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HARMONICES MUNDI #0606_1/ 2006
(  Satoshi Kinoshita )
| Series: | Paintings: Landscape 2 | | Medium: | Acrylic on stretched canvas | | Size (inches): | 11.7 x 8.3 | | Size (mm): | 297 x 210 | | Catalog #: | PA_0103 | | Description: | Signed, titled, date, copyright in magic ink on the reverse.
"The Science of the Harmony of the World" (1619) by Johannes Kepler.
Preface to Book I: On the Reason for the Knowledge and Proof of the Regular Plane Figures which create Harmonic Proportions, with their origin, classes, order and differences.
Translated by Christopher White with the assistance of Sylvia Brewda.
Introduction:
In the work known as Harmonice Mundi, the German scientist and mathematician, Johannes Kepler (1571-1630) presented to the world the culminating application to questions of astronomy of the method which he had defined in his first book (Mysterium Cosmographicum (1599).
Many know of Harmonice Mundi as the work in which Kepler announced the third of his laws of planetary motion: the ratio of the cube of the (average) radius of the planet's orbit to the square of its periodic time is equal to a constant for all planets. This law, which applies as well to all the planets and systems of moons discovered since Kepler, does not however define the true importance of this work. Here, Kepler pulled together his studies in music, geometry, epistemology and astronomy and created a theory of the solar system which opens the door to critical advances in all of physics.
This ground-breaking work has never been published in English, except for Book V, which is the culmination of the entire work, but which appears mystical and unrigorous if read alone. The effect is essentially the opposite of what Kepler describes here as being done to Euclid, where the crown of the work was chopped off, here only the crown has been presented without the foundation which Kepler carefully built. Book I of Harmonice Mundi is the most difficult section to read, but provides the scientific language which Kepler will need throughout the rest of the work.
The language is based on the process, described in Book X of Euclid's Elements, of constructing line lengths which are in knowable, although irrational ratios to a given line. Kepler considers that this process is absolutely key to the understanding of the regular polygons, which in turn he considers as the basis for consonant (sweet-sounding) intervals in music as well as for the five Platonic Solids which he used to explicate the number of the planets and the relative sizes of their orbits. Thus, from the investigation of constructable numbers, Kepler moves to the construction of polygons and their star figures, and contrasts those which can be constructed with others which cannot, whether or not they can be approximated.
In this introduction, the reader can get some sense of Kepler's sense of the sacred nature of scientific inquiry, both in his descriptions of how it should be carried out, and his unabashed attacks against those who demean it. As Kepler had said years earlier in one of his calendars: "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 into the world itself, not with letters but rather with essential objects, saying: Man, stretch thy reason hither, so that thou mayest comprehend these things." (quoted by Max Casper in his biography, Kepler, as translated by C. Doris Hellman)
Note: Continued on the following "page" as "PA_103" - Harmonices Mundi #0606_2/ 2006.
-www.schillerinstitute.org/transl/trans_kepler.html
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