Harmony and Symmetry. Celestial regularities shaping human culture. E-Book

Gudrun Wolfschmidt

• Herausgeber: tredition
• Kategorie: Religion und Spiritualität
• Serie: European Society for Astronomy in Culture - SEAC Publications
• Sprache: Englisch
• Veröffentlichungsjahr: 2020

Seitenzahl: 985

Beschreibung

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.

Leseprobe

Harmony and Symmetry

Celestial regularities shaping human culture

Proceedings of the SEAC 2018 Conference in Graz

Figure 0.1:

Apian’s Astronomicum Caesareum, Deferens Martis

(UB Graz)

European Society for Astronomy in Culture

SEAC Publications; Vol. 01

Sonja Draxler, Max E. Lippitsch & Gudrun Wolfschmidt

Harmony and Symmetry

Celestial regularities shaping human culture

Proceedings of the SEAC 2018 Conference in Graz

Hamburg: tredition 2020

European Society for Astronomy in Culture SEAC Publications (ISSN 2701-889X), ed. by Gudrun Wolfschmidt, University of Hamburg

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. Hamburg: tredition (SEAC Publications; Vol. 01) 2020.

Front Cover: Johannes Kepler: Mysterium Cosmographicum (Tübingen 1596).

Frontispice: Apian’s Astronomicum Caesareum, Deferens Martis (UB Graz)

Title Page: Logo SEAC

Back Cover: Calendar Table with gods of the day and Zodiac in Cistercian monastery Stift Rein, Zodiac sign Capricorn, Andreas Pleninger, 1607 (Photo: Kurt Roth)

SEAC Publications (ISSN 2701-889X), ed. by Gudrun Wolfschmidt,Center for History of Science and Technology, Hamburg Observatory, University of Hamburg https://www.fhsev.de/Wolfschmidt/GNT/research/nuncius.php#SEAC

The publication including all its parts is protected by copyright. Any exploitation is not permitted without the consent of the publisher and the author. This is especially true for reproductions, translations, microfilming as well as storage and processing in electronic systems.

Verlag und Druck: tredition GmbH, Halenreie 40–44, 22359 Hamburg, Germany

ISBN – 978-3-347-14632-7 (Paperback), 978-3-347-14633-4 (Hardcover),

978-3-347-14634-1 (e-Book), © 2020 Gudrun Wolfschmidt.

Table of Contents

Preface: Harmony and Symmetry –

Celestial regularities shaping human culture

Sonja Draxler, Max E. Lippitsch & Gudrun Wolfschmidt

0.1.1 References

0.1.2 Sponsoring

1 Prehistoric Times

Common features of megalithic stone rows in western Switzerland

Rita Gautschy

1.1.1 Introduction

1.1.2 Method

1.1.3 Site 1: Yverdon-les-Bains Clendy

1.1.4 Site 2: Lutry La Possession

1.1.5 Site 3: Sion Chemin des Collines

1.1.6 Conclusion

1.1.7 Appendix

1.1.8 Bibliography

The summer solstice sun at Lepenski Vir

Aleksandra Bajić & Hristivoje Pavlović

1.2.1 Introduction

1.2.2 Methodology

1.2.3 Results

1.2.4 Observation

1.2.5 Archaeological Findings, which reinforce the Assumption that Lepinski Vir was the Place where the Sun was Observed

1.2.6 Conclusions

1.2.7 References

Structure of the sacred space, astronomical orientation and functional evolution of the rock-cut monument near the village of Lilyach, Kyustendil region, Bulgaria

Alexey Stoev, Penka Maglova, Vassil Markov, Dimitriya Spasova & Anton Genov

1.3.1 Introduction

1.3.2 Methodology

1.3.3 Archaeoastronomical research

1.3.4 Conclusion

1.3.5 References

Eneolithic Calendar in the Magura Cave, Bulgaria

Penka Maglova, Alexey Stoev & Mina Spasova

1.4.1 Introduction

1.4.2 Eneolithic monochrome paintings of the Magura cave

1.4.3 Methods of research

1.4.4 Results – Analysis of the Solar Hall paintings

1.4.5 Reading the Eneolithic calendar

1.4.6 Discussion

1.4.7 References

Calendrical Interpretation of Spirals in Irish Megalithic Art

Marc Türler

1.5.1 Introduction

1.5.2 A dynamic approach of the art

1.5.3 Observable properties of astronomical cycles

1.5.4 Calendrical interpretation of five spiral motifs

1.5.5 Discussion

1.5.6 Conclusion

1.5.7 References

Vršac Circles a possible archaeoastronomy related site celebrating the rebirth and life in the South Banat district of Serbia Marc Frîncu, Aleksandra Bajić, Leonard Dorogostaisky & Tamaš Fodor

1.6.1 Introduction

1.6.2 Overview of the area

1.6.3 Research methodology

1.6.4 Archaeoastronomical analysis

1.6.5 Discussion

1.6.6 Bibliography

2 Bronze Age and Iron Age

The Orientations of the Chamber-Tombs at Mavro Spelio, Crete: a clue to their historical significance

Göran Henriksson & Mary Blomberg (1934–2020)

2.1.1 Introduction

2.1.2 Methods

2.1.3 Chamber tombs

2.1.4 Cults rooms

2.1.5 Chamber tombs at Mavro Spelio

2.1.6 Bibliography

Games for Cosmos – How the Minoan elite ruled their people by mastering ritual performance and the cycles of time

Marianna P. Ridderstad

2.2.1 Introduction

2.2.2 Outline of the Minoan culture

2.2.3 3. Games in the Minoan culture – Minoan gameboards

2.2.4 Games in the Minoan culture – Representations of games and sports in art

2.2.5 ‘Games for cosmos’: the meaning of games in Minoan ritual life

2.2.6 Conclusions

2.2.7 Bibliography

The Hittite Rock Sanctuary of Yazılıkaya: A Time-Keeping Device from ca. 1230 B.C.

Eberhard Zangger & Rita Gautschy

2.3.1 The Sanctuary

2.3.2 Indications for a Technical Function of Yazılıkaya

2.3.3 Astronomical Calculations to Determine Horizon Profiles

2.3.4 Chamber A: Keeping Track of Days, Months, and Years

2.3.5 Conclusions

2.3.6 Bibliography

A Statistical Analysis of the Motifs on Bronze Age Golden Hats Marc Thuillard

2.4.1 Introduction

2.4.2 Method

2.4.3 Results

2.4.4 Discussion

2.4.5 Conclusion

2.4.6 Bibliography

2.4.7 Annex: Software Program

Exceptional evidence of a prehistoric meteorite impact at the archaeological site of Stöttham (Chiemgau, SE-Germany)

Barbara Rappenglück, Michael Hiltl & Kord Ernstson

2.5.1 Introduction

2.5.2 The archaeological site of Chieming-Stöttham

2.5.3 A sample of ‘slag’ containing non-ferrous metal

2.5.4 Results

2.5.5 A more accurate dating of the Chiemgau meteorite impact

2.5.6 Summary

2.5.7 Bibliography

Archaeoastronomical “Stratigraphy”: Investigations on a Cisalpine Celtic Enclosure

Stefano Spagocci & Adriano Gaspani

2.6.1 Introduction

2.6.2 Site Alignments

2.6.3 The Dating Algorithm

2.6.4 Site Dating

2.6.5 Built by a Priestess?

2.6.6 Final Remarks

2.6.7 Bibliography

3 Mythology and Ethnoastronomy

A Catchy World Model:The Concept(s) of Cosmic Mountain(s) Used by Ancient Cultures

Michael A. Rappenglück

3.1.1 Mountains – General Remarks

3.1.2 Cosmogony: The Primordial Hill, the Womb of the World, the World Cave

3.1.3 World Mountain, Water Cycle, Milky Way, and the Four Rivers

3.1.4 Cosmology: The 3D-shape of the World Mountain

3.1.5 The World Mountain as a spatial-temporal structure

3.1.6 The World Mountain: transcendence and the beyond

3.1.7 Conclusion

3.1.8 Bibliography

Skyscape as a Cultural Fulfilment of a Cognitive Task

Jadran Kale

3.2.1 Introduction

3.2.2 The Ethnography of a Socially ‘Small’ Sky

3.2.3 Cognitive Foundations of ‘Small’ and ‘Large’ Skies

3.2.4 Travelling with Mentalscapes

3.2.5 Conclusion

3.2.6 Bibliography

4 Babylonian Astronomy

Babylonian Constellations in Stellarium 0.19.*

Susanne M. Hoffmann

4.1.1 Introduction

4.1.2 MUL.APIN Sky Culture – the – 2nd millennium

4.1.3 Seleucid Sky Culture – the – 1st millennium

4.1.4 Method

4.1.5 Result and Uncertainies

4.1.6 Conclusion

4.1.7 References

4.1.8 Appendix 1 (Pictures)

4.1.9 Appendix 2

Celestial regularity as a basis of time-reckoning

Hermann Hunger

4.2.1 Introduction – calendar and time

4.2.2 Subdivision of day and night

4.2.3 Measuring devices

4.2.4 Bibliography

Ziggurats: An Astro-Archaeological Analysis

Vance Tiede

4.3.1 Introduction

4.3.2 Historical Evidence

4.3.3 Research Objectives

4.3.4 Research Significance

4.3.5 Limitations

4.3.6 Methodology

4.3.7 Analysis

4.3.8 Conclusion

4.3.9 Bibliography

5 Greek and Roman Astronomy

Where does astronomy sit? Astronomy in some of its contexts

Liba Taub

5.1.1 Introduction

5.1.2 Sensible Models

5.1.3 Theoretical and practical astronomy

5.1.4 Astronomy and philosophy: the astronomer as philosopher

5.1.5 Bibliography

On the Orientation of Roman Cities in the Illyrian Coast: a Statistical and Comparative Study

Juan Antonio Belmonte, Andrea Rodríguez-Antón & A. César González-García

5.2.1 Introduction

5.2.2 Data on Illyrian cities and discussion

5.2.3 Appendix: Data on ancient Roman cities of Histria and Dalmatia

5.2.4 Conclusion

5.2.5 References

Archeoastronomical research in Felix Romuliana (The palace, neither on Heaven nor on the Earth)

Aleksandra Bajić & Milan S. Dimitrijević

5.3.1 Introduction

5.3.2 Where is that Groma (or Umblicus)?

5.3.3 The Temples

5.3.4 Magura, the Sacred Hill

5.3.5 Conclusions

5.3.6 Bibliography

6 The Middle Ages and beyond

Diachronic evolution of the orientation of early Christian and medieval churches of Rome

Isabella Leone, S. Gaudenzi, Franco Meddi, Vito Francesco Polcaro (1945–2018) & F. Carnevale

6.1.1 Introduction

6.1.2 Measurement methodology

6.1.3 Results

6.1.4 Data Analysis

6.1.5 Discussion and conclusion

6.1.6 Acknowledgements

6.1.7 Bibliography

The orientation of Early Christian and medieval churches inside and next to the Roman centuria of northern and central Italy

Eva Spinazzè

6.2.1 Introduction

6.2.2 Methodology

6.2.3 Calendars

6.2.4 Analysis and Results

6.2.5 Conclusion

6.2.6 References

The astrological cycle of Schifanoia: a digital representation

Manuela Incerti

6.3.1 Museums and digital

6.3.2 Historical notes on the Palace, the frescoes and its patrons

6.3.3 Multimedia tools and the renovation of the museum

6.3.4 The 3D model, information and interactive storytelling

6.3.5 Digital technologies for Astronomical Heritage: the lines of development for the near future

6.3.6 Project contributors

6.3.7 Bibliography

Astronomical Treasures in Stift Rein

Sonja Draxler & Max E. Lippitsch

6.4.1 Introduction

6.4.2 Motus astrorum

6.4.3 Wurmprecht Calendar

6.4.4 Sacrobosco’s De sphaera

6.4.5 Apian’s Astronomicum Caesareum

6.4.6 Great Comet of 1577

6.4.7 Calendar table

6.4.8 Representative rooms of the monastery

6.4.9 References

The change of worldview during Renaissance and its impacts on the architecture in the Czech lands during 16th and early 17th century

Nikolaos Ragkos

6.5.1 Introduction

6.5.2 The cultural movement of Renaissance – Its origin, ambience and changes

6.5.3 Renaissance beyond the Italian Alps

6.5.4 The evolution of the science of astronomy during the Renaissance

6.5.5 Renaissance architecture in the Czech Lands

6.5.6 Precedent case studies – Methods and Data

6.5.7 Results and discussion

6.5.8 Conclusion

6.5.9 References

A 17th century “Mountain Calendar” from Żywiec (Poland): an erudite’s invention or a local Mountaineers’ tradition?

Mariusz Ziółkowski, Maciej Sobczyk, Bartlomiej Ćmielewski & Wojciech Mirocha

6.6.1 The factographical basis of the study

6.6.2 Analysis

6.6.3 Interpretation

6.6.4 Bibliography

Schloss Eggenberg – A Symbolic World

Barbara Kaiser

6.7.1 Introduction

6.7.2 Prince Eggenberg

6.7.3 The new residence

6.7.4 Utopia

6.7.5 The private universe

6.7.6 The architectural calendar

6.7.7 Coincidentia Oppositorum – The Uniting of Opposites

6.7.8 Sunt Coelo Digni – The Planetary Room

6.7.9 Saturn

6.7.10 Mercury

6.7.11 Bibliography

7 Johannes Kepler

Johannes’ Kepler’s Political Cosmology, Psychological Astrology and the Archaeology of Knowledge in the Seventeenth Century

Nicholas Campion

7.1.1 Introduction

7.1.2 The Cosmos as a State

7.1.3 Conclusion

7.1.4 Bibliography

Meteorological astrology by Johannes Kepler and Georg Krafft’s prediction for ice drift on the Neva River in

Karine Dilanian

7.2.1 Introduction

7.2.2 Methodology

7.2.3 The author of the calendar

7.2.4 The content and the structure of Krafft’s article

7.2.5 Interrelation of Krafft’s text with the other texts and philosophical concepts: Kepler, Pico and Ptolemy

7.2.6 Musical harmony, human soul and astrology

7.2.7 Methodology of astrological meteorological prediction: Kepler and Krafft

7.2.8 Conclusion

7.2.9 Bibliography

The ancient doctrine of the Great Year and its possible influence on Johannes Kepler and Dionysius Exiguus

Sepp Rothwangl

7.3.1 Introduction

7.3.2 The ancient doctrine of a Great Planetary Year

7.3.3 Epochs based upon planetary massing in other cultures

7.3.4 Johannes Kepler and chronolgy

7.3.5 Kepler’s own search for a date of the creation with the Great Year doctrine

7.3.6 Early Christian dissemination of the Great Year

7.3.7 Dionysisus Exiguus inventing Anno Domini

7.3.8 Comparison and conclusion

7.3.9 Bibliography

The harmony of Johannes Kepler: Elliptical form in geometry and music

Uliva Velo

7.4.1 Kepler and his “Harmonies of the World”

7.4.2 Interconnections

7.4.3 The ellipse and its composition

7.4.4 Conclusion

7.4.5 Bibliography

Graz and Kepler – working, living, and commemoration Bruno P. Besser, Mohammed Y. Boudjada, Max E. Lippitsch & Sonja Draxler

7.5.1 Kepler’s commemoration

7.5.2 Plaques for Johannes Kepler

7.5.3 Monuments at public places

7.5.4 Educational institutes named after Kepler

7.5.5 Buildings remembering Kepler

7.5.6 Artwork remembering Johannes Kepler

7.5.7 Further memorials

7.5.8 Bibliography

7.5.9 Original Documents from Johannes Kepler in Graz

8 Meso- and South America

TOLUPAN Universe: A Mesoamerican Cosmovision

Javier Mejuto & Eduardo Rodas-Quito

8.1.1 Introduction

8.1.2 Tomam Family

8.1.3 The Moons and the Suns

8.1.4 The Eclipses

8.1.5 The Stars

8.1.6 Discussion

8.1.7 Conclusions

8.1.8 References

Identification of Seri’s Constellations from Memory and Experience Arturo Morales Blanco, Alejandro Aguilar Zeleny, Julio Saucedo Morales & Raul Perez-Enriquez

8.2.1 Introduction

8.2.2 Memory and tradition

8.2.3 Family of Morales Colosio

8.2.4 Experiences

8.2.5 Seri’s Constellations and stars

8.2.6 Ethnographical relations

8.2.7 Zaamth or Crab

8.2.8 Haapjc or Deer hunter

8.2.9 Caamoilcoj or Wheel game

8.2.10 Coohamc or Women and their Husband

8.2.11 Stories in coiqui hitom

8.2.12 Conclusions

8.2.13 Bibliography

The calendrical period of 13 days as a basis to explain the solar orientation of architectural structures in Mesoamerica

Jesús Galindo Trejo

8.3.1 Introduction

8.3.2 Calendric-astronomical orientation

8.3.3 A general pattern of solar orientations in Mesoamerica

8.3.4 Observational proposal of the origin of trecena in the Mesoamerican calendrical system

8.3.5 Conclusions

8.3.6 References

Significant orientations of structures in Copán, Honduras

Hasso Hohmann

8.4.1 Introduction

8.4.2 Alignment of the Structures of Courtyard A

8.4.3 Creating a Hypothesis

8.4.4 One Possibility of How to Construct the Observation Point

8.4.5 Bibliography

The use of the Palenque ratio in the Lunar Series as a means to perform long-time calculations linking the ruling dynasty with its patron deities

Stanisław Iwaniszewski

8.5.1 Introduction

8.5.2 The use of the Lunar Series at Palenque

8.5.3 11960-day intervals at Palenque

8.5.4 Conclusions

8.5.5 References

Solar alignments and observational techniques in Mesoamerica

Ivan Šprajc

8.6.1 Introduction

8.6.2 Methodology

8.6.3 Results and Discussion

8.6.4 Conclusion

8.6.5 References

Meaning and Coincidences. A study into the archeoastronomy of Inka structures and their ritual significance

José Nicolás Balbi

8.7.1 Presentation

8.7.2 Conclusions

8.7.3 Bibliography

The Ceremonial Centre of Llactapata and the Coricancha of Cusco: A Comparison

John McKim Malville & Gery R. Ziegler

8.8.1 History and Observations

8.8.2 Llactapata’s Sector I

8.8.3 State Organized Pilgrimage

8.8.4 The Michihuayunca Ushnu

8.8.5 Conclusions

8.8.6 Bibliography

The “Intihuatana” of Saywite (Perú): an archaeoastronomical investigation on the role of time marker of the gnomon Silvia Motta, Adriano Gaspani, Nicolas Balbi, Gustavo Manuel Corrado, Sixto Giménez Benítez & José Luis Pino Matos

8.9.1 Introduction

8.9.2 Conclusion

8.9.3 Bibliography

9 Middle East and Eastern Asia

Kaaba a house built under the Sun

Reza Assasi

9.1.1 Kaaba a house built under the Sun

9.1.2 Bibliography

A Short History of Archeoastronomy in Japan: With focus on alignment studies of stone circle, settlement and burials

Akira Goto

9.2.1 Introduction

9.2.2 Pioneer Studies by the British

9.2.3 Burials and Stone Circles of the Jomon Period

9.2.4 Yayoi Settlement Studies

9.2.5 Kofun Orientation Revisited

9.2.6 The Recent Situation in Japan

9.2.7 Conclusion

9.2.8 Bibliography

10 Computational Astronomy

A Virtual Park of Astronomical Instruments

Georg Zotti

10.1.1 Introduction

10.1.2 Software Components for Interactive Simulation in Historical Astronomy

10.1.3 Serious Gaming under Stellarium’s Skies

10.1.4 Three Modes of Program Connection

10.1.5 Discussion and conclusions

10.1.6 Bibliography

11 Appendix

SEAC Conference in Graz – Information

11.1.1 SEAC 26th Scientific Committee

11.1.2 SEAC 26th Local Organizig Committee

SEAC 2018 in Graz: List of Participants

Index

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: [email protected], [email protected].

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:

ΤΗΝ ΔΕ ΓΗΝ ΕΙΝΑΙ ΜΕΤΕΩΡΟΝ ΥΠΟ ΜΗΔΕΝΟΣ ΚΡΑΤΟΥΜΕΝΗΝ ΜΕΝΟΥΣΑΝ ΔΕ ΔΙΑ ΤΩΝ ΟΜΟΙΑΝ ΠΑΝΤΩΝ ΑΠΟΣΤΑΣΙΝ

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 ῾Αρμονία 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, and structure means regularity, the repetition of similar units. This is true for the repetition of spatial elements, especially in architecture, as well as for temporal elements of social behaviour, especially in political and religious ceremonies and rituals. Astronomy as the oldest of natural sciences was always strongly connected with these regularities, providing the reliable background of repeated and therefor symmetric numbers to human societies. Astronomers were not hunting products of phantastic ideas in the ivory tower but had their place in the midst of the interests of society. Their observations and predictions were important for temporal and spatial structuring of daily life, providing orientation in a purely practical, but also in its spiritual meaning, thus connecting natural phenomena with astrological and religious interpretations of the world. The celestial sphere, regarded as the sky of astronomy and meteorology, as well as the heaven of divine numina, from the early times of Anaximander and Pythagoras till Copernicus and Kepler was equated with symmetry, harmony, and beauty. Till today this has been reflected in the structure of cultural creations, from architectural objects to musical forms. Symmetry and harmony are the only reliable features of human life, and thus are extraordinarily suitable to form the motto for this conference.

The organizers of the conference appreciate, that the motto was well accepted by the participants. About a quarter of the contributions alluded on the motto even in the title, many more mentioned it in the text. This proves that harmony and symmetry can stand their ground even in view of a now nearly complete evidence for a totally rational science.

0.1.1 References

POPPER, KARL RAIMUND: “Some notes on early Greek cosmology.” Henry Dan Broadhead Memorial Lecture, Christchurch, May 7, 1973. In: The world of Parmenides. London, New York: Routledge 1998.

ARISTOTLE: De caelo II, 13 296 a 11–21.

ARISTOTLE: Physics IV, 8 214b, 31–33. Translation by R. P. HARDIE & R. K. GAYE.

IAMBLICHUS: The life of Pythagoras, or, Pythagoric life. Translated by K.S. THOMAS TAYLOR. London: J. M. Watkins 1818.

ILIEVSKI, P.: “The origin and semantic development of the term harmony.” In: Illinois Classical Studies18 (1993), pp. 19–29.

0.1.2 Sponsoring

Support of this work by the following institutions is gratefully acknowledged:

1 Prehistoric Times