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Kepler is a key figure in the 17th-century scientific revolution. He is best known for his laws of planetary motion , based on his works Astronomia nova , Harmonices Mundi , and Epitome of Copernican Astronomy. These works also provided one of the foundations for Isaac Newton 's theory of universal gravitation. Kepler was a mathematics teacher at a seminary school in Graz , where he became an associate of Prince Hans Ulrich von Eggenberg.
He also taught mathematics in Linz , and was an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics , invented an improved version of the refracting telescope the Keplerian telescope , and was mentioned in the telescopic discoveries of his contemporary Galileo Galilei.
He was a corresponding member of the Accademia dei Lincei in Rome. Kepler lived in an era when there was no clear distinction between astronomy and astrology , but there was a strong division between astronomy a branch of mathematics within the liberal arts and physics a branch of natural philosophy.
Kepler also incorporated religious arguments and reasoning into his work, motivated by the religious conviction and belief that God had created the world according to an intelligible plan that is accessible through the natural light of reason. His grandfather, Sebald Kepler, had been Lord Mayor of the city. By the time Johannes was born, he had two brothers and one sister and the Kepler family fortune was in decline. His father, Heinrich Kepler, earned a precarious living as a mercenary , and he left the family when Johannes was five years old.
He was believed to have died in the Eighty Years' War in the Netherlands. His mother, Katharina Guldenmann , an innkeeper's daughter, was a healer and herbalist. Born prematurely, Johannes claimed to have been weak and sickly as a child. Nevertheless, he often impressed travelers at his grandfather's inn with his phenomenal mathematical faculty. He was introduced to astronomy at an early age, and developed a love for it that would span his entire life. At age six, he observed the Great Comet of , writing that he "was taken by [his] mother to a high place to look at it.
He became a Copernican at that time. In a student disputation, he defended heliocentrism from both a theoretical and theological perspective, maintaining that the Sun was the principal source of motive power in the universe. He accepted the position in April , at the age of Kepler's first major astronomical work, Mysterium Cosmographicum The Cosmographic Mystery , was the first published defense of the Copernican system.
Kepler claimed to have had an epiphany on July 19, , while teaching in Graz , demonstrating the periodic conjunction of Saturn and Jupiter in the zodiac: After failing to find a unique arrangement of polygons that fit known astronomical observations even with extra planets added to the system , Kepler began experimenting with 3-dimensional polyhedra.
He found that each of the five Platonic solids could be inscribed and circumscribed by spherical orbs ; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets— Mercury , Venus , Earth , Mars , Jupiter, and Saturn.
By ordering the solids selectively— octahedron , icosahedron , dodecahedron , tetrahedron , cube —Kepler found that the spheres could be placed at intervals corresponding to the relative sizes of each planet's path, assuming the planets circle the Sun. Kepler also found a formula relating the size of each planet's orb to the length of its orbital period: However, Kepler later rejected this formula, because it was not precise enough.
As he indicated in the title, Kepler thought he had revealed God's geometrical plan for the universe. Much of Kepler's enthusiasm for the Copernican system stemmed from his theological convictions about the connection between the physical and the spiritual ; the universe itself was an image of God, with the Sun corresponding to the Father, the stellar sphere to the Son , and the intervening space between to the Holy Spirit.
His first manuscript of Mysterium contained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism. Mysterium was published late in , and Kepler received his copies and began sending them to prominent astronomers and patrons early in ; it was not widely read, but it established Kepler's reputation as a highly skilled astronomer.
The effusive dedication, to powerful patrons as well as to the men who controlled his position in Graz, also provided a crucial doorway into the patronage system.
Though the details would be modified in light of his later work, Kepler never relinquished the Platonist polyhedral-spherist cosmology of Mysterium Cosmographicum. His subsequent main astronomical works were in some sense only further developments of it, concerned with finding more precise inner and outer dimensions for the spheres by calculating the eccentricities of the planetary orbits within it.
In , Kepler published an expanded second edition of Mysterium , half as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication. In terms of the impact of Mysterium , it can be seen as an important first step in modernizing the theory proposed by Nicolaus Copernicus in his " De Revolutionibus orbium coelestium ". Whilst Copernicus sought to advance a heliocentric system in this book, he resorted to Ptolemaic devices viz.
Her father Jobst initially opposed a marriage. Even though Kepler had inherited his grandfather's nobility, Kepler's poverty made him an unacceptable match. Jobst relented after Kepler completed work on Mysterium , but the engagement nearly fell apart while Kepler was away tending to the details of publication.
Barbara and Johannes were married on April 27, In the first years of their marriage, the Keplers had two children Heinrich and Susanna , both of whom died in infancy. In , they had a daughter Susanna ; in , a son Friedrich ; and in , another son Ludwig. Following the publication of Mysterium and with the blessing of the Graz school inspectors, Kepler began an ambitious program to extend and elaborate his work.
He planned four additional books: Ursus did not reply directly, but republished Kepler's flattering letter to pursue his priority dispute over what is now called the Tychonic system with Tycho. Despite this black mark, Tycho also began corresponding with Kepler, starting with a harsh but legitimate critique of Kepler's system; among a host of objections, Tycho took issue with the use of inaccurate numerical data taken from Copernicus.
Through their letters, Tycho and Kepler discussed a broad range of astronomical problems, dwelling on lunar phenomena and Copernican theory particularly its theological viability. But without the significantly more accurate data of Tycho's observatory, Kepler had no way to address many of these issues.
Instead, he turned his attention to chronology and "harmony," the numerological relationships among music, mathematics and the physical world, and their astrological consequences. By assuming the Earth to possess a soul a property he would later invoke to explain how the sun causes the motion of planets , he established a speculative system connecting astrological aspects and astronomical distances to weather and other earthly phenomena.
By , however, he again felt his work limited by the inaccuracy of available data—just as growing religious tension was also threatening his continued employment in Graz. In December of that year, Tycho invited Kepler to visit him in Prague ; on January 1, before he even received the invitation , Kepler set off in the hopes that Tycho's patronage could solve his philosophical problems as well as his social and financial ones. Over the next two months, he stayed as a guest, analyzing some of Tycho's observations of Mars; Tycho guarded his data closely, but was impressed by Kepler's theoretical ideas and soon allowed him more access.
Kepler planned to test his theory  from Mysterium Cosmographicum based on the Mars data, but he estimated that the work would take up to two years since he was not allowed to simply copy the data for his own use. With the help of Johannes Jessenius , Kepler attempted to negotiate a more formal employment arrangement with Tycho, but negotiations broke down in an angry argument and Kepler left for Prague on April 6.
Kepler and Tycho soon reconciled and eventually reached an agreement on salary and living arrangements, and in June, Kepler returned home to Graz to collect his family. Political and religious difficulties in Graz dashed his hopes of returning immediately to Brahe; in hopes of continuing his astronomical studies, Kepler sought an appointment as a mathematician to Archduke Ferdinand.
To that end, Kepler composed an essay—dedicated to Ferdinand—in which he proposed a force-based theory of lunar motion: These observations formed the basis of his explorations of the laws of optics that would culminate in Astronomiae Pars Optica. On August 2, , after refusing to convert to Catholicism, Kepler and his family were banished from Graz.
Several months later, Kepler returned, now with the rest of his household, to Prague. Through most of , he was supported directly by Tycho, who assigned him to analyzing planetary observations and writing a tract against Tycho's by then deceased rival, Ursus.
In September, Tycho secured him a commission as a collaborator on the new project he had proposed to the emperor: Two days after Tycho's unexpected death on October 24, , Kepler was appointed his successor as the imperial mathematician with the responsibility to complete his unfinished work. The next 11 years as imperial mathematician would be the most productive of his life. Kepler's primary obligation as imperial mathematician was to provide astrological advice to the emperor.
In addition to horoscopes for allies and foreign leaders, the emperor sought Kepler's advice in times of political trouble. Rudolph was actively interested in the work of many of his court scholars including numerous alchemists and kept up with Kepler's work in physical astronomy as well. Officially, the only acceptable religious doctrines in Prague were Catholic and Utraquist , but Kepler's position in the imperial court allowed him to practice his Lutheran faith unhindered.
The emperor nominally provided an ample income for his family, but the difficulties of the over-extended imperial treasury meant that actually getting hold of enough money to meet financial obligations was a continual struggle. Partly because of financial troubles, his life at home with Barbara was unpleasant, marred with bickering and bouts of sickness.
As Kepler slowly continued analyzing Tycho's Mars observations—now available to him in their entirety—and began the slow process of tabulating the Rudolphine Tables , Kepler also picked up the investigation of the laws of optics from his lunar essay of Both lunar and solar eclipses presented unexplained phenomena, such as unexpected shadow sizes, the red color of a total lunar eclipse, and the reportedly unusual light surrounding a total solar eclipse.
Related issues of atmospheric refraction applied to all astronomical observations. Through most of , Kepler paused his other work to focus on optical theory; the resulting manuscript, presented to the emperor on January 1, , was published as Astronomiae Pars Optica The Optical Part of Astronomy.
In it, Kepler described the inverse-square law governing the intensity of light, reflection by flat and curved mirrors, and principles of pinhole cameras , as well as the astronomical implications of optics such as parallax and the apparent sizes of heavenly bodies. He also extended his study of optics to the human eye, and is generally considered by neuroscientists to be the first to recognize that images are projected inverted and reversed by the eye's lens onto the retina.
The solution to this dilemma was not of particular importance to Kepler as he did not see it as pertaining to optics, although he did suggest that the image was later corrected "in the hollows of the brain" due to the "activity of the Soul. He argued that if a focus of a conic section were allowed to move along the line joining the foci, the geometric form would morph or degenerate, one into another. In this way, an ellipse becomes a parabola when a focus moves toward infinity, and when two foci of an ellipse merge into one another, a circle is formed.
As the foci of a hyperbola merge into one another, the hyperbola becomes a pair of straight lines. He also assumed that if a straight line is extended to infinity it will meet itself at a single point at infinity , thus having the properties of a large circle.
In October , a bright new evening star SN appeared, but Kepler did not believe the rumors until he saw it himself. Kepler began systematically observing the nova. Astrologically, the end of marked the beginning of a fiery trigon , the start of the about year cycle of great conjunctions ; astrologers associated the two previous such periods with the rise of Charlemagne c.
It was in this context, as the imperial mathematician and astrologer to the emperor, that Kepler described the new star two years later in his De Stella Nova. In it, Kepler addressed the star's astronomical properties while taking a skeptical approach to the many astrological interpretations then circulating.
He noted its fading luminosity, speculated about its origin, and used the lack of observed parallax to argue that it was in the sphere of fixed stars, further undermining the doctrine of the immutability of the heavens the idea accepted since Aristotle that the celestial spheres were perfect and unchanging.
The birth of a new star implied the variability of the heavens. In an appendix, Kepler also discussed the recent chronology work of the Polish historian Laurentius Suslyga ; he calculated that, if Suslyga was correct that accepted timelines were four years behind, then the Star of Bethlehem —analogous to the present new star—would have coincided with the first great conjunction of the earlier year cycle.
The extended line of research that culminated in Astronomia nova A New Astronomy —including the first two laws of planetary motion —began with the analysis, under Tycho's direction, of Mars' orbit. Kepler calculated and recalculated various approximations of Mars' orbit using an equant the mathematical tool that Copernicus had eliminated with his system , eventually creating a model that generally agreed with Tycho's observations to within two arcminutes the average measurement error.
But he was not satisfied with the complex and still slightly inaccurate result; at certain points the model differed from the data by up to eight arcminutes. The wide array of traditional mathematical astronomy methods having failed him, Kepler set about trying to fit an ovoid orbit to the data. In Kepler's religious view of the cosmos, the Sun a symbol of God the Father was the source of motive force in the solar system. As a physical basis, Kepler drew by analogy on William Gilbert's theory of the magnetic soul of the Earth from De Magnete and on his own work on optics.
Kepler supposed that the motive power or motive species  radiated by the Sun weakens with distance, causing faster or slower motion as planets move closer or farther from it.
In Terra Nuova began work in Mali with an anthropological research project on traditional medicine in Kolokani. In , Terra Nuova began to produce a monthly newsletter, a space for debate and discussion in the NGO sector called 'Terra Nuova Forum' which came out regularly until From to , two multiannual projects were carried out in the Dominican Republic. One of these was multi-sectoral, based in the region of Cibao in which community trainers worked with mostly Haitian workers, and the other focussed on communication and social action with the largest feminist centre in the country.
In a training programme was set up to train indigenous primary school teachers in the Peruvian Amazon, with an intercultural, bilingual educational approach. This project went ahead for 10 years and led the Peruvian state to take over the original approach, in a scheme that was jointly managed with indigenous organisations, and the establishment of the EIB at the primary teacher training college in Iquitos.
In Terra Nuova began to work with craftsmen in the slums of Nairobi, Kenya, thanks to its partnership with the Undugu Society of Kenya. This work was to continue in subsequent years with other partners, until the MAE Jua Kali project was concluded in July In Terra Nuova staged its first operations in Brazil: The last project to be carried out in this country was a scheme to support the cooperative movement in the Bahia region in TN worked in this country until From until TN was operational in Argentina, particularly in the area of promoting human rights, alongside the organisation Servicio Paz y Justicia, founded by Nobel prizewinner Perez Esquivel.
In we opened a project for street children in Uganda, which concluded in ; over the same period we worked in Nicaragua and Guatemala with street children and youth including child labour and teenagers living on the streets. In we arrived in Somalia, where work continues to this day in an extremely challenging context. Following the Decree of 4 th December , n. The first part was called 'Environment explorers — processes of education on sustainable development', and ran in , and the second, 'Environment explorers — Experiences in the North and the South: Also in , we initiated a project called 'Slaves or Children — information and awareness-raising project to fight child prostitution, pornography and sex trafficking' to support the activities of the recently launched Ecpat Italia, created with the support of the Province of Rome.
Accordingly, it seems to me that the vast majority of those who play these games are looking for a very different kind of ride. Paul 'Phinehas' Schwanz Aug 03, at The only thing that surprises me about the sex scene in SL is that people are surprised it's there.
Claiming that SL with its sex scene is the real face of liberty might lead one to conclude that all of those players picking WOW over SL don't find liberty's face particularly attractive. Mike Sellers Aug 03, at Aug 03, at Personally I enjoyed the piece! It's just an example, and I think we can all agree, definately not a mis representation. I'm a TSO'er myself, and although we don't have as much artistic freedom as SL'ers, the things going on there, sex or otherwise, are just amazing.
Players are using it as a playground or sandbox for their fantasies. And because these games are so open-ended there's no limit to where people's minds and imaginations will take them! Linn Aug 04, at Thomas' use of the word "anarchy" later in the piece might be a more accurate description which, I imagine, is why you have the word liberty in quotes. Drawing a parallel to punk music in his article also seems appropriate.
If he'd claimed that punk music is the voice of liberty and a paragon of what people really want to listen to, I might have raised a similar objection.
Certainly some people do enjoy punk music, but looking at listening and MMOG playing habits as a whole, it appears that people readily choose restraint over this type of 'liberty' in large numbers.
It seems plausible to me that the described sex scene in SL is simply another face of the game's tendency toward anarchy. No doubt there are other factors involved when it comes to subscription numbers, but I don't think I'm way off base in pointing out that people often choose restraint over anarchy.
To some degree, I think the subscriptions reflect this tendency as well as others. Aug 04, at And while there's definitely a lot of wild fantasy going on there, in fact, many or most of the people in SL choose restraint over anarchy.
Which is not the impression the article conveys. Mark Wallace Aug 04, at Jack Matador Aug 04, at What MOST people still want, to this day, is a fairly passive form of entertainment that they can just sit back and watch. While the internet has stolen a lot of "viewing hours" away from television, it's only been able to do so because it also allows people to wander around consuming "content" for hours without producing any.
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