Books - Johannes Kepler
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Synchronicity by C.G. Jung Routledge & Kegan Paul PLC (1972) Paperback Used Price: $15.99 ![]() |
Product Description:
To Jung, synchonicity is a meaningful coincidence in time, a psychic factor which is independant of space and time. This revolutionary concept of synchronicity both challenges and complements the physicist's classical view of casualty. It also forces is to a basic reconsideration of the meaning of chance, probability, coincidence and the singular events in our lives. Customer Review: Synchronicity Explained: "Synchronicity An Acausal Connecting Principle" is a must read for those interested in the subject of synchronicity. At 115 pages this book is deceiving at first glance as it appears to be a quick read. However, it is difficult to get through, not because it is uninteresting - but really because it is fascinating and much of the thought in this work is new and is counter to traditional thinking. The translation is good, although it would be nice to have a new simplified version released which "dumbs down" some of the complex concepts. A fascinating book and well worth the time and effort. Customer Review: The devil in the details: It's way too hard to read. If you have the time to really dive in and stay it, I'll probably be interesting...but for me, it was too technical. Customer Review: fabulous: This book makes me look at the whole universe in a new way. Still, it is early psychology, and each person must take what is important for themselves. Parts of it deal with analyzing statistics, and while I understand why, I don't care - i.e., I just want to eat the pancakes, I don't want to read the recipe. That said, the book spoke to me in all good ways. Customer Review: Thoughtful, insightful essay: C G. Jung here tackles the question of "meaningful coincidences" whether omens, divination (the I Ching, ESP, and the occult (he cites Albertus Magnus) and concludes that there is objective evidence for subjective control over the universe. This fundamental issue of subjective control is strikingly at odds with natural sciences and falls outside the bounds of scientific inquiry. He then outlines a theory which is both similar to and somewhat beyond later developments (it shares non-local elements with Bell's Theorem, for example, but adds semantic elements). Jung's theory also seems to be to be both a precursor and a missing piece of semiotic theories of the occult (which have recently become much more accepted in anthropological schools of thought). Because both of these suggest inherent meaning rather than mere imitation, they are quite compatible both in theory and practice. All in all, I would highly recommend this essay. It may be dated in a few ways, but it lays groundwork for a lot of what has come later in a way which is complimentary with later developments rather than outmoded by them. Customer Review: Well-Received: This product was delivered in a timely manner and was just as the description had listed... Positive purchase experience.
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Kepler's Witch : An Astronomer's Discovery of Cosmic Order Amid Religious War, Political Intrigue, and the Heresy Trial of His Mother by James A. Connor (2004) Hardcover Used Price: $4.50 ![]() |
Product Description: Foreword by David Koch of NASA's Kepler Mission Isaac Newton said that if he had seen farther than others, it was because he was standing on the shoulders of giants: Nicolaus Copernicus, Tycho Brahe, Galileo Galilei, and Johannes Kepler. James A. Connor focuses on one of those giants in his fascinating and largely untold story of the "Protestant Galileo," Johannes Kepler. Set against the backdrop of the witchcraft trial of his mother, Kepler's Witch vividly brings to life the tidal forces of the Reformation and Counter-Reformation, submerging us into these turbulent times, revealing not only the surprisingly spiritual nature of early modern science, but Kepler's role as a neglected hero of conscience. The doorway into Kepler's life and times begins with the sensational witchcraft trial of his elderly mother, Katharina, an eccentric woman who, like Kepler, was too smart for the world she lived in. The story is filled with crooked judges, sadistic bailiffs, and nasty neighbors bent on the destruction of this single, half-mad old woman. Using never-before translated transcripts of the trial, Connor explains that witches in the seventeenth century were the terrorists of their day. Tragically, thousands of people -- mostly women -- had gone to the stake by the time of Katharina Kepler's trial. Johannes Kepler's life thus became a pilgrimage, a spiritual journey into the modern world through disease and horrible injustice on the eve of Europe's terrible and bloody Thirty Years' War. Kepler was concerned with more than scientific discoveries and achievement -- he fought for peace and reconciliation between the Christian churches, even when it nearly cost him his life. Exiled twice by Catholic princes and excommunicated by his fellow Lutherans, he was unbowed in his scientific and moral vision. Besides the witchcraft trial records and testimonies, Connor has translated many of Kepler's diary entries and correspondence into English for the first time. With a great respect for the history of these times and the life of this man, Connor's unforgettable story illuminates Kepler, a man of science, as well as Kepler, a man of uncommon faith and courage. |
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Tycho & Kepler by Kitty Ferguson Walker & Company (2002) Hardcover Used Price: $4.74 ![]() |
Product Description: On his deathbed in 1601, the greatest naked-eye astronomer, Tycho Brahe, told his young colleague, Johannes Kepler, "Let me not have lived in vain." For more than thirty years, Tycho had made meticulous observations of planetary movements and the positions of the stars, from which he developed his Tychonic system of the universe-a highly original, if incorrect, scheme that attempted to reconcile the ancient belief in an unmoving Earth with Copernicus's revolutionary re-arrangement of the solar system. Tycho knew that Kepler, the brilliant young mathematician he had engaged to interpret his findings, believed in Copernicus's formation, in which all the planets circled the Sun; and he was afraid his system-the product of a lifetime of effort to explain how the universe worked-would be abandoned. In point of fact, it was. From his study of Tycho's observations came Kepler's stunning Three Laws of Planetary Motion-ever since the cornerstone of cosmology and our understanding of the heavens. Yet, as Kitty Ferguson reveals, neither of these giant figures would have his reputation today without the other; and the story of how their lives and talents were fatefully intertwined is one of the most memorable sagas in the long history of science. Set in a turbulent and colorful era in European history, at the turning point when medieval gave way to modern, Tycho & Kepler is both a highly original dual biography and a masterful recreation of how science advances. From Tycho's fabulous Uraniborg Observatory on an island off the Danish coast, to the court of the Holy Roman Emperor, Rudolph II, to the religious conflict of the Thirty Years' War that rocked all of Europe, to Kepler's extraordinary leaps of understanding, Ferguson recounts a fascinating interplay of science and religion, politics and personality. Her insights recolor the established personalities of Tycho and Kepler, and her book opens a rich window onto our place in the universe. |
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Johannes Kepler: Giant of Faith and Science (Sowers) by John Hudson Tiner Mott Media (MI) (1999) Paperback Our Price: $7.99 Used Price: $1.35 ![]() |
Product Description: This giant of astronomy considered his studies to be a way of looking into God's creation. Customer Review: Brilliant man, so-so book, mediocre depth: John Hudson Tiner's Johannes Kepler: Giant of Faith and Science is a biography that recounts Kepler's life in a simplistic and easy-to-follow way. The entire story is documented in major "chapters" of Kepler's life, and each event is described with commentary and dialogue between Kepler and the other prevalent characters. Not only are Kepler's scientific works covered, but his struggles with the church and society are also described. Johannes Kepler was a giant of science as well as faith. One cannot understand the history of science without understand those who are behind in. In doing so, the author makes a valuable contribution to those wish to understand not only science but the interplay between science and society. This book is a good elementary description of Kepler's life, but for someone who is looking for an in-depth and sophisticated opinion may find it lacking. However, it certainly is suitable for younger students or anyone just wanting a quick read. One thumb up :o) Customer Review: Science and faith blended in this man's life.: John Hudson Tiner dones a fine job of writing this easy reading book of Kepler's life. I cannot comment on how well he makes the subject matter easy to understand for the intended audience, since I am not experienced in that area, but I can tell it is a great book for high school and older -- a book written for young people that adults can read without feeling like it is written beneath them. One great feature of this book, and other books by Tiner in this series, is the fact that he explains scientific facts in such a way that those not familiar with them can gain an understanding of some of the contributions of this man to astronomy. Pictures, some from Kepler's works, throughout the book make the book even more valuable. Any biography on Kepler is not true to the man if his faith and science are separated. Raised in a less than ideal family situation, Kepler lived in incredible times so far as the fighting over religious beliefs is concerned. Though he held firmly to and held dearly his own faith and gave up much because of it, he did not wish to become involved in the fighting over it. He also freely acknowledged that God gained glory from whatever scientific study he did. Kepler's contribution to astonomy was immense. As an example, he was provided with much needed observational data from Tycho that allowed him to determine the orbital path of Mars (around the Sun). This opened the door to determine the orbital path of other heavenly bodies as well. At one point he was motivated to discover the truth about the heavenly bodies to help dispel the superstition that caused his own mother to be tried inappropriately as a witch. This book provides a good starting point for learning about the life of Kepler. Such reading is wholesome and inspiring and good for teaching excellent values in life. To continue my study of Kepler, I am presently reading the book on him titled Kepler by Max Casper, Dover pub., 1993, a book clearly written for adults which includes much more detail. Tiner's book was a good preliminary for this latter book. |
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Epitome of Copernican Astronomy & Harmonies of the World (Great Minds Series) by Johannes Kepler Prometheus Books (1995) Paperback List Price: Used Price: $5.95 ![]() |
Product Description: The brilliant German mathematician Johannes Kepler (1571-1630), one of the founders of modern astronomy, revolutionised the Copernican heliocentric theory of the universe with his three laws of motion: that the planets move not in circular but elliptical orbits, that their speed is greatest when nearest the sun, and that the sun and planets form an integrated system. This volume contains two of his most important works: "The Epitome of Copernican Astronomy" (books 4 and 5 of which are translated here) is a textbook of Copernican science, remarkable for the prominence given to physical astronomy and for the extension to the Jovian system of the laws recently discovered to regulate the motions of the Planets; and "Harmonies of the World" (book 5 of which is translated here) expounds an elaborate system of celestial harmonies depending on the varying velocities of the planets. Customer Review: Great book: If you're interested in the universe and music and math and all that that pertains too, purchase this book. Customer Review: Kepler's Tribute to Copernicus: In this volume, Kepler combines much of his work into what he believes to be a more accessible understanding of the planetary orbits. I would recommend this book for the serious student of Astronomy, because although it is less demanding than 'Astronomia Nova', it is quite in depth and certain adjustments are made to the Copernican cosmology which the reader must have some familiarity with. A final notice: this edition of the 'Epitome..' is only sections 4 & 5. The prior sections have never been brought into English. Customer Review: A small sample..: This is a republication of an old translation. If you haven't read Kepler's own words, then this book will be both more and less than you expected. It is both a mathematical and philosophically speculative text, which in some sections can get quite technical.(Warning: the title is a bit deceiving. Only part of the Epitome is included.) I would only give 3 stars to this book, except that english translations of Kepler's works are very few, and this book is the most financially accessible of those currently on the market. I therefore recommend it as a good first exposure. There's no substitute to reading the original words of great thinkers, especially in gaining insight into their way of approaching the world. If you haven't read Kepler's own words, then this book will be both more and less than you expected. It is both a mathematical and phylsophically speculative text, which in some sections can get quite technical.(Warning: the title is a bit deceiving. Only part of the Epitome is included.) I would only give 3 stars to this book, except that english translations of Kepler's works are very few, and this book is the most financially accessible of those currently on the market. I therefore recommend it as a good first exposure. There's no substitute to reading the original words of great thinkers, especially in gaining insight into their way of approaching the world. |
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Johannes Kepler: And the New Astronomy (Oxford Portraits in Science) by James R. Voelkel Oxford University Press, USA (1999) Hardcover Our Price: $32.95 Used Price: $4.09 ![]() |
Product Description: Johannes Kepler (1571-1630) is remembered as one of the greatest medieval astronomers in the tradition of Copernicus and Galileo, a man who made major contributions to physics, astronomy, and mathematics. Born in Germany and trained as a theologian, Kepler did not hesitate to challenge church doctrine by supporting the iconoclastic theory of a Sun-centered solar system. As Imperial Mathematician to the Holy Roman Emperor, he conducted careful observations of the night sky, which led to his discovery of the three Laws of Planetary Motion and the orbit of Mars. He also devised the Rudolphine Tables on planetary movements, and made key improvements to the telescope. Voelkel vividly describes the scientific achievements, providing enough background in physics and trigonometry so even beginners can enjoy this book. The author also gives us a captivating account of Kepler's tumultuous life, plagued by misery, disease, and fervent religious prosecution by the Catholic Church. Oxford Portraits in Science is an ongoing series of scientific biographies for young adults. Written by top scholars and writers, each biography examines the personality of its subject as well as the thought process leading to his or her discoveries. These illustrated biographies combine accessible technical information with compelling personal stories to portray the scientists whose work has shaped our understanding of the natural world. |
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Kepler: A novel by John Banville Vintage (1993) Paperback List Price: Used Price: $3.44 ![]() |
Customer Review: Elliptical Prose: A short review, for a change: I agree with the other reviewers that these "scientific" novels of the early Banville do not hold an early Renaissance tallow candle to his later work.--Please see my review of Doctor Copernicus in re this lack--but just to reiterate, Banville is still Banville, in a celestial sphere above the scrum of other writers. Yes, as one reviewer has noted, the letters in Harmonia Mundi, the fourth part of the novel, form a chronological circuit of some sort. Call it an ellipse if you must, but methinks this is a wee bit of preciousness on Banville's part. The other reviewers have covered all the other, ahem, shall we say, foci? - Good period detail (q.v. C.V. Wedgwood's account of the Thirty Years' War if you want more horrors from this ghastly period of history.), interesting insights into Kepler's moods, states of mind etc. And, most of all, Banville's elegant prose in embryonic stage. How would you describe a layer of fallen snow? Banville describes it thus: "Cold it had been that morning, the sky like a bruised gland and a taste of metal in the air, and everything holding its breath under an astonishment of fallen snow." Even in these early works, Banville can still astonish. Customer Review: Novel of ideas - not Banville's forte: Kepler is a well written historical novel written during a time when Banville was attempting to write what he considered 'European novels of ideas'. In writing about the mind of a great scientist, has found a way to write about creativity without going down the established, oft cliched route of writing about writing, or painting. However it is fundamentally a poor book, which Banville has subsequently admitted. It artfully chronicles the ideas of Kepler, his struggle, but fails to invoke this in a passionate or beautiful manner. Banville's best novels are works of art. As Beckett said of Joyce, his work is not about anything, it is about the work itself. Kepler is a novel about something, a novel of ideas. It does not work well. Customer Review: Excellent Biographical Novel: Close on the heels of finishing Banville's novel Doctor Copernicus, a story based on the life of Nicholas Copernicus, I started reading this novel on the life of Johannes Kepler. I had enjoyed Mr. Banville's book on Copernicus but I found that I enjoyed this book on Kepler even more. In terms of structure and power of prose, the two books are much the same but in Kepler Banville seems to know his man much better. Doctor Copernicus powerfully evokes its time period and setting but it does so at the expense of the main character in some ways. Here, Kepler and his story seem to be more the driving force which made for an even more interesting read. Many of the main conflicts of Kepler's life are here--his struggles with Brahe, his problems with his wife, his mother's trial for witchcraft, his endless search for riches & fame along with truth--and they are brought out well through the eyes of the main character. Banville's mastery of beautiful prose my still lie in the years following this early novel; however, he was a writer of incredible power from his earliest books. For someone interested in science as I am, reading this book is a no-brainer: it needs to be read. However, any reader will find much to enjoy here. Customer Review: Elliptically told, fitting Kepler's own perigrinations: This earlier historical novel in the scientific series Banville wrote in the 80s sparkles with detail. Especially in the first section, you feel the damp of a castle, the gloom of a chamber, and smell the slops and suds. It's slow going at the start, "Mysterium Cosmagraphicum," as Kepler squares off against Brahe, and tries to gain favor with the Emperor. But this part, in hindsight, dazzles the most for the density of texture, in the prose and what it describes. You glimpse the tension between teaching schoolkids basic skills and Kepler's longing to plunge into elevated research--certainly I could relate to this as a teacher! Banville sketches easily the battle between living in a decaying world and pondering in an ethereal realm timeless (so Kepler thinks) truths. Part II lacks a title but shows how Kepler the husband must deal with the mundane among an increasingly perilous era when witches are burnt and Protestants are expelled, and how he must make a living thanks to the formidable tension created by his relationship with his father-in-law and his wife. The household and domestic strife both ring with recognizable scenes, despite the superficial differences in decor and diet, and show Banville's ability to capture drama in the everyday affairs that we too share, if in less fraught situations. Throughout the novel, a loved one's loss and the ebb and flow of intimacy within a family as expressed through Kepler's ruminations make for eloquent, yet unadorned prose that convinces you of its truth. Part III, "Dioptrice," focuses upon his mathematical ambitions and the possibilities and competition opened up by Galileo and his telescope. Here again, the exile from favor he endures balances well with the cosmological theories he seeks to verify slowly and painfully. For "Harmonia Mundi," part IV takes the form of not only letters to colleagues and friends relating his discoveries, but these letters, from 1605-11, form themselves an arc or an ellipse! I've never seen this before in a book. The letters start in 1605, progress chronologically to 1611, and then slowly retreat again from the verification of his contention that planets move elliptically back gradually to 1605. For part V, fittingly titled "Somnium," the later years of Kepler are movingly described as once more he must wander out of favor with the imperial contenders within an ideologically divided Central Europe. This book moves at an uncertain pace, mimicking its protagonist. At times, it drags, perhaps intentionally illustrating the frustrations frequently felt by Kepler within a society that does not understand his devotion to the stars or his introspective fits and starts of genius. You get--to my surprise--few of the details of Prague parading itself that I had expected, given how in the non-fictional "Prague Pictures," (also reviewed by me on Amazon) written two decades after "Kepler," the struggles of Kepler and Brahe are grippingly told by Banville in exactly this Czech context. The prose does not leap out as vividly in later sections as the former ones, but one quote remains in my mind. Banville provides Kepler's recollection of the loss of his virginity to a teenaged girl he meets at a pub. "Yet beyond the act itself, that frantic froglike swim to the edge of the cataract's edge, he had found something touching in her skinny flanks and her frail chest, that rank rose under its furred cap of bone." (38) The female body and the sexual act have been depicted millions of ways perhaps in literature; at this late state, Banville still can make such familiar scenes vivid again. Customer Review: Yawn!: I picked this book up from the library after reading that Banville won the Booker Prize for "The Sea". Plus, I love reading history books about 16th and 17th century science. So I figured: How could I go wrong? Well, the good thing about "Kepler" is that it was short. If it had been more than 200 pages, I just wouldn't have made it through. I liked the beginning part of the book, when Kepler meets Tycho for the first time, but after that it went downhill. Simply put: The last half of the book was a snoozer. Nothing much happens. Which is a shame, because Kepler was an extraordinarily interesting historical figure. I was waiting to be riveted, and it just didn't happen. I really tried hard to like this book, but it just didn't do it for me.
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Kepler by Max Caspar Dover Publications (1993) Paperback List Price: Used Price: $7.02 ![]() |
Product Description: Definitive biography by foremost scholar offers fascinating erudite picture of great mathematician’s scientific accomplishments: formulation of laws of planetary motion, work with optics and calculus, much more. Also detailed chronicle of Kepler’s public and personal life (childhood and youth, education, mother’s trial as a witch, fear of religious persecution, etc.). Introduction and Notes by Owen Gingerich. Bibliography. Customer Review: Quite good: This biography is fine, but it cannot be recommended above Koestler's biography, which is more beautifully written and, I think, not as scholarly inferior as some people say. The discrepancy in terms of style seems to be due in part to this translation being rather clumsy (although I have not compared it with the German original). Let us consider some comparisons between this book and Koestler's in this regard. Where Koestler has (quoting Kepler) "geometry was implanted into man ... and not merely conveyed to his mind through the eyes" (p. 262), Caspar reads: "geometry ... has been transferred to man ... [and] not received inside through the eyes" (p. 381). Or (again quoting Kepler): "be greeted, double knob, children of Mars" (Caspar, p. 201) versus "hail, burning twin, offspring of Mars" (Koestler, p. 377). Now it may be said that Koestler operates with a poetic licence (which is probably true in the latter case, but often not), but so should this book, which is also a popular account with no footnotes or references. No footnotes or references, that is, except those added by the translator/editor. And in these she reveals her appalling lack of taste. She is extremely inconsistent in what gets a footnote and what does not, which seems to be due, firstly, to the fact that she does not know the material very well, and, secondly, to the fact that she shamelessly wants to refer to her own work whenever possible. And she completely destroys the flair of Caspar's stylish sentence "[Kepler] did not start with doubt, as another soon did, but with an unquestioned faith in ratio" (p. 377) by inserting a dimwitted attempt at a joke: "Ed. note: Doubtless, reference here is to Descartes (1596-1650)." Quibbles aside, this is of course still a very interesting book. Here are some of my favourite themes: "Aesthetic-artistic consideration of the universe" (p. 382). "I consider it my duty and task ... to advocate ... what I ... have recognized as true and whose beauty fills me with unbelievable rapture on contemplation." (Kepler, p. 298). "I may say with truth that whenever I consider in my thoughts the beautiful order, how one thing issues out of and is derived from another, then it is as though I had read a divine text, written onto the world itself ... saying: Man, stretch thy reason hither, so that thou mayest comprehend these things" (p. 152). Mathematics a means to this end. "Kepler consciously renounced [Archimedean] rigor and wanted to take over from Archimedes only so much as 'is sufficient for the pleasure of the lovers of geometry.'" (p. 234). "Don't sentence me completely to the treadmill of mathematical calculations and leave me time for philosophical speculations, which are my sole delight. Each one has his own particular pleasure, one the tables and nativities, I the flower of astronomy, the artistic structure of the motions." (Kepler, p. 308). Man's cognitive abilities designed for this purpose. "[T]he world partakes of quantity and the mind of man grasps nothing better than quantities for the recognition of which he was obviously created." (p. 96). "Nature loves these relationships in everything that is capable of thus being related. They are also loved by the intellect of man who is an image of the Creator." (p. 94). Cf. also p. 93 and above. The universe designed for this purpose. "The earth's axis in inclined to the ecliptic in consideration of the people distributed over the whole surface of the earth, so that the change of the heavenly phenomena should extend to all places on the earth and consequently all people have a share in it. ... Sun and moon have the same apparent sizes, so that the eclipses, one of the spectacles arranged by the Creator for instructing observing creatures in the orbital relations of the sun and the moon, can occur. The earth moves around the sun to make it possible for man to get to know the world and its dimensions." (p. 296). Reception of the above. These ideas were quite well received e.g. in the case of the Mysterium Cosmographicum: "Professor Georg Limnäus in Jena ... is ecstatic that at last someone had again revived the time-honoured Platonic art of philosophising. ... [Tycho Brahe] takes unusual pleasure in the book: ... the zeal, the fine understanding and acumen ought to be praised [even though] certain details give him pause." (p. 69-70). It was different with the more modern physics of the Astronomia Nova: "Kepler ran up against rejection and lack of understanding on all sides. Maestlin, Fabricius, Longomontanus and others shook their heads." (p. 135). Customer Review: The Complete Story of Johannes Kepler the Heretic Astronomer: This biography is simply the best on the life and trials of Johannes Kepler.Anyone,who is exploring the field of astronomy,should invest their time in reading this great book.It's the fascinating story of a genius scientist having to deal with the heretical zeitgeist and relentless religious persecution of his times.Ironically,more from his own protestant leadership rather than the catholic church.Kepler was like the modern Socrates during this epoch leading to the Age of Reason. Kepler supported the Greek Copernican world model,which was in direct oppossion to the teachings of all christian-jewish European schools.Kepler did not want to 'drag the owls of knowledge to Athens',yet to bring their greek pagan wisdom to the heart of the European centers of learning.This is just an excellent book for any astute historian with a budding interest in the laws of the stars above us. Customer Review: If you dig Kepler, you'll love this book: Like the other reviewers have said, this book is simply the best combination of an account of Kepler's life, theories, and works. Customer Review: Widely considered Kepler's definitive biography: Although written in 1948, Caspar's biography is today still the most comprehensive attempt to portray the person of Kepler in a unified manner. This work reflects Caspar's lifetime of work dedicated to Kepler's many publications, manuscripts, and correspondences, and, thanks to additional citations made by editor Owen Gingerich, the reader may now find where nearly all of these passages derive from. Both the common reader and serious student may benefit from this book, for it combines Kepler's scientific studies with the deeply personal conflicts of an early modern genius. Caspar's biography is fundamental not only for studies made on Kepler, but also for the Scientific Revolution in general. Customer Review: If you are at all serious......: ....about Kepler, you must have this book. Period. By the way, Arthur Koestler's Sleepwalkers (and the Kepler chapters which were published under the title The Watershed) rely heavily on Caspar's book.
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The Eye of Heaven: Ptolemy, Copernicus, Kepler (Masters of Modern Physics) by Owen Gingerich Springer (1997) Hardcover Our Price: $49.95 Used Price: $21.61 ![]() |
Product Description: "I can think of few better ways of introducing students to the history of astronomy than by using The Eye of Heaven as a text....This is science at its best....Not only does Gingerich make you think, he also forces you back in time and makes you think as astronomers did then. Students need this inspiration." David Hughes, New Scientist Astronomer and historian Owen Gingerich provides a fascinating introduction to three giants of early astronomy: Ptolemy, Copernicus, and Kepler. In these collected essays, Gingerich examines the revolution in man's conception of the universe brought about by the shift from the earth-centered cosmos of Ptolemy to the sun-centered model of Copernicus. And if you're really serious, you'll get a copy of the paper by James Evans in Am. J. Phys 56 (Nov, 1988) 1009-1024. It answered tons of technical questions for me. Just do it, you'll thank me (and Jim Evans!). |
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Variations on a Theme by Kepler (Colloquium Publications (Amer Mathematical Soc)) by V. Guillemin, Shlomo Sternberg American Mathematical Society (1990) Hardcover Used Price: $10.94 ![]() |
Product Description:
This book is based on the Colloquium Lectures presented by Shlomo Sternberg during the Joint Mathematics Meetings in Louisville, Kentucky in January 1990. The authors delve into the mysterious role that groups, especially Lie groups, play in revealing the laws of nature by focusing on the familiar example of Kepler motion: the motion of a planet under the attraction of the sun according to Kepler's laws. Newton realized that Kepler's second law---equal areas are swept out in equal times---has to do with the fact that the force is directed radially to the sun. Kepler's second law is really the assertion of the conservation of angular momentum, reflecting the rotational symmetry of the system about the origin of the force. In today's language, we would say that the group O(3) (the orthogonal group in three dimensions) is responsible for Kepler's second law. By the end of the nineteenth century, the inverse square law of attraction was seen to have O(4) symmetry (where O(4) acts on a portion of the six-dimensional phase space of the planet). Even larger groups have since been found to be involved in Kepler motion. In quantum mechanics, the example of Kepler motion manifests itself as the hydrogen atom. Exploring this circle of ideas, the first part of the book was written with the general mathematical reader in mind. The remainder of the book is aimed at specialists. It begins with a demonstration that the Kepler problem and the hydrogen atom exhibit O(4) symmetry and that the form of this symmetry determines the inverse square law in classical mechanics and the spectrum of the hydrogen atom in quantum mechanics. The space of regularized elliptical motions of the Kepler problem (also known as the Kepler manifold) plays a central role in this book. The last portion of the book studies the various cosmological models in this same conformal class (and having varying isometry groups) from the viewpoint of projective geometry. The computation of the hydrogen spectrum provides an illustration of the principle that enlarging the phase space can simplify the equations of motion in the classical setting and aid in the quantization problem in the quantum setting. The authors provide a short summary of the homological quantization of constraints and a list of recent applications to many interesting finite-dimensional settings. The book closes with an outline of Kostant's theory, in which a unitary representation is associated to the minimal nilpotent orbit of SO(4,4) and in which electromagnetism and gravitation are unified in a Kaluza-Klein type theory in six dimensions. |










