Wolfschmidt Harmony and Symmetry. Celestial regularities shaping human culture.

Proceedings of the SEAC 2018 Conference in Graz. Edited by Sonja Draxler, Max E. Lippitsch & Gudrun Wolfschmidt. SEAC Publications; Vol. 01
1. Auflage 2020
ISBN: 978-3-347-14634-1
Verlag: tredition
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, Band 1, 440 Seiten

Reihe: European Society for Astronomy in Culture - SEAC Publications

For the SEAC conference in Graz (2018) and for the Proceedings the motto 'Harmony and symmetry - celestial regularities shaping human culture' was chosen. There were at least two strong reasons for this motto: First, the connection between astronomy and human culture has an extremely long tradition, and one of its absolute high points is the astronomer Johannes Kepler, who spent his entire life searching for the relationship between the movement of heavenly lights and ideas about harmonious structures and regular bodies. Kepler started his scientific career and authored his first book, the Mysterium cosmographicum, in Graz. Kepler argued in his first publication for the twelve-fold partition of the zodiac with arguments derived from the monochord, anticipating the procedure he developed in his Harmonices mundi. Five contributions deal with Kepler, including the harmony in musical theory. The second reason was the Eggenberg Castle. This palace, built for the nobleman Hans Ulrich von Eggenberg (1568-1634), is a remarkable piece of symmetry and harmony and an outstanding example of a strong connection between astronomy and culture. Seven contributions have the topic astronomy, astrology and architecture with the emphasis on astronomical orientation, symmetry and harmony in the Middle Ages and Renaissance. The Proceedings with ten chapters and 44 contributions range besides the mentioned 'Middle Ages and beyond' and Johannes Kepler from Prehistoric Times, Bronze and Iron Age, Mythology and Ethnoastronomy, Babylonian Astronomy, Greek and Roman Astronomy, Meso- and South America, Middle East and Eastern Asia and Computational Astronomy. The celestial sphere, regarded as the sky of astronomy, as well as the heaven of divine numina, from Antiquity to Copernicus and Kepler was equated with symmetry, harmony, and beauty. Until today, this has been reflected in the structure of cultural creations, from architectural objects to musical forms.

Homepage https://www.fhsev.de/Wolfschmidt/index.html Nuncius Hamburgensis - Beiträge zur Geschichte der Naturwissenschaften https://www.fhsev.de/Wolfschmidt/GNT/research/nuncius.php Publikationen https://www.fhsev.de/Wolfschmidt/publikat.php#2020

Autoren/Hrsg.

Wolfschmidt, Gudrun

Leseproben

Preface Harmony and Symmetry –
Celestial regularities shaping human culture Sonja Draxler1, Max E. Lippitsch1 & Gudrun Wolfschmidt2 1 Institute of Physics, Karl-Franzens University Graz, Austria 2 Hamburg Observatory, University of Hamburg Email: Email: [e-mail], [e-mail]. It is a well-established procedure for SEAC annual conferences to set a special motto defining the general theme of the conference. The contributors are in no way obliged to abide by this motto, but a look at the Proceedings of previous conferences shows that the motto is valued by the majority of participants, and many contributors aim at least to relate their own work and the conference motto. The Graz conference took place under the motto “Harmony and symmetry – celestial regularities shaping human culture”. There were at least two strong reasons for this motto: First, the connection between astronomy and human culture has an extremely long tradition, and one of its absolute high points is the astronomer Johannes Kepler, who spent his entire life searching for the relationship between the movement of heavenly lights and ideas about harmonious structures and regular bodies. Kepler started his scientific career and authored his first book, the Mysterium cosmographicum, in Graz. The second reason was the Eggenberg Castle. This palace, built for the nobleman Hans Ulrich von Eggenberg (1568–1634), is a remarkable piece of symmetry and harmony and an outstanding example of a strong connection between astronomy and culture. The Conference Chair is grateful for the opportunity to integrate this wonderful place into the program of the conference. What is the meaning of the keywords harmony and symmetry? In everyday language, they stand in a rather vague way for a certain kind of beauty and concinnity. In a scientific context, especially in mathematics and the physical sciences, symmetry has got a well-defined meaning: The symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. This definition obviously reminds us of astronomy: The celestial sphere remains unchanged when rotated by 360° or 24 hours. The mathematical tool for dealing with symmetries is group theory. Their importance in physics was established in 1918 by the German mathematician Emmy Noether. Her theory related, in an unprecedented way, symmetries with conservation laws and became exceedingly fruitful in theoretical physics. But, though highly appreciating Emmy Noether’s work, we have to state: The basic idea was not new. We have to go back about 2.600 years, when Ionian Greeks had begun to speculate about the very essence of the world and the position of men in the universe. The first well-known name is Thales of Miletus, and, as Aristotle reports, he had stated that earth rested upon water like a piece of wood. His pupil Anaximander (c. 610–546 BC) adopted a quite different position: ??? ?? G?? ????? ????O??? ??? ??????S ??????????? ?????S?? ?? ??? ?O? ?????? ????O? ???S??S?? But the earth is unsupported, held by nothing, remaining amidst and standing away equally from all. As we learn from ancient comments on this saying, even in antiquity it was understood in a sense that there is no need for a support holding the earth: The invariance of the earth’s position is deduced solely from the spherical symmetry of the cosmos. Karl Popper (1973) is wrong in assuming that equal forces in all directions hold the earth. Being at the centre of a totally symmetric world the earth has no reason at all to leave its place. Thus, the first connection between symmetry and conservation is postulated: In modern terms, the spherical symmetry of the cosmos with respect to its centre causes conservation of rest in that centre. Thus, the first application of symmetry arguments was related with the question of Earth’s position in the cosmos, that is in an astronomical context. Aristotle discarded the opinion of Anaximander. One of his objections was, told in the language of modern physics: Symmetry could hold only for a point, for an extended solid the symmetry would be broken, and every part of it would move away from the centre, thus producing an expanding earth. Most interestingly, however, Aristotle used the symmetry argument in another context: against the existence of the void (the vacuum): as with those who for a like reason say the earth is at rest, so, too, in the void things must be at rest; for there is no place to which things can move more or less than to another. Or, expressed in modern language: A perfectly empty space by necessity is symmetric in all possible symmetry elements. Hence every quantity must be preserved, and nothing could change. Since this would be unreasonable, the void cannot exist. The consequence again anticipates a concept of modern physics: Space must be filled, at least with some kind of information on (local) asymmetries of space. This is the birth of modern field theory and again provides an astronomical context. While the term symmetry was given an unambiguous meaning by scientific definition, the situation is more difficult for harmony. From the natural sciences, the term has disappeared. Its use is restricted to musical theory, and even in that field it has several meanings. Obviously, no connection between harmony and astronomy has survived. In ancient times, on the other hand, harmony was one of the key words of the Pythagoreans, who attributed a harmonic movement to the planets. The first known appearance of the word ???µ???a is in Homer’s Iliad and Odyssey, where it denotes an “element… for fastening together with bolts different parts of whole” (Ilieski 1933), a joint for fixing planks in ship building. This ability, to join different parts to form a whole, provided a steep carrier for the term harmony: A few generations after Homer, harmony had developed to a goddess, joining even her disparate parents, love goddess Aphrodite and war god Ares. The most important role harmony was to play in musical theory. The first to deal with this topic, reportedly was the sage Pythagoras (c. 570–480 BC). His biographer Iamblichus (c. 245–c. 325 AD), following the mathematician Nikomachos (c. 60–120 AD), bequeaths the nice story of the sage passing by “a brazier’s shop where he heard the hammers beating, producing sounds that harmonized….” (Iamblichus: The life of Pythagoras 26, transl. K.S.T. Taylor. London 1818). From extensive experimental work Pythagoras attained the insight that there is a close connection between the physical quantity of size (spatial length and temporal duration) and the esthetic quality of perception. This he impressively demonstrated using the monochord, a single string with an appliance to change the string’s length. From this simple device he learned the basics of musical acoustics. His followers were convinced that size and sound where closely connected with each other, and consequently they attributed a special kind of sound to the most special object, the universe. In that time this meant the planetary system (earth, counter-earth, seven planets including sun and moon) and the sphere of fixed stars. This structure consists of ten elements, and there was a specific musical action, a peculiar harmony attributed to every single element. The Pythagorean ideas survived much longer than their community. During antiquity, in the Middle Ages, but also in modern times a considerable number of scientists kept alive Pythagorean thinking. Also here in Graz, some of these remarkable scientists were working and teaching, for example Nobel Prize winner Erwin Schrödinger, the spectroscopist Joseph Brandmüller, and, of course, Johannes Kepler. This great thinker in his first publication argued for the twelve-fold partition of the zodiac with arguments derived from the monochord, anticipating the procedure he developed in his Harmonices mundi. Astronomy provides a unique type of symmetry: While time itself is proceeding without any symmetry (no moment equals any other), the spatial structures periodically return to the same configuration in fixed temporal distances: Every noon the sun’s path culminates in the same direction. The face of the moon changes its size in regular, predictable times. The appearance of Venus as evening or morning star follows a time pattern that can be rationally understood. While it was completely unpredictable, when a disease or an accident would terminate our life, the movement of the celestial luminaries remained the same over many generations. Astronomy, to use an exaggerated formulation, is the only trustable thing in the world, the only knowledge you can rely on. You can believe in inscrutable numina or trust in recurrent heavenly phenomena. Culture is impossible without structure,...