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Bill Gates
Bill Gates, born in 1955, American business executive, who serves as chairman of Microsoft Corporation, the leading computer software company in the United States. Gates cofounded Microsoft in 1975 with high school friend Paul Allen. The company’s success made Gates one of the most influential figures in the computer industry and, eventually, one of the richest people in the world.
Born in Seattle, Washington, William Henry Gates III attended public school through the sixth grade. In the seventh grade he entered Seattle’s exclusive Lakeside School, where he met Allen. Gates was first introduced to computers and programming languages in 1968, when he was in the eighth grade. That year Lakeside bought a teletype machine that connected to a mainframe computer over phone lines. At the time, the school was one of the few that provided students with access to a computer.
Soon afterward, Gates, Allen, and other students convinced a local computer company to give them free access to its PDP-10, a new minicomputer made by Digital Equipment Corporation. In exchange for the computer time, the students tried to find flaws in the system. Gates spent much of his free time on the PDP-10 learning programming languages such as BASIC, Fortran, and LISP. In 1972 Gates and Allen founded Traf-O-Data, a company that designed and built computerized car-counting machines for traffic analysis. The project introduced them to the programmable 8008 microprocessor from Intel Corporation.
While attending Harvard University in Cambridge, Massachusetts, in 1975, Gates teamed with Allen to develop a version of the BASIC programming language for the Altair 8800, the first personal computer. They licensed the software to the manufacturer of the Altair, Micro Instrumentation and Telemetry Systems (MITS), and formed Microsoft (originally Micro-soft) to develop versions of BASIC for other computer companies. Gates decided to drop out of Harvard in his junior year to devote his time to Microsoft. In 1980 Microsoft closed a pivotal deal with International Business Machines Corporation (IBM) to provide the operating system for the IBM PC personal computer. As part of the deal, Microsoft retained the right to license the operating system to other companies.
The success of the IBM PC made the operating system, MS-DOS, an industry standard. Microsoft’s revenues skyrocketed as other computer makers licensed MS-DOS and demand for personal computers surged. In 1986 Microsoft offered its stock to the public; by 1987 rapid appreciation of the stock had made Gates, 31, the youngest ever self-made billionaire. In the 1990s, as Microsoft’s Windows operating system and Office application software achieved worldwide market dominance, Gates amassed a fortune worth tens of billions of dollars. Alongside his successes, however, Gates was accused of using his company’s power to stifle competition. In 2000 a federal judge found Microsoft guilty of violating antitrust laws and ordered it split into two companies. An appeals court overturned the breakup order in 2001 but upheld the judge's ruling that Microsoft had abused its power to protect its Windows monopoly. In November 2001 Microsoft reached a settlement with the U.S. Justice Department and nine states, and a year later, the settlement was upheld by a federal district court judge. (For more information on the history of Microsoft, see Microsoft Corporation.)
Gates has made personal investments in other high-technology companies. He sits on the board of one biotechnology company and has invested in a number of others. In 1989 he founded Corbis Corporation, which now owns the largest collection of digital images in the world.
In the late 1990s Gates became more involved in philanthropy. With his wife he established the Bill & Melinda Gates Foundation, which, ranked by assets, quickly became the largest foundation in the world. Gates has also authored two books: The Road Ahead (1995; revised, 1996), which details his vision of technology’s role in society, and Business @ the Speed of Thought (1999), which discusses the role technology can play in running a business.
In 1998 Gates appointed an executive vice president of Microsoft, Steve Ballmer, to the position of president, but Gates continued to serve as Microsoft’s chairman and chief executive officer (CEO). In 2000 Gates transferred the title of CEO to Ballmer. While remaining chairman, Gates also took on the title of chief software architect to focus on the development of new products and technologies.
In June 2006 Gates announced that he would begin transitioning from a full-time role at Microsoft to a full-time role at the Bill & Melinda Gates Foundation. He relinquished his title of chief software architect to Ray Ozzie, a veteran leader in computer technology and creator of Lotus Notes. Gates planned to remain chairman of Microsoft and to continue as its largest shareholder, but he said that by July 2008 he would have only a part-time role at the company he cofounded.
Taken from :
Microsoft ® Encarta ® 2008. © 1993-2007 Microsoft Corporation. All rights reserved.
Born in Seattle, Washington, William Henry Gates III attended public school through the sixth grade. In the seventh grade he entered Seattle’s exclusive Lakeside School, where he met Allen. Gates was first introduced to computers and programming languages in 1968, when he was in the eighth grade. That year Lakeside bought a teletype machine that connected to a mainframe computer over phone lines. At the time, the school was one of the few that provided students with access to a computer.
Soon afterward, Gates, Allen, and other students convinced a local computer company to give them free access to its PDP-10, a new minicomputer made by Digital Equipment Corporation. In exchange for the computer time, the students tried to find flaws in the system. Gates spent much of his free time on the PDP-10 learning programming languages such as BASIC, Fortran, and LISP. In 1972 Gates and Allen founded Traf-O-Data, a company that designed and built computerized car-counting machines for traffic analysis. The project introduced them to the programmable 8008 microprocessor from Intel Corporation.
While attending Harvard University in Cambridge, Massachusetts, in 1975, Gates teamed with Allen to develop a version of the BASIC programming language for the Altair 8800, the first personal computer. They licensed the software to the manufacturer of the Altair, Micro Instrumentation and Telemetry Systems (MITS), and formed Microsoft (originally Micro-soft) to develop versions of BASIC for other computer companies. Gates decided to drop out of Harvard in his junior year to devote his time to Microsoft. In 1980 Microsoft closed a pivotal deal with International Business Machines Corporation (IBM) to provide the operating system for the IBM PC personal computer. As part of the deal, Microsoft retained the right to license the operating system to other companies.
The success of the IBM PC made the operating system, MS-DOS, an industry standard. Microsoft’s revenues skyrocketed as other computer makers licensed MS-DOS and demand for personal computers surged. In 1986 Microsoft offered its stock to the public; by 1987 rapid appreciation of the stock had made Gates, 31, the youngest ever self-made billionaire. In the 1990s, as Microsoft’s Windows operating system and Office application software achieved worldwide market dominance, Gates amassed a fortune worth tens of billions of dollars. Alongside his successes, however, Gates was accused of using his company’s power to stifle competition. In 2000 a federal judge found Microsoft guilty of violating antitrust laws and ordered it split into two companies. An appeals court overturned the breakup order in 2001 but upheld the judge's ruling that Microsoft had abused its power to protect its Windows monopoly. In November 2001 Microsoft reached a settlement with the U.S. Justice Department and nine states, and a year later, the settlement was upheld by a federal district court judge. (For more information on the history of Microsoft, see Microsoft Corporation.)
Gates has made personal investments in other high-technology companies. He sits on the board of one biotechnology company and has invested in a number of others. In 1989 he founded Corbis Corporation, which now owns the largest collection of digital images in the world.
In the late 1990s Gates became more involved in philanthropy. With his wife he established the Bill & Melinda Gates Foundation, which, ranked by assets, quickly became the largest foundation in the world. Gates has also authored two books: The Road Ahead (1995; revised, 1996), which details his vision of technology’s role in society, and Business @ the Speed of Thought (1999), which discusses the role technology can play in running a business.
In 1998 Gates appointed an executive vice president of Microsoft, Steve Ballmer, to the position of president, but Gates continued to serve as Microsoft’s chairman and chief executive officer (CEO). In 2000 Gates transferred the title of CEO to Ballmer. While remaining chairman, Gates also took on the title of chief software architect to focus on the development of new products and technologies.
In June 2006 Gates announced that he would begin transitioning from a full-time role at Microsoft to a full-time role at the Bill & Melinda Gates Foundation. He relinquished his title of chief software architect to Ray Ozzie, a veteran leader in computer technology and creator of Lotus Notes. Gates planned to remain chairman of Microsoft and to continue as its largest shareholder, but he said that by July 2008 he would have only a part-time role at the company he cofounded.
Taken from :
Microsoft ® Encarta ® 2008. © 1993-2007 Microsoft Corporation. All rights reserved.
Dalton, John
Dalton, John
Dalton, John (b. Sept. 6, 1766, Eaglesfield, Cumberland. Eng.- d. July 27, 1844, Manchester), British chemist and physicist who developed the atomic theory of matter and hence is known as one of the fathers of modern physical science.
Dalton was the son of a Quaker weaver. When only 12 he took charge of a Quaker school in Cumberland and two years later taught with his brother at a school in Kendal, where he was to remain for 12 years. He then became a teacher of mathematics and natural philosophy at New College in Manchester, a college established by the Presbyterians to give a first-class education to both layman and candidates for the ministry, the doors of Cambridge and Oxford being open at that time only to members of the Church of England. He resigned this position in 1800 to become secretary of the Manchester Literary and Philosophical Society and served as a public and private teacher of mathematics and chemistry. In 1817 he became president of the Philosophical Society, an honorary office that he held until his death
In the early days of his teaching, Dalton's way of life was influenced by a wealthy Quaker, a capable meteorologist and instrument maker, who interested him in the problems of mathematics and meteorology. His first scientific work, which he began in 1787 and continued until the end of his life, was to keep a diary - which was ultimately to contain 200,000 entries - of meteorological observations recording the changeable climate of the lake district in which he lived. In 1793 Dalton published Meteorological Observations and Essays. He then became interested in preparing collections of botanical and insect species. Stimulated by a spectacular aurora display in 1788, he began observations about aurora phenomena - luminous, sometimes colored displays in the sky caused by electrical disturbances in the atmosphere. His writings on the aurora borealis reveal independent thinking unhampered by the conclusions of others. As Dalton himself notes, "Having been in my progress so often misled by taking for granted the results of others, I have determined to write as little as possible but what I can attest by my own experience." In his work on the aurora he concluded that some relationship must exist between the aurora beams and the Earth's magnetism: "Now, from the conclusions in the preceding sections, we are under the necessity of considering the beams of the aurora borealis of a ferruginous (iron-like) nature, because nothing else is known to be magnetic, and consequently, that there exists in the higher regions of the atmosphere an elastic fluid partaking of the properties of iron, or rather of magnetic steel, and that this fluid, doubtless from its magnetic property, assumes the form of cylindric beams."
Some of his studies in meteorology led him to conclusions about the origin of trade winds involving the Earth's rotation and variation in temperature - unaware, perhaps, that this theory had already been proposed in 1735 by George Hadley. These are only some of the subjects on which he wrote essays that he read before the Philosophical Society: others included such topics as the barometer, thermometer, hygrometer, rainfall, the formation
1
of clouds, evaporation and distribution and character of atmospheric moisture, including the concept of the dew point. He was the first to confirm the theory that rain is caused not by any alteration in atmospheric pressure but by a diminution of temperature. In his studies with water he determined the point of the maximum density of water to be 42.5° F (later shown to be 39.16° F. Along with his other researches he also became interested in color blindness, a condition that he and his brother shared. The results of this work were published in an essay, "Extraordinary Facts Relating to the Vision of Colors" (1794), in which he postulated that deficiency in color perception was caused by discoloration of the liquid medium of the eyeball. Although Dalton's theory lost credence in his own lifetime, the meticulous, systematic nature of his research was so broadly recognized that Daltonism became a common term for color blindness.
An indefatigable investigator or researcher, Dalton had an unusual talent for formulating a theory from a variety of data. The mental capacity of the man is illustrated by his major work that was to begin at the turn of the century - his work in chemistry. Although he taught chemistry for six years at New College, he had no experience in chemical research. He embarked on this study with the same intuitiveness, independence of mind, dedication, and genius for creative synthesis of a theory from the available facts that he had demonstrated in his other work. His early studies on gases led to development of the law of partial pressures (known as Dalton's law; q.v.), which states that the total pressure of a mixture of gases equals the sum of the pressures of the gases in the mixture, each gas acting independently. These experiments also resulted in his theory according to which gas expands as it rises in temperature (the so-called Charles's law, which should really be credited to Dalton). On the strength of the data gained in these studies he devised other experiments that proved the solubility of gases in water and the rate of diffusion of gases. His analysis of the atmosphere showed it to be constant in com-position to 15,000 feet. He devised a system of chemical symbols and, having ascertained the relative weights of atoms (particles of matter), in 1803 arranged them into a table. In addition, he formulated the theory that a chemical combination of different elements occurs in simple numerical ratios by weight, which led to the development of the laws of definite and multiple proportions. Dalton discovered butylene and determined the composition of ether, finding its correct formula. Finally, he developed his masterpiece of synthesis - the atomic theory, the thesis that all elements are composed of tiny, indestructible particles called atoms that are all alike and have the same atomic weight.
Dalton's studies and writings, many included in his New System of Chemical Philosophy (part I, 1808; part II, 1810), cast light on the man. Dedicated to scientific research, independent in his approach, often diffident in seeking help in scientific papers that would aid him - or misguide him, as he often thought - he was a genius in synthesizing facts and ideas. Almost a recluse, with few friends, and unmarried, he was deeply dedicated to a search for the answer to scientific problems. His homemade equipment was crude, and his data were not usually exact, but they were good enough to give his alert and creative mind clues to the probable answer. Dalton remained a man of simple wants and uniform habits, keeping his dress and manners consistent with his Quaker faith.
2
Dalton's record keeping, although remarkable for quantity, often lacked exactness in dating, probably because he revised his manuscripts as secretary of the Philosophical Society between the time of the oral presentation and the publication. The exact date of some of his work, especially the atomic theory, is still in doubt because of this opportunity for revision. His documents were destroyed during the bombings of England in World War II. A fellow of the Royal Society, from whom he received the Gold Medal in 1826, and a corresponding member of the French Academy of Sciences, John Dalton was also cofounder of the British Association for the Advancement of Science. At his death more than 40,000 people came to Manchester to pay their final respects. (A.B.Ga.)
BIBLIOGRAPHY. H.E. Roscoe, John Dalton and the Rise of Modern Chemistry (1895), the most authoritative biography, and with A. Harden. A New View of the Origin of Dalton's Atomic Theory (1896), original material on Dalton's research: D.S.L. Cardwell (ed.), John Dalton and the Progress of Science (1968); J.B. Conant and L.K. Nash (eds.), Harvard Case Histories in Experimental Science, vol. 1 (1957), probably the most critical analysis of Dalton's work; Frank Greenaway. John Dalton and the Atom (1966).
3
Dalton, John (b. Sept. 6, 1766, Eaglesfield, Cumberland. Eng.- d. July 27, 1844, Manchester), British chemist and physicist who developed the atomic theory of matter and hence is known as one of the fathers of modern physical science.
Dalton was the son of a Quaker weaver. When only 12 he took charge of a Quaker school in Cumberland and two years later taught with his brother at a school in Kendal, where he was to remain for 12 years. He then became a teacher of mathematics and natural philosophy at New College in Manchester, a college established by the Presbyterians to give a first-class education to both layman and candidates for the ministry, the doors of Cambridge and Oxford being open at that time only to members of the Church of England. He resigned this position in 1800 to become secretary of the Manchester Literary and Philosophical Society and served as a public and private teacher of mathematics and chemistry. In 1817 he became president of the Philosophical Society, an honorary office that he held until his death
In the early days of his teaching, Dalton's way of life was influenced by a wealthy Quaker, a capable meteorologist and instrument maker, who interested him in the problems of mathematics and meteorology. His first scientific work, which he began in 1787 and continued until the end of his life, was to keep a diary - which was ultimately to contain 200,000 entries - of meteorological observations recording the changeable climate of the lake district in which he lived. In 1793 Dalton published Meteorological Observations and Essays. He then became interested in preparing collections of botanical and insect species. Stimulated by a spectacular aurora display in 1788, he began observations about aurora phenomena - luminous, sometimes colored displays in the sky caused by electrical disturbances in the atmosphere. His writings on the aurora borealis reveal independent thinking unhampered by the conclusions of others. As Dalton himself notes, "Having been in my progress so often misled by taking for granted the results of others, I have determined to write as little as possible but what I can attest by my own experience." In his work on the aurora he concluded that some relationship must exist between the aurora beams and the Earth's magnetism: "Now, from the conclusions in the preceding sections, we are under the necessity of considering the beams of the aurora borealis of a ferruginous (iron-like) nature, because nothing else is known to be magnetic, and consequently, that there exists in the higher regions of the atmosphere an elastic fluid partaking of the properties of iron, or rather of magnetic steel, and that this fluid, doubtless from its magnetic property, assumes the form of cylindric beams."
Some of his studies in meteorology led him to conclusions about the origin of trade winds involving the Earth's rotation and variation in temperature - unaware, perhaps, that this theory had already been proposed in 1735 by George Hadley. These are only some of the subjects on which he wrote essays that he read before the Philosophical Society: others included such topics as the barometer, thermometer, hygrometer, rainfall, the formation
1
of clouds, evaporation and distribution and character of atmospheric moisture, including the concept of the dew point. He was the first to confirm the theory that rain is caused not by any alteration in atmospheric pressure but by a diminution of temperature. In his studies with water he determined the point of the maximum density of water to be 42.5° F (later shown to be 39.16° F. Along with his other researches he also became interested in color blindness, a condition that he and his brother shared. The results of this work were published in an essay, "Extraordinary Facts Relating to the Vision of Colors" (1794), in which he postulated that deficiency in color perception was caused by discoloration of the liquid medium of the eyeball. Although Dalton's theory lost credence in his own lifetime, the meticulous, systematic nature of his research was so broadly recognized that Daltonism became a common term for color blindness.
An indefatigable investigator or researcher, Dalton had an unusual talent for formulating a theory from a variety of data. The mental capacity of the man is illustrated by his major work that was to begin at the turn of the century - his work in chemistry. Although he taught chemistry for six years at New College, he had no experience in chemical research. He embarked on this study with the same intuitiveness, independence of mind, dedication, and genius for creative synthesis of a theory from the available facts that he had demonstrated in his other work. His early studies on gases led to development of the law of partial pressures (known as Dalton's law; q.v.), which states that the total pressure of a mixture of gases equals the sum of the pressures of the gases in the mixture, each gas acting independently. These experiments also resulted in his theory according to which gas expands as it rises in temperature (the so-called Charles's law, which should really be credited to Dalton). On the strength of the data gained in these studies he devised other experiments that proved the solubility of gases in water and the rate of diffusion of gases. His analysis of the atmosphere showed it to be constant in com-position to 15,000 feet. He devised a system of chemical symbols and, having ascertained the relative weights of atoms (particles of matter), in 1803 arranged them into a table. In addition, he formulated the theory that a chemical combination of different elements occurs in simple numerical ratios by weight, which led to the development of the laws of definite and multiple proportions. Dalton discovered butylene and determined the composition of ether, finding its correct formula. Finally, he developed his masterpiece of synthesis - the atomic theory, the thesis that all elements are composed of tiny, indestructible particles called atoms that are all alike and have the same atomic weight.
Dalton's studies and writings, many included in his New System of Chemical Philosophy (part I, 1808; part II, 1810), cast light on the man. Dedicated to scientific research, independent in his approach, often diffident in seeking help in scientific papers that would aid him - or misguide him, as he often thought - he was a genius in synthesizing facts and ideas. Almost a recluse, with few friends, and unmarried, he was deeply dedicated to a search for the answer to scientific problems. His homemade equipment was crude, and his data were not usually exact, but they were good enough to give his alert and creative mind clues to the probable answer. Dalton remained a man of simple wants and uniform habits, keeping his dress and manners consistent with his Quaker faith.
2
Dalton's record keeping, although remarkable for quantity, often lacked exactness in dating, probably because he revised his manuscripts as secretary of the Philosophical Society between the time of the oral presentation and the publication. The exact date of some of his work, especially the atomic theory, is still in doubt because of this opportunity for revision. His documents were destroyed during the bombings of England in World War II. A fellow of the Royal Society, from whom he received the Gold Medal in 1826, and a corresponding member of the French Academy of Sciences, John Dalton was also cofounder of the British Association for the Advancement of Science. At his death more than 40,000 people came to Manchester to pay their final respects. (A.B.Ga.)
BIBLIOGRAPHY. H.E. Roscoe, John Dalton and the Rise of Modern Chemistry (1895), the most authoritative biography, and with A. Harden. A New View of the Origin of Dalton's Atomic Theory (1896), original material on Dalton's research: D.S.L. Cardwell (ed.), John Dalton and the Progress of Science (1968); J.B. Conant and L.K. Nash (eds.), Harvard Case Histories in Experimental Science, vol. 1 (1957), probably the most critical analysis of Dalton's work; Frank Greenaway. John Dalton and the Atom (1966).
3
Galileo Galilei
Galileo Galilei
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Born: 15 Feb 1564 in Pisa (now in Italy)
Died: 8 Jan 1642 in Arcetri (near Florence) (now in Italy)
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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.
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In the year 1582-83 Ostilio Ricci, who was the mathematician of the Tuscan Court and a former pupil of Tartaglia, taught a course on Euclid's Elements at the University of Pisa which Galileo attended. During the summer of 1583 Galileo was back in Florence with his family and Vincenzo encouraged him to read Galen to further his medical studies. However Galileo, still reluctant to study medicine, invited Ricci (also in Florence where the Tuscan court spent the summer and autumn) to his home to meet his father. Ricci tried to persuade Vincenzo to allow his son to study mathematics since this was where his interests lay. Certainly Vincenzo did not like the idea and resisted strongly but eventually he gave way a little and Galileo was able to study the works of Euclid and Archimedes from the Italian translations which Tartaglia had made. Of course he was still officially enrolled as a medical student at Pisa but eventually, by 1585, he gave up this course and left without completing his degree.
Galileo began teaching mathematics, first privately in Florence and then during 1585-86 at Siena where he held a public appointment. During the summer of 1586 he taught at Vallombrosa, and in this year he wrote his first scientific book The little balance [La Balancitta] which described Archimedes' method of finding the specific gravities (that is the relative densities) of substances using a balance. In the following year he travelled to Rome to visit Clavius who was professor of mathematics at the Jesuit Collegio Romano there. A topic which was very popular with the Jesuit mathematicians at this time was centres of gravity and Galileo brought with him some results which he had discovered on this topic. Despite making a very favourable impression on Clavius, Galileo failed to gain an appointment to teach mathematics at the University of Bologna.
After leaving Rome Galileo remained in contact with Clavius by correspondence and Guidobaldo del Monte was also a regular correspondent. Certainly the theorems which Galileo had proved on the centres of gravity of solids, and left in Rome, were discussed in this correspondence. It is also likely that Galileo received lecture notes from courses which had been given at the Collegio Romano, for he made copies of such material which still survive today. The correspondence began around 1588 and continued for many years. Also in 1588 Galileo received a prestigious invitation to lecture on the dimensions and location of hell in Dante's Inferno at the Academy in Florence.
Fantoni left the chair of mathematics at the University of Pisa in 1589 and Galileo was appointed to fill the post (although this was only a nominal position to provide financial support for Galileo). Not only did he receive strong recommendations from Clavius, but he also had acquired an excellent reputation through his lectures at the Florence Academy in the previous year. The young mathematician had rapidly acquired the reputation that was necessary to gain such a position, but there were still higher positions at which he might aim. Galileo spent three years holding this post at the university of Pisa and during this time he wrote De Motu a series of essays on the theory of motion which he never published. It is likely that he never published this material because he was less than satisfied with it, and this is fair for despite containing some important steps forward, it also contained some incorrect ideas. Perhaps the most important new ideas which De Motu contains is that one can test theories by conducting experiments. In particular the
2
work contains his important idea that one could test theories about falling bodies using an inclined plane to slow down the rate of descent.
In 1591 Vincenzo Galilei, Galileo's father, died and since Galileo was the eldest son he had to provide financial support for the rest of the family and in particular have the necessary financial means to provide dowries for his two younger sisters. Being professor of mathematics at Pisa was not well paid, so Galileo looked for a more lucrative post. With strong recommendations from Guidobaldo del Monte, Galileo was appointed professor of mathematics at the University of Padua (the university of the Republic of Venice) in 1592 at a salary of three times what he had received at Pisa. On 7 December 1592 he gave his inaugural lecture and began a period of eighteen years at the university, years which he later described as the happiest of his life. At Padua his duties were mainly to teach Euclid's geometry and standard (geocentric) astronomy to medical students, who would need to know some astronomy in order to make use of astrology in their medical practice. However, Galileo argued against Aristotle's view of astronomy and natural philosophy in three public lectures he gave in connection with the appearance of a New Star (now known as 'Kepler's supernova') in 1604. The belief at this time was that of Aristotle, namely that all changes in the heavens had to occur in the lunar region close to the Earth, the realm of the fixed stars being permanent. Galileo used parallax arguments to prove that the New Star could not be close to the Earth. In a personal letter written to Kepler in 1598, Galileo had stated that he was a Copernican (believer in the theories of Copernicus). However, no public sign of this belief was to appear until many years later.
At Padua, Galileo began a long term relationship with Maria Gamba, who was from Venice, but they did not marry perhaps because Galileo felt his financial situation was not good enough. In 1600 their first child Virginia was born, followed by a second daughter Livia in the following year. In 1606 their son Vincenzo was born.
We mentioned above an error in Galileo's theory of motion as he set it out in De Motu around 1590. He was quite mistaken in his belief that the force acting on a body was the relative difference between its specific gravity and that of the substance through which it moved. Galileo wrote to his friend Paolo Sarpi, a fine mathematician who was consultor to the Venetian government, in 1604 and it is clear from his letter that by this time he had realised his mistake. In fact he had returned to work on the theory of motion in 1602 and over the following two years, through his study of inclined planes and the pendulum, he had formulated the correct law of falling bodies and had worked out that a projectile follows a parabolic path. However, these famous results would not be published for another 35 years.
In May 1609, Galileo received a letter from Paolo Sarpi telling him about a spyglass that a Dutchman had shown in Venice. Galileo wrote in the Starry Messenger (Sidereus Nuncius) in April 1610:-
About ten months ago a report reached my ears that a certain Fleming had constructed a spyglass by means of which visible objects, though very distant from the eye of the observer, were distinctly seen as if nearby. Of this truly remarkable effect several
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experiences were related, to which some persons believed while other denied them. A few days later the report was confirmed by a letter I received from a Frenchman in Paris, Jacques Badovere, which caused me to apply myself wholeheartedly to investigate means by which I might arrive at the invention of a similar instrument. This I did soon afterwards, my basis being the doctrine of refraction.
From these reports, and using his own technical skills as a mathematician and as a craftsman, Galileo began to make a series of telescopes whose optical performance was much better than that of the Dutch instrument. His first telescope was made from available lenses and gave a magnification of about four times. To improve on this Galileo learned how to grind and polish his own lenses and by August 1609 he had an instrument with a magnification of around eight or nine. Galileo immediately saw the commercial and military applications of his telescope (which he called a perspicillum) for ships at sea. He kept Sarpi informed of his progress and Sarpi arranged a demonstration for the Venetian Senate. They were very impressed and, in return for a large increase in his salary, Galileo gave the sole rights for the manufacture of telescopes to the Venetian Senate. It seems a particularly good move on his part since he must have known that such rights were meaningless, particularly since he always acknowledged that the telescope was not his invention!
By the end of 1609 Galileo had turned his telescope on the night sky and began to make remarkable discoveries. Swerdlow writes (see [16]):-
In about two months, December and January, he made more discoveries that changed the world than anyone has ever made before or since.
The astronomical discoveries he made with his telescopes were described in a short book called the Starry Messenger published in Venice in May 1610. This work caused a sensation. Galileo claimed to have seen mountains on the Moon, to have proved the Milky Way was made up of tiny stars, and to have seen four small bodies orbiting Jupiter. These last, with an eye to getting a position in Florence, he quickly named 'the Medicean stars'. He had also sent Cosimo de Medici, the Grand Duke of Tuscany, an excellent telescope for himself.
The Venetian Senate, perhaps realising that the rights to manufacture telescopes that Galileo had given them were worthless, froze his salary. However he had succeeded in impressing Cosimo and, in June 1610, only a month after his famous little book was published, Galileo resigned his post at Padua and became Chief Mathematician at the University of Pisa (without any teaching duties) and 'Mathematician and Philosopher' to the Grand Duke of Tuscany. In 1611 he visited Rome where he was treated as a leading celebrity; the Collegio Romano put on a grand dinner with speeches to honour Galileo's remarkable discoveries. He was also made a member of the Accademia dei Lincei (in fact the sixth member) and this was an honour which was especially important to Galileo who signed himself 'Galileo Galilei Linceo' from this time on.
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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.
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Castelli defended the Copernican position vigorously and wrote to Galileo afterwards telling him how successful he had been in putting the arguments. Galileo, less convinced that Castelli had won the argument, wrote Letter to Castelli to him arguing that the Bible had to be interpreted in the light of what science had shown to be true. Galileo had several opponents in Florence and they made sure that a copy of the Letter to Castelli was sent to the Inquisition in Rome. However, after examining its contents they found little to which they could object.
The Catholic Church's most important figure at this time in dealing with interpretations of the Holy Scripture was Cardinal Robert Bellarmine. He seems at this time to have seen little reason for the Church to be concerned regarding the Copernican theory. The point at issue was whether Copernicus had simply put forward a mathematical theory which enabled the calculation of the positions of the heavenly bodies to be made more simply or whether he was proposing a physical reality. At this time Bellarmine viewed the theory as an elegant mathematical one which did not threaten the established Christian belief regarding the structure of the universe.
In 1616 Galileo wrote the Letter to the Grand Duchess which vigorously attacked the followers of Aristotle. In this work, which he addressed to the Grand Duchess Christina of Lorraine, he argued strongly for a non-literal interpretation of Holy Scripture when the literal interpretation would contradict facts about the physical world proved by mathematical science. In this Galileo stated quite clearly that for him the Copernican theory is not just a mathematical calculating tool, but is a physical reality:-
I hold that the Sun is located at the centre of the revolutions of the heavenly orbs and does not change place, and that the Earth rotates on itself and moves around it. Moreover ... I confirm this view not only by refuting Ptolemy's and Aristotle's arguments, but also by producing many for the other side, especially some pertaining to physical effects whose causes perhaps cannot be determined in any other way, and other astronomical discoveries; these discoveries clearly confute the Ptolemaic system, and they agree admirably with this other position and confirm it.
Pope Paul V ordered Bellarmine to have the Sacred Congregation of the Index decide on the Copernican theory. The cardinals of the Inquisition met on 24 February 1616 and took evidence from theological experts. They condemned the teachings of Copernicus, and Bellarmine conveyed their decision to Galileo who had not been personally involved in the trial. Galileo was forbidden to hold Copernican views but later events made him less concerned about this decision of the Inquisition. Most importantly Maffeo Barberini, who was an admirer of Galileo, was elected as Pope Urban VIII. This happened just as Galileo's book Il saggiatore (The Assayer) was about to be published by the Accademia dei Lincei in 1623 and Galileo was quick to dedicate this work to the new Pope. The work described Galileo's new scientific method and contains a famous quote regarding mathematics:-
Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the
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language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth.
Pope Urban VIII invited Galileo to papal audiences on six occasions and led Galileo to believe that the Catholic Church would not make an issue of the Copernican theory. Galileo, therefore, decided to publish his views believing that he could do so without serious consequences from the Church. However by this stage in his life Galileo's health was poor with frequent bouts of severe illness and so even though he began to write his famous Dialogue in 1624 it took him six years to complete the work.
Galileo attempted to obtain permission from Rome to publish the Dialogue in 1630 but this did not prove easy. Eventually he received permission from Florence, and not Rome. In February 1632 Galileo published Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican. It takes the form of a dialogue between Salviati, who argues for the Copernican system, and Simplicio who is an Aristotelian philosopher. The climax of the book is an argument by Salviati that the Earth moves which was based on Galileo's theory of the tides. Galileo's theory of the tides was entirely false despite being postulated after Kepler had already put forward the correct explanation. It was unfortunate, given the remarkable truths the Dialogue supported, that the argument which Galileo thought to give the strongest proof of Copernicus's theory should be incorrect.
Shortly after publication of Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican the Inquisition banned its sale and ordered Galileo to appear in Rome before them. Illness prevented him from travelling to Rome until 1633. Galileo's accusation at the trial which followed was that he had breached the conditions laid down by the Inquisition in 1616. However a different version of this decision was produced at the trial rather than the one Galileo had been given at the time. The truth of the Copernican theory was not an issue therefore; it was taken as a fact at the trial that this theory was false. This was logical, of course, since the judgement of 1616 had declared it totally false.
Found guilty, Galileo was condemned to lifelong imprisonment, but the sentence was carried out somewhat sympathetically and it amounted to house arrest rather than a prison sentence. He was able to live first with the Archbishop of Siena, then later to return to his home in Arcetri, near Florence, but had to spend the rest of his life watched over by officers from the Inquisition. In 1634 he suffered a severe blow when his daughter Virginia, Sister Maria Celeste, died. She had been a great support to her father through his illnesses and Galileo was shattered and could not work for many months. When he did manage to restart work, he began to write Discourses and mathematical demonstrations concerning the two new sciences.
After Galileo had completed work on the Discourses it was smuggled out of Italy, and taken to Leyden in Holland where it was published. It was his most rigorous mathematical work which treated problems on impetus, moments, and centres of gravity.
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Much of this work went back to the unpublished ideas in De Motu from around 1590 and the improvements which he had worked out during 1602-1604. In the Discourses he developed his ideas of the inclined plane writing:-
I assume that the speed acquired by the same movable object over different inclinations of the plane are equal whenever the heights of those planes are equal.
He then described an experiment using a pendulum to verify his property of inclined planes and used these ideas to give a theorem on acceleration of bodies in free fall:-
The time in which a certain distance is traversed by an object moving under uniform acceleration from rest is equal to the time in which the same distance would be traversed by the same movable object moving at a uniform speed of one half the maximum and final speed of the previous uniformly accelerated motion.
After giving further results of this type he gives his famous result that the distance that a body moves from rest under uniform acceleration is proportional to the square of the time taken.
One would expect that Galileo's understanding of the pendulum, which he had since he was a young man, would have led him to design a pendulum clock. In fact he only seems to have thought of this possibility near the end of his life and around 1640 he did design the first pendulum clock. Galileo died in early 1642 but the significance of his clock design was certainly realised by his son Vincenzo who tried to make a clock to Galileo's plan, but failed.
It was a sad end for so great a man to die condemned of heresy. His will indicated that he wished to be buried beside his father in the family tomb in the Basilica of Santa Croce but his relatives feared, quite rightly, that this would provoke opposition from the Church. His body was concealed and only placed in a fine tomb in the church in 1737 by the civil authorities against the wishes of many in the Church. On 31 October 1992, 350 years after Galileo's death, Pope John Paul II gave an address on behalf of the Catholic Church in which he admitted that errors had been made by the theological advisors in the case of Galileo. He declared the Galileo case closed, but he did not admit that the Church was wrong to convict Galileo on a charge of heresy because of his belief that the Earth rotates round the sun.
Article by: J J O'Connor and E F Robertson
November 2002
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Born: 15 Feb 1564 in Pisa (now in Italy)
Died: 8 Jan 1642 in Arcetri (near Florence) (now in Italy)
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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.
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In the year 1582-83 Ostilio Ricci, who was the mathematician of the Tuscan Court and a former pupil of Tartaglia, taught a course on Euclid's Elements at the University of Pisa which Galileo attended. During the summer of 1583 Galileo was back in Florence with his family and Vincenzo encouraged him to read Galen to further his medical studies. However Galileo, still reluctant to study medicine, invited Ricci (also in Florence where the Tuscan court spent the summer and autumn) to his home to meet his father. Ricci tried to persuade Vincenzo to allow his son to study mathematics since this was where his interests lay. Certainly Vincenzo did not like the idea and resisted strongly but eventually he gave way a little and Galileo was able to study the works of Euclid and Archimedes from the Italian translations which Tartaglia had made. Of course he was still officially enrolled as a medical student at Pisa but eventually, by 1585, he gave up this course and left without completing his degree.
Galileo began teaching mathematics, first privately in Florence and then during 1585-86 at Siena where he held a public appointment. During the summer of 1586 he taught at Vallombrosa, and in this year he wrote his first scientific book The little balance [La Balancitta] which described Archimedes' method of finding the specific gravities (that is the relative densities) of substances using a balance. In the following year he travelled to Rome to visit Clavius who was professor of mathematics at the Jesuit Collegio Romano there. A topic which was very popular with the Jesuit mathematicians at this time was centres of gravity and Galileo brought with him some results which he had discovered on this topic. Despite making a very favourable impression on Clavius, Galileo failed to gain an appointment to teach mathematics at the University of Bologna.
After leaving Rome Galileo remained in contact with Clavius by correspondence and Guidobaldo del Monte was also a regular correspondent. Certainly the theorems which Galileo had proved on the centres of gravity of solids, and left in Rome, were discussed in this correspondence. It is also likely that Galileo received lecture notes from courses which had been given at the Collegio Romano, for he made copies of such material which still survive today. The correspondence began around 1588 and continued for many years. Also in 1588 Galileo received a prestigious invitation to lecture on the dimensions and location of hell in Dante's Inferno at the Academy in Florence.
Fantoni left the chair of mathematics at the University of Pisa in 1589 and Galileo was appointed to fill the post (although this was only a nominal position to provide financial support for Galileo). Not only did he receive strong recommendations from Clavius, but he also had acquired an excellent reputation through his lectures at the Florence Academy in the previous year. The young mathematician had rapidly acquired the reputation that was necessary to gain such a position, but there were still higher positions at which he might aim. Galileo spent three years holding this post at the university of Pisa and during this time he wrote De Motu a series of essays on the theory of motion which he never published. It is likely that he never published this material because he was less than satisfied with it, and this is fair for despite containing some important steps forward, it also contained some incorrect ideas. Perhaps the most important new ideas which De Motu contains is that one can test theories by conducting experiments. In particular the
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work contains his important idea that one could test theories about falling bodies using an inclined plane to slow down the rate of descent.
In 1591 Vincenzo Galilei, Galileo's father, died and since Galileo was the eldest son he had to provide financial support for the rest of the family and in particular have the necessary financial means to provide dowries for his two younger sisters. Being professor of mathematics at Pisa was not well paid, so Galileo looked for a more lucrative post. With strong recommendations from Guidobaldo del Monte, Galileo was appointed professor of mathematics at the University of Padua (the university of the Republic of Venice) in 1592 at a salary of three times what he had received at Pisa. On 7 December 1592 he gave his inaugural lecture and began a period of eighteen years at the university, years which he later described as the happiest of his life. At Padua his duties were mainly to teach Euclid's geometry and standard (geocentric) astronomy to medical students, who would need to know some astronomy in order to make use of astrology in their medical practice. However, Galileo argued against Aristotle's view of astronomy and natural philosophy in three public lectures he gave in connection with the appearance of a New Star (now known as 'Kepler's supernova') in 1604. The belief at this time was that of Aristotle, namely that all changes in the heavens had to occur in the lunar region close to the Earth, the realm of the fixed stars being permanent. Galileo used parallax arguments to prove that the New Star could not be close to the Earth. In a personal letter written to Kepler in 1598, Galileo had stated that he was a Copernican (believer in the theories of Copernicus). However, no public sign of this belief was to appear until many years later.
At Padua, Galileo began a long term relationship with Maria Gamba, who was from Venice, but they did not marry perhaps because Galileo felt his financial situation was not good enough. In 1600 their first child Virginia was born, followed by a second daughter Livia in the following year. In 1606 their son Vincenzo was born.
We mentioned above an error in Galileo's theory of motion as he set it out in De Motu around 1590. He was quite mistaken in his belief that the force acting on a body was the relative difference between its specific gravity and that of the substance through which it moved. Galileo wrote to his friend Paolo Sarpi, a fine mathematician who was consultor to the Venetian government, in 1604 and it is clear from his letter that by this time he had realised his mistake. In fact he had returned to work on the theory of motion in 1602 and over the following two years, through his study of inclined planes and the pendulum, he had formulated the correct law of falling bodies and had worked out that a projectile follows a parabolic path. However, these famous results would not be published for another 35 years.
In May 1609, Galileo received a letter from Paolo Sarpi telling him about a spyglass that a Dutchman had shown in Venice. Galileo wrote in the Starry Messenger (Sidereus Nuncius) in April 1610:-
About ten months ago a report reached my ears that a certain Fleming had constructed a spyglass by means of which visible objects, though very distant from the eye of the observer, were distinctly seen as if nearby. Of this truly remarkable effect several
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experiences were related, to which some persons believed while other denied them. A few days later the report was confirmed by a letter I received from a Frenchman in Paris, Jacques Badovere, which caused me to apply myself wholeheartedly to investigate means by which I might arrive at the invention of a similar instrument. This I did soon afterwards, my basis being the doctrine of refraction.
From these reports, and using his own technical skills as a mathematician and as a craftsman, Galileo began to make a series of telescopes whose optical performance was much better than that of the Dutch instrument. His first telescope was made from available lenses and gave a magnification of about four times. To improve on this Galileo learned how to grind and polish his own lenses and by August 1609 he had an instrument with a magnification of around eight or nine. Galileo immediately saw the commercial and military applications of his telescope (which he called a perspicillum) for ships at sea. He kept Sarpi informed of his progress and Sarpi arranged a demonstration for the Venetian Senate. They were very impressed and, in return for a large increase in his salary, Galileo gave the sole rights for the manufacture of telescopes to the Venetian Senate. It seems a particularly good move on his part since he must have known that such rights were meaningless, particularly since he always acknowledged that the telescope was not his invention!
By the end of 1609 Galileo had turned his telescope on the night sky and began to make remarkable discoveries. Swerdlow writes (see [16]):-
In about two months, December and January, he made more discoveries that changed the world than anyone has ever made before or since.
The astronomical discoveries he made with his telescopes were described in a short book called the Starry Messenger published in Venice in May 1610. This work caused a sensation. Galileo claimed to have seen mountains on the Moon, to have proved the Milky Way was made up of tiny stars, and to have seen four small bodies orbiting Jupiter. These last, with an eye to getting a position in Florence, he quickly named 'the Medicean stars'. He had also sent Cosimo de Medici, the Grand Duke of Tuscany, an excellent telescope for himself.
The Venetian Senate, perhaps realising that the rights to manufacture telescopes that Galileo had given them were worthless, froze his salary. However he had succeeded in impressing Cosimo and, in June 1610, only a month after his famous little book was published, Galileo resigned his post at Padua and became Chief Mathematician at the University of Pisa (without any teaching duties) and 'Mathematician and Philosopher' to the Grand Duke of Tuscany. In 1611 he visited Rome where he was treated as a leading celebrity; the Collegio Romano put on a grand dinner with speeches to honour Galileo's remarkable discoveries. He was also made a member of the Accademia dei Lincei (in fact the sixth member) and this was an honour which was especially important to Galileo who signed himself 'Galileo Galilei Linceo' from this time on.
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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.
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Castelli defended the Copernican position vigorously and wrote to Galileo afterwards telling him how successful he had been in putting the arguments. Galileo, less convinced that Castelli had won the argument, wrote Letter to Castelli to him arguing that the Bible had to be interpreted in the light of what science had shown to be true. Galileo had several opponents in Florence and they made sure that a copy of the Letter to Castelli was sent to the Inquisition in Rome. However, after examining its contents they found little to which they could object.
The Catholic Church's most important figure at this time in dealing with interpretations of the Holy Scripture was Cardinal Robert Bellarmine. He seems at this time to have seen little reason for the Church to be concerned regarding the Copernican theory. The point at issue was whether Copernicus had simply put forward a mathematical theory which enabled the calculation of the positions of the heavenly bodies to be made more simply or whether he was proposing a physical reality. At this time Bellarmine viewed the theory as an elegant mathematical one which did not threaten the established Christian belief regarding the structure of the universe.
In 1616 Galileo wrote the Letter to the Grand Duchess which vigorously attacked the followers of Aristotle. In this work, which he addressed to the Grand Duchess Christina of Lorraine, he argued strongly for a non-literal interpretation of Holy Scripture when the literal interpretation would contradict facts about the physical world proved by mathematical science. In this Galileo stated quite clearly that for him the Copernican theory is not just a mathematical calculating tool, but is a physical reality:-
I hold that the Sun is located at the centre of the revolutions of the heavenly orbs and does not change place, and that the Earth rotates on itself and moves around it. Moreover ... I confirm this view not only by refuting Ptolemy's and Aristotle's arguments, but also by producing many for the other side, especially some pertaining to physical effects whose causes perhaps cannot be determined in any other way, and other astronomical discoveries; these discoveries clearly confute the Ptolemaic system, and they agree admirably with this other position and confirm it.
Pope Paul V ordered Bellarmine to have the Sacred Congregation of the Index decide on the Copernican theory. The cardinals of the Inquisition met on 24 February 1616 and took evidence from theological experts. They condemned the teachings of Copernicus, and Bellarmine conveyed their decision to Galileo who had not been personally involved in the trial. Galileo was forbidden to hold Copernican views but later events made him less concerned about this decision of the Inquisition. Most importantly Maffeo Barberini, who was an admirer of Galileo, was elected as Pope Urban VIII. This happened just as Galileo's book Il saggiatore (The Assayer) was about to be published by the Accademia dei Lincei in 1623 and Galileo was quick to dedicate this work to the new Pope. The work described Galileo's new scientific method and contains a famous quote regarding mathematics:-
Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the
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language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth.
Pope Urban VIII invited Galileo to papal audiences on six occasions and led Galileo to believe that the Catholic Church would not make an issue of the Copernican theory. Galileo, therefore, decided to publish his views believing that he could do so without serious consequences from the Church. However by this stage in his life Galileo's health was poor with frequent bouts of severe illness and so even though he began to write his famous Dialogue in 1624 it took him six years to complete the work.
Galileo attempted to obtain permission from Rome to publish the Dialogue in 1630 but this did not prove easy. Eventually he received permission from Florence, and not Rome. In February 1632 Galileo published Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican. It takes the form of a dialogue between Salviati, who argues for the Copernican system, and Simplicio who is an Aristotelian philosopher. The climax of the book is an argument by Salviati that the Earth moves which was based on Galileo's theory of the tides. Galileo's theory of the tides was entirely false despite being postulated after Kepler had already put forward the correct explanation. It was unfortunate, given the remarkable truths the Dialogue supported, that the argument which Galileo thought to give the strongest proof of Copernicus's theory should be incorrect.
Shortly after publication of Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican the Inquisition banned its sale and ordered Galileo to appear in Rome before them. Illness prevented him from travelling to Rome until 1633. Galileo's accusation at the trial which followed was that he had breached the conditions laid down by the Inquisition in 1616. However a different version of this decision was produced at the trial rather than the one Galileo had been given at the time. The truth of the Copernican theory was not an issue therefore; it was taken as a fact at the trial that this theory was false. This was logical, of course, since the judgement of 1616 had declared it totally false.
Found guilty, Galileo was condemned to lifelong imprisonment, but the sentence was carried out somewhat sympathetically and it amounted to house arrest rather than a prison sentence. He was able to live first with the Archbishop of Siena, then later to return to his home in Arcetri, near Florence, but had to spend the rest of his life watched over by officers from the Inquisition. In 1634 he suffered a severe blow when his daughter Virginia, Sister Maria Celeste, died. She had been a great support to her father through his illnesses and Galileo was shattered and could not work for many months. When he did manage to restart work, he began to write Discourses and mathematical demonstrations concerning the two new sciences.
After Galileo had completed work on the Discourses it was smuggled out of Italy, and taken to Leyden in Holland where it was published. It was his most rigorous mathematical work which treated problems on impetus, moments, and centres of gravity.
7
Much of this work went back to the unpublished ideas in De Motu from around 1590 and the improvements which he had worked out during 1602-1604. In the Discourses he developed his ideas of the inclined plane writing:-
I assume that the speed acquired by the same movable object over different inclinations of the plane are equal whenever the heights of those planes are equal.
He then described an experiment using a pendulum to verify his property of inclined planes and used these ideas to give a theorem on acceleration of bodies in free fall:-
The time in which a certain distance is traversed by an object moving under uniform acceleration from rest is equal to the time in which the same distance would be traversed by the same movable object moving at a uniform speed of one half the maximum and final speed of the previous uniformly accelerated motion.
After giving further results of this type he gives his famous result that the distance that a body moves from rest under uniform acceleration is proportional to the square of the time taken.
One would expect that Galileo's understanding of the pendulum, which he had since he was a young man, would have led him to design a pendulum clock. In fact he only seems to have thought of this possibility near the end of his life and around 1640 he did design the first pendulum clock. Galileo died in early 1642 but the significance of his clock design was certainly realised by his son Vincenzo who tried to make a clock to Galileo's plan, but failed.
It was a sad end for so great a man to die condemned of heresy. His will indicated that he wished to be buried beside his father in the family tomb in the Basilica of Santa Croce but his relatives feared, quite rightly, that this would provoke opposition from the Church. His body was concealed and only placed in a fine tomb in the church in 1737 by the civil authorities against the wishes of many in the Church. On 31 October 1992, 350 years after Galileo's death, Pope John Paul II gave an address on behalf of the Catholic Church in which he admitted that errors had been made by the theological advisors in the case of Galileo. He declared the Galileo case closed, but he did not admit that the Church was wrong to convict Galileo on a charge of heresy because of his belief that the Earth rotates round the sun.
Article by: J J O'Connor and E F Robertson
November 2002
Johannes Kepler
Johannes Kepler
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Born: 27 Dec 1571 in Weil der Stadt, Württemberg, Holy Roman Empire (now Germany)
Died: 15 Nov 1630 in Regensburg (now in Germany)
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Johannes Kepler is now chiefly remembered for discovering the three laws of planetary motion that bear his name published in 1609 and 1619). He also did important work in optics (1604, 1611), discovered two new regular polyhedra (1619), gave the first mathematical treatment of close packing of equal spheres (leading to an explanation of the shape of the cells of a honeycomb, 1611), gave the first proof of how logarithms worked (1624), and devised a method of finding the volumes of solids of revolution that (with hindsight!) can be seen as contributing to the development of calculus (1615, 1616). Moreover, he calculated the most exact astronomical tables hitherto known, whose continued accuracy did much to establish the truth of heliocentric astronomy (Rudolphine Tables, Ulm, 1627).
A large quantity of Kepler's correspondence survives. Many of his letters are almost the equivalent of a scientific paper (there were as yet no scientific journals), and correspondents seem to have kept them because they were interesting. In consequence, we know rather a lot about Kepler's life, and indeed about his character. It is partly because of this that Kepler has had something of a career as a more or less fictional character (see historiographic note).
Childhood
Kepler was born in the small town of Weil der Stadt in Swabia and moved to
nearby Leonberg with his parents in 1576. His father was a mercenary soldier and his mother the daughter of an innkeeper. Johannes was their first child. His father left home for the last time when Johannes was five, and is believed to have died in the war in the Netherlands. As a child, Kepler lived with his mother in his grandfather's inn. He tells us that he used to help by serving in the inn. One imagines customers were sometimes bemused by the child's unusual competence at arithmetic.
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Kepler's early education was in a local school and then at a nearby seminary, from which, intending to be ordained, he went on to enrol at the University of Tübingen, then (as now) a bastion of Lutheran orthodoxy.
Kepler's opinions
Throughout his life, Kepler was a profoundly religious man. All his writings contain numerous references to God, and he saw his work as a fulfilment of his Christian duty to understand the works of God. Man being, as Kepler believed, made in the image of God, was clearly capable of understanding the Universe that He had created. Moreover, Kepler was convinced that God had made the Universe according to a mathematical plan (a belief found in the works of Plato and associated with Pythagoras). Since it was generally accepted at the time that mathematics provided a secure method of arriving at truths about the world (Euclid's common notions and postulates being regarded as actually true), we have here a strategy for understanding the Universe. Since some authors have given Kepler a name for irrationality, it is worth noting that this rather hopeful epistemology is very far indeed from the mystic's conviction that things can only be understood in an imprecise way that relies upon insights that are not subject to reason. Kepler does indeed repeatedly thank God for granting him insights, but the insights are presented as rational.
University education
At this time, it was usual for all students at a university to attend courses on "mathematics". In principle this included the four mathematical sciences: arithmetic, geometry, astronomy and music. It seems, however, that what was taught depended on the particular university. At Tübingen Kepler was taught astronomy by one of the leading astronomers of the day, Michael Maestlin (1550 - 1631). The astronomy of the curriculum was, of course, geocentric astronomy, that is the current version of the Ptolemaic system, in which all seven planets - Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn - moved round the Earth, their positions against the fixed stars being calculated by combining circular motions. This system was more or less in accord with current (Aristotelian) notions of physics, though there were certain difficulties, such as whether one might consider as 'uniform' (and therefore acceptable as obviously eternal) a circular motion that was not uniform about its own centre but about another point (called an 'equant'). However, it seems that on the whole astronomers (who saw themselves as 'mathematicians') were content to carry on calculating positions of planets and leave it to natural philosophers to worry about whether the mathematical models corresponded to physical mechanisms. Kepler did not take this attitude. His earliest published work (1596) proposes to consider the actual paths of the planets, not the circles used to construct them.
At Tübingen, Kepler studied not only mathematics but also Greek and Hebrew (both necessary for reading the scriptures in their original languages). Teaching was in Latin. At the end of his first year Kepler got 'A's for everything except mathematics. Probably Maestlin was trying to tell him he could do better, because Kepler was in fact one of the
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select pupils to whom he chose to teach more advanced astronomy by introducing them to the new, heliocentric cosmological system of Copernicus. It was from Maestlin that Kepler learned that the preface to On the revolutions, explaining that this was 'only mathematics', was not by Copernicus. Kepler seems to have accepted almost instantly that the Copernican system was physically true; his reasons for accepting it will be discussed in connection with his first cosmological model (see below).
It seems that even in Kepler's student days there were indications that his religious beliefs were not entirely in accord with the orthodox Lutheranism current in Tübingen and formulated in the 'Augsburg Confession' (Confessio Augustana). Kepler's problems with this Protestant orthodoxy concerned the supposed relation between matter and 'spirit' (a non-material entity) in the doctrine of the Eucharist. This ties up with Kepler's astronomy to the extent that he apparently found somewhat similar intellectual difficulties in explaining how 'force' from the Sun could affect the planets. In his writings, Kepler is given to laying his opinions on the line - which is very convenient for historians. In real life, it seems likely that a similar tendency to openness led the authorities at Tübingen to entertain well-founded doubts about his religious orthodoxy. These may explain why Maestlin persuaded Kepler to abandon plans for ordination and instead take up a post teaching mathematics in Graz. Religious intolerance sharpened in the following years. Kepler was excommunicated in 1612. This caused him much pain, but despite his (by then) relatively high social standing, as Imperial Mathematician, he never succeeded in getting the ban lifted.
Kepler's first cosmological model (1596)
Instead of the seven planets in standard geocentric astronomy the Copernican system had only six, the Moon having become a body of kind previously unknown to astronomy, which Kepler was later to call a 'satellite' (a name he coined in 1610 to describe the moons that Galileo had discovered were orbiting Jupiter, literally meaning 'attendant'). Why six planets?
Moreover, in geocentric astronomy there was no way of using observations to find the relative sizes of the planetary orbs; they were simply assumed to be in contact. This seemed to require no explanation, since it fitted nicely with natural philosophers' belief that the whole system was turned from the movement of the outermost sphere, one (or maybe two) beyond the sphere of the 'fixed' stars (the ones whose pattern made the constellations), beyond the sphere of Saturn. In the Copernican system, the fact that the annual component of each planetary motion was a reflection of the annual motion of the Earth allowed one to use observations to calculate the size of each planet's path, and it turned out that there were huge spaces between the planets. Why these particular spaces?
Kepler's answer to these questions, described in his Mystery of the Cosmos (Mysterium cosmographicum, Tübingen, 1596), looks bizarre to twentieth-century readers (see the figure on the right). He suggested that if a sphere were drawn to touch the inside of the
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path of Saturn, and a cube were inscribed in the sphere, then the sphere inscribed in that cube would be the sphere circumscribing the path of Jupiter. Then if a regular tetrahedron were drawn in the sphere inscribing the path of Jupiter, the insphere of the tetrahedron would be the sphere circumscribing the path of Mars, and so inwards, putting the regular dodecahedron between Mars and Earth, the regular icosahedron between Earth and Venus, and the regular octahedron between Venus and Mercury. This explains the number of planets perfectly: there are only five convex regular solids (as is proved in Euclid's Elements , Book 13). It also gives a convincing fit with the sizes of the paths as deduced by Copernicus, the greatest error being less than 10% (which is spectacularly good for a cosmological model even now). Kepler did not express himself in terms of percentage errors, and his is in fact the first mathematical cosmological model, but it is easy to see why he believed that the observational evidence supported his theory.
Kepler saw his cosmological theory as providing evidence for the Copernican theory. Before presenting his own theory he gave arguments to establish the plausibility of the Copernican theory itself. Kepler asserts that its advantages over the geocentric theory are in its greater explanatory power. For instance, the Copernican theory can explain why Venus and Mercury are never seen very far from the Sun (they lie between Earth and the Sun) whereas in the geocentric theory there is no explanation of this fact. Kepler lists nine such questions in the first chapter of the Mysterium cosmographicum.
Kepler carried out this work while he was teaching in Graz, but the book was seen through the press in Tübingen by Maestlin. The agreement with values deduced from observation was not exact, and Kepler hoped that better observations would improve the agreement, so he sent a copy of the Mysterium cosmographicum to one of the foremost observational astronomers of the time, Tycho Brahe (1546 - 1601). Tycho, then working in Prague (at that time the capital of the Holy Roman Empire), had in fact already written to Maestlin in search of a mathematical assistant. Kepler got the job.
The 'War with Mars'
Naturally enough, Tycho's priorities were not the same as Kepler's, and Kepler soon found himself working on the intractable problem of the orbit of Mars [(See Appendix below)]. He continued to work on this after Tycho died (in 1601) and Kepler succeeded him as Imperial Mathematician. Conventionally, orbits were compounded of circles, and rather few observational values were required to fix the relative radii and positions of the circles. Tycho had made a huge number of observations and Kepler determined to make the best possible use of them. Essentially, he had so many observations available that once he had constructed a possible orbit he was able to check it against further observations until satisfactory agreement was reached. Kepler concluded that the orbit of Mars was an ellipse with the Sun in one of its foci (a result which when extended to all the planets is now called "Kepler's First Law"), and that a line joining the planet to the Sun swept out equal areas in equal times as the planet described its orbit ("Kepler's Second Law"), that is the area is used as a measure of time. After this work was published in New Astronomy ... (Astronomia nova, ..., Heidelberg, 1609), Kepler found
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orbits for the other planets, thus establishing that the two laws held for them too. Both laws relate the motion of the planet to the Sun; Kepler's Copernicanism was crucial to his reasoning and to his deductions.
The actual process of calculation for Mars was immensely laborious - there are nearly a thousand surviving folio sheets of arithmetic - and Kepler himself refers to this work as 'my war with Mars', but the result was an orbit which agrees with modern results so exactly that the comparison has to make allowance for secular changes in the orbit since Kepler's time.
Observational error
It was crucial to Kepler's method of checking possible orbits against observations that he have an idea of what should be accepted as adequate agreement. From this arises the first explicit use of the concept of observational error. Kepler may have owed this notion at least partly to Tycho, who made detailed checks on the performance of his instruments (see the biography of Brahe).
Optics, and the New Star of 1604
The work on Mars was essentially completed by 1605, but there were delays in getting the book published. Meanwhile, in response to concerns about the different apparent diameter of the Moon when observed directly and when observed using a camera obscura, Kepler did some work on optics, and came up with the first correct mathematical theory of the camera obscura and the first correct explanation of the working of the human eye, with an upside-down picture formed on the retina. These results were published in Supplements to Witelo, on the optical part of astronomy (Ad Vitellionem paralipomena, quibus astronomiae pars optica traditur, Frankfurt, 1604). He also wrote about the New Star of 1604, now usually called 'Kepler's supernova', rejecting numerous explanations, and remarking at one point that of course this star could just be a special creation 'but before we come to [that] I think we should try everything else' (On the New Star, De stella nova, Prague, 1606, Chapter 22, KGW 1, p. 257, line 23).
Following Galileo's use of the telescope in discovering the moons of Jupiter, published in his Sidereal Messenger (Venice, 1610), to which Kepler had written an enthusiastic reply (1610), Kepler wrote a study of the properties of lenses (the first such work on optics) in which he presented a new design of telescope, using two convex lenses (Dioptrice, Prague, 1611). This design, in which the final image is inverted, was so successful that it is now usually known not as a Keplerian telescope but simply as the astronomical telescope.
Leaving Prague for Linz
Kepler's years in Prague were relatively peaceful, and scientifically extremely productive. In fact, even when things went badly, he seems never to have allowed external circumstances to prevent him from getting on with his work. Things began to go very
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badly in late 1611. First, his seven year old son died. Kepler wrote to a friend that this death was particularly hard to bear because the child reminded him so much of himself at that age. Then Kepler's wife died. Then the Emperor Rudolf, whose health was failing, was forced to abdicate in favour of his brother Matthias, who, like Rudolf, was a Catholic but (unlike Rudolf) did not believe in tolerance of Protestants. Kepler had to leave Prague. Before he departed he had his wife's body moved into the son's grave, and wrote a Latin epitaph for them. He and his remaining children moved to Linz (now in Austria).
Marriage and wine barrels
Kepler seems to have married his first wife, Barbara, for love (though the marriage was arranged through a broker). The second marriage, in 1613, was a matter of practical necessity; he needed someone to look after the children. Kepler's new wife, Susanna, had a crash course in Kepler's character: the dedicatory letter to the resultant book explains that at the wedding celebrations he noticed that the volumes of wine barrels were estimated by means of a rod slipped in diagonally through the bung-hole, and he began to wonder how that could work. The result was a study of the volumes of solids of revolution (New Stereometry of wine barrels ..., Nova stereometria doliorum ..., Linz, 1615) in which Kepler, basing himself on the work of Archimedes, used a resolution into 'indivisibles'. This method was later developed by Bonaventura Cavalieri (c. 1598 - 1647) and is part of the ancestry of the infinitesimal calculus.
The Harmony of the World
Kepler's main task as Imperial Mathematician was to write astronomical tables, based on Tycho's observations, but what he really wanted to do was write The Harmony of the World, planned since 1599 as a development of his Mystery of the Cosmos. This second work on cosmology (Harmonices mundi libri V, Linz, 1619) presents a more elaborate mathematical model than the earlier one, though the polyhedra are still there. The mathematics in this work includes the first systematic treatment of tessellations, a proof that there are only thirteen convex uniform polyhedra (the Archimedean solids) and the first account of two non-convex regular polyhedra (all in Book 2). The Harmony of the World also contains what is now known as 'Kepler's Third Law', that for any two planets the ratio of the squares of their periods will be the same as the ratio of the cubes of the mean radii of their orbits. From the first, Kepler had sought a rule relating the sizes of the orbits to the periods, but there was no slow series of steps towards this law as there had been towards the other two. In fact, although the Third Law plays an important part in some of the final sections of the printed version of the Harmony of the World, it was not actually discovered until the work was in press. Kepler made last-minute revisions. He himself tells the story of the eventual success:
...and if you want the exact moment in time, it was conceived mentally on 8th March in this year one thousand six hundred and eighteen, but submitted to calculation in an unlucky way, and therefore rejected as false, and finally returning on the 15th of May and adopting a new line of attack, stormed the darkness of my mind. So strong was the support from the combination of my labour of seventeen years on the observations of
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Brahe and the present study, which conspired together, that at first I believed I was dreaming, and assuming my conclusion among my basic premises. But it is absolutely certain and exact that "the proportion between the periodic times of any two planets is precisely the sesquialterate proportion of their mean distances ..."
(Harmonice mundi Book 5, Chapter 3, trans. Aiton, Duncan and Field, p. 411).
Witchcraft trial
While Kepler was working on his Harmony of the World, his mother was charged with witchcraft. He enlisted the help of the legal faculty at Tübingen. Katharina Kepler was eventually released, at least partly as a result of technical objections arising from the authorities' failure to follow the correct legal procedures in the use of torture. The surviving documents are chilling. However, Kepler continued to work. In the coach, on his journey to Württemberg to defend his mother, he read a work on music theory by Vincenzo Galilei (c.1520 - 1591, Galileo's father), to which there are numerous references in The Harmony of the World.
Astronomical Tables
Calculating tables, the normal business for an astronomer, always involved heavy arithmetic. Kepler was accordingly delighted when in 1616 he came across Napier's work on logarithms (published in 1614). However, Maestlin promptly told him first that it was unseemly for a serious mathematician to rejoice over a mere aid to calculation and second that it was unwise to trust logarithms because no-one understood how they worked. (Similar comments were made about computers in the early 1960s.) Kepler's answer to the second objection was to publish a proof of how logarithms worked, based on an impeccably respectable source: Euclid's Elements Book 5. Kepler calculated tables of eight-figure logarithms, which were published with the Rudolphine Tables (Ulm, 1628). The astronomical tables used not only Tycho's observations, but also Kepler's first two laws. All astronomical tables that made use of new observations were accurate for the first few years after publication. What was remarkable about the Rudolphine Tables was that they proved to be accurate over decades. And as the years mounted up, the continued accuracy of the tables was, naturally, seen as an argument for the correctness of Kepler's laws, and thus for the correctness of the heliocentric astronomy. Kepler's fulfilment of his dull official task as Imperial Mathematician led to the fulfilment of his dearest wish, to help establish Copernicanism.
Wallenstein
By the time the Rudolphine Tables were published Kepler was, in fact, no longer working for the Emperor (he had left Linz in 1626), but for Albrecht von Wallenstein (1583 - 1632), one of the few successful military leaders in the Thirty Years' War (1618 - 1648).
Wallenstein, like the emperor Rudolf, expected Kepler to give him advice based on astrology. Kepler naturally had to obey, but repeatedly points out that he does not believe precise predictions can be made. Like most people of the time, Kepler accepted the
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principle of astrology, that heavenly bodies could influence what happened on Earth (the clearest examples being the Sun causing the seasons and the Moon the tides) but as a Copernican he did not believe in the physical reality of the constellations. His astrology was based only on the angles between the positions of heavenly bodies ('astrological aspects'). He expresses utter contempt for the complicated systems of conventional astrology.
Death
Kepler died in Regensburg, after a short illness. He was staying in the city on his way to collect some money owing to him in connection with the Rudolphine Tables. He was buried in the local church, but this was destroyed in the course of the Thirty Years' War and nothing remains of the tomb.
Historiographic note
Much has sometimes been made of supposedly non-rational elements in Kepler's scientific activity. Believing astrologers frequently claim his work provides a scientifically respectable antecedent to their own. In his influential Sleepwalkers the late Arthur Koestler made Kepler's battle with Mars into an argument for the inherent irrationality of modern science. There have been many tacit followers of these two persuasions. Both are, however, based on very partial reading of Kepler's work. In particular, Koestler seems not to have had the mathematical expertise to understand Kepler's procedures. Closer study shows Koestler was simply mistaken in his assessment.
The truly important non-rational element in Kepler's work is his Christianity. Kepler's extensive and successful use of mathematics makes his work look 'modern', but we are in fact dealing with a Christian Natural Philosopher, for whom understanding the nature of the Universe included understanding the nature of its Creator.
Article by: J. V. Field, London
April 1999
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Born: 27 Dec 1571 in Weil der Stadt, Württemberg, Holy Roman Empire (now Germany)
Died: 15 Nov 1630 in Regensburg (now in Germany)
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Johannes Kepler is now chiefly remembered for discovering the three laws of planetary motion that bear his name published in 1609 and 1619). He also did important work in optics (1604, 1611), discovered two new regular polyhedra (1619), gave the first mathematical treatment of close packing of equal spheres (leading to an explanation of the shape of the cells of a honeycomb, 1611), gave the first proof of how logarithms worked (1624), and devised a method of finding the volumes of solids of revolution that (with hindsight!) can be seen as contributing to the development of calculus (1615, 1616). Moreover, he calculated the most exact astronomical tables hitherto known, whose continued accuracy did much to establish the truth of heliocentric astronomy (Rudolphine Tables, Ulm, 1627).
A large quantity of Kepler's correspondence survives. Many of his letters are almost the equivalent of a scientific paper (there were as yet no scientific journals), and correspondents seem to have kept them because they were interesting. In consequence, we know rather a lot about Kepler's life, and indeed about his character. It is partly because of this that Kepler has had something of a career as a more or less fictional character (see historiographic note).
Childhood
Kepler was born in the small town of Weil der Stadt in Swabia and moved to
nearby Leonberg with his parents in 1576. His father was a mercenary soldier and his mother the daughter of an innkeeper. Johannes was their first child. His father left home for the last time when Johannes was five, and is believed to have died in the war in the Netherlands. As a child, Kepler lived with his mother in his grandfather's inn. He tells us that he used to help by serving in the inn. One imagines customers were sometimes bemused by the child's unusual competence at arithmetic.
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Kepler's early education was in a local school and then at a nearby seminary, from which, intending to be ordained, he went on to enrol at the University of Tübingen, then (as now) a bastion of Lutheran orthodoxy.
Kepler's opinions
Throughout his life, Kepler was a profoundly religious man. All his writings contain numerous references to God, and he saw his work as a fulfilment of his Christian duty to understand the works of God. Man being, as Kepler believed, made in the image of God, was clearly capable of understanding the Universe that He had created. Moreover, Kepler was convinced that God had made the Universe according to a mathematical plan (a belief found in the works of Plato and associated with Pythagoras). Since it was generally accepted at the time that mathematics provided a secure method of arriving at truths about the world (Euclid's common notions and postulates being regarded as actually true), we have here a strategy for understanding the Universe. Since some authors have given Kepler a name for irrationality, it is worth noting that this rather hopeful epistemology is very far indeed from the mystic's conviction that things can only be understood in an imprecise way that relies upon insights that are not subject to reason. Kepler does indeed repeatedly thank God for granting him insights, but the insights are presented as rational.
University education
At this time, it was usual for all students at a university to attend courses on "mathematics". In principle this included the four mathematical sciences: arithmetic, geometry, astronomy and music. It seems, however, that what was taught depended on the particular university. At Tübingen Kepler was taught astronomy by one of the leading astronomers of the day, Michael Maestlin (1550 - 1631). The astronomy of the curriculum was, of course, geocentric astronomy, that is the current version of the Ptolemaic system, in which all seven planets - Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn - moved round the Earth, their positions against the fixed stars being calculated by combining circular motions. This system was more or less in accord with current (Aristotelian) notions of physics, though there were certain difficulties, such as whether one might consider as 'uniform' (and therefore acceptable as obviously eternal) a circular motion that was not uniform about its own centre but about another point (called an 'equant'). However, it seems that on the whole astronomers (who saw themselves as 'mathematicians') were content to carry on calculating positions of planets and leave it to natural philosophers to worry about whether the mathematical models corresponded to physical mechanisms. Kepler did not take this attitude. His earliest published work (1596) proposes to consider the actual paths of the planets, not the circles used to construct them.
At Tübingen, Kepler studied not only mathematics but also Greek and Hebrew (both necessary for reading the scriptures in their original languages). Teaching was in Latin. At the end of his first year Kepler got 'A's for everything except mathematics. Probably Maestlin was trying to tell him he could do better, because Kepler was in fact one of the
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select pupils to whom he chose to teach more advanced astronomy by introducing them to the new, heliocentric cosmological system of Copernicus. It was from Maestlin that Kepler learned that the preface to On the revolutions, explaining that this was 'only mathematics', was not by Copernicus. Kepler seems to have accepted almost instantly that the Copernican system was physically true; his reasons for accepting it will be discussed in connection with his first cosmological model (see below).
It seems that even in Kepler's student days there were indications that his religious beliefs were not entirely in accord with the orthodox Lutheranism current in Tübingen and formulated in the 'Augsburg Confession' (Confessio Augustana). Kepler's problems with this Protestant orthodoxy concerned the supposed relation between matter and 'spirit' (a non-material entity) in the doctrine of the Eucharist. This ties up with Kepler's astronomy to the extent that he apparently found somewhat similar intellectual difficulties in explaining how 'force' from the Sun could affect the planets. In his writings, Kepler is given to laying his opinions on the line - which is very convenient for historians. In real life, it seems likely that a similar tendency to openness led the authorities at Tübingen to entertain well-founded doubts about his religious orthodoxy. These may explain why Maestlin persuaded Kepler to abandon plans for ordination and instead take up a post teaching mathematics in Graz. Religious intolerance sharpened in the following years. Kepler was excommunicated in 1612. This caused him much pain, but despite his (by then) relatively high social standing, as Imperial Mathematician, he never succeeded in getting the ban lifted.
Kepler's first cosmological model (1596)
Instead of the seven planets in standard geocentric astronomy the Copernican system had only six, the Moon having become a body of kind previously unknown to astronomy, which Kepler was later to call a 'satellite' (a name he coined in 1610 to describe the moons that Galileo had discovered were orbiting Jupiter, literally meaning 'attendant'). Why six planets?
Moreover, in geocentric astronomy there was no way of using observations to find the relative sizes of the planetary orbs; they were simply assumed to be in contact. This seemed to require no explanation, since it fitted nicely with natural philosophers' belief that the whole system was turned from the movement of the outermost sphere, one (or maybe two) beyond the sphere of the 'fixed' stars (the ones whose pattern made the constellations), beyond the sphere of Saturn. In the Copernican system, the fact that the annual component of each planetary motion was a reflection of the annual motion of the Earth allowed one to use observations to calculate the size of each planet's path, and it turned out that there were huge spaces between the planets. Why these particular spaces?
Kepler's answer to these questions, described in his Mystery of the Cosmos (Mysterium cosmographicum, Tübingen, 1596), looks bizarre to twentieth-century readers (see the figure on the right). He suggested that if a sphere were drawn to touch the inside of the
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path of Saturn, and a cube were inscribed in the sphere, then the sphere inscribed in that cube would be the sphere circumscribing the path of Jupiter. Then if a regular tetrahedron were drawn in the sphere inscribing the path of Jupiter, the insphere of the tetrahedron would be the sphere circumscribing the path of Mars, and so inwards, putting the regular dodecahedron between Mars and Earth, the regular icosahedron between Earth and Venus, and the regular octahedron between Venus and Mercury. This explains the number of planets perfectly: there are only five convex regular solids (as is proved in Euclid's Elements , Book 13). It also gives a convincing fit with the sizes of the paths as deduced by Copernicus, the greatest error being less than 10% (which is spectacularly good for a cosmological model even now). Kepler did not express himself in terms of percentage errors, and his is in fact the first mathematical cosmological model, but it is easy to see why he believed that the observational evidence supported his theory.
Kepler saw his cosmological theory as providing evidence for the Copernican theory. Before presenting his own theory he gave arguments to establish the plausibility of the Copernican theory itself. Kepler asserts that its advantages over the geocentric theory are in its greater explanatory power. For instance, the Copernican theory can explain why Venus and Mercury are never seen very far from the Sun (they lie between Earth and the Sun) whereas in the geocentric theory there is no explanation of this fact. Kepler lists nine such questions in the first chapter of the Mysterium cosmographicum.
Kepler carried out this work while he was teaching in Graz, but the book was seen through the press in Tübingen by Maestlin. The agreement with values deduced from observation was not exact, and Kepler hoped that better observations would improve the agreement, so he sent a copy of the Mysterium cosmographicum to one of the foremost observational astronomers of the time, Tycho Brahe (1546 - 1601). Tycho, then working in Prague (at that time the capital of the Holy Roman Empire), had in fact already written to Maestlin in search of a mathematical assistant. Kepler got the job.
The 'War with Mars'
Naturally enough, Tycho's priorities were not the same as Kepler's, and Kepler soon found himself working on the intractable problem of the orbit of Mars [(See Appendix below)]. He continued to work on this after Tycho died (in 1601) and Kepler succeeded him as Imperial Mathematician. Conventionally, orbits were compounded of circles, and rather few observational values were required to fix the relative radii and positions of the circles. Tycho had made a huge number of observations and Kepler determined to make the best possible use of them. Essentially, he had so many observations available that once he had constructed a possible orbit he was able to check it against further observations until satisfactory agreement was reached. Kepler concluded that the orbit of Mars was an ellipse with the Sun in one of its foci (a result which when extended to all the planets is now called "Kepler's First Law"), and that a line joining the planet to the Sun swept out equal areas in equal times as the planet described its orbit ("Kepler's Second Law"), that is the area is used as a measure of time. After this work was published in New Astronomy ... (Astronomia nova, ..., Heidelberg, 1609), Kepler found
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orbits for the other planets, thus establishing that the two laws held for them too. Both laws relate the motion of the planet to the Sun; Kepler's Copernicanism was crucial to his reasoning and to his deductions.
The actual process of calculation for Mars was immensely laborious - there are nearly a thousand surviving folio sheets of arithmetic - and Kepler himself refers to this work as 'my war with Mars', but the result was an orbit which agrees with modern results so exactly that the comparison has to make allowance for secular changes in the orbit since Kepler's time.
Observational error
It was crucial to Kepler's method of checking possible orbits against observations that he have an idea of what should be accepted as adequate agreement. From this arises the first explicit use of the concept of observational error. Kepler may have owed this notion at least partly to Tycho, who made detailed checks on the performance of his instruments (see the biography of Brahe).
Optics, and the New Star of 1604
The work on Mars was essentially completed by 1605, but there were delays in getting the book published. Meanwhile, in response to concerns about the different apparent diameter of the Moon when observed directly and when observed using a camera obscura, Kepler did some work on optics, and came up with the first correct mathematical theory of the camera obscura and the first correct explanation of the working of the human eye, with an upside-down picture formed on the retina. These results were published in Supplements to Witelo, on the optical part of astronomy (Ad Vitellionem paralipomena, quibus astronomiae pars optica traditur, Frankfurt, 1604). He also wrote about the New Star of 1604, now usually called 'Kepler's supernova', rejecting numerous explanations, and remarking at one point that of course this star could just be a special creation 'but before we come to [that] I think we should try everything else' (On the New Star, De stella nova, Prague, 1606, Chapter 22, KGW 1, p. 257, line 23).
Following Galileo's use of the telescope in discovering the moons of Jupiter, published in his Sidereal Messenger (Venice, 1610), to which Kepler had written an enthusiastic reply (1610), Kepler wrote a study of the properties of lenses (the first such work on optics) in which he presented a new design of telescope, using two convex lenses (Dioptrice, Prague, 1611). This design, in which the final image is inverted, was so successful that it is now usually known not as a Keplerian telescope but simply as the astronomical telescope.
Leaving Prague for Linz
Kepler's years in Prague were relatively peaceful, and scientifically extremely productive. In fact, even when things went badly, he seems never to have allowed external circumstances to prevent him from getting on with his work. Things began to go very
5
badly in late 1611. First, his seven year old son died. Kepler wrote to a friend that this death was particularly hard to bear because the child reminded him so much of himself at that age. Then Kepler's wife died. Then the Emperor Rudolf, whose health was failing, was forced to abdicate in favour of his brother Matthias, who, like Rudolf, was a Catholic but (unlike Rudolf) did not believe in tolerance of Protestants. Kepler had to leave Prague. Before he departed he had his wife's body moved into the son's grave, and wrote a Latin epitaph for them. He and his remaining children moved to Linz (now in Austria).
Marriage and wine barrels
Kepler seems to have married his first wife, Barbara, for love (though the marriage was arranged through a broker). The second marriage, in 1613, was a matter of practical necessity; he needed someone to look after the children. Kepler's new wife, Susanna, had a crash course in Kepler's character: the dedicatory letter to the resultant book explains that at the wedding celebrations he noticed that the volumes of wine barrels were estimated by means of a rod slipped in diagonally through the bung-hole, and he began to wonder how that could work. The result was a study of the volumes of solids of revolution (New Stereometry of wine barrels ..., Nova stereometria doliorum ..., Linz, 1615) in which Kepler, basing himself on the work of Archimedes, used a resolution into 'indivisibles'. This method was later developed by Bonaventura Cavalieri (c. 1598 - 1647) and is part of the ancestry of the infinitesimal calculus.
The Harmony of the World
Kepler's main task as Imperial Mathematician was to write astronomical tables, based on Tycho's observations, but what he really wanted to do was write The Harmony of the World, planned since 1599 as a development of his Mystery of the Cosmos. This second work on cosmology (Harmonices mundi libri V, Linz, 1619) presents a more elaborate mathematical model than the earlier one, though the polyhedra are still there. The mathematics in this work includes the first systematic treatment of tessellations, a proof that there are only thirteen convex uniform polyhedra (the Archimedean solids) and the first account of two non-convex regular polyhedra (all in Book 2). The Harmony of the World also contains what is now known as 'Kepler's Third Law', that for any two planets the ratio of the squares of their periods will be the same as the ratio of the cubes of the mean radii of their orbits. From the first, Kepler had sought a rule relating the sizes of the orbits to the periods, but there was no slow series of steps towards this law as there had been towards the other two. In fact, although the Third Law plays an important part in some of the final sections of the printed version of the Harmony of the World, it was not actually discovered until the work was in press. Kepler made last-minute revisions. He himself tells the story of the eventual success:
...and if you want the exact moment in time, it was conceived mentally on 8th March in this year one thousand six hundred and eighteen, but submitted to calculation in an unlucky way, and therefore rejected as false, and finally returning on the 15th of May and adopting a new line of attack, stormed the darkness of my mind. So strong was the support from the combination of my labour of seventeen years on the observations of
6
Brahe and the present study, which conspired together, that at first I believed I was dreaming, and assuming my conclusion among my basic premises. But it is absolutely certain and exact that "the proportion between the periodic times of any two planets is precisely the sesquialterate proportion of their mean distances ..."
(Harmonice mundi Book 5, Chapter 3, trans. Aiton, Duncan and Field, p. 411).
Witchcraft trial
While Kepler was working on his Harmony of the World, his mother was charged with witchcraft. He enlisted the help of the legal faculty at Tübingen. Katharina Kepler was eventually released, at least partly as a result of technical objections arising from the authorities' failure to follow the correct legal procedures in the use of torture. The surviving documents are chilling. However, Kepler continued to work. In the coach, on his journey to Württemberg to defend his mother, he read a work on music theory by Vincenzo Galilei (c.1520 - 1591, Galileo's father), to which there are numerous references in The Harmony of the World.
Astronomical Tables
Calculating tables, the normal business for an astronomer, always involved heavy arithmetic. Kepler was accordingly delighted when in 1616 he came across Napier's work on logarithms (published in 1614). However, Maestlin promptly told him first that it was unseemly for a serious mathematician to rejoice over a mere aid to calculation and second that it was unwise to trust logarithms because no-one understood how they worked. (Similar comments were made about computers in the early 1960s.) Kepler's answer to the second objection was to publish a proof of how logarithms worked, based on an impeccably respectable source: Euclid's Elements Book 5. Kepler calculated tables of eight-figure logarithms, which were published with the Rudolphine Tables (Ulm, 1628). The astronomical tables used not only Tycho's observations, but also Kepler's first two laws. All astronomical tables that made use of new observations were accurate for the first few years after publication. What was remarkable about the Rudolphine Tables was that they proved to be accurate over decades. And as the years mounted up, the continued accuracy of the tables was, naturally, seen as an argument for the correctness of Kepler's laws, and thus for the correctness of the heliocentric astronomy. Kepler's fulfilment of his dull official task as Imperial Mathematician led to the fulfilment of his dearest wish, to help establish Copernicanism.
Wallenstein
By the time the Rudolphine Tables were published Kepler was, in fact, no longer working for the Emperor (he had left Linz in 1626), but for Albrecht von Wallenstein (1583 - 1632), one of the few successful military leaders in the Thirty Years' War (1618 - 1648).
Wallenstein, like the emperor Rudolf, expected Kepler to give him advice based on astrology. Kepler naturally had to obey, but repeatedly points out that he does not believe precise predictions can be made. Like most people of the time, Kepler accepted the
7
principle of astrology, that heavenly bodies could influence what happened on Earth (the clearest examples being the Sun causing the seasons and the Moon the tides) but as a Copernican he did not believe in the physical reality of the constellations. His astrology was based only on the angles between the positions of heavenly bodies ('astrological aspects'). He expresses utter contempt for the complicated systems of conventional astrology.
Death
Kepler died in Regensburg, after a short illness. He was staying in the city on his way to collect some money owing to him in connection with the Rudolphine Tables. He was buried in the local church, but this was destroyed in the course of the Thirty Years' War and nothing remains of the tomb.
Historiographic note
Much has sometimes been made of supposedly non-rational elements in Kepler's scientific activity. Believing astrologers frequently claim his work provides a scientifically respectable antecedent to their own. In his influential Sleepwalkers the late Arthur Koestler made Kepler's battle with Mars into an argument for the inherent irrationality of modern science. There have been many tacit followers of these two persuasions. Both are, however, based on very partial reading of Kepler's work. In particular, Koestler seems not to have had the mathematical expertise to understand Kepler's procedures. Closer study shows Koestler was simply mistaken in his assessment.
The truly important non-rational element in Kepler's work is his Christianity. Kepler's extensive and successful use of mathematics makes his work look 'modern', but we are in fact dealing with a Christian Natural Philosopher, for whom understanding the nature of the Universe included understanding the nature of its Creator.
Article by: J. V. Field, London
April 1999
Marin Mersenne
Marin Mersenne
--------------------------------------------------------------------------------
Born: 8 Sept 1588 in Oizé in Maine, France
Died: 1 Sept 1648 in Paris, France
--------------------------------------------------------------------------------
Marin Mersenne was born into a working class family in the small town of Oizé in the province of Maine on 8 September 1588 and was baptised on the same day. From an early age he showed signs of devotion and eagerness to study. So, despite their financial situation, Marin's parents sent him to the Collège du Mans where he took grammar classes. Later, at the age of sixteen, Mersenne asked to go to the newly established Jesuit School in La Flèche which had been set up as a model school for the benefit of all children regardless of their parents' financial situation. It turns out that Descartes, who was eight years younger than Mersenne, was enrolled at the same school although they are not thought to have become friends until much later.
Mersenne's father wanted his son to have a career in the Church. Mersenne, however, was devoted to study, which he loved, and, showing that he was ready for responsibilities of the world, had decided to further his education in Paris. He left for Paris staying en route at a convent of the Minims. This experience so inspired Mersenne that he agreed to join their Order if one day he decided to lead a monastic life. After reaching Paris he studied at the Collège Royale du France, continuing there his education in philosophy and also attending classes in theology at the Sorbonne where he also obtained the degree of Magister Atrium in Philosophy. He finished his studies in 1611 and, having had a privileged education, realised that he was now ready for the calm and studious life of a monastery.
The Order of the Minims, having been set up by St Francis of Paula in 1436, was thriving at this time. They believed they were the least (minimi) of all the religions on earth, and devoted themselves to prayer, study, and scholarship. They wore a habit made of coarse black wool with broad sleeves and girded by a thin black cord (as seen in the portraits of Mersenne). Charles VIII introduced the Order into France and, due to their great simplicity, the monks were named 'les bons hommes'. After the French Revolution the Order dwindled considerably in number and today there exists only a few convents in Italy. Mersenne entered the Order on 16 July 1611, and was ordained a priest in Paris in July 1612 after a two and a half month probationary period in the monasteries at Nigeon
1
and Meaux. His first posting was in 1614 to the monastery in Nevers where he taught philosophy and theology to the younger members of the community. In fact one of his students, Hilarion de Coste, later became his confidant and biographer. It was during this period of his life that he is thought to have discovered the cycloid - a geometric curve.
After two years teaching Mersenne was elected superior of the Place Royale monastery in Paris where he remained, except for brief journeys, until his death in 1648. It is believed that the Church supported him for most of his life, although in later years a fellow monk, Jacques Hallé, helped out with money and granted him access to his library. From the beginning of his time in Paris, mathematical problems played an important role in his life. Very early on he had links with important scholars in Paris whom he met often, exchanging ideas and discussing projects. The Minims realised that the biggest service he could give was through his books and they never asked any more of him.
In 1623 he published his first two papers consisting of studies against atheism and scepticism in France; L'usage de la raison and L'analyse de la vie spirituelle. Continuing his theological writing he had then wanted to disprove magic, however a fellow monk pointed out that it wasn't appropriate, leading to his publication of Quaestiones celeberrime in genesim that includes the disapproval of magicians in the Scriptures. This book contains 1900 columns of text from the Bible in its first six chapters. It was because of this publication that, in September 1624 when he returned to Paris, he met Gassendi who had been asked to comment on Mersenne's results, and later became his closest friend.
At this time France was going through a period of anti-witchcraft, expelling any sorcerers. L'impiété des deistes, in French, was aimed at the French public so that they might read and understand what was happening. It was during this time that Mersenne started to think about the theological criticism directed against Descartes and Galileo. In fact Mersenne's attitude to Galileo changed over a number of years as Garber points out in [16]:-
Marin Mersenne was central to the new mathematical approach to nature in Paris in the 1630s and 1640s. Intellectually, he was one of the most enthusiastic practitioners of that program, and published a number of influential books in those important decades. But Mersenne started his career in a rather different way. In the early 1620s, Mersenne was known in Paris primarily as a writer on religious topics, and a staunch defender of Aristotle against attacks by those who would replace him by a new philosophy. ... In the early 1620s, Mersenne listed Galileo among the innovators in natural philosophy whose views should be rejected. However, by the early 1630s, less than a decade later, Mersenne had become one of Galileo's most ardent supporters.
Mersenne was beginning to realise that alongside religion it was science that really interested him. Mathematics was the area he studied in greatest depth, believing that without it no science was possible. He always had a philosophical approach to mathematics and believed that the cause of the sciences is the cause of God, see [5]. So, in La vérité des sciences he proved, via many great discoveries, the value of the human
2
mind. It was around this time that Mersenne started to become a coordinator for all European scholars. From 1623 he began to make a careful selection of savants who met at his convent in Paris or corresponded with him from all across Europe and even from as far afield as Constantinople and Transylvania (present-day Hungary). His regular visitors, or correspondents, included Peiresc, Gassendi, Descartes, Roberval, Beeckman, J B van Helmont, Fermat, Hobbes, Etienne Pascal, and his son Blaise Pascal. He set up meetings of scholars from around Europe during which they would read and review scientific papers, both national and international, exchange contacts with other scholars and plan and discuss experiments and other work. This came to be known as the Académie Parisiensis and sometimes among friends as the Académie Mersenne. It was notably one of most resourceful centres of research at that time, meeting weekly at members' houses and later in Mersenne's cell due to his weakened health. The list of Mersenne's correspondents kept increasing and Mersenne himself did not hesitate to travel to meetings with scholars all around Europe.
Mersenne had a strong interest in music and spent a lot of time researching acoustics and the speed of sound. In 1627 he published one of his most famous works, L'harmonie universelle. In this work he was the first to publish the laws relating to the vibrating string: its frequency is proportional to the square root of the tension, and inversely proportional to the length, to the diameter and to the square root of the specific weight of the string, provided all other conditions remain the same when one of these quantities is altered. Mersenne had already started encouraging the talents of others and helped them to share their ideas and results with other scholars. When Roberval arrived in Paris, after joining Mersenne's circle of scholars, his talent was soon recognised by Mersenne who encouraged him to work on the cycloid.
The period between 1627 and 1634 was a transitional period in Mersenne's life. During this time he travelled to Holland for several months between 1629 and 1630. His main reason was to seek a cure for an illness with the help of spa water but he used the opportunity to visit scholars in the surrounding areas. The greater maturity in his writing in the seven years since his last publication became apparent when Questions inouyes and Questions harmoniques were printed in 1634. In October 1644 Mersenne travelled to Provence and Italy where he learnt of the barometer experiment from Torricelli. On his return to Paris, he reported this news to encourage French scholars to carry out the experiments too.
Throughout his lifetime Mersenne helped many potential scientists by steering them in the right direction and advising some on the next step to take. He became a role model for Huygens whom Mersenne took under his wing and through his encouraging letters inspired Huygens' Theory of Music. Huygens had intended to move to Paris in 1646 to be near Mersenne in order to enable them to contact each other more easily, however Huygens didn't move until several years after Mersenne had died so they never met.
Galileo also has to be grateful to Mersenne for making his work known outside Italy. Mersenne insisted on publishing Galileo's work and without this Galileo's ideas might never have become as widely known. Continuing his travels into his old age, in 1646
3
Mersenne set off on a trip to Bordeaux. There he met Pierre Trichet whom he helped make his mark. The success of the scientific life over in Bordeaux and Guyenne, which later formed the Académie Royale des Sciences, was largely due to the advice and experience Mersenne was able to offer. He returned to Paris in 1647.
Mersenne fell ill after his visit to see Descartes in July 1648 and, unfortunately, his health never improved. He was advised to mix wine with his water to help him get better, however Minims do not drink wine. He had an abscess on the lung but the surgeon was unable to find it. Mersenne himself pointed out that the incision, which he asked for, had been attempted too low. Gassendi was there for Mersenne throughout his illness and remained with him until his death on 1 September 1648 in Paris, just 8 days from his 60th birthday. He never gave up his life-long desire to advance science. He even asked, in his will, that his body be used for biological research.
After Mersenne's death, letters in his cell were found from 78 different correspondents including Fermat, Huygens, Pell, Galileo and Torricelli. Also several physics instruments were found in his cell and a lot of Mersenne's library was retrieved from which L'optique et la catoptrique was published in 1651. Inside this publication one of Roberval's texts was inserted. Later all the letters he sent and received from other scholars were accumulated and published in several volumes. These letters read like an international review of mechanics in the early 17th century. Mersenne was aware of all the science that was going on, what all the scientists were doing, and only wanted for them all to work together in advancing science.
Mersenne studied the cycloid for several years quoting his research in Quaestiones in Genesim (1623), Synopsis mathematica (1626) and Questions inouyes (1634). He gave the definition of a cycloid as the locus of a point at distance h from the centre of a circle of radius a, that rolls along a straight line. He stated the obvious properties including the length of the base line equals the circumference of the rolling circle. We note that Mersenne referred to the cycloid as the 'roulette' but the term cycloid was adopted later. He attempted to find the area under the curve by integration but having failed, so he put the question to Roberval. In 1638 he announced that Roberval had indeed found the area under the cycloid.
Mersenne's name is best remembered today for Mersenne primes. He tried to find a formula that would represent all primes but, although he failed in this, his work on numbers of the form
2p - 1, p prime
has been of continuing interest in the investigation of large primes. It is easy to prove that if the number n = 2p - 1 is prime then p must be a prime. In 1644 Mersenne claimed that n is prime if p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257 but composite for the other 44 primes p smaller than 257.
4
Over the years it has been found that Mersenne was wrong about 5 of the primes of the form 2p - 1 where p is less than or equal to 257 (he claimed two that didn't lead to a prime (67 and 257) and missed 3 that did: 61, 89, 107). Drake [13] has tried to both understand the source of Mersenne's work on these primes, and also to try to determine the rule that was being used. He suggests Frenicle de Bessy may be the source and also suggests that the errors might be misprints by the printer. Drake reconstructs Mersenne's rule for exponents as that they must differ by not more than one from a value of 2n or by not more than three from a value of 2 to the power 2n.
Mersenne undertook experiments to test Galileo's law of motion for falling bodies. In 1634 he presented the results that he had obtained when measuring the acceleration of falling bodies from heights of 147, 108 and 48 feet. These confirmed the time-squared law that Galileo had published in his Dialogue on the two chief world systems of 1632 but they also raised questions about the numerical data. One problem he tried to solve was whether acceleration was continuous as Galileo maintained or discontinuous as Descartes believed. Mersenne thought Galileo's assumption that a falling body passes through infinite degrees of speed was incompatible with a genuinely mechanistic explanation of acceleration. These ideas are discussed in detail in [24] and [25].
In some of his non-mathematical works Mersenne looks at permutations and combinations. He states practical rules for calculating the number of combinations or permutations, solving the problem of finding the number of permutations with or without repetitions and gives an example the making of anagrams. His main reason to study combinatorial analysis was, however, to optimise musical composition as he explains in The book on the art of singing well which is Book Six of Harmonie universelle (1636). In an unpublished manuscript preserved in the Bibliothèque Nationale at Paris he gave the 40320 permutations of 8 notes.
During the final four years of his life, Mersenne spent a lot of time investigating the barometer. Pascal had already proved that air was not weightless and it was Mersenne who found the density of air to be approximately 1/19th that of water. He was informed of the barometer experiment, consisting of a glass tube about 3 feet long sealed at one end and filled with pure mercury, through several letters from De Verdus but it was not until October 1644, when he visited Torricelli in Italy, that he saw the experiment carried out. Torricelli used the pressure of the air to explain why the mercury moved up the glass tube. Mersenne was doubtful that the air pressure actually supported the mercury and on his return attempted to re-do the experiment but did not have the necessary equipment. Mersenne explained the problem to Etienne Pascal, his son Blaise Pascal, Petit, Roberval, and others in Paris. There is some confusion as to who, in 1647, initially suggested the experiments with the Torricellian tube and the mountain, later to be called the Puy de Dome experiments. Certainly Mersenne had briefed both Huygens and Le Tenneur but it was not until three weeks after Mersenne's death in 1648 that these experiments were carried out. They consisted of collecting results both at the foot of the Puy de Dome and at the summit. Tests were made as to whether the level of mercury in the column was lower when at the top of the mountain than it was at the bottom. If this had proved to be true, they realised that this would be due to the pressure of the air alone. Perier, who
5
finally conducted the experiments, did indeed find that there was a significant difference in the level of the mercury hence drawing the correct conclusion that the air pressure was supporting it.
An interesting question is how Mersenne managed to pursue his scientific ideas freely at a time when the Church (of which he was a devoted member) moved to prevent such discussion. This topic is considered in detail in [18] where Hine writes:-
During the first half of the seventeenth century, debate over the Copernican hypothesis had spread beyond the ranks of astronomers and had stirred up so much controversy that the Church decided to intervene. In 1616 a theological examining body concluded that the idea of the earth's motion was philosophically false and in conflict with the Scriptures, and it suspended Copernicus' book until corrected. Historians have generally assumed that this decision and the subsequent condemnation of Galileo had such a devastating effect that scientific progress in Catholic countries was greatly retarded. However, the attitude of Mersenne, who was both a faithful member of a religious order and a central figure in the development of French science, does not support such a conclusion. An examination of Mersenne's reaction to Copernicanism indicates that no matter how disturbing the Church's decision, it was still possible, at least in France, to study Copernican ideas and to find them useful, despite some reservations. Mersenne was affected by such decisions of the Church, but less so than one might suppose.
Article by: J J O'Connor and E F Robertson based on an honours project by Jessica Daniell (University of St Andrews).
August 2005
--------------------------------------------------------------------------------
Born: 8 Sept 1588 in Oizé in Maine, France
Died: 1 Sept 1648 in Paris, France
--------------------------------------------------------------------------------
Marin Mersenne was born into a working class family in the small town of Oizé in the province of Maine on 8 September 1588 and was baptised on the same day. From an early age he showed signs of devotion and eagerness to study. So, despite their financial situation, Marin's parents sent him to the Collège du Mans where he took grammar classes. Later, at the age of sixteen, Mersenne asked to go to the newly established Jesuit School in La Flèche which had been set up as a model school for the benefit of all children regardless of their parents' financial situation. It turns out that Descartes, who was eight years younger than Mersenne, was enrolled at the same school although they are not thought to have become friends until much later.
Mersenne's father wanted his son to have a career in the Church. Mersenne, however, was devoted to study, which he loved, and, showing that he was ready for responsibilities of the world, had decided to further his education in Paris. He left for Paris staying en route at a convent of the Minims. This experience so inspired Mersenne that he agreed to join their Order if one day he decided to lead a monastic life. After reaching Paris he studied at the Collège Royale du France, continuing there his education in philosophy and also attending classes in theology at the Sorbonne where he also obtained the degree of Magister Atrium in Philosophy. He finished his studies in 1611 and, having had a privileged education, realised that he was now ready for the calm and studious life of a monastery.
The Order of the Minims, having been set up by St Francis of Paula in 1436, was thriving at this time. They believed they were the least (minimi) of all the religions on earth, and devoted themselves to prayer, study, and scholarship. They wore a habit made of coarse black wool with broad sleeves and girded by a thin black cord (as seen in the portraits of Mersenne). Charles VIII introduced the Order into France and, due to their great simplicity, the monks were named 'les bons hommes'. After the French Revolution the Order dwindled considerably in number and today there exists only a few convents in Italy. Mersenne entered the Order on 16 July 1611, and was ordained a priest in Paris in July 1612 after a two and a half month probationary period in the monasteries at Nigeon
1
and Meaux. His first posting was in 1614 to the monastery in Nevers where he taught philosophy and theology to the younger members of the community. In fact one of his students, Hilarion de Coste, later became his confidant and biographer. It was during this period of his life that he is thought to have discovered the cycloid - a geometric curve.
After two years teaching Mersenne was elected superior of the Place Royale monastery in Paris where he remained, except for brief journeys, until his death in 1648. It is believed that the Church supported him for most of his life, although in later years a fellow monk, Jacques Hallé, helped out with money and granted him access to his library. From the beginning of his time in Paris, mathematical problems played an important role in his life. Very early on he had links with important scholars in Paris whom he met often, exchanging ideas and discussing projects. The Minims realised that the biggest service he could give was through his books and they never asked any more of him.
In 1623 he published his first two papers consisting of studies against atheism and scepticism in France; L'usage de la raison and L'analyse de la vie spirituelle. Continuing his theological writing he had then wanted to disprove magic, however a fellow monk pointed out that it wasn't appropriate, leading to his publication of Quaestiones celeberrime in genesim that includes the disapproval of magicians in the Scriptures. This book contains 1900 columns of text from the Bible in its first six chapters. It was because of this publication that, in September 1624 when he returned to Paris, he met Gassendi who had been asked to comment on Mersenne's results, and later became his closest friend.
At this time France was going through a period of anti-witchcraft, expelling any sorcerers. L'impiété des deistes, in French, was aimed at the French public so that they might read and understand what was happening. It was during this time that Mersenne started to think about the theological criticism directed against Descartes and Galileo. In fact Mersenne's attitude to Galileo changed over a number of years as Garber points out in [16]:-
Marin Mersenne was central to the new mathematical approach to nature in Paris in the 1630s and 1640s. Intellectually, he was one of the most enthusiastic practitioners of that program, and published a number of influential books in those important decades. But Mersenne started his career in a rather different way. In the early 1620s, Mersenne was known in Paris primarily as a writer on religious topics, and a staunch defender of Aristotle against attacks by those who would replace him by a new philosophy. ... In the early 1620s, Mersenne listed Galileo among the innovators in natural philosophy whose views should be rejected. However, by the early 1630s, less than a decade later, Mersenne had become one of Galileo's most ardent supporters.
Mersenne was beginning to realise that alongside religion it was science that really interested him. Mathematics was the area he studied in greatest depth, believing that without it no science was possible. He always had a philosophical approach to mathematics and believed that the cause of the sciences is the cause of God, see [5]. So, in La vérité des sciences he proved, via many great discoveries, the value of the human
2
mind. It was around this time that Mersenne started to become a coordinator for all European scholars. From 1623 he began to make a careful selection of savants who met at his convent in Paris or corresponded with him from all across Europe and even from as far afield as Constantinople and Transylvania (present-day Hungary). His regular visitors, or correspondents, included Peiresc, Gassendi, Descartes, Roberval, Beeckman, J B van Helmont, Fermat, Hobbes, Etienne Pascal, and his son Blaise Pascal. He set up meetings of scholars from around Europe during which they would read and review scientific papers, both national and international, exchange contacts with other scholars and plan and discuss experiments and other work. This came to be known as the Académie Parisiensis and sometimes among friends as the Académie Mersenne. It was notably one of most resourceful centres of research at that time, meeting weekly at members' houses and later in Mersenne's cell due to his weakened health. The list of Mersenne's correspondents kept increasing and Mersenne himself did not hesitate to travel to meetings with scholars all around Europe.
Mersenne had a strong interest in music and spent a lot of time researching acoustics and the speed of sound. In 1627 he published one of his most famous works, L'harmonie universelle. In this work he was the first to publish the laws relating to the vibrating string: its frequency is proportional to the square root of the tension, and inversely proportional to the length, to the diameter and to the square root of the specific weight of the string, provided all other conditions remain the same when one of these quantities is altered. Mersenne had already started encouraging the talents of others and helped them to share their ideas and results with other scholars. When Roberval arrived in Paris, after joining Mersenne's circle of scholars, his talent was soon recognised by Mersenne who encouraged him to work on the cycloid.
The period between 1627 and 1634 was a transitional period in Mersenne's life. During this time he travelled to Holland for several months between 1629 and 1630. His main reason was to seek a cure for an illness with the help of spa water but he used the opportunity to visit scholars in the surrounding areas. The greater maturity in his writing in the seven years since his last publication became apparent when Questions inouyes and Questions harmoniques were printed in 1634. In October 1644 Mersenne travelled to Provence and Italy where he learnt of the barometer experiment from Torricelli. On his return to Paris, he reported this news to encourage French scholars to carry out the experiments too.
Throughout his lifetime Mersenne helped many potential scientists by steering them in the right direction and advising some on the next step to take. He became a role model for Huygens whom Mersenne took under his wing and through his encouraging letters inspired Huygens' Theory of Music. Huygens had intended to move to Paris in 1646 to be near Mersenne in order to enable them to contact each other more easily, however Huygens didn't move until several years after Mersenne had died so they never met.
Galileo also has to be grateful to Mersenne for making his work known outside Italy. Mersenne insisted on publishing Galileo's work and without this Galileo's ideas might never have become as widely known. Continuing his travels into his old age, in 1646
3
Mersenne set off on a trip to Bordeaux. There he met Pierre Trichet whom he helped make his mark. The success of the scientific life over in Bordeaux and Guyenne, which later formed the Académie Royale des Sciences, was largely due to the advice and experience Mersenne was able to offer. He returned to Paris in 1647.
Mersenne fell ill after his visit to see Descartes in July 1648 and, unfortunately, his health never improved. He was advised to mix wine with his water to help him get better, however Minims do not drink wine. He had an abscess on the lung but the surgeon was unable to find it. Mersenne himself pointed out that the incision, which he asked for, had been attempted too low. Gassendi was there for Mersenne throughout his illness and remained with him until his death on 1 September 1648 in Paris, just 8 days from his 60th birthday. He never gave up his life-long desire to advance science. He even asked, in his will, that his body be used for biological research.
After Mersenne's death, letters in his cell were found from 78 different correspondents including Fermat, Huygens, Pell, Galileo and Torricelli. Also several physics instruments were found in his cell and a lot of Mersenne's library was retrieved from which L'optique et la catoptrique was published in 1651. Inside this publication one of Roberval's texts was inserted. Later all the letters he sent and received from other scholars were accumulated and published in several volumes. These letters read like an international review of mechanics in the early 17th century. Mersenne was aware of all the science that was going on, what all the scientists were doing, and only wanted for them all to work together in advancing science.
Mersenne studied the cycloid for several years quoting his research in Quaestiones in Genesim (1623), Synopsis mathematica (1626) and Questions inouyes (1634). He gave the definition of a cycloid as the locus of a point at distance h from the centre of a circle of radius a, that rolls along a straight line. He stated the obvious properties including the length of the base line equals the circumference of the rolling circle. We note that Mersenne referred to the cycloid as the 'roulette' but the term cycloid was adopted later. He attempted to find the area under the curve by integration but having failed, so he put the question to Roberval. In 1638 he announced that Roberval had indeed found the area under the cycloid.
Mersenne's name is best remembered today for Mersenne primes. He tried to find a formula that would represent all primes but, although he failed in this, his work on numbers of the form
2p - 1, p prime
has been of continuing interest in the investigation of large primes. It is easy to prove that if the number n = 2p - 1 is prime then p must be a prime. In 1644 Mersenne claimed that n is prime if p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257 but composite for the other 44 primes p smaller than 257.
4
Over the years it has been found that Mersenne was wrong about 5 of the primes of the form 2p - 1 where p is less than or equal to 257 (he claimed two that didn't lead to a prime (67 and 257) and missed 3 that did: 61, 89, 107). Drake [13] has tried to both understand the source of Mersenne's work on these primes, and also to try to determine the rule that was being used. He suggests Frenicle de Bessy may be the source and also suggests that the errors might be misprints by the printer. Drake reconstructs Mersenne's rule for exponents as that they must differ by not more than one from a value of 2n or by not more than three from a value of 2 to the power 2n.
Mersenne undertook experiments to test Galileo's law of motion for falling bodies. In 1634 he presented the results that he had obtained when measuring the acceleration of falling bodies from heights of 147, 108 and 48 feet. These confirmed the time-squared law that Galileo had published in his Dialogue on the two chief world systems of 1632 but they also raised questions about the numerical data. One problem he tried to solve was whether acceleration was continuous as Galileo maintained or discontinuous as Descartes believed. Mersenne thought Galileo's assumption that a falling body passes through infinite degrees of speed was incompatible with a genuinely mechanistic explanation of acceleration. These ideas are discussed in detail in [24] and [25].
In some of his non-mathematical works Mersenne looks at permutations and combinations. He states practical rules for calculating the number of combinations or permutations, solving the problem of finding the number of permutations with or without repetitions and gives an example the making of anagrams. His main reason to study combinatorial analysis was, however, to optimise musical composition as he explains in The book on the art of singing well which is Book Six of Harmonie universelle (1636). In an unpublished manuscript preserved in the Bibliothèque Nationale at Paris he gave the 40320 permutations of 8 notes.
During the final four years of his life, Mersenne spent a lot of time investigating the barometer. Pascal had already proved that air was not weightless and it was Mersenne who found the density of air to be approximately 1/19th that of water. He was informed of the barometer experiment, consisting of a glass tube about 3 feet long sealed at one end and filled with pure mercury, through several letters from De Verdus but it was not until October 1644, when he visited Torricelli in Italy, that he saw the experiment carried out. Torricelli used the pressure of the air to explain why the mercury moved up the glass tube. Mersenne was doubtful that the air pressure actually supported the mercury and on his return attempted to re-do the experiment but did not have the necessary equipment. Mersenne explained the problem to Etienne Pascal, his son Blaise Pascal, Petit, Roberval, and others in Paris. There is some confusion as to who, in 1647, initially suggested the experiments with the Torricellian tube and the mountain, later to be called the Puy de Dome experiments. Certainly Mersenne had briefed both Huygens and Le Tenneur but it was not until three weeks after Mersenne's death in 1648 that these experiments were carried out. They consisted of collecting results both at the foot of the Puy de Dome and at the summit. Tests were made as to whether the level of mercury in the column was lower when at the top of the mountain than it was at the bottom. If this had proved to be true, they realised that this would be due to the pressure of the air alone. Perier, who
5
finally conducted the experiments, did indeed find that there was a significant difference in the level of the mercury hence drawing the correct conclusion that the air pressure was supporting it.
An interesting question is how Mersenne managed to pursue his scientific ideas freely at a time when the Church (of which he was a devoted member) moved to prevent such discussion. This topic is considered in detail in [18] where Hine writes:-
During the first half of the seventeenth century, debate over the Copernican hypothesis had spread beyond the ranks of astronomers and had stirred up so much controversy that the Church decided to intervene. In 1616 a theological examining body concluded that the idea of the earth's motion was philosophically false and in conflict with the Scriptures, and it suspended Copernicus' book until corrected. Historians have generally assumed that this decision and the subsequent condemnation of Galileo had such a devastating effect that scientific progress in Catholic countries was greatly retarded. However, the attitude of Mersenne, who was both a faithful member of a religious order and a central figure in the development of French science, does not support such a conclusion. An examination of Mersenne's reaction to Copernicanism indicates that no matter how disturbing the Church's decision, it was still possible, at least in France, to study Copernican ideas and to find them useful, despite some reservations. Mersenne was affected by such decisions of the Church, but less so than one might suppose.
Article by: J J O'Connor and E F Robertson based on an honours project by Jessica Daniell (University of St Andrews).
August 2005
Max Karl Ernst Ludwig Planck
Max Karl Ernst Ludwig Planck
--------------------------------------------------------------------------------
Born: 23 April 1858 in Kiel, Schleswig-Holstein, Germany
Died: 4 Oct 1947 in Göttingen, Germany
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Max Planck came from an academic family, his father Julius Wilhelm Planck being Professor of Constitutional Law in the University of Kiel at the time of his birth, and both his grandfather and great-grandfather had been professors of theology at Göttingen. His mother, Emma Patzig, was his father's second wife. Both Max's parents were relatively old when he was born, his father being 41 and his mother being 37. He was born into a large family, being his father's sixth child (two of the children were from his first marriage to Mathilde Voigt), and he was brought up in a tradition which greatly respected scholarship, honesty, fairness, and generosity. The values he was given as a young child quickly became the values that he would cherish throughout his life, showing the utmost respect for the institutions of state and church.
Max began his elementary schooling in Kiel. In the spring of 1867 his family moved to Munich when his father was appointed Professor there. This city provided a stimulating environment for the young boy who enjoyed its culture, particularly the music, and loved walking and climbing in the mountains when the family took excursions to Upper Bavaria. He attended secondary school there, entering the famous Maximilian Gymnasium in May 1867. He did well at school, but not brilliantly, usually coming somewhere between third and eighth in his class. Music was perhaps his best subject and he was awarded the school prize in catechism and good conduct almost every year. One might have expected him to excel in mathematics and science, but certainly in his early school years, although he did well, there was no sign of outstanding talent in these subjects. However, towards the end of his school career, his teacher Hermann Müller raised his level of interest in physics and mathematics, and he became deeply impressed by the absolute nature of the law of conservation of energy. A school report for 1872 reads:-
Justifiably favoured by both teachers and classmates ... and despite having childish ways, he has a very clear, logical mind. Shows great promise.
1
In July 1874, at the age of 16, he passed his school leaving examination with distinction but, having talents for a wide variety of subjects particularly music (he played piano and organ extremely well), he still did not have a clear idea of what he should to study at university. Before he began his studies at the University of Munich he discussed the possibility of a musical career with a musician who told him that if he had to ask the question he'd better study something else.
He entered the University of Munich on 21 October 1874 and was taught physics by Philipp von Jolly and Wilhelm Beetz, and mathematics by Ludwig Seidel and Gustav Bauer. After taking mostly mathematics classes at the start of his course, he enquired about the prospects of research in physics from Philipp von Jolly, the professor of physics at Munich, and was told that physics was essentially a complete science with little prospect of further developments. Fortunately Planck decided to study physics despite the bleak future for research that was presented to him.
In [7] Planck describes why he chose physics:-
The outside world is something independent from man, something absolute, and the quest for the laws which apply to this absolute appeared to me as the most sublime scientific pursuit in life.
The off-putting comments from his physics professor clearly set the tone for his time at the University of Munich for Planck wrote later:-
I did not have the good fortune of a prominent scientist or teacher directing the specific course of my education.
He was ill during the summer term of 1875 which caused him to give up studying for a while. It was customary for German students to move between universities at this time and indeed Planck moved to study at the University of Berlin from October 1877 where his teachers included Weierstrass, Helmholtz and Kirchhoff. He later wrote that he admired Kirchhoff greatly but found him dry and monotonous as a teacher. However it is likely to be the contrast between the research attitude of his teachers at Munich and those at Berlin which prompted the quote we gave above (made many years later). One important part of his education at Berlin came, however, through independent study for at this stage he read Rudolf Clausius's articles on thermodynamics. Again the absolute nature of the second law of thermodynamics impressed him.
Planck returned to Munich and received his doctorate in July 1879 at the age of 21 with a thesis on the second law of thermodynamics entitled On the Second Law of Mechanical Theory of Heat. The award of the doctorate was made "summa cum laude'' on 28 July 1879. Following this Planck continued to work for his habilitation which was awarded on 14 June 1880, after he had submitted his thesis on entropy and the mechanical theory of heat, and he became a Privatdozent at Munich University. Such a teaching post was unpaid so Planck received no income to support himself. He lived with his parents during the five years that he held this post, but felt rather guilty that he was continuing to live at
2
their expense. During this time he became friends with Carl Runge and it turned into a long lasting and academically fruitful friendship.
On 2 May 1885 Planck was appointed extraordinary professor of theoretical physics in Kiel and held this chair for four years. This now made him financially secure so he could now marry Marie Merck whom he had known for many years. She was the daughter of a Munich banker, and the pair were married on 31 March 1887. He now worked on thermodynamics publishing three excellent papers on applications to physical chemistry and thermoelectricity.
After the death of Kirchhoff in October 1887, the University of Berlin looked for a world leading physicist to replace him and to become a colleague of Helmholtz. They approached Ludwig Boltzmann but he was not interested, and the same proved true for Heinrich Hertz. In 1888 the appointment of Planck was proposed by the Faculty of Philosophy at the University of Berlin, strongly recommended by Helmholtz:-
Planck's papers are very favourably distinguished from those of the majority of his colleagues in that he tries to carry through the strict consequences of thermomechanics constructively, without adding additional hypotheses, and carefully separates the secure from the doubtful ... His papers ... clearly show him to be a man of original ideas who is making his own paths [and] that he has a comprehensive overview of the various areas of science.
Planck was appointed as an extraordinary professor of theoretical physics at the University of Berlin on 29 November 1888, at the same time became director of the Institute for Theoretical Physics. He was promoted to ordinary professor on 23 May 1892 and held the chair until he retired on 1 October 1927. His colleagues and friends included Emil du Bois-Reymond (the famous physiologist and brother of Paul du Bois-Reymond), Helmholtz, Pringsheim, Wien, as well as theologians, historians, and philologists. He continued to indulge his passion for music having a harmonium built with 104 tones in each octave, and holding concerts in his own home.
While in Berlin Planck did his most brilliant work and delivered outstanding lectures. He studied thermodynamics, in particular examining the distribution of energy according to wavelength. By combining the formulae of Wien and Rayleigh, Planck announced in October 1900 a formula now known as Planck's radiation formula. Within two months Planck made a complete theoretical deduction of his formula renouncing classical physics and introducing the quanta of energy. On 14 December 1900 he presented his theoretical explanation involving quanta of energy at a meeting of the Physikalische Gesellschaft in Berlin. In doing so he had to reject his belief that the second law of thermodynamics was an absolute law of nature, and accept Boltzmann's interpretation that it was a statistical law. In a letter written a year later Planck described proposing the theoretical interpretation of the radiation formula saying:-
... the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be.
3
Planck received the Nobel Prize for Physics in 1918 for his achievement. He described in his Nobel Lecture given on 2 June 1920, in much more detail than we have given above, how he made his discoveries. We now give some extracts from the lecture:-
For many years, [my aim] was to solve the problem of energy distribution in the normal spectrum of radiating heat. After Gustav Kirchhoff has shown that the state of the heat radiation which takes place in a cavity bounded by any emitting and absorbing material at uniform temperature is totally independent of the nature of the material, a universal function was demonstrated which was dependent only on temperature and wavelength, but not in any way on the properties of the material. The discovery of this remarkable function promised deeper insight into the connection between energy and temperature which is, in fact, the major problem in thermodynamics and so in all of molecular physics. ...
At that time I held what would be considered today naively charming and agreeable expectations, that the laws of classical electrodynamics would, if approached in a sufficiently general manner avoiding special hypotheses, allow us to understand the most significant part of the process we would expect, and so to achieve the desired aim. ...
[A number of different approaches] showed more and more clearly that an important connecting element or term, essential to completely grasp the basis of the problem, had to be missing. ...
I was busy... from the day I [established a new radiation formula], with the task of finding a real physical interpretation of the formula, and this problem led me automatically to consider the connection between entropy and probability, that is, Boltzmann's train of ideas; eventually after some weeks of the hardest work of my life, light entered the darkness, and a new inconceivable perspective opened up before me. ...
Because [a constant in the radiation law] represents the product of energy and time ... I described it as the elementary quantum of action. ... As long as it was looked on as infinitely small ... everything was fine; but in the general case, however, a gap opened wide somewhere or other, which became more striking the weaker and faster the vibrations considered. That all efforts to bridge the chasm foundered soon left little doubt. Either the quantum of action was a fictional quantity, then the whole deduction of the radiation law was essentially an illusion representing only an empty play on formulas of no significance, or the derivation of the radiation law was based on a sound physical conception. In this case the quantum of action must play a fundamental role in physics, and here was something completely new, never heard of before, which seemed to require us to basically revise all our physical thinking, built as this was, from the time of the establishment of the infinitesimal calculus by Leibniz and Newton, on accepting the continuity of all causative connections. Experiment decided it was the second alternative.
At first the theory met resistance but, due to the successful work of Niels Bohr in 1913 calculating positions of spectral lines using the theory, it became generally accepted.
4
Planck himself in [7] explains how despite having invented quantum theory he did not understand it himself at first:-
I tried immediately to weld the elementary quantum of action somehow in the framework of classical theory. But in the face of all such attempts this constant showed itself to be obdurate ... My futile attempts to put the elementary quantum of action into the classical theory continued for a number of years and they cost me a great deal of effort.
Planck who was 42 years old when he made his historic quantum announcement, took only a minor part in the further development of quantum theory. This was left to Einstein with theories of light quanta, Poincaré who proved mathematically that the quanta was a necessary consequence of Planck's radiation law, Niels Bohr with his theory of the atom, Paul Dirac and others. Sadly his life was filled with tragedy in the years following his remarkable initiation of the study of quantum mechanics. His wife Marie died on 17 October 1909. They had four children; two sons Erwin and Karl, and twin daughters Margarete and Emma. Two years after the death of his first wife, Planck married again, to Marga von Hösslin the niece of Marie his first wife, on 14 March 1911. They had one child, a son Hermann. Karl, the younger of Planck's sons from his first marriage, was killed in 1916 during World War I. Both his daughters died in childbirth, Margarete in 1917 and Emma in 1919. His son Erwin became his best friend and advisor, but as we relate below Erwin died in even more terrible circumstances.
Planck always took on administrative duties, in addition to his research activities, such as Secretary of the Mathematics and Natural Science Section of the Prussian Academy of Sciences, a post he held from 1912 until 1943. He had been elected to the Academy in 1894. Planck was much involved with the German Physical Society, being treasurer and a committee member. He was chairman of the Society from 1905 to 1908 and then again from 1915 to 1916. Planck was also honoured by being elected an honorary member in 1927. Two years later an award, the Max Planck Medal, was established and Planck himself became the first recipient. He was on the committee of the Kaiser Wilhelm Gesellschaft, the main German research organisation, from 1916 and was president of the Society from 1930 until 1937 (it was renamed the Max Planck Society). This was the time that the Nazis rose to power, and he tried his best to prevent political issues to take over from scientific ones. He could not prevent the reorganisation of the Society by the Nazis and refused to accept the presidency of the reorganised Society.
He remained in Germany during World War II through what must have been times of the deepest difficulty. In 1942 he explained why he was still in Berlin:-
I've been here in Berlin at the university since 1889 ... so I'm quite an old-timer. But there really aren't any genuine old Berliners, people who were born here; in the academic word everybody moves around frequently. People go from one university to the next one, but in that sense I'm actually very sedentary. But once I arrived in Berlin, it wasn't easy to move away; for ultimately, this is the centre of all intellectual activity in the whole of Germany.
5
However, being in Berlin towards the end of World War II, was very dangerous. He moved to Rogätz, near Magdeburg, in 1943. His home in the suburb of Grunewald in Berlin was destroyed by fire after an air raid in February 1944. Loosing his home and possessions was bad, but loosing his irreplaceable scientific notebooks was a tragedy for him and for science. Worse was to follow. His son Erwin was suspected of being involved in the plot to assassinate Hitler on 20 July 1944 and was executed by the Gestapo early in 1945. In [4] Heilbron describes the impact of wars on Planck and his family:-
He would remember, even in his old age, the sight of Prussian and Austrian troops marching into his native town when he was six years old. Throughout his life, war would cause him deep personal sorrow. He lost his eldest son during World War I. In World War II, his house in Berlin was burned down in an air raid. In 1945 his other son was executed when declared guilty of complicity in a plot to kill Hitler.
Planck was 87 years old at the end of World War II and he was taken to Göttingen by the allies. Remarkably, given his age, he was able to put effort into reconstructing German science and he again became president of the Kaiser Wilhelm Gesellschaft in 1945-1946. For the second time he defended German science through a period of exceptional difficulty.
Article by: J J O'Connor and E F Robertson
October 2003
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Born: 23 April 1858 in Kiel, Schleswig-Holstein, Germany
Died: 4 Oct 1947 in Göttingen, Germany
--------------------------------------------------------------------------------
Max Planck came from an academic family, his father Julius Wilhelm Planck being Professor of Constitutional Law in the University of Kiel at the time of his birth, and both his grandfather and great-grandfather had been professors of theology at Göttingen. His mother, Emma Patzig, was his father's second wife. Both Max's parents were relatively old when he was born, his father being 41 and his mother being 37. He was born into a large family, being his father's sixth child (two of the children were from his first marriage to Mathilde Voigt), and he was brought up in a tradition which greatly respected scholarship, honesty, fairness, and generosity. The values he was given as a young child quickly became the values that he would cherish throughout his life, showing the utmost respect for the institutions of state and church.
Max began his elementary schooling in Kiel. In the spring of 1867 his family moved to Munich when his father was appointed Professor there. This city provided a stimulating environment for the young boy who enjoyed its culture, particularly the music, and loved walking and climbing in the mountains when the family took excursions to Upper Bavaria. He attended secondary school there, entering the famous Maximilian Gymnasium in May 1867. He did well at school, but not brilliantly, usually coming somewhere between third and eighth in his class. Music was perhaps his best subject and he was awarded the school prize in catechism and good conduct almost every year. One might have expected him to excel in mathematics and science, but certainly in his early school years, although he did well, there was no sign of outstanding talent in these subjects. However, towards the end of his school career, his teacher Hermann Müller raised his level of interest in physics and mathematics, and he became deeply impressed by the absolute nature of the law of conservation of energy. A school report for 1872 reads:-
Justifiably favoured by both teachers and classmates ... and despite having childish ways, he has a very clear, logical mind. Shows great promise.
1
In July 1874, at the age of 16, he passed his school leaving examination with distinction but, having talents for a wide variety of subjects particularly music (he played piano and organ extremely well), he still did not have a clear idea of what he should to study at university. Before he began his studies at the University of Munich he discussed the possibility of a musical career with a musician who told him that if he had to ask the question he'd better study something else.
He entered the University of Munich on 21 October 1874 and was taught physics by Philipp von Jolly and Wilhelm Beetz, and mathematics by Ludwig Seidel and Gustav Bauer. After taking mostly mathematics classes at the start of his course, he enquired about the prospects of research in physics from Philipp von Jolly, the professor of physics at Munich, and was told that physics was essentially a complete science with little prospect of further developments. Fortunately Planck decided to study physics despite the bleak future for research that was presented to him.
In [7] Planck describes why he chose physics:-
The outside world is something independent from man, something absolute, and the quest for the laws which apply to this absolute appeared to me as the most sublime scientific pursuit in life.
The off-putting comments from his physics professor clearly set the tone for his time at the University of Munich for Planck wrote later:-
I did not have the good fortune of a prominent scientist or teacher directing the specific course of my education.
He was ill during the summer term of 1875 which caused him to give up studying for a while. It was customary for German students to move between universities at this time and indeed Planck moved to study at the University of Berlin from October 1877 where his teachers included Weierstrass, Helmholtz and Kirchhoff. He later wrote that he admired Kirchhoff greatly but found him dry and monotonous as a teacher. However it is likely to be the contrast between the research attitude of his teachers at Munich and those at Berlin which prompted the quote we gave above (made many years later). One important part of his education at Berlin came, however, through independent study for at this stage he read Rudolf Clausius's articles on thermodynamics. Again the absolute nature of the second law of thermodynamics impressed him.
Planck returned to Munich and received his doctorate in July 1879 at the age of 21 with a thesis on the second law of thermodynamics entitled On the Second Law of Mechanical Theory of Heat. The award of the doctorate was made "summa cum laude'' on 28 July 1879. Following this Planck continued to work for his habilitation which was awarded on 14 June 1880, after he had submitted his thesis on entropy and the mechanical theory of heat, and he became a Privatdozent at Munich University. Such a teaching post was unpaid so Planck received no income to support himself. He lived with his parents during the five years that he held this post, but felt rather guilty that he was continuing to live at
2
their expense. During this time he became friends with Carl Runge and it turned into a long lasting and academically fruitful friendship.
On 2 May 1885 Planck was appointed extraordinary professor of theoretical physics in Kiel and held this chair for four years. This now made him financially secure so he could now marry Marie Merck whom he had known for many years. She was the daughter of a Munich banker, and the pair were married on 31 March 1887. He now worked on thermodynamics publishing three excellent papers on applications to physical chemistry and thermoelectricity.
After the death of Kirchhoff in October 1887, the University of Berlin looked for a world leading physicist to replace him and to become a colleague of Helmholtz. They approached Ludwig Boltzmann but he was not interested, and the same proved true for Heinrich Hertz. In 1888 the appointment of Planck was proposed by the Faculty of Philosophy at the University of Berlin, strongly recommended by Helmholtz:-
Planck's papers are very favourably distinguished from those of the majority of his colleagues in that he tries to carry through the strict consequences of thermomechanics constructively, without adding additional hypotheses, and carefully separates the secure from the doubtful ... His papers ... clearly show him to be a man of original ideas who is making his own paths [and] that he has a comprehensive overview of the various areas of science.
Planck was appointed as an extraordinary professor of theoretical physics at the University of Berlin on 29 November 1888, at the same time became director of the Institute for Theoretical Physics. He was promoted to ordinary professor on 23 May 1892 and held the chair until he retired on 1 October 1927. His colleagues and friends included Emil du Bois-Reymond (the famous physiologist and brother of Paul du Bois-Reymond), Helmholtz, Pringsheim, Wien, as well as theologians, historians, and philologists. He continued to indulge his passion for music having a harmonium built with 104 tones in each octave, and holding concerts in his own home.
While in Berlin Planck did his most brilliant work and delivered outstanding lectures. He studied thermodynamics, in particular examining the distribution of energy according to wavelength. By combining the formulae of Wien and Rayleigh, Planck announced in October 1900 a formula now known as Planck's radiation formula. Within two months Planck made a complete theoretical deduction of his formula renouncing classical physics and introducing the quanta of energy. On 14 December 1900 he presented his theoretical explanation involving quanta of energy at a meeting of the Physikalische Gesellschaft in Berlin. In doing so he had to reject his belief that the second law of thermodynamics was an absolute law of nature, and accept Boltzmann's interpretation that it was a statistical law. In a letter written a year later Planck described proposing the theoretical interpretation of the radiation formula saying:-
... the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be.
3
Planck received the Nobel Prize for Physics in 1918 for his achievement. He described in his Nobel Lecture given on 2 June 1920, in much more detail than we have given above, how he made his discoveries. We now give some extracts from the lecture:-
For many years, [my aim] was to solve the problem of energy distribution in the normal spectrum of radiating heat. After Gustav Kirchhoff has shown that the state of the heat radiation which takes place in a cavity bounded by any emitting and absorbing material at uniform temperature is totally independent of the nature of the material, a universal function was demonstrated which was dependent only on temperature and wavelength, but not in any way on the properties of the material. The discovery of this remarkable function promised deeper insight into the connection between energy and temperature which is, in fact, the major problem in thermodynamics and so in all of molecular physics. ...
At that time I held what would be considered today naively charming and agreeable expectations, that the laws of classical electrodynamics would, if approached in a sufficiently general manner avoiding special hypotheses, allow us to understand the most significant part of the process we would expect, and so to achieve the desired aim. ...
[A number of different approaches] showed more and more clearly that an important connecting element or term, essential to completely grasp the basis of the problem, had to be missing. ...
I was busy... from the day I [established a new radiation formula], with the task of finding a real physical interpretation of the formula, and this problem led me automatically to consider the connection between entropy and probability, that is, Boltzmann's train of ideas; eventually after some weeks of the hardest work of my life, light entered the darkness, and a new inconceivable perspective opened up before me. ...
Because [a constant in the radiation law] represents the product of energy and time ... I described it as the elementary quantum of action. ... As long as it was looked on as infinitely small ... everything was fine; but in the general case, however, a gap opened wide somewhere or other, which became more striking the weaker and faster the vibrations considered. That all efforts to bridge the chasm foundered soon left little doubt. Either the quantum of action was a fictional quantity, then the whole deduction of the radiation law was essentially an illusion representing only an empty play on formulas of no significance, or the derivation of the radiation law was based on a sound physical conception. In this case the quantum of action must play a fundamental role in physics, and here was something completely new, never heard of before, which seemed to require us to basically revise all our physical thinking, built as this was, from the time of the establishment of the infinitesimal calculus by Leibniz and Newton, on accepting the continuity of all causative connections. Experiment decided it was the second alternative.
At first the theory met resistance but, due to the successful work of Niels Bohr in 1913 calculating positions of spectral lines using the theory, it became generally accepted.
4
Planck himself in [7] explains how despite having invented quantum theory he did not understand it himself at first:-
I tried immediately to weld the elementary quantum of action somehow in the framework of classical theory. But in the face of all such attempts this constant showed itself to be obdurate ... My futile attempts to put the elementary quantum of action into the classical theory continued for a number of years and they cost me a great deal of effort.
Planck who was 42 years old when he made his historic quantum announcement, took only a minor part in the further development of quantum theory. This was left to Einstein with theories of light quanta, Poincaré who proved mathematically that the quanta was a necessary consequence of Planck's radiation law, Niels Bohr with his theory of the atom, Paul Dirac and others. Sadly his life was filled with tragedy in the years following his remarkable initiation of the study of quantum mechanics. His wife Marie died on 17 October 1909. They had four children; two sons Erwin and Karl, and twin daughters Margarete and Emma. Two years after the death of his first wife, Planck married again, to Marga von Hösslin the niece of Marie his first wife, on 14 March 1911. They had one child, a son Hermann. Karl, the younger of Planck's sons from his first marriage, was killed in 1916 during World War I. Both his daughters died in childbirth, Margarete in 1917 and Emma in 1919. His son Erwin became his best friend and advisor, but as we relate below Erwin died in even more terrible circumstances.
Planck always took on administrative duties, in addition to his research activities, such as Secretary of the Mathematics and Natural Science Section of the Prussian Academy of Sciences, a post he held from 1912 until 1943. He had been elected to the Academy in 1894. Planck was much involved with the German Physical Society, being treasurer and a committee member. He was chairman of the Society from 1905 to 1908 and then again from 1915 to 1916. Planck was also honoured by being elected an honorary member in 1927. Two years later an award, the Max Planck Medal, was established and Planck himself became the first recipient. He was on the committee of the Kaiser Wilhelm Gesellschaft, the main German research organisation, from 1916 and was president of the Society from 1930 until 1937 (it was renamed the Max Planck Society). This was the time that the Nazis rose to power, and he tried his best to prevent political issues to take over from scientific ones. He could not prevent the reorganisation of the Society by the Nazis and refused to accept the presidency of the reorganised Society.
He remained in Germany during World War II through what must have been times of the deepest difficulty. In 1942 he explained why he was still in Berlin:-
I've been here in Berlin at the university since 1889 ... so I'm quite an old-timer. But there really aren't any genuine old Berliners, people who were born here; in the academic word everybody moves around frequently. People go from one university to the next one, but in that sense I'm actually very sedentary. But once I arrived in Berlin, it wasn't easy to move away; for ultimately, this is the centre of all intellectual activity in the whole of Germany.
5
However, being in Berlin towards the end of World War II, was very dangerous. He moved to Rogätz, near Magdeburg, in 1943. His home in the suburb of Grunewald in Berlin was destroyed by fire after an air raid in February 1944. Loosing his home and possessions was bad, but loosing his irreplaceable scientific notebooks was a tragedy for him and for science. Worse was to follow. His son Erwin was suspected of being involved in the plot to assassinate Hitler on 20 July 1944 and was executed by the Gestapo early in 1945. In [4] Heilbron describes the impact of wars on Planck and his family:-
He would remember, even in his old age, the sight of Prussian and Austrian troops marching into his native town when he was six years old. Throughout his life, war would cause him deep personal sorrow. He lost his eldest son during World War I. In World War II, his house in Berlin was burned down in an air raid. In 1945 his other son was executed when declared guilty of complicity in a plot to kill Hitler.
Planck was 87 years old at the end of World War II and he was taken to Göttingen by the allies. Remarkably, given his age, he was able to put effort into reconstructing German science and he again became president of the Kaiser Wilhelm Gesellschaft in 1945-1946. For the second time he defended German science through a period of exceptional difficulty.
Article by: J J O'Connor and E F Robertson
October 2003
Michael Faraday
Michael Faraday
--------------------------------------------------------------------------------
Born: 22 Sept 1791 in Newington Butts, Surrey (now London) England
Died: 25 Aug 1867 in Hampton Court, Middlesex, England
--------------------------------------------------------------------------------
Michael Faraday did not directly contribute to mathematics so should not really qualify to have his biography in this archive. However he was such a major figure and his science had such a large impact on the work of those developing mathematical theories that it is proper that he is included. We say more about this below.
Faraday's father, James Faraday, was a blacksmith who came from Yorkshire in the north of England while his mother Margaret Hastwell, also from the north of England, was the daughter of a farmer. Early in 1791 James and Margaret moved to Newington Butts, which was then a village outside London, where James hoped that work was more plentiful. They already had two children, a boy Robert and a girl, before they moved to Newington Butts and Michael was born only a few months after their move.
Work was not easy to find and the family moved again, remaining in or around London. By 1795, when Michael was around five years, the family were living in Jacob's Wells Mews in London. They had rooms over a coachhouse and, by this time, a second daughter had been born. Times were hard particularly since Michael's father had poor health and was not able to provide much for his family.
The family were held closely together by a strong religious faith, being members of the Sandemanians, a form of the Protestant Church which had split from the Church of Scotland. The Sandemanians believed in the literal truth of the Bible and tried to recreate the sense of love and community which had characterised the early Christian Church. The religious influence was important for Faraday since the theories he developed later in his life were strongly influenced by a belief in a unity of the world.
Michael attended a day school where he learnt to read, write and count. When Faraday was thirteen years old he had to find work to help the family finances and he was employed running errands for George Riebau who had a bookselling business. In 1805, after a year as an errand-boy, Faraday was taken on by Riebau as an apprentice bookbinder. He spent seven years serving his apprenticeship with Riebau. Not only did
1
he bind books but he also read them. Riebau wrote a letter in 1813 in which he described how Faraday spent his days as an apprentice (see for example [4]):-
After the regular hours of business, he was chiefly employed in drawing and copying from the Artist's Repository, a work published in numbers which he took in weekly. ... Dr Watts's Improvements of the mind was then read and frequently took in his pocket, when he went an early walk in the morning, visiting some other works of art or searching for some mineral or vegetable curiosity. ... His mind ever engaged, besides attending to bookbinding which he executed in a proper manner.
His mode of living temperate, seldom drinking any other than pure water, and when done his day's work, would set himself down in the workshop ... If I had any curious book from my customers to bind, with plates, he would copy such as he thought singular or clever ...
Faraday himself wrote of this time in his life:-
Whilst an apprentice, I loved to read the scientific books which were under my hands ...
From 1810 Faraday attended lectures at John Tatum's house. He attended lectures on many different topics but he was particularly interested in those on electricity, galvanism and mechanics. At Tatum's house he made two special friends, J Huxtable who was a medical student, and Benjamin Abbott who was a clerk. In 1812 Faraday attended lectures by Humphry Davy at the Royal Institution and made careful copies of the notes he had taken. In fact these lectures would become Faraday's passport to a scientific career.
In 1812, intent on improving his literary skills, he carried out a correspondence with Abbott. He had already tried to leave bookbinding and the route he tried was certainly an ambitious one. He had written to Sir Joseph Banks, the President of the Royal Society, asking how he could become involved in scientific work. Perhaps not surprisingly he had received no reply. When his apprenticeship ended in October 1812, Faraday got a job as a bookbinder but still he attempted to get into science and again he took a somewhat ambitious route for a young man with little formal education. He wrote to Humphry Davy, who had been his hero since he attended his chemistry lectures, sending him copies of the notes he had taken at Davy's lectures. Davy, unlike Banks, replied to Faraday and arranged a meeting. He advised Faraday to keep working as a bookbinder, saying:-
Science [is] a harsh mistress, and in a pecuniary point of view but poorly rewarding those who devote themselves to her service.
Shortly after the interview Davy's assistant had to be sacked for fighting and Davy sent for Faraday and invited him to fill the empty post. In 1813 Faraday took up the position at the Royal Institution.
2
In October 1813 Davy set out on a scientific tour of Europe and he took Faraday with him as his assistant and secretary. Faraday met Ampère and other scientists in Paris. They travelled on towards Italy where they spent time in Genoa, Florence, Rome and Naples. Heading north again they visited Milan where Faraday met Volta. The trip was an important one for Faraday [4]:-
These eighteen months abroad had taken the place, in Faraday's life, of the years spent at university by other men. He gained a working knowledge of French and Italian; he had added considerably to his scientific attainments, and had met and talked with many of the leading foreign men of science; but, above all, the tour had been what was most valuable to him at that time, a broadening influence.
On his return to London, Faraday was re-engaged at the Royal Institution as an assistant. His work there was mainly involved with chemical experiments in the laboratory. He also began lecturing on chemistry topics at the Philosophical Society. He published his first paper in 1816 on caustic lime from Tuscany.
In 1821 Faraday married Sarah Barnard whom he had met when attending the Sandemanian church. Faraday was made Superintendent of the House and Laboratory at the Royal Institution and given additional rooms to make his marriage possible.
The year 1821 marked another important time in Faraday's researches. He had worked almost entirely on chemistry topics yet one of his interests from his days as a bookbinder had been electricity. In 1820 several scientists in Paris including Arago and Ampère made significant advances in establishing a relation between electricity and magnetism. Davy became interested and this gave Faraday the opportunity to work on the topic. He published On some new electro-magnetical motions, and on the theory of magnetism in the Quarterly Journal of Science in October 1821. Pearce Williams writes [1]:-
It records the first conversion of electrical into mechanical energy. It also contained the first notion of the line of force.
It is Faraday's work on electricity which has prompted us to add him to this archive. However we must note that Faraday was in no sense a mathematician and almost all his biographers describe him as "mathematically illiterate". He never learnt any mathematics and his contributions to electricity were purely that of an experimentalist. Why then include him in an archive of mathematicians? Well, it was Faraday's work which led to deep mathematical theories of electricity and magnetism. In particular the remarkable mathematical theories on the topic developed by Maxwell would not have been possible without Faraday's discovery of various laws. This is a point which Maxwell himself stressed on a number of occasions.
In the ten years from 1821 to 1831 Faraday again undertook research on chemistry. His two most important pieces of work on chemistry during that period was liquefying chlorine in 1823 and isolating benzene in 1825. Between these dates, in 1824, he was elected a fellow of the Royal Society. This was a difficult time for Faraday since Davy
3
was at this time President of the Royal Society and could not see the man who he still thought of as his assistant as becoming a Fellow. Although Davy opposed his election, he was over-ruled by the other Fellows. Faraday never held the incident against Davy, always holding him in the highest regard.
Faraday introduced a series of six Christmas lectures for children at the Royal Institution in 1826. In 1831 Faraday returned to his work on electricity and made what is arguably his most important discovery, namely that of electro-magnetic induction. This discovery was the opposite of that which he had made ten years earlier. He showed that a magnet could induce an electrical current in a wire. Thus he was able to convert mechanical energy into electrical energy and discover the first dynamo. Again he made lines of force central to his thinking. He published his first paper in what was to become a series on Experimental researches on electricity in 1831. He read the paper before the Royal Society on 24 November of that year.
In 1832 Faraday began to receive honours for his major contributions to science. In that year he received an honorary degree from the University of Oxford. In February 1833 he became Fullerian Professor of Chemistry at the Royal Institution. Further honours such as the Royal Medal and the Copley Medal, both from the Royal Society, were to follow. In 1836 he was made a Member of the Senate of the University of London, which was a Crown appointment.
During this period, beginning in 1833, Faraday made important discoveries in electrochemistry. He went on to work on electrostatics and by 1838 he [1]:-
... was in a position to put all the pieces together into a coherent theory of electricity.
The extremely high workload eventually told on Faraday's health and in 1839 he suffered a nervous breakdown. He did recover his health and by 1845 he began intense research activity again. The work which he undertook at this time was the result of mathematical developments in the subject. Faraday's ideas on lines of force had received a mathematical treatment from William Thomson. He wrote to Faraday on 6 August 1845 telling him of his mathematical predictions that a magnetic field should affect the plane of polarised light. Faraday had attempted to detect this experimentally many years earlier but without success. Now, with the idea reinforced by Thomson, he tried again and on 13 September 1845 he was successful in showing that a strong magnetic field could rotate the plane of polarisation, and moreover that the angle of rotation was proportional to the strength of the magnetic field. Faraday wrote (see for example [1]):-
That which is magnetic in the forces of matter has been affected, and in turn has affected that which is truly magnetic in the force of light.
He followed his line of experiments which led him to discover diamagnetism.
By the mid 1850s Faraday's mental abilities began to decline. At around the same time Maxwell was building on the foundations Faraday had created developing a mathematical
4
theory which would always have been out of reach for Faraday. However Faraday continued to lecture at the Royal Institution but declined the offer of the Presidency of the Royal Society in 1857.
He continued to give the children's Christmas lectures. In 1859-60 he gave the Christmas lectures on the various forces of matter. At the following Christmas he gave the children's lectures on the chemical history of the candle. These two final series of lectures by Faraday were published and have become classics. The Christmas lectures at the Royal Institution, begun by Faraday, continue today but now reach a much greater audience since they are televised. I [EFR] have watched these lectures with great interest over many years. They are a joy for anyone interested as I am in the "public understanding of science". I particularly remember lectures by Carl Sagan on "the planets" and mathematics lectures by Chris Zeeman and Ian Stewart.
The Royal Institution literature states:-
[Faraday's] magnetic laboratory, where many of his most important discoveries were made, was restored in 1972 to the form it was known to have had in 1854. A museum, adjacent to the laboratory, houses a unique collection of original apparatus arranged to illustrate the most important aspects of Faraday's immense contribution to the advancement of science in his fifty years at the Royal Institution.
Martin, in [4], gives this indication of Faraday's character:-
He was by any sense and by any standard a good man; and yet his goodness was not of the kind that make others uncomfortable in his presence. His strong personal sense of duty did not take the gaiety out of his life. ... his virtues were those of action, not of mere abstention ...
Article by: J J O'Connor and E F Robertson
May 2001
--------------------------------------------------------------------------------
Born: 22 Sept 1791 in Newington Butts, Surrey (now London) England
Died: 25 Aug 1867 in Hampton Court, Middlesex, England
--------------------------------------------------------------------------------
Michael Faraday did not directly contribute to mathematics so should not really qualify to have his biography in this archive. However he was such a major figure and his science had such a large impact on the work of those developing mathematical theories that it is proper that he is included. We say more about this below.
Faraday's father, James Faraday, was a blacksmith who came from Yorkshire in the north of England while his mother Margaret Hastwell, also from the north of England, was the daughter of a farmer. Early in 1791 James and Margaret moved to Newington Butts, which was then a village outside London, where James hoped that work was more plentiful. They already had two children, a boy Robert and a girl, before they moved to Newington Butts and Michael was born only a few months after their move.
Work was not easy to find and the family moved again, remaining in or around London. By 1795, when Michael was around five years, the family were living in Jacob's Wells Mews in London. They had rooms over a coachhouse and, by this time, a second daughter had been born. Times were hard particularly since Michael's father had poor health and was not able to provide much for his family.
The family were held closely together by a strong religious faith, being members of the Sandemanians, a form of the Protestant Church which had split from the Church of Scotland. The Sandemanians believed in the literal truth of the Bible and tried to recreate the sense of love and community which had characterised the early Christian Church. The religious influence was important for Faraday since the theories he developed later in his life were strongly influenced by a belief in a unity of the world.
Michael attended a day school where he learnt to read, write and count. When Faraday was thirteen years old he had to find work to help the family finances and he was employed running errands for George Riebau who had a bookselling business. In 1805, after a year as an errand-boy, Faraday was taken on by Riebau as an apprentice bookbinder. He spent seven years serving his apprenticeship with Riebau. Not only did
1
he bind books but he also read them. Riebau wrote a letter in 1813 in which he described how Faraday spent his days as an apprentice (see for example [4]):-
After the regular hours of business, he was chiefly employed in drawing and copying from the Artist's Repository, a work published in numbers which he took in weekly. ... Dr Watts's Improvements of the mind was then read and frequently took in his pocket, when he went an early walk in the morning, visiting some other works of art or searching for some mineral or vegetable curiosity. ... His mind ever engaged, besides attending to bookbinding which he executed in a proper manner.
His mode of living temperate, seldom drinking any other than pure water, and when done his day's work, would set himself down in the workshop ... If I had any curious book from my customers to bind, with plates, he would copy such as he thought singular or clever ...
Faraday himself wrote of this time in his life:-
Whilst an apprentice, I loved to read the scientific books which were under my hands ...
From 1810 Faraday attended lectures at John Tatum's house. He attended lectures on many different topics but he was particularly interested in those on electricity, galvanism and mechanics. At Tatum's house he made two special friends, J Huxtable who was a medical student, and Benjamin Abbott who was a clerk. In 1812 Faraday attended lectures by Humphry Davy at the Royal Institution and made careful copies of the notes he had taken. In fact these lectures would become Faraday's passport to a scientific career.
In 1812, intent on improving his literary skills, he carried out a correspondence with Abbott. He had already tried to leave bookbinding and the route he tried was certainly an ambitious one. He had written to Sir Joseph Banks, the President of the Royal Society, asking how he could become involved in scientific work. Perhaps not surprisingly he had received no reply. When his apprenticeship ended in October 1812, Faraday got a job as a bookbinder but still he attempted to get into science and again he took a somewhat ambitious route for a young man with little formal education. He wrote to Humphry Davy, who had been his hero since he attended his chemistry lectures, sending him copies of the notes he had taken at Davy's lectures. Davy, unlike Banks, replied to Faraday and arranged a meeting. He advised Faraday to keep working as a bookbinder, saying:-
Science [is] a harsh mistress, and in a pecuniary point of view but poorly rewarding those who devote themselves to her service.
Shortly after the interview Davy's assistant had to be sacked for fighting and Davy sent for Faraday and invited him to fill the empty post. In 1813 Faraday took up the position at the Royal Institution.
2
In October 1813 Davy set out on a scientific tour of Europe and he took Faraday with him as his assistant and secretary. Faraday met Ampère and other scientists in Paris. They travelled on towards Italy where they spent time in Genoa, Florence, Rome and Naples. Heading north again they visited Milan where Faraday met Volta. The trip was an important one for Faraday [4]:-
These eighteen months abroad had taken the place, in Faraday's life, of the years spent at university by other men. He gained a working knowledge of French and Italian; he had added considerably to his scientific attainments, and had met and talked with many of the leading foreign men of science; but, above all, the tour had been what was most valuable to him at that time, a broadening influence.
On his return to London, Faraday was re-engaged at the Royal Institution as an assistant. His work there was mainly involved with chemical experiments in the laboratory. He also began lecturing on chemistry topics at the Philosophical Society. He published his first paper in 1816 on caustic lime from Tuscany.
In 1821 Faraday married Sarah Barnard whom he had met when attending the Sandemanian church. Faraday was made Superintendent of the House and Laboratory at the Royal Institution and given additional rooms to make his marriage possible.
The year 1821 marked another important time in Faraday's researches. He had worked almost entirely on chemistry topics yet one of his interests from his days as a bookbinder had been electricity. In 1820 several scientists in Paris including Arago and Ampère made significant advances in establishing a relation between electricity and magnetism. Davy became interested and this gave Faraday the opportunity to work on the topic. He published On some new electro-magnetical motions, and on the theory of magnetism in the Quarterly Journal of Science in October 1821. Pearce Williams writes [1]:-
It records the first conversion of electrical into mechanical energy. It also contained the first notion of the line of force.
It is Faraday's work on electricity which has prompted us to add him to this archive. However we must note that Faraday was in no sense a mathematician and almost all his biographers describe him as "mathematically illiterate". He never learnt any mathematics and his contributions to electricity were purely that of an experimentalist. Why then include him in an archive of mathematicians? Well, it was Faraday's work which led to deep mathematical theories of electricity and magnetism. In particular the remarkable mathematical theories on the topic developed by Maxwell would not have been possible without Faraday's discovery of various laws. This is a point which Maxwell himself stressed on a number of occasions.
In the ten years from 1821 to 1831 Faraday again undertook research on chemistry. His two most important pieces of work on chemistry during that period was liquefying chlorine in 1823 and isolating benzene in 1825. Between these dates, in 1824, he was elected a fellow of the Royal Society. This was a difficult time for Faraday since Davy
3
was at this time President of the Royal Society and could not see the man who he still thought of as his assistant as becoming a Fellow. Although Davy opposed his election, he was over-ruled by the other Fellows. Faraday never held the incident against Davy, always holding him in the highest regard.
Faraday introduced a series of six Christmas lectures for children at the Royal Institution in 1826. In 1831 Faraday returned to his work on electricity and made what is arguably his most important discovery, namely that of electro-magnetic induction. This discovery was the opposite of that which he had made ten years earlier. He showed that a magnet could induce an electrical current in a wire. Thus he was able to convert mechanical energy into electrical energy and discover the first dynamo. Again he made lines of force central to his thinking. He published his first paper in what was to become a series on Experimental researches on electricity in 1831. He read the paper before the Royal Society on 24 November of that year.
In 1832 Faraday began to receive honours for his major contributions to science. In that year he received an honorary degree from the University of Oxford. In February 1833 he became Fullerian Professor of Chemistry at the Royal Institution. Further honours such as the Royal Medal and the Copley Medal, both from the Royal Society, were to follow. In 1836 he was made a Member of the Senate of the University of London, which was a Crown appointment.
During this period, beginning in 1833, Faraday made important discoveries in electrochemistry. He went on to work on electrostatics and by 1838 he [1]:-
... was in a position to put all the pieces together into a coherent theory of electricity.
The extremely high workload eventually told on Faraday's health and in 1839 he suffered a nervous breakdown. He did recover his health and by 1845 he began intense research activity again. The work which he undertook at this time was the result of mathematical developments in the subject. Faraday's ideas on lines of force had received a mathematical treatment from William Thomson. He wrote to Faraday on 6 August 1845 telling him of his mathematical predictions that a magnetic field should affect the plane of polarised light. Faraday had attempted to detect this experimentally many years earlier but without success. Now, with the idea reinforced by Thomson, he tried again and on 13 September 1845 he was successful in showing that a strong magnetic field could rotate the plane of polarisation, and moreover that the angle of rotation was proportional to the strength of the magnetic field. Faraday wrote (see for example [1]):-
That which is magnetic in the forces of matter has been affected, and in turn has affected that which is truly magnetic in the force of light.
He followed his line of experiments which led him to discover diamagnetism.
By the mid 1850s Faraday's mental abilities began to decline. At around the same time Maxwell was building on the foundations Faraday had created developing a mathematical
4
theory which would always have been out of reach for Faraday. However Faraday continued to lecture at the Royal Institution but declined the offer of the Presidency of the Royal Society in 1857.
He continued to give the children's Christmas lectures. In 1859-60 he gave the Christmas lectures on the various forces of matter. At the following Christmas he gave the children's lectures on the chemical history of the candle. These two final series of lectures by Faraday were published and have become classics. The Christmas lectures at the Royal Institution, begun by Faraday, continue today but now reach a much greater audience since they are televised. I [EFR] have watched these lectures with great interest over many years. They are a joy for anyone interested as I am in the "public understanding of science". I particularly remember lectures by Carl Sagan on "the planets" and mathematics lectures by Chris Zeeman and Ian Stewart.
The Royal Institution literature states:-
[Faraday's] magnetic laboratory, where many of his most important discoveries were made, was restored in 1972 to the form it was known to have had in 1854. A museum, adjacent to the laboratory, houses a unique collection of original apparatus arranged to illustrate the most important aspects of Faraday's immense contribution to the advancement of science in his fifty years at the Royal Institution.
Martin, in [4], gives this indication of Faraday's character:-
He was by any sense and by any standard a good man; and yet his goodness was not of the kind that make others uncomfortable in his presence. His strong personal sense of duty did not take the gaiety out of his life. ... his virtues were those of action, not of mere abstention ...
Article by: J J O'Connor and E F Robertson
May 2001
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