First Translation Of Kepler's 'New Astronomy'
Click here for Full Issue of EIR Volume 20, Number 44, November 12, 1993 ITillScience & TechnologyFirst translation ofKepler's 'New Astronomy'Kepler said, "The occasions by which people come to understandcelestial things seem to me not much less marvellous than the natureqf the celestial things themselves. "A reviewfrom Sylvia Brewda.Johannes Kepler: New Astronomytranslated by William DonohoeCambridge University Press, Cambridge, U.K.,1992665 pages, hardbound, 140The New Astronomy, or, as it was originally titled, Commen tary on the Motions o/the Star Mars, is the work, publishedin 1609, in which the great German astronomer JohannesKepler ( 157 1- 1630) announced his discovery that the orbitsof the planets are ellipses, rather than various compoundingsof circular motion, and that the rate at which a given planettravels is inversely proportional to its distance from the Sun(a law which later became, because of the approximationused by Kepler for calculation, the law of equal areas).The appearance of the first English translation of thisgroundbreaking work by the father of modern astronomy,and one of the greatest scientists known, is cause for rejoic ing, even though the book is not easy reading for those notfamiliar with the terms and operations of observational as tronomy. As Kepler himself says, unlike the tales of thediscoveries of Columbus, Magellan, and the Portuguese mar iners, "the difficulties and thorns of my discoveries infest thevery reading" about these mathematical discoveries.This is only the second complete English translation ofany of Kepler's book-length writings, none of which is avail16Science & Technologyable in other languages except German and the original Latin.To those not fluent in either language, other works of the mostcelebrated astronomical physicist have only been available asselections or in brief pieces which Kepler himself consideredsecondary within his life's work. The translator and the pub lisher are therefore to be thanked for making this completeversion of a major work available, in an edition marked byscrupulous attention to the technical apparatus (calculations,star positions, diagrams) of the original. However, the readermust be wary of the attempts, embedded in this edition, toexplain Kepler's achievements as the result of his abandon ment of his previous commitment to the outlook of ChristianPlatonism in favor of an Aristotelian adherence to data, andthe reduction of the reasons for things to the mere physicalcauses by which they occur. In fact, the publication of thismonumental work may have been in part prompted by theidea that here, Kepler could be portrayed as he is describedin the Foreword by Prof. Owen Gingerich of Harvard, ashaving "passed through the refiner's fire," with the "youthfulspeculations of his Mysterium Cosmographicum . . . behindhim." These comments are of particular importance since theentire translation is characterized in the acknowledgementsas "still very much his project." It is true that, because of thetask he had set himself, Kepler does not specify as muchas elsewhere the hypothetical foundations of his analysis.However, the misunderstanding indicated by describing thiswork as "a foundation for the development of classical [i.e.,Newtonian] physics" is refuted by Kepler's own wordsthroughout. For example, Kepler places an attack on theproto-Newtonian Ramus, and his demand for "an astronomyEIRNovember 12, 1993 1993 EIR News Service Inc. All Rights Reserved. Reproduction in whole or in part without permission strictly prohibited.
FIGURE 1Relations between the five Platonic solids(a) Dodecahedron and icosahedron(b) Dodecahedron and cube(c) Cube and octahedron(d) Cube and tetrahedronThe dodecahedron can generate the icosahedron (20 triangular faces) by placing the center of a triangle over each vertex (a). The cubecan be generatedJrom the dodecahedron by connecting non-neighboring pairs of vertices (b), while the octahedron and tetrahedron canbe constructedJrom the cube, the octahedron by placing the center of its eight triangular faces over each of the vertices of the cube (c),and the tetrahedron (four triangular faces) by connecting each non-neighboring vertex of the cube. Although the icosahedron can regen erate the dodecahedron, and the octahedron and tetrahedron can be used to generate the cube and each other, there is no way to use thecube, octahedron, or tetrahedron to generate the dodecahedron/icosahedron pair. Although Kepler never references this characteristicof the dodecahedron, it is consistent with his original conception of the planetary system, which begins with the dodecahedron, and alsowith the Pythagoreans' attribution of the highest quality to the dodecahedron, which they described as defining the essence of the heav enly bodies, or as Plato and Timaeus say, as "the construction which God used to paint the zodiac of the universe."constructed without hypotheses," directly after the title page,an attack which the translator mistakenly references as anendorsement in his Introduction. Throughout the book, foot notes detail the errors which Kepler made in computation,and often reflect the translator's amazed incomprehensionthat Kepler could arrive at accurate conclusions despite them.EIRNovember 12, 1993The 'secret' of methodThe secret of the work which is recorded in this book isKepler's method, which led him to become the first scientificelaborator of the concept of the quantum field, which is thebasis for all significant advances in physics since. To under stand his method, let us start where he started, in the book heScience & Technology17
wrote at the age of 25 with the seemingly immodest title, TheSecret of the Universe (usually referred to by its Latin name,Mysterium Cosmographicum). Here, Kepler lays out the firstknown use of quantum field theory for physical science withhis use of the five Platonic solids as the necessary determi nants of the planetary system.Most people today, including scientists, have only thevaguest familiarity with these solids, which were vividlypresent to the mind of "anyone having a slight acquaintancewith geometry" in Kepler's time. These solids are the onlyones that can be formed in three-dimensional space withfaces that are equal, regular plane figures and equal solidangles ("vertices" or comers), and that can both be circum scribed by a single sphere (all the vertices of the figure justtouch the inside of the sphere), and in which a sphere can beinscribed, just touching the center of each face. These solidscan therefore be thought of as representing the ways in whichthe boundary of a sphere or an interior spherical space can bedivided. As Kepler described this for the case of plane fig ures, a square can be thought of as inscribed in a circle,just touching it with each of its four vertices (comers), andtherefore dividing the circle evenly into four pieces, or arcs.In the same way, the eight vertices of a cube, for example,can be considered as creating a division of the inside of thespherical shell into six surface segments, each in the shapeof a square drawn onto a sphere.The most dense such division that can be made by thesefive solids is that made by the one with the most vertices,which is the dodecahedron, which has 12 pentagonal faces,which come together in 20 vertices. It is also the dodecahe dron which can generate the other four solids (Figure 1),and therefore any relation involving the five Platonic solidsnecessarily involves the characteristic of the dodecahedron,which is the Golden Section ratio, which Kepler called theDivine Proportion, the ratio by which one can divide a lineso that the smaller piece has the same ratio to the larger thatthe larger has to the whole. This is the ratio found in thepentagon (the plane figure which is the face of the dodecahe dron) between the lengths of the side and the diagonal (be tween any non-neighboring pairs of vertices). Relationshipsinvolving this same ratio [( 1 V5)/2) : 1] are found in thedodecahedron, for example between the radius of the circum scribing sphere and the length of an edge, which is the prod uct of the Golden Section and V3 : 2.In the introduction to Mysterium Cosmographicum.Kepler records his discovery as the thought originally cameto him: "The Earth is the circle which is the measure of all.Construct a dodecahedron around it. The circle surroundingthat will be Mars. Round Mars construct a tetrahedron. Thecircle surrounding that will be Jupiter. Round Jupiter con struct a cube. The circle surrounding that will be Saturn[the outermost planet known at the time]. Now construct anicosahedron inside the Earth. The circle inscribed within thatwill be Venus. Inside Venus inscribe an octahedron. Thecircle inscribed within that will be Mercury."18Science & TechnologyThe idea of quantum fieldThe concept which Kepler expresses here, and the basisof his first work and all his succeeding marvelous elabora tions and improvements, was that there was not merely a wayin which all space and time relations were lawfully ordered,as the "field" of our planetary system is, but that this orderingis not merely some evenly changing function but such asto generate specific loci at which singularities can occur.Compare the usual modem idea of gravity, as a force decreas ing smoothly with the distance from the attracting body, tothe idea that there were particular distances from the Sun, atwhich planets could occur. This is why Lyndon LaRouchehas described Kepler as the first elaborator of the quantumfield, since Kepler understood not only the existence of field type relationships (such as gravity and magnetism) whichdefine the relationships between bodies, but he grasped thefundamental point that in real, self-sustaining systems, suchfields are ordered in a quantized way, w hich determines theloci (possible places or pathways) of the bodies.What is a quantum field? A series of examples can help alayman to develop this concept. First, consider a vibratingstring, or to make the visualization clearer, a string fixed atone end which you are shaking at the other. If you shake thestring at a particular rate, you will see a point in the middlestay still, while the rest of the string is moving up and down.This is called a node, and is a simple example of a type ofquantization. If the string is the same for all its length, thatstationary point will be exactly in the middle, and it can onlybe set up at a particular rate of shaking (oscillation). If youshake faster or slower, or if you try to hold another point still,it won't work. Both space and time are therefore quantizedwith respect to that string. You can change the rate of shakingso that you will set up two, three, or more such nodes, buteach at particular points along the string and only at a particu lar frequency. In somewhat the same way, a drumhead (likea string but in two dimensions) which is struck producespatterns of vibrating and stationary areas, which can be seenby watching where grains of sand settle when the surfacevibrates (Figure 2).These examples are clearly special cases, because of theartificial boundaries, and the fact that the energy is being sup plied from outside. How could Kepler say that the spacearound the Sun is ordered in a similar way? How could thishelp him to determine the laws of planetary motion which arestill valid today, laws which also govern the motions of theouter planets and of systems of moons, of which he knewnothing? To answer these questions demands that the readerconfront some of the most basic dogmas of professional sci ence today. However, recent occurrences in science itselfought to convince us that this body of theory is in need of suchcritical examination. Witness the hysterical denial with whichthe proven repeatability of the cold fusion phenomenon hasbeen met; the deafening silence which greeted the appearanceof a number of "spokes" or areas of different reflectivity inone of the major rings of Saturn, as well as the spectacularEIRNovember 12, 1993
FIGURE2A simple example of quantizationThe grains of sand show the stationary areas by the pattern they form on adrumhead that is being vibrated.appearance of a "braided" structure in a fine outer ring (whichprompted one scientist to exclaim, "Obviously, the rings aredoing the right thing: It's just that we don't understand therules"); and the proof that according to Newtonian mechanics,there is no lawful way to predict the outcome of a collisionbetween three or more bodies if there is the slightest uncertain ty about the relative masses and velocities of the bodies.Consider the case of the spectrum of light emitted byhydrogen gas. This is one of the best-known physical factsin science today, and is used as a measuring rod for manyareas of physics, such as astronomy. The reason is that, whenhydrogen is heated, it emits light only at certain very clearlydefined and consistent frequencies (colors). However, if thespace around the nucleus were homogeneous, the electronsshould be able to revolve at any distance from the nucleus,to expand or contract the radii of their orbits in a continuousway, and therefore to emit light of all frequencies (since lightis emitted when an electron changes from one orbit to anotherof lower energy, nearer to the nucleus, and the frequency ofthe light is determined by the amount of energy involved).Therefore, there must be an ordering of the atom as a systemwhich defines only certain transitions in the electrons' orbitsas possible: those transitions which correspond to the particu lar frequencies of the emitted light.In the same way that Kepler considered quantized order ings of the space in the solar system, scientists should ask:What ordering must exist in the micro-space of the atom? InEIRNovember 12, 1993one formulation by the French physicist Louis de Broglie,the electron orbits could be defined as those in which thewave-forms associated with the electrons could exist asstanding waves (like the waves on the string). De Broglieknew that electrons behave like waves rather than particlesunder certain experimental conditions. For example, in pass ing through a slit or by a straight-edge, electrons form exactlythe same diffraction patterns as water waves or visible light,but on a scale five orders of magnitude smaller than light.He calculated wave-length which pertains to the hydrogenelectrons and used it to determine the lengths or circumfer ences of the particular orbits which they could occupy andcreate standing waves, and thus' the energies which could beemitted in the transitions between them. These tum out to beexactly what are observed in the hydrogen spectrum.What has this to do with the orbits of the planets? onemight ask. Are we saying, or did Kepler say, that the planetswere actually waves? No, but this example indicates thekinds of experimental evidence, known but ignored by thevast majority of scientists today, which demands the applica tion of Kepler's method.In the tradition of Plato and CusaIn the New Astronomy, Kepler presents the results of hismethod, rather than its basis. However, the method whichKepler used to achieve these results remained consistentthroughout his work, as proven by his later masterpiece,Harmonice Mundi (Harmony of the World). As Kepler speci fied in Mysterium Cosmographicum, and as he reaffirmed inhis footnotes to that book, written 25 years later, after histriumphant proclamation of the three laws which bear hisname, his method is that of Plato and the great Renaissancephilosopher and scientist, Cardinal Nicolaus of Cusa. Therehe referred to Plato's formulation, which he took as the axi omatic basis of science, that "by a most perfect Creator itwas absolutely necessary that a most beautiful work shouldbe produced. 'For it neither is nor was right' (as Cicero . . .quotes from Plato's Timaeus) 'that he who is the best shouldmake anything except the most beautiful. ' " From Cusa,he noted in particular the absolute distinction and hierarchyexisting between curved and straight lines: "For in this onerespect Nicolaus of Cusa and others seem to me divine: thatthey attached so much importance to the relationship betweena straight and a curved line, and dared to liken a curve toGod, a straight line to his creatures. " Here, Kepler referred,among other points, to Cusa's proof that no polygon canactually equal a circle, but that the circle was of a differentorder, and could generate those figures made with straightlines, but not the other way around (Figure 3).It was from this methodological base that Kepler was ableto conceive of the planetary system as one ordered whole,because nothing would be created were it not so ordered, andthat he could be certain that the ordering bad to come fromthe Sun, rather than the relatively tiny Earth. Thus, he wasable to assert, before the empirical evidence provided by sun.Science & Technology19
FIGURE 3FIGURE 4Quadrature of the circleKepler's model of thespots was discovered, that the Sun itself, as the center anddefining singularity of this system, must rotate on its axis.In Mysterium Cosmographicum, Kepler also attempts toexplain the eccentricities of the planets, the fact that theplanets did not appear to make perfect circles around the Sun.At the time, it was assumed that all motion of the planetswas compounded from circular motion, and therefore theCopernican hypothesis was that the planets traced out circles(or actually sections of spheres, since each travels in a planeslightly tilted with respect to the orbits of the others) arounddifferent points, all close to the Sun but none exactly coincid ing with it. Kepler could not accept such an idea, and insteaddepicted each planet as travelling in a course bounded by twocircles of slightly different radii, but each centered on theSun. This then represented the spherical shell, inside whicha Platonic solid was constructed; within which, in tum, asphere could be inscribed, representing the outer boundaryof the shell within which the next planet moved (Figure 4).While Kepler did not specify the relation of this arrangementto Cusa's analysis of the relation between a circle and thesquares inscribed and circumscribed with it, the relation isclear. As Cusa knew, the squares can be replaced with octa gons, sixteen-sided figures and so on, without either the outeror inner figure ever '"'''''''-''''''11' with the perimeter of thecircle. Thus, there is always non-zero width between thelinear figure and the curved. LaRouche has pointed outcan be made smaller thanthat this width, even thoughany given value, must always. the singularity which, and thus the transidefines both the inner andtion between "inside-ness"way, Kepler's formulationwhich is almost zero on the a trorlonllc:aiand which determineswhich the matter of the planetthe transition between the·Platonic solid, which is beingbounded by this shell, and theone out. One can considerthe difference between the ·and circumscribed fig, the spherical shell is thefaces and edges of the solidlocus of the points at whichwith respect to this figure;terminate, thus ofof the shell touches thefrom the outside, the exteriorcenters of the faces of thesolid, points which are notof these planes, but notsingular, determining thetheir extent. Thus, the matter this singular location definesthe space surrounding it, and in a way which is different,and exterior areas.although related, in the·It should be noted thatshells are the loci for thedescribed in his 1988 paperthe solar system (see 21 stCentury Science & Tpr-,mn'I J 'v, July-August 1988, "Howthe Solar System Was. In this model, certain ringsare defined by theof a rotating plasma with a20Science & TechnologyEIRNovember 12, 1993
non-zero magnetic field, the matter of the field arranges itselfin these ring areas in shapes like those of concentric smokerings, and at a certain moment each ring snaps, and the matterin it condenses into a blob at the point on its circumferen
Nov 12, 1993 · First translation of Kepler's 'New Astronomy' Kepler said, "The occasions by which people come to understand celestial things seem to me not much less marvellous than the nature qf the celestial things themselves. "A review from Sylvia Brewda. Johannes Kepler: New Astronomy translated by Wil
brief overview of CUDA see Appendix A - Quick Refresher on CUDA). The following table compares parameters of different Compute Capabilities for Fermi and Kepler GPU architectures: Compute Capability of Fermi and Kepler GPUs FERMI GF100 FERMI GF104 KEPLER GK104 KEPLER
Appendix A ‐ Quick Refresher on CUDA). The following table compares parameters of different Compute Capabilities for Fermi and Kepler GPU architectures: FERMI GF100 FERMI GF104 KEPLER GK104 KEPLER GK110 Comp
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Kepler’s First Law - The orbit of each planet is an ellipse with the Sun at one focus. Kepler’s Second Law - The line joining any planet to the Sun sweeps out equal areas in equal times. Kepler’s Third Law - The squares of the periods o
Accepted translation 74 Constraints on literal translation 75 Natural translation 75 Re-creative translation 76 Literary translation 77 The sub-text 77 The notion of theKno-equivalent1 word - 78 The role of context 80 8 The Other Translation Procedures 81 Transference 81 Naturalisation 82 Cultural equivalent 82 Functional equivalent 83
translation, idiomatic translation and communicative translation. From 116 data of passive voice in I Am Number Four novel, there is 1 or 0.9% datum belongs to word-for-word translation, there are 46 or 39.6% data belong to literal translation, there is 1 or 0.9% datum belongs to faithful translation, there are 6 or
Anatomy of a journal 1. Introduction This short activity will walk you through the different elements which form a Journal. Learning outcomes By the end of the activity you will be able to: Understand what an academic journal is Identify a journal article inside a journal Understand what a peer reviewed journal is 2. What is a journal? Firstly, let's look at a description of a .
