six to age thirteen, he also had religious education at home where he was taught Judaism. Two years later he entered the Luitpold Gymnasium and after this his religious education was given at school. He studied mathematics, in particular the calculus, beginning around 1891.
In 1894 Einstein’s family moved to Milan but Einstein remained in Munich. In 1895 Einstein failed an examination that would have allowed him to study for a diploma as an electrical engineer at the Eidgenössische Technische Hochschule in Zurich. Einstein renounced German citizenship in 1896 and was to be stateless for a number of years. He did not even apply for Swiss citizenship until 1899, citizenship being granted in 1901.
Following the failing of the entrance exam to the ETH, Einstein attended secondary school at Aarau planning to use this route to enter the ETH in Zurich.
Einstein graduated in 1900 as a teacher of mathematics and physics. One of his friends at ETH was Marcel Grossmann who was in the same class as Einstein. Einstein tried to obtain a post, writing to Hurwitz who held out some hope of a position but nothing came of it. Three of Einstein’s fellow students, including Grossmann, were appointed assistants at ETH in Zurich but clearly Einstein had not impressed enough and still in 1901 he was writing round universities in the hope of obtaining a job, but without success.
He did manage to avoid Swiss military service on the grounds that he had flat feet and varicose veins. By mid 1901 he had a temporary job as a teacher, teaching mathematics at the Technical High School in Winterthur.
Another temporary position teaching in a private school in Schaffhausen followed. Then Grossmann’s father tried to help Einstein get a job by recommending him to the director of the patent office in Bern. Einstein was appointed as a technical expert third class.
Einstein worked in this patent office from 1902 to 1909, holding a temporary post when he was first appointed, but by 1904 the position was made permanent and in 1906 he was promoted to technical expert second class. While in the Bern patent office he completed an astonishing range of theoretical physics publications, written in his spare time without the benefit of close contact with scientific literature or colleagues.
Einstein earned a doctorate from the University of Zurich in 1905 for a thesis On a new determination of molecular dimensions. He dedicated the thesis to Grossmann.
In the first of three papers, all written in 1905, Einstein examined the phenomenon discovered by Max Planck, according to which electromagnetic energy seemed to be emitted from radiating objects in discrete quantities. The energy of these quanta was directly proportional to the frequency of the radiation. This seemed to contradict classical electromagnetic theory, based on Maxwell’s equations and the laws of thermodynamics which assumed that electromagnetic energy consisted of waves which could contain any small amount of energy. Einstein used Planck’s quantum hypothesis to describe the electromagnetic radiation of light.
Einstein’s second 1905 paper proposed what is today called the special theory of relativity. He based his new theory on a reinterpretation of the classical principle of relativity, namely that the laws of physics had to have the same form in any frame of reference. As a second fundamental hypothesis, Einstein assumed that the speed of light remained constant in all frames of reference, as required by Maxwell’s theory.
Later in 1905 Einstein showed how mass and energy were equivalent. Einstein was not the first to propose all the components of special theory of relativity. His contribution is unifying important parts of classical mechanics and Maxwell’s electrodynamics.
The third of Einstein’s papers of 1905 concerned statistical mechanics, a field of that had been studied by Ludwig Boltzmann and Josiah Gibbs.
After 1905 Einstein continued working in the areas described above. He made important contributions to quantum theory, but he sought to extend the special theory of relativity to phenomena involving acceleration. The key appeared in 1907 with the principle of equivalence, in which gravitational acceleration was held to be indistinguishable from acceleration caused by mechanical forces. Gravitational mass was therefore identical with inertial mass.
In 1908 Einstein became a lecturer at the University of Bern after submitting his Habilitation thesis Consequences for the constitution of radiation following from the energy distribution law of black bodies. The following year he become professor of physics at the University of Zurich, having resigned his lectureship at Bern and his job in the patent office in Bern.
By 1909 Einstein was recognised as a leading scientific thinker and in that year he resigned from the patent office. He was appointed a full professor at the Karl-Ferdinand University in Prague in 1911. In fact 1911 was a very significant year for Einstein since he was able to make preliminary predictions about how a ray of light from a distant star, passing near the Sun, would appear to be bent slightly, in the direction of the Sun. This would be highly significant as it would lead to the first experimental evidence in favour of Einstein’s theory.
About 1912, Einstein began a new phase of his gravitational research, with the help of his mathematician friend Marcel Grossmann, by expressing his work in terms of the tensor calculus of Tullio Levi-Civita and Gregorio Ricci-Curbastro. Einstein called his new work the general theory of relativity. He moved from Prague to Zurich in 1912 to take up a chair at the Eidgenössische Technische Hochschule in Zurich.
Einstein returned to Germany in 1914 but did not reapply for German citizenship. What he accepted was an impressive offer. It was a research position in the Prussian Academy of Sciences together with a chair (but no teaching duties) at the University of Berlin. He was also offered the directorship of the Kaiser Wilhelm Institute of Physics in Berlin which was about to be established.
After a number of false starts Einstein published, late in 1915, the definitive version of general theory. Just before publishing this work he lectured on general relativity at Göttingen.
When British eclipse expeditions in 1919 confirmed his predictions, Einstein was idolised by the popular press. Einstein received the Nobel Prize in 1921 but not for relativity rather for his 1905 work on the photoelectric effect. In fact he was not present in December 1922 to receive the prize being on a voyage to Japan. Around this time he made many international visits. He had visited Paris earlier in 1922 and during 1923 he visited Palestine. After making his last major scientific discovery on the association of waves with matter in 1924 he made further visits in 1925, this time to South America.
To this historical list we could add further such men as Wilhelm Roentgen, A. H. Becquerel, J. J. Thomson, Marie and Pierre Curie, Ernest Rutherford, A. A. Michelson and E. W. Morley, Josef Stefan, Ludwig Boltzmann, Wilhelm Wien, Niels Bohr, Arthur Compton, Werner Heisenberg, Louis de Broglie, Erwin Schrödinger, Paul Dirac, Richard Feynman, Nathan Rosen, David Bohm, John Bell, Steven Hawking, Richard Gott, and many others who have added to our knowledge of the universe.
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