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Old Wednesday, September 19, 2007
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Albert Einstein was born at Ulm, in Württemberg, Germany, on March 14, 1879. Six weeks later the family moved to Munich, where he later on began his schooling at the Luitpold Gymnasium. Later, they moved to Italy and Albert continued his education at Aarau, Switzerland and in 1896 he entered the Swiss Federal Polytechnic School in Zurich to be trained as a teacher in physics and mathematics. In 1901, the year he gained his diploma, he acquired Swiss citizenship and, as he was unable to find a teaching post, he accepted a position as technical assistant in the Swiss Patent Office. In 1905 he obtained his doctor's degree.

During his stay at the Patent Office, and in his spare time, he produced much of his remarkable work and in 1908 he was appointed Privatdozent in Berne. In 1909 he became Professor Extraordinary at Zurich, in 1911 Professor of Theoretical Physics at Prague, returning to Zurich in the following year to fill a similar post. In 1914 he was appointed Director of the Kaiser Wilhelm Physical Institute and Professor in the University of Berlin. He became a German citizen in 1914 and remained in Berlin until 1933 when he renounced his citizenship for political reasons and emigrated to America to take the position of Professor of Theoretical Physics at Princeton*. He became a United States citizen in 1940 and retired from his post in 1945.

After World War II, Einstein was a leading figure in the World Government Movement, he was offered the Presidency of the State of Israel, which he declined, and he collaborated with Dr. Chaim Weizmann in establishing the Hebrew University of Jerusalem.

Einstein always appeared to have a clear view of the problems of physics and the determination to solve them. He had a strategy of his own and was able to visualize the main stages on the way to his goal. He regarded his major achievements as mere stepping-stones for the next advance.

At the start of his scientific work, Einstein realized the inadequacies of Newtonian mechanics and his special theory of relativity stemmed from an attempt to reconcile the laws of mechanics with the laws of the electromagnetic field. He dealt with classical problems of statistical mechanics and problems in which they were merged with quantum theory: this led to an explanation of the Brownian movement of molecules. He investigated the thermal properties of light with a low radiation density and his observations laid the foundation of the photon theory of light.

In his early days in Berlin, Einstein postulated that the correct interpretation of the special theory of relativity must also furnish a theory of gravitation and in 1916 he published his paper on the general theory of relativity. During this time he also contributed to the problems of the theory of radiation and statistical mechanics.

In the 1920's, Einstein embarked on the construction of unified field theories, although he continued to work on the probabilistic interpretation of quantum theory, and he persevered with this work in America. He contributed to statistical mechanics by his development of the quantum theory of a monatomic gas and he has also accomplished valuable work in connection with atomic transition probabilities and relativistic cosmology.

After his retirement he continued to work towards the unification of the basic concepts of physics, taking the opposite approach, geometrisation, to the majority of physicists.

Einstein's researches are, of course, well chronicled and his more important works include Special Theory of Relativity (1905), Relativity (English translations, 1920 and 1950), General Theory of Relativity (1916), Investigations on Theory of Brownian Movement (1926), and The Evolution of Physics (1938). Among his non-scientific works, About Zionism (1930), Why War? (1933), My Philosophy (1934), and Out of My Later Years (1950) are perhaps the most important.

Albert Einstein received honorary doctorate degrees in science, medicine and philosophy from many European and American universities. During the 1920's he lectured in Europe, America and the Far East and he was awarded Fellowships or Memberships of all the leading scientific academies throughout the world. He gained numerous awards in recognition of his work, including the Copley Medal of the Royal Society of London in 1925, and the Franklin Medal of the Franklin Institute in 1935.

Einstein's gifts inevitably resulted in his dwelling much in intellectual solitude and, for relaxation, music played an important part in his life. He married Mileva Maric in 1903 and they had a daughter and two sons; their marriage was dissolved in 1919 and in the same year he married his cousin, Elsa Löwenthal, who died in 1936. He died on April 18, 1955 at Princeton, New Jersey.
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Sir Isaac Newton
I INTRODUCTION
Newton, Sir Isaac (1642-1727), mathematician and physicist, one of the foremost scientific intellects of all time. Born at Woolsthorpe, near Grantham in Lincolnshire, where he attended school, he entered Cambridge University in 1661; he was elected a Fellow of Trinity College in 1667, and Lucasian Professor of Mathematics in 1669. He remained at the university, lecturing in most years, until 1696. Of these Cambridge years, in which Newton was at the height of his creative power, he singled out 1665-1666 (spent largely in Lincolnshire because of plague in Cambridge) as "the prime of my age for invention". During two to three years of intense mental effort he prepared Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) commonly known as the Principia, although this was not published until 1687.

As a firm opponent of the attempt by King James II to make the universities into Catholic institutions, Newton was elected Member of Parliament for the University of Cambridge to the Convention Parliament of 1689, and sat again in 1701-1702. Meanwhile, in 1696 he had moved to London as Warden of the Royal Mint. He became Master of the Mint in 1699, an office he retained to his death. He was elected a Fellow of the Royal Society of London in 1671, and in 1703 he became President, being annually re-elected for the rest of his life. His major work, Opticks, appeared the next year; he was knighted in Cambridge in 1705.

As Newtonian science became increasingly accepted on the Continent, and especially after a general peace was restored in 1714, following the War of the Spanish Succession, Newton became the most highly esteemed natural philosopher in Europe. His last decades were passed in revising his major works, polishing his studies of ancient history, and defending himself against critics, as well as carrying out his official duties. Newton was modest, diffident, and a man of simple tastes. He was angered by criticism or opposition, and harboured resentment; he was harsh towards enemies but generous to friends. In government, and at the Royal Society, he proved an able administrator. He never married and lived modestly, but was buried with great pomp in Westminster Abbey.

Newton has been regarded for almost 300 years as the founding examplar of modern physical science, his achievements in experimental investigation being as innovative as those in mathematical research. With equal, if not greater, energy and originality he also plunged into chemistry, the early history of Western civilization, and theology; among his special studies was an investigation of the form and dimensions, as described in the Bible, of Solomon's Temple in Jerusalem.

II OPTICS
In 1664, while still a student, Newton read recent work on optics and light by the English physicists Robert Boyle and Robert Hooke; he also studied both the mathematics and the physics of the French philosopher and scientist René Descartes. He investigated the refraction of light by a glass prism; developing over a few years a series of increasingly elaborate, refined, and exact experiments, Newton discovered measurable, mathematical patterns in the phenomenon of colour. He found white light to be a mixture of infinitely varied coloured rays (manifest in the rainbow and the spectrum), each ray definable by the angle through which it is refracted on entering or leaving a given transparent medium. He correlated this notion with his study of the interference colours of thin films (for example, of oil on water, or soap bubbles), using a simple technique of extreme acuity to measure the thickness of such films. He held that light consisted of streams of minute particles. From his experiments he could infer the magnitudes of the transparent "corpuscles" forming the surfaces of bodies, which, according to their dimensions, so interacted with white light as to reflect, selectively, the different observed colours of those surfaces.

The roots of these unconventional ideas were with Newton by about 1668; when first expressed (tersely and partially) in public in 1672 and 1675, they provoked hostile criticism, mainly because colours were thought to be modified forms of homogeneous white light. Doubts, and Newton's rejoinders, were printed in the learned journals. Notably, the scepticism of Christiaan Huygens and the failure of the French physicist Edmé Mariotte to duplicate Newton's refraction experiments in 1681 set scientists on the Continent against him for a generation. The publication of Opticks, largely written by 1692, was delayed by Newton until the critics were dead. The book was still imperfect: the colours of diffraction defeated Newton. Nevertheless, Opticks established itself, from about 1715, as a model of the interweaving of theory with quantitative experimentation.

III MATHEMATICS
In mathematics too, early brilliance appeared in Newton's student notes. He may have learnt geometry at school, though he always spoke of himself as self-taught; certainly he advanced through studying the writings of his compatriots William Oughtred and John Wallis, and of Descartes and the Dutch school. Newton made contributions to all branches of mathematics then studied, but is especially famous for his solutions to the contemporary problems in analytical geometry of drawing tangents to curves (differentiation) and defining areas bounded by curves (integration). Not only did Newton discover that these problems were inverse to each other, but he discovered general methods of resolving problems of curvature, embraced in his "method of fluxions" and "inverse method of fluxions", respectively equivalent to Leibniz's later differential and integral calculus. Newton used the term "fluxion" (from Latin meaning "flow") because he imagined a quantity "flowing" from one magnitude to another. Fluxions were expressed algebraically, as Leibniz's differentials were, but Newton made extensive use also (especially in the Principia) of analogous geometrical arguments. Late in life, Newton expressed regret for the algebraic style of recent mathematical progress, preferring the geometrical method of the Classical Greeks, which he regarded as clearer and more rigorous.

Newton's work on pure mathematics was virtually hidden from all but his correspondents until 1704, when he published, with Opticks, a tract on the quadrature of curves (integration) and another on the classification of the cubic curves. His Cambridge lectures, delivered from about 1673 to 1683, were published in 1707.

The Calculus Priority Dispute
Newton had the essence of the methods of fluxions by 1666. The first to become known, privately, to other mathematicians, in 1668, was his method of integration by infinite series. In Paris in 1675 Gottfried Wilhelm Leibniz independently evolved the first ideas of his differential calculus, outlined to Newton in 1677. Newton had already described some of his mathematical discoveries to Leibniz, not including his method of fluxions. In 1684 Leibniz published his first paper on calculus; a small group of mathematicians took up his ideas.

In the 1690s Newton's friends proclaimed the priority of Newton's methods of fluxions. Supporters of Leibniz asserted that he had communicated the differential method to Newton, although Leibniz had claimed no such thing. Newtonians then asserted, rightly, that Leibniz had seen papers of Newton's during a London visit in 1676; in reality, Leibniz had taken no notice of material on fluxions. A violent dispute sprang up, part public, part private, extended by Leibniz to attacks on Newton's theory of gravitation and his ideas about God and creation; it was not ended even by Leibniz's death in 1716. The dispute delayed the reception of Newtonian science on the Continent, and dissuaded British mathematicians from sharing the researches of Continental colleagues for a century.

IV MECHANICS AND GRAVITATION
According to the well-known story, it was on seeing an apple fall in his orchard at some time during 1665 or 1666 that Newton conceived that the same force governed the motion of the Moon and the apple. He calculated the force needed to hold the Moon in its orbit, as compared with the force pulling an object to the ground. He also calculated the centripetal force needed to hold a stone in a sling, and the relation between the length of a pendulum and the time of its swing. These early explorations were not soon exploited by Newton, though he studied astronomy and the problems of planetary motion.

Correspondence with Hooke (1679-1680) redirected Newton to the problem of the path of a body subjected to a centrally directed force that varies as the inverse square of the distance; he determined it to be an ellipse, so informing Edmond Halley in August 1684. Halley's interest led Newton to demonstrate the relationship afresh, to compose a brief tract on mechanics, and finally to write the Principia.

Book I of the Principia states the foundations of the science of mechanics, developing upon them the mathematics of orbital motion round centres of force. Newton identified gravitation as the fundamental force controlling the motions of the celestial bodies. He never found its cause. To contemporaries who found the idea of attractions across empty space unintelligible, he conceded that they might prove to be caused by the impacts of unseen particles.

Book II inaugurates the theory of fluids: Newton solves problems of fluids in movement and of motion through fluids. From the density of air he calculated the speed of sound waves.

Book III shows the law of gravitation at work in the universe: Newton demonstrates it from the revolutions of the six known planets, including the Earth, and their satellites. However, he could never quite perfect the difficult theory of the Moon's motion. Comets were shown to obey the same law; in later editions, Newton added conjectures on the possibility of their return. He calculated the relative masses of heavenly bodies from their gravitational forces, and the oblateness of Earth and Jupiter, already observed. He explained tidal ebb and flow and the precession of the equinoxes from the forces exerted by the Sun and Moon. All this was done by exact computation.

Newton's work in mechanics was accepted at once in Britain, and universally after half a century. Since then it has been ranked among humanity's greatest achievements in abstract thought. It was extended and perfected by others, notably Pierre Simon de Laplace, without changing its basis and it survived into the late 19th century before it began to show signs of failing. See Quantum Theory; Relativity.

V ALCHEMY AND CHEMISTRY
Newton left a mass of manuscripts on the subjects of alchemy and chemistry, then closely related topics. Most of these were extracts from books, bibliographies, dictionaries, and so on, but a few are original. He began intensive experimentation in 1669, continuing till he left Cambridge, seeking to unravel the meaning that he hoped was hidden in alchemical obscurity and mysticism. He sought understanding of the nature and structure of all matter, formed from the "solid, massy, hard, impenetrable, movable particles" that he believed God had created. Most importantly in the "Queries" appended to "Opticks" and in the essay "On the Nature of Acids" (1710), Newton published an incomplete theory of chemical force, concealing his exploration of the alchemists, which became known a century after his death.

VI HISTORICAL AND CHRONOLOGICAL STUDIES
Newton owned more books on humanistic learning than on mathematics and science; all his life he studied them deeply. His unpublished "classical scholia"—explanatory notes intended for use in a future edition of the Principia—reveal his knowledge of pre-Socratic philosophy; he read the Fathers of the Church even more deeply. Newton sought to reconcile Greek mythology and record with the Bible, considered the prime authority on the early history of mankind. In his work on chronology he undertook to make Jewish and pagan dates compatible, and to fix them absolutely from an astronomical argument about the earliest constellation figures devised by the Greeks. He put the fall of Troy at 904 BC, about 500 years later than other scholars; this was not well received.

VII RELIGIOUS CONVICTIONS AND PERSONALITY
Newton also wrote on Judaeo-Christian prophecy, whose decipherment was essential, he thought, to the understanding of God. His book on the subject, which was reprinted well into the Victorian Age, represented lifelong study. Its message was that Christianity went astray in the 4th century AD, when the first Council of Nicaea propounded erroneous doctrines of the nature of Christ. The full extent of Newton's unorthodoxy was recognized only in the present century: but although a critic of accepted Trinitarian dogmas and the Council of Nicaea, he possessed a deep religious sense, venerated the Bible and accepted its account of creation. In late editions of his scientific works he expressed a strong sense of God's providential role in nature.

VIII PUBLICATIONS
Newton published an edition of Geographia generalis by the German geographer Varenius in 1672. His own letters on optics appeared in print from 1672 to 1676. Then he published nothing until the Principia (published in Latin in 1687; revised in 1713 and 1726; and translated into English in 1729). This was followed by Opticks in 1704; a revised edition in Latin appeared in 1706. Posthumously published writings include The Chronology of Ancient Kingdoms Amended (1728), The System of the World (1728), the first draft of Book III of the Principia, and Observations upon the Prophecies of Daniel and the Apocalypse of St John (1733).
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Johannes Kepler

Johannes Kepler was born at 2:30 PM on December 27, 1571, in Weil der Stadt, Württemburg, in the Holy Roman Empire of German Nationality. He was a sickly child and his parents were poor. But his evident intelligence earned him a scholarship to the University of Tübingen to study for the Lutheran ministry. There he was introduced to the ideas of Copernicus and delighted in them. In 1596, while a mathematics teacher in Graz, he wrote the first outspoken defense of the Copernican system, the Mysterium Cosmographicum.

Kepler's family was Lutheran and he adhered to the Augsburg Confession a defining document for Lutheranism. However, he did not adhere to the Lutheran position on the real presence and refused to sign the Formula of Concord. Because of his refusal he was excluded from the sacrament in the Lutheran church. This and his refusal to convert to Catholicism left him alienated by both the Lutherans and the Catholics. Thus he had no refuge during the Thirty-Years War.
The Holy Roman Empire of German Nationality at the Time of Kepler


Kepler was forced to leave his teaching post at Graz due to the counter Reformation because he was Lutheran and moved to Prague to work with the renowned Danish astronomer, Tycho Brahe. He inherited Tycho's post as Imperial Mathematician when Tycho died in 1601. Using the precise data that Tycho had collected, Kepler discovered that the orbit of Mars was an ellipse. In 1609 he published Astronomia Nova, delineating his discoveries, which are now called Kepler's first two laws of planetary motion. And what is just as important about this work, "it is the first published account wherein a scientist documents how he has coped with the multitude of imperfect data to forge a theory of surpassing accuracy" (O. Gingerich in forward to Johannes Kepler New Astronomy translated by W. Donahue, Cambridge Univ Press, 1992), a fundamental law of nature. Today we call this the scientific method.

In 1612 Lutherans were forced out of Prague, so Kepler moved on to Linz. His wife and two sons had recently died. He remarried happily, but had many personal and financial troubles. Two infant daughters died and Kepler had to return to Württemburg where he successfully defended his mother against charges of witchcraft. In 1619 he published Harmonices Mundi, in which he describes his "third law."

In spite of more forced relocations, Kepler published the seven-volume Epitome Astronomiae in 1621. This was his most influential work and discussed all of heliocentric astronomy in a systematic way. He then went on to complete the Rudolphine Tables that Tycho had started long ago. These included calculations using logarithms, which he developed, and provided perpetual tables for calculating planetary positions for any past or future date. Kepler used the tables to predict a pair of transits by Mercury and Venus of the Sun, although he did not live to witness the events.

Johannes Kepler died in Regensburg in 1630, while on a journey from his home in Sagan to collect a debt. His grave was demolished within two years because of the Thirty Years War. Frail of body, but robust in mind and spirit, Kepler was scrupulously honest to the data.
A List of Kepler's Firsts
First to correctly explain planetary motion, thereby, becoming founder of celestial mechanics and the first "natural laws" in the modern sense; being universal, verifiable, precise.

In his book Astronomia Pars Optica, for which he earned the title of founder of modern optics he was the:
First to investigate the formation of pictures with a pin hole camera;
First to explain the process of vision by refraction within the eye;
First to formulate eyeglass designing for nearsightedness and farsightedness;
First to explain the use of both eyes for depth perception.

In his book Dioptrice (a term coined by Kepler and still used today) he was the:
First to describe: real, virtual, upright and inverted images and magnification;
First to explain the principles of how a telescope works;
First to discover and describe the properties of total internal reflection.

In addition:
His book Stereometrica Doliorum formed the basis of integral calculus.
First to explain that the tides are caused by the Moon (Galileo reproved him for this).
Tried to use stellar parallax caused by the Earth's orbit to measure the distance to the stars; the same principle as depth perception. Today this branch of research is called astrometry.
First to suggest that the Sun rotates about its axis in Astronomia Nova
First to derive the birth year of Christ, that is now universally accepted.
First to derive logarithms purely based on mathematics, independent of Napier's tables published in 1614.
He coined the word "satellite" in his pamphlet Narratio de Observatis a se quatuor Iovis sattelitibus erronibus
Kepler's Laws of Planetary Motion

Kepler was assigned the task by Tycho Brahe to analyze the observations that Tycho had made of Mars. Of all the planets, the predicted position of Mars had the largest errors and therefore posed the greatest problem. Tycho's data were the best available before the invention of the telescope and the accuracy was good enough for Kepler to show that Mars' orbit would precisely fit an ellipse. In 1605 he announced The First Law:

Planets move in ellipses with the Sun at one focus.


The figure below illustrates two orbits with the same semi-major axis, focus and orbital period: one a circle with an eccentricity of 0.0; the other an ellipse with an eccentricity of 0.8.
Circular and Elliptical Orbits Having the Same Period and Focus

Prior to this in 1602, Kepler found from trying to calculate the position of the Earth in its orbit that as it sweeps out an area defined by the Sun and the orbital path of the Earth that:

The radius vector describes equal areas in equal times. (The Second Law)


Kepler published these two laws in 1609 in his book Astronomia Nova.

For a circle the motion is uniform as shown above, but in order for an object along an elliptical orbit to sweep out the area at a uniform rate, the object moves quickly when the radius vector is short and the object moves slowly when the radius vector is long.

On May 15, 1618 he discovered The Third Law:

The squares of the periodic times are to each other as the cubes of the mean distances.


This law he published in 1619 in his Harmonices Mundi . It was this law, not an apple, that lead Newton to his law of gravitation. Kepler can truly be called the founder of celestial mechanics.
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Galileo Galilei

The Italian scientist Galileo Galilei (1564-1642) is renowned for his epoch-making contributions to astronomy, physics, and scientific philosophy.

Galileo was born in Pisa on Feb. 15, 1564, the first child of Vincenzio Galilei, a merchant and musician and an abrasive champion of advanced musical theories of the day. The family moved to Florence in 1574, and that year Galileo started his formal education in the nearby monastery of Vallombrosa. Seven years later he matriculated as a student of medicine at the University of Pisa.

In 1583, while Galileo was at home on vacation, he began to study mathematics and the physical sciences. His zeal astonished Ostilio Ricci, a family friend and professor at the Academy of Design. Ricci was a student of Nicolò Tartaglia, the famed algebraist and translator into Latin of several of Archimedes' works. Galileo's life-long admiration for Archimedes started, therefore, as his scientific studies got under way.

Galileo's new interest brought to an end his medical studies, but in Pisa at that time there was only one notable science teacher, Francisco Buonamico, and he was an Aristotelian. Galileo seems, however, to have been an eager disciple of his, as shown by Galileo's Juvenilia, dating from 1584, mostly paraphrases of Aristotelian physics and cosmology. Because of financial difficulties Galileo had to leave the University of Pisa in 1585 before he got his degree.

Early Work

Back in Florence, Galileo spent 3 years vainly searching for a suitable teaching position. He was more successful in furthering his grasp of mathematics and physics. He produced two treatises which, although circulated in manuscript form only, made his name well known. One was La bilancetta (The Little Balance), describing the hydrostatic principles of balancing; the other was a study on the center of gravity of various solids. These topics, obviously demanding a geometrical approach, were not the only evidence of his devotion to geometry and Archimedes. In a lecture given in 1588 before the Florentine Academy on the topography of Dante's Inferno, Galileo seized on details that readily lent themselves to a display of his prowess in geometry. He showed himself a perfect master both of the poet's text and of the incisiveness and sweep of geometrical lore.

Galileo's rising reputation as a mathematician and natural philosopher (physicist) gained him a teaching post at the University of Pisa in 1589. The 3 years he spent there are memorable for two things. First, he became exposed through reading a work of Giovanni Battista Benedetti to the "Parisian tradition" of physics, which originated during the 14th century with the speculations of Jean Buridan and Nicole Oresme at the University of Paris. This meant the breakaway point in Galileo's thought from Aristotelian physics and the start of his preoccupation with a truly satisfactory formulation of the impetus theory. Second, right at the beginning of his academic career, he showed himself an eager participant in disputes and controversies. With biting sarcasm he lampooned the custom of wearing academic gowns. The most he was willing to condone was the use of ordinary clothes, but only after pointing out that the best thing was to go naked.

The death of Galileo's father in 1591 put on his shoulders the care of his mother, brothers, and sisters. He had to look for a better position, which he found in 1592 at the University of Padua, part of the Venetian Republic. The 18 years he spent there were, according to his own admission, the happiest of his life. He often visited Venice and made many influential friends, among them Giovanfrancesco Sagredo, whom he later immortalized in the Dialogue as the representative of judiciousness and good sense.

In 1604 Galileo publicly declared that he was a Copernican. In three public lectures given in Venice, before an overflow audience, he argued that the new star which appeared earlier that year was major evidence in support of the doctrine of Copernicus. (Actually the new star merely proved that there was something seriously wrong with the Aristotelian doctrine of the heavens.) More important was a letter Galileo wrote that year to Father Paolo Sarpi, in which he stated that "the distances covered in natural motion are proportional to the squares of the number of time intervals, and therefore, the distances covered in equal times are as the odd numbers beginning from one." By natural motion, Galileo meant the unimpeded fall of a body, and what he proposed was the law of free fall, later written as s = 1/2 (gt2), where s is distance, t is time, and g is the acceleration due to gravity at sea level.

In 1606 came the publication of The Operations of the Geometrical and Military Compass, which reveals the experimentalist and craftsman in Galileo. In this booklet he went overboard in defending his originality against charges from rather insignificant sources. It was craftsmanship, not theorizing, which put the crowning touch on his stay in Padua. In mid-1609 he learned about the success of some Dutch spectacle makers in combining lenses into what later came to be called a telescope. He feverishly set to work, and on August 25 he presented to the Venetian Senate a telescope as his own invention. The success was tremendous. He obtained a lifelong contract at the University of Padua, but he also stirred up just resentment when it was learned that he was not the original inventor.

Astronomical Works

Galileo's success in making a workable and sufficiently powerful telescope with a magnifying power of about 40 was due to intuition rather than to rigorous reasoning in optics. It was also the intuitive stroke of a genius that made him turn the telescope toward the sky sometime in the fall of 1609, a feat which a dozen other people could very well have done during the previous 4 to 5 years. Science had few luckier moments. Within a few months he gathered astonishing evidence about mountains on the moon, about moons circling Jupiter, and about an incredibly large number of stars, especially in the belt of the Milky Way. On March 12, 1610, all these sensational items were printed in Venice under the title Sidereus nuncius (The Starry Messenger), a booklet which took the world of science by storm. The view of the heavens drastically changed, and so did Galileo's life.

Historians agree that Galileo's decision to secure for himself the position of court mathematician in Florence at the court of Cosimo II (the job also included the casting of horoscopes for his princely patron) reveals a heavy strain of selfishness in his character. He wanted nothing, not even a modest amount of teaching, to impede him in pursuing his ambition to become the founder of new physics and new astronomy. In 1610 he left behind in Padua his common-law wife, Marina Gamba, and his young son, Vincenzio, and placed his two daughters, aged 12 and 13, in the convent of S. Matteo in Arcetri. The older, Sister Maria Celeste as nun, was later a great comfort to her father.

Galileo's move to Florence turned out to be highly unwise, as events soon showed. In the beginning, however, everything was pure bliss. He made a triumphal visit to Rome in 1611. The next year saw the publication of his Discourse on Bodies in Water. There he disclosed his discovery of the phases of Venus (a most important proof of the truth of the Copernican theory), but the work was also the source of heated controversies. In 1613 Galileo published his observations of sunspots, which embroiled him for many years in bitter disputes with the German Jesuit Christopher Scheiner of the University of Ingolstadt, whose observations of sunspots had already been published in January 1612 under the pseudonym Apelles.

First Condemnation

But Galileo's real aim was to make a sweeping account of the Copernican universe and of the new physics it necessitated. A major obstacle was the generally shared, though officially never sanctioned, belief that the biblical revelation imposed geocentrism in general and the motionlessness of the earth in particular. To counter the scriptural difficulties, he waded deep into theology. With the help of some enlightened ecclesiastics, such as Monsignor Piero Dini and Father Benedetto Castelli, a Benedictine from Monte Cassino and his best scientific pupil, Galileo produced essays in the form of letters, which now rank among the best writings of biblical theology of those times. As the letters (the longest one was addressed to Grand Duchess Christina of Tuscany) circulated widely, a confrontation with the Church authorities became inevitable. The disciplinary instruction handed down in 1616 by Cardinal Robert Bellarmine forbade Galileo to "hold, teach and defend in any manner whatsoever, in words or in print" the Copernican doctrine of the motion of the earth.

Galileo knew, of course, both the force and the limits of what in substance was a disciplinary measure. It could be reversed, and he eagerly looked for any evidence indicating precisely that. He obeyed partly out of prudence, partly because he remained to the end a devout and loyal Catholic. Although his yearning for fame was powerful, there can be no doubt about the sincerity of his often-voiced claim that by his advocacy of Copernicanism he wanted to serve the long-range interest of the Church in a world of science. The first favorable sign came in 1620, when Cardinal Maffeo Barberini composed a poem in honor of Galileo. Three years later the cardinal became Pope Urban VIII. How encouraged Galileo must have felt can be seen from the fact that he dedicated to the new pope his freshly composed Assayer, one of the finest pieces of polemics ever produced in the philosophy of science.

The next year Galileo had six audiences with Urban VIII, who promised a pension for Galileo's son, Vincenzio, but gave Galileo no firm assurance about changing the injunction of 1616. But before departing for Florence, Galileo was informed that the Pope had remarked that "the Holy Church had never, and would never, condemn it [Copernicanism] as heretical but only as rash, though there was no danger that anyone would ever demonstrate it to be necessarily true." This was more than enough to give Galileo the necessary encouragement to go ahead with the great undertaking of his life.

The Dialogue

Galileo spent 6 years writing his Dialogue concerning the Two Chief World Systems. When the final manuscript copy was being made in March 1630, Father Castelli dispatched the news to Galileo that Urban VIII insisted in a private conversation with him that, had he been the pope in 1616, the censuring of Copernicanism would have never taken place. Galileo also learned about the benevolent attitude of the Pope's official theologian, Father Nicolò Riccardi, Master of the Sacred Palace. The book was published with ecclesiastical approbation on Feb. 21, 1632.

Its contents are easy to summarize, as its four main topics are discussed in dialogue form on four consecutive days. Of the three interlocutors, Simplicius represented Aristotle, Salviati was Galileo's spokesman, and Sagredo played the role of the judicious arbiter leaning heavily toward Galileo. The First Day is devoted to the criticism of the alleged perfection of the universe and especially of its superlunary region, as claimed by Aristotle. Here Galileo made ample use of his discovery of the "imperfections" of the moon, namely, of its rugged surface revealed by the telescope. The Second Day is a discussion of the advantages of the rotation of the earth on its axis for the explanation of various celestial phenomena. During the Third Day the orbital motion of the earth around the sun is debated, the principal issues being the parallax of stars and the undisturbed state of affairs on the surface of the earth in spite of its double motion. In this connection Galileo gave the most detailed account of his ideas of the relativity of motion and of the inertial motion. Bafflingly enough, he came to contradict his best-posited principles when he offered during the Fourth Day the tides as proof of the earth's twofold motion. The inconsistencies and arbitrariness that characterize his discourse there could not help undermine an otherwise magnificent effort presented in a most attractive style.

Second Condemnation

The Dialogue certainly proved that for all his rhetorical provisos Galileo held, taught, and defended the doctrine of Copernicus. It did not help Galileo either that he put into the mouth of the discredited Simplicius an argument which was a favorite with Urban VIII. Galileo was summoned to Rome to appear before the Inquisition. Legally speaking, his prosecutors were justified. Galileo did not speak the truth when he claimed before his judges that he did not hold Copernicanism since the precept was given to him in 1616 to abandon it. The justices had their point, but it was the letter of the law, not its spirit, that they vindicated. More importantly, they miscarried justice, aborted philosophical truth, and gravely compromised sound theology. In that misguided defense of orthodoxy the only sad solace for Galileo's supporters consisted in the fact that the highest authority of the Church did not become implicated, as the Catholic René Descartes, the Protestant Gottfried Wilhelm von Leibniz, and others were quick to point out during the coming decades.

The proceedings dragged on from the fall of 1632 to the summer of 1633. During that time Galileo was allowed to stay at the home of the Florentine ambassador in Rome and was detained by the Holy Office only from June 21, the day preceding his abjuration, until the end of the month. He was never subjected to physical coercion. However, he had to inflict the supreme torture upon himself by abjuring the doctrine that the earth moved. One hundred years later a writer with vivid imagination dramatized the event by claiming that following his abjuration Galileo muttered the words "Eppur si muove (And yet it does move)."

On his way back to Florence, Galileo enjoyed the hospitality of the archbishop of Siena for some 5 months and then received permission in December to live in his own villa at Arcetri. He was not supposed to have any visitors, but this injunction was not obeyed. Nor was ecclesiastical prohibition a serious obstacle to the printing of his works outside Italy. In 1634 Father Marin Mersenne published in French translation a manuscript of Galileo on mechanics composed during his Paduan period. In Holland the Elzeviers brought out his Dialogue in Latin in 1635 and shortly afterward his great theological letter to Grand Duchess Christina. But the most important event in this connection took place in 1638, when Galileo's Two New Sciences saw print in Leiden.

Two New Sciences

The first draft of the work went back to Galileo's professorship at Padua. But cosmology replaced pure physics as the center of his attention until 1633. His condemnation was in a sense a gain for physics. He had no sooner regained his composure in Siena than he was at work preparing for publication old, long-neglected manuscripts. The Two New Sciences, like the Dialogue, is in the dialogue form and the discussions are divided into Four Days. The First Day is largely taken up with the mechanical resistance of materials, with ample allowance for speculations on the atomic constitution of matter. There are also long discussions on the question of vacuum and on the isochronism of the vibrations of pendulums. During the Second Day all these and other topics, among them the properties of levers, are discussed in a strictly mathematical manner, in an almost positivist spirit, with no attention being given to "underlying causes." Equally "dry" and mathematical is the analysis of uniform and accelerated motion during the Third Day, and the same holds true of the topic of the Fourth Day, the analysis of projectile motion. There Galileo proved that the longest shot occurred when the cannon was set at an angle of 45 degrees. He arrived at this result by recognizing that the motions of the cannonball in the vertical and in the horizontal directions "can combine without changing, disturbing or impeding each other" into a parabolic path.

Galileo found the justification for such a geometrical analysis of motion partly because it led to a striking correspondence with factual data. More importantly, he believed that the universe was structured along the patterns of geometry. In 1604 he could have had experimental verification of the law of free fall, which he derived on a purely theoretical basis, but it is not known that he sought at that time such an experimental proof. He was a Christian Platonist as far as scientific method was concerned. This is why he praised Copernicus repeatedly in the Dialogue for his belief in the voice of reason, although it contradicted sense experience. Such a faith rested on the conviction that the world was a product of a personal, rational Creator who disposed everything according to weight, measure, and number.

This biblically inspired faith was stated by Galileo most eloquently in the closing pages of the First Day of the Dialogue. There he described the human mind as the most excellent product of the Creator, precisely because it could recognize mathematical truths. This faith is possibly the most precious bequest of the great Florentine, who spent his last years partially blind. His disciple Vincenzio Viviani sensed this well as he described the last hours of Galileo: "On the night of Jan. 8, 1642, with philosophical and Christian firmness he rendered up his soul to its Creator, sending it, as he liked to believe, to enjoy and to watch from a closer vantage point those eternal and immutable marvels which he, by means of a fragile device, had brought closer to our mortal eyes with such eagerness and impatience."

Further Reading

Galileo's chief works are available in excellent translations: Dialogue concerning the Two Chief World Systems (translated by Stillman Drake, 1953); Dialogues concerning Two New Sciences (translated by H. Crew and A. de Salvio, 1914; repr. 1952); and The Discoveries and Opinions of Galileo (edited and translated by Stillman Drake, 1957), which contains The Starry Messenger, the Letters on Sunspots, the Letter to Grand Duchess Christina, and the Assayer.

Stillman Drake also wrote Galileo Studies: Personality, Tradition, and Revolution (1970), which discusses Galileo and 16th-century science. An excellently written, relatively short biography is James Brodrick, Galileo: The Man, His Work, His Misfortunes (1965). Giorgio de Santillana, The Crime of Galileo (1955), and Jerome J. Langford, Galileo: Science and the Church (1966), treat Galileo's condemnation and trial. His philosophy of science is the principal consideration in Ludovico Geymonat, Galileo Galilei (1965). A Galileo bibliography of some 2,000 entries, covering the period 1940-1965, is in Galileo: Man of Science (1968), edited by Ernan McMullin, a volume of essays commemorating the four-hundredth anniversary of Galileo's birth
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