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

By Gudrun Wolfschmidt

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.

• Language: English
• Publisher: tredition
• Release date: Dec 29, 2020
• ISBN: 9783347146341

Book preview

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:

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 Studies 18 (1993), pp. 19–29.

0.1.2 Sponsoring

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

1 Prehistoric Times

Common features of megalithic stone rows in western Switzerland

Rita Gautschy

University of Basel, Switzerland

Email: [e-mail]

Abstract: Several recent investigations suggest that monuments such as temples, tombs or stone rows were orientated towards distinctive points on the horizon such as the directions of sunrise or sunset at the solstices or equinoxes (e. g. González-García & Belmonte 2015), or the rising or setting Moon during the lunistices. This paper investigates whether three accessible megalithic monuments in western Switzerland with stone rows consisting of ten or more stones show common features in orientation.

Keywords: megalithic stone rows; Switzerland; orientation; solstices; lunistices

1.1.1 Introduction

Similar to other countries, numerous megalithic monuments can be found throughout Switzerland, but only few of them are well known and easily accessible (Schwegler 2019). Concerning stone rows from Neolithic times, excavations were conducted at the following locations: Bevaix, Falera, Gorgier, Saint-Aubin, Yverdonles-Bains, Lutry and Sion. Except for Falera all of these locations are situated in western Switzerland. The sites of Bevaix, Saint-Aubin and Gorgier are located in close proximity to each other close to the boarder of Lake Neuchâtel. The stones from Bevaix and Saint-Aubin Derrière la Croix (Grau Bitterli et al. 2002) were transferred to a museum, the Laténium in Neuchâtel. The three stones in Gorgier (pierres de Guénégou) are tilted and surrounded by a forest. Their connecting line points into the direction of another standing stone (menhir du bois) at a distance of about 90 metres away (Schwegler 2019, http://www.ssdi. ch/Inventar/NE/2 023.10.pdf). The remains of another stone can be seen on top of a hill approximately 25 metres southwest of the tilted stones. It is unclear whether these five stones once belonged to the same site or to a different monument. Thus, the present investigation is limited to the following three stone rows, all of them consisting of ten or more standing stones (Fig. 1.1 left): the one in Yverdon-les-Bains (Clendy; Site 1) on the boarders of Lake Neuchâtel, the one in Lutry (La Possession; Site 2) close to the Lake Geneva, and the one in Sion (Chemin de Collines; Site 3) in the vicinity of the river Rhône. Each of these monuments is unique in some way. In Yverdon-les-Bains the site was covered by water for at least three millennia, hence one can be relatively sure that all stones of the final stage of the monument are still extant. In Lutry, excellent data concerning stratigraphy and the dating of the monument is available (Burri-Wyser et al. 2016). Finally, the stone row in Sion can be investigated in connection with its contemporary neighbouring cist cemetery and settlement (Moinat et al. 2007).

1.1.2 Method

It has to be stressed that the stones of all three monuments were re-erected (Yverdonles-Bains) or first moved several metres and then repositioned (Lutry and Sion). Thus, maps of the original locations of the stone sockets and measurements taken during excavation play a vital role in addition to the features still visible and measurable on site today. Azimuths and horizon altitudes were measured on site with the help of a compass-inclinometer which – theoretically – allows for a precision of the measurement to half of a degree. However, the azimuths determined on today’s positions of the standing stones turned out to match indications in the maps of their original location and with azimuth values obtained during excavation within 1° to 2°. The investigations were further hampered by the fact that in all cases it was impossible to take photographs and to create horizon panoramas based on these images from the original position of the monuments. In Yverdon-les-Bains and Lutry geographical latitude was kept constant and the panoramas photographed from the shore of the lakes. Afterwards, an artificial panorama based on Shuttle Radar Topography Mission (SRTM) data created for the original location of the monument (Deuschle 2019) was used for establishing the field-of-view in the panorama images. Due to this procedure – images taken several metres away from the original location – the accuracy of the azimuths in the resulting precision of the horizon panoramas is 2° to 3°. The precision of the altitude measurements is better, namely about 0.5° to 1°. Wherever possible, altitude measurements in a wide field-of-view were taken from the original stone positions and compared extensively with the values in the artificial panoramas. Nevertheless, only rough statements concerning the orientation of the monuments can be made.

Figure 1.1:

Left: Location of the three long stone rows in western Switzerland Right: Map of the megalithic monument in Yverdon-les-Bains

Drawing: Rita Gautschy, after Voruz (1992), p. 39. Drawing: Rita Gautschy, after Walker (2014), p. 13.

1.1.3 Site 1: Yverdon-les-Bains Clendy

The site in Yverdon-les-Bains was discovered in the 1880s during engineering works when the water level of Lake Neuchâtel sank several metres. But soon again it was covered by dense undergrowth. In 1981 the site was investigated by archaeologists. However, an official report of the investigation has never been published. Some of the stones are up to 4.5 metres tall and few of them are worked to resemble anthropomorphic forms. Concerning the dating of the monument, estimates range from 4500 BCE to 2000 BCE – these estimates are mainly based on the typology of the standing stones (Voruz 1992, 54–60). It is assumed that the site was reworked at least once. Thus, the layout at the moment of discovery rather reflects a later stage than the original design of the monument. The megalithic monument lies very close to several settlements that are dated from 5000 BCE onwards. Their location and the excavations done there allow for a rather precise reconstruction of the lake boarder in different times (Voruz 1992, 43). Around 850 BCE at the latest the site was covered by lake water until its discovery in 1887. This means that there is a reasonable chance that no stones were removed and that the context reflects the last stage of the monument’s use.

However, in 1986 the 45 fallen stones were re-erected by a local building company. Regrettably, most stones were aligned along straight lines. Fortunately, the exact original position of all stones had been mapped. Fig. 1.1, right, shows the location of the stones prior to their reposition (black) as well as their actual position on site today (grey). Azimuths were measured along the features visible on site today and afterwards compared with azimuth values which can be read from the original map (Voruz 1992, 47) and values measured on site by others (Walker 2014, 13; Weidmann 2016, 188).

It seems that the average orientation of the two almost 50 metres long stone rows – the so-called northern row and central row – has been respected during the process of repositioning of the stones: the orientations measured on site today accord with the indications in the map within one degree respectively. The original intersection of the northern and the central row lies on the eastern end of the northern stone row. This spot was originally occupied by a semi-circular feature – today the structure is straightened. Since the view into the northeastern direction from this spot was affected by the densely spaced stones this may imply that the south-western – open – direction was the more important one. There was a circular structure approximately in the centre of the site along the central row, but today these stones are part of the row. The three separate monumental groups of stones in the south-eastern part of the site that contain the largest stones are prominent. Today the site is crossed by the minor river Calamin. Taking photographs for a horizon panorama directly from the site turned out to be impossible – due to the dense vegetation and the buildings in the industrial zone of Yverdon-les-Bains almost none of the horizon is visible. Thus, the images for the panorama were taken from the shore of the lake, which is about 400 metres distant. Afterwards, an artificial panorama based on Shuttle Radar Topography Mission (SRTM) data created for the original location of the monument (Deuschle 2019) was used for establishing the field-of-view in the images. The northern stone row runs parallel to and very close to the boarder of Lake Neuchâtel in Neolithic times (Voruz 1992, 43). Additionally, it points at a landmark, the Dent de Vaulion (Fig. 1.2 above). Taking into account the altitude of the local horizon of about 2.5°, the Sun set approximately 50 days before and after the winter solstice behind the Dent de Vaulion in 3000 BCE (δ = –14.9° ± 0.8°). However, the orientation of this stone row was very likely motivated by landscape factors rather than by any astronomical-religious-agricultural ones. The azimuth of the central stone row neither points at a prominent landmark, nor can it be connected in any way with the setting Sun. But it coincides approximately with azimuths of the setting Moon at Major Southern Lunar Standstills (LSMS in Fig. 1.2 above; δ = –29.5° ± 0.7°). Hence, the orientation of this stone row may be motivated by some religious conceptions in connection with the Moon. Since the semi-circular structures are no longer extant in their original form, they have not been further considered in the current investigation.

Figure 1.2:

Above: Horizon panorama to the west of the megalithic monument in Yverdon-les-Bains.

Middle: Horizon panorama to the west of the megalithic monument in Lutry.

Below: Horizon panorama to the west of the megalithic monument in Sion.

Abbreviations used: WS – winter solstice; EQU – equinox; SS – summer solstice; LSMS – Major Southern Lunar Standstill; LSmS – Minor Southern Lunar Standstill; LSmN – Minor Northern Lunar Standstill; LSMN – Major Northern Lunar Standstill. The white arrows mark the orientation of the central (220°) and the northern (245°) stone row.

© Rita Gautschy.

1.1.4 Site 2: Lutry La Possession

The stones in Lutry were discovered standing in situ during construction works for a car park. They were excavated in 1984 and displaced a few metres from the location in which they were discovered. The results of the excavations have been published by Elena Burri-Wyser and her colleagues (Burri-Wyser et al. 2016). The stone row is composed of 24 standing stones that were contiguous, which results in the impression that they form a wall (Fig. 1.3 above). It was possible to trace the stratigraphy across the whole site and the different layers were radiocarbon-dated. Hence, it is known that all stones of the row were erected at the same time, namely between 2570 and 2350 BCE. The monument was built within an open landscape close to the river Lutrive. The standing stones were still frequented between 1500 and 1400 BCE (Burri-Wyser et al. 2016, 34), but prior to 1200 BCE the site was abandoned in the course of a period of natural forest densification.

The stone row is curvi-linear, straight for 14 metres and curved at its western end for about seven metres (Fig. 1.3 above). Possibly, the eastern end once contained a similarly curved part, but multiple flooding of the river Lutrive caused the destruction of the standing stones in this section of the monument. The monument faces Lake Geneva. The tallest stone once stood in the centre of the monument, but its top was destroyed during discovery. On either side of the tallest stone the stones were graded by height. All these stones were contiguous – the only discontinuity within the preserved assemblage is due to the removal of stone 24 on the eastern end which already happened in prehistoric times (Burri-Wyser et al. 2016, 50).

The stone row was erected parallel to the shore of the lake, but on a terrace 10 metres above the Lake Geneva, and perpendicular to the slope of the hill slightly to the west of the river Lutrive. Due to the neighbouring car park and houses it was impossible to photograph a horizon panorama on site – the images were taken about 200 metres off-site from the boarder of the lake. The straight part of the monument possesses azimuths of 122°/302°. The western end of the straight part points roughly towards the setting Sun at summer solstice (Fig. 1.2 middle; azimuth of 302°; δ = +23.7° ± 0.8° in 2570 BCE). Along the eastern horizon the orientation of the preserved curved part and of the straight part of the stone row do not coincide with any astronomically significant direction such as the rising Sun or Moon. However, if the archaeologists are correct and a symmetric reconstruction of the monument in the eastern part – destroyed by flooding – in analogy to the curved western part can be assumed, then the eastern part once may have pointed roughly into the direction of the rising Sun at winter solstice. Toward west the curved part of the stone row is oriented approximately into the direction of the setting Sun at the equinox (Fig. 1.2 middle; azimuth of 272°; δ = +2.8° ± 0.8° in 2570 BCE).

1.1.5 Site 3: Sion Chemin des Collines

Construction works in Sion in 1961 led to the discovery of one of the most important prehistoric sites in Switzerland. Excavations lasted until 1992. The Neolithic complex of the 4th millennium BCE at the site Sion Chemin des Collines includes a settlement, a cist cemetery and a stone row that was built at the southeastern end of the settlement (Baudais et al. 1989/90). The site lies close to the river Sionne that is nowadays culverted, and in the vicinity of the river Rhône. All monuments were removed from their original position and put into a park ca. 200 metres further west of their original position. The monument consists of a stone row with nine stones that is very roughly oriented east-west, and two additional stones that are displaced about 2 metres to the north (Fig. 1.3 below). To the south three shapeless stone blocs were found, it is doubtful whether they belonged to the monument (Baudais et al. 1989/90, 23). Alternatively, one could interpret the eastern end of the stone row as cromlechlike structure similar to the one that was found in the centre of the monument in Yverdon-les-Bains. Five of the standing stones possess engravings, amongst others a sun or a star. Due to the engravings and the level of the foundation stones the monument can be securely dated to the Middle Neolithic (ca. 4000–3500 BCE). Only five of the eleven standing stones are preserved intact – the remaining ones were damaged during discovery (Voruz 1990, 190).

Azimuth measurements taken on the relocated site agree within 1° with values read from the map drawn during excavations (Bocksberger 1964, 145) and with values measured by others (Weidmann 2016, 188). Hence, the orientation of the monument with respect to the cardinal directions has been preserved during the relocation process. Since the original position of the monument is no longer accessible and the offset amounting to ca. 200 metres westwards, the following analysis rests mainly upon the artificial horizon panorama (Deuschle 2019) created for the find spot of the monument. On the western side the stone row points in the direction of the Mont d’Orge – one of the closer mountain peaks in the vicinity of Sion (Fig. 1.2 below). Taking the altitude of the local horizon of about 11.5° into account, the Sun sets about ten days after the spring equinox and ten days before the autumn equinox at an azimuth of 264°(δ = 4.2 ± 1.1° in 4000 BCE). On the eastern horizon there is no coincidence with a prominent landmark. Taking the altitude of the local horizon of about 6° into account the Sun rises approximately three weeks after the spring equinox and three weeks before the autumn equinox at an azimuth of 84°(δ = 8.4° ± 1.0° in 4000 BCE). The neighbouring settlement and the cist cemetery are orientated differently: according to Denis Weidmann (2016, 188; 192; 194) the main axes of the cists scatter around the azimuth of the rising Sun at summer solstice and the main axis of the settlement roughly accords with the direction of the setting Sun at winter solstice. Since the stone row – which was located on the south-eastern end of the settlement – shows a different orientation I suggest that its orientation on the western side towards Mont d’Orge was intended.

Figure 1.3:

Above: Map of the megalithic monument in Lutry

Below: Map of the megalithic monument in Sion, Chemin des Collines

Above: Drawing: Rita Gautschy after Voruz (1990), p. 193.

Below: Drawing: Rita Gautschy, after Bocksberger (1964), p. 145.

1.1.6 Conclusion

The topographical situation of three long stone rows in western Switzerland was investigated and their orientation measured. It should be kept in mind that all these monuments were either re-erected (Yverdon-les-Bains) or moved by several metres and then repositioned (Lutry and Sion). Thus, azimuths measured on-site today may deviate slightly from the original ones. However, the measurements accord well (within 1° – 2°) with indications in maps drawn during the excavations. The most obvious similarity between the stone rows is their common connection with water – two of them were situated very close to the shore of a lake and in immediate vicinity of a small river, and the third one in Sion lies close to the rivers Sionne and Rhône. Thus, the presence of water was a decisive factor for the siting of the monument. One of the two stone rows in Yverdon-les-Bains follows the ancient shore of Lake Neuchâtel. It seems that the function of the northern stone row in Yverdon-les-Bains was to mark the border between water and earth, a liminal space – physically and maybe also spiritually – that allows trespassing from outside to inside, from exclusivity to inclusivity or vice versa. It may also have been a liminal place between the death and the living: since over 90% of the known Neolithic sites in Switzerland are settlements it has been proposed that amongst other things people were buried in water, thus leaving no archaeological traces (Doppler 2017, 172). In Lutry, the stone row is situated about 10 metres above Lake Geneva, but very close to the river Lutrive. The overall appearance of the monument suggests that the water of the lake and the entities associated with it should be blocked and kept outside. Maybe it is no coincidence – and perhaps explains the very unusual contiguous design of the standing stones – that this monument was erected at a time when the lakeside dwellings were abandoned due to rising lake water levels. In Sion, the stone row was situated at the south-eastern end of a necropolis and a settlement. It was probably erected parallel to the river Rhône flowing in a distance of about 500 metres today. Hence, in all three cases the stone rows are presumably oriented parallel to a lake or a broad stream and at the same time perpendicular to a small river. Connections with water bodies and courses have also been recognised for some Irish tombs and Welsh cairns (Prendergast (2016, 14) and references therein). The second similarity between the stone rows is a supposedly preference of the western horizon: the northern stone row in Yverdon-les-Bains and the one in Sion point to a landmark on the western horizon. The sample of known stone rows in Switzerland is generally small – nine in total up to now (Schwegler 2019) – and the number of those that are still existing (five) even smaller. Hence, it is not surprising that concerning the possible intended astronomical orientation of these monuments, no coherent picture emerges. The orientation of the central stone row in Yverdon-les-Bains coincides approximately with the direction of the setting Moon at Major Southern Lunar Standstills. Lutry may be explained with an interest in the points of sunrise and sunset at the solstices and equinoxes. Finally, the direction of the stone row in Sion very roughly concurs with the points of sunrise and sunset on the local horizon at the equinoxes. In my opinion the decisive factor for the orientation of these monuments was their position with respect to the adjacent bodies of water – parallel to a lake or a broad stream and perpendicular to a small river. Astronomical orientation played a secondary role only, if any at all.

Acknowledgements

I thank Frank Prendergast for helpful comments, suggestions and language improvements of the first draft.

1.1.7 Appendix

Table 1.1:

Summary of all data discussed in the text

1.1.8 Bibliography

BAUDAIS, D.; BRUNIER, C.; CURDY, P.; DAVID-ELBIALI, M.; FAVRE, S.; GALLAY, A.; MAY, O.; MOINAT, P.; MOTTET, M.; VORUZ, J.-L. & A. WINIGER: ‘Le néolithique de la région de Sion (Valais). Un bilan.’ In: Bulletin du Centre Genevois d’Anthropologie 2 (1989–1990), pp. 5–56.

BOCKSBERGER, O.-J.: ‘Découvertes archéologiques récentes à l’ouest de Sion: nouvelles données sur le néolithique valaisan.’ In: Bulletin de La Murithienne 81 (1964), pp. 141–152.

BURRI-WYSER, E.; CHEVALIER, A.; FAVRE, S. & A. STEUDLER (eds.): Destins des mégalithes vaudois. Lausanne (Cahier d’archéologie romande; 159) 2016.

DEUSCHLE, U.: Create a panorama, http://www. udeuschle.selfhost.pro/panoramas/makepanoramas_en.htm (last accessed 11 July 2019).

DOPPLER, T.: ‘Einblicke in individuelle Lebensgeschichten und kulturelle Praktiken.’ In: Lebensweisen in der Steinzeit. Ed. by B. RÖDER, S. BOLLIGER SCHREYER & S. SCHREYER. Baden 2017, pp. 172–1176.

GONZALEZ-GARCÍA, A. CÉSAR & JUAN A. BELMONTE: ‘Orientation of Hittite Monuments.’ In: Handbook of Archaeoastronomy and Ethnoastronomy. Ed. by CLIVE L. N. RUGGLES. New York 2015, pp. 1783–1792.

GRAU BITTERLI, M.-H.; LEUVREY, J.-M. & J. RIEDER: ‘Zwei neue Fundgebiete mit Megalithen am Nordufer des Neuenburgersees.’ In: Bulletin d’Archéologie Suisse 25 (2002), pp. 20–30.

MOINAT, P.; BAUDAIS, D. & C. BRUNIER: ‘Les sites de l’avenue Ritz et du chemin des Collines: deux exemples de nécropole en ville de Sion.’ In: Les cistes de Chamblandes et la place des coffres dans les pratiques funéraires du Néolithique moyen occidental. Ed. by P. MOINAT & P. CHAMBON. Lausanne (Cahier d’archéologie romande; 110) 2007, pp. 277–296.

PRENDERGAST, F.: ‘Interpreting megalithic tomb orientation and siting within broader cultural contexts.’ In: Modern Archaeoastronomy: From Material Culture to Cosmology. Ed. by D. BROWN. Journal of Physics: Conference Series 685 (2016), pp. 1–25.

SCHWEGLER, U.: SSDI: Schweizerische Stein-Denkmäler. Inventar, http://www.ssdi.ch (last accessed 11 July 2019).

VORUZ, J.-L.: ‘Litholâtrie néolithique: les statues-menhirs de Suisse romande.’ In: Mégalithisme et Société. Table ronde C.N.R.S. des Sables d’Olonne (Vendée) 2–4 Novembre 1987. Ed. by R. Joussaume. La Roche sur Yon 1990, pp. 187–207.

VORUZ, J.-L.: ‘Hommes et Dieux du Néolithique: les statuesmenhirs d’Yverdon.’ In: Jahrbuch der Schweizerischen Gesellschaft für Ur- und Frühgeschichte 75 (1992), pp. 37–64.

WALKER, R.: Megalithanlage Yverdon-les-Bains-Clendy. Analyse des Designs und möglicher archäo-astronomischer Aspekte, Version 4.7, 05/2014, http://www.ursusmajor.ch/downloads/megalithanlage-yverdon-clendy-v-4_7.pdf (last accessed 27 December 2018).

WEIDMANN, D.: ‘Des questions d’orientation.’ In: Destins des mégalithes vaudois. Ed. by E. BURRI-WYSER, A. CHEVALIER, S. FAVRE & A. STEUDLER. Lausanne (Cahier d’archéologie romande; 159) 2016, pp. 187–196.

The summer solstice sun at Lepenski Vir

Aleksandra Bajić & Hristivoje Pavlović

Association for research in Archaeoastronomy and Ethno astronomy Vlašići, Belgrade, Serbia

Email: [e-mail]

Abstract: Lepenski Vir is a late Mesolithic settlement, situated on the right bank of the Danube in the Iron Gate Gorge, which was flourishing by the end of the seventh millennium BC. It is famous for the unusual trapezoidal buildings and the oldest monumental sculptures in Europe. The site was discovered in 1965. In 1972 it was moved 100 m northwest from the original position and to a 28.81 m higher elevation to be preserved from flooding by the Danube following the construction of the Kladovo dam. According to the available maps, the vast majority of the houses were oriented towards the steep volcanic hill named Treskavac, at the opposite side of the Danube, in Romania. This paper will demonstrate that this orientation was actually towards an astronomical event: summer solstice sunrise. As seen from any point in the original Mesolithic settlement, as well as from the majority of the houses, the summer solstice Sun rose on the flattened hilltop. Therefore, the astronomical event was an important criterion to choose the location of the settlement.

Keywords: Lepenski Vir; Treskavac; solstice; sunrise, Mesolithic, Archeoastronomy

1.2.1 Introduction

A spectacular double sunrise at dawn on summer solstice can be observed from the new position of the settlement. The first sunrays appeared in a narrow notch on the horizon on 21 June, 2017, 06:09 local (summer) time. The solar disc rolls up the north slope of Treskavac Hill for a minute or two, then disappears behind the flat hilltop (Fig. 1.4).

Four minutes later, it rises again at the top. Thus, thanks to the topography of the local horizon, one can determine the summer solstice.

Knowing that 8,200 years ago, the Earth’s axis was significantly more inclined in respect to the ecliptic than it is today and the summer solstice Sun rose more than 1° closer to the north, the phenomenon of double sunrise was visible from a certain position to the south (or lower), closer to the original position of the Mesolithic settlement. Although the original position is submerged now and the settlement relocated, a precise technical documentation on its relocation still exists, developed by a team of experts from the Institute for the Protection of Cultural Monuments of Serbia (Čanak-Medić, 1970, p. 8). This documentation, together with the achievements of modern geodesy and accurate (satellite) geospatial positioning, enables archaeoastronomical analysis of the site.

1.2.2 Methodology

1. Modern geodetic system WGS/UTM 84 (Serbia belongs to UTM zone 34 N), with the geographical coordinates expressed in meters, makes it possible to calculate the azimuths and the distances between any pair of points for which the coordinates are known. Therefore, an accurate geo-spatial survey (by Novatel GNSS device, with the accuracy of ±15 cm) was performed at the centre of the relocated settlement (the ZERO point), at the junction of its longitudinal and transversal axis (as determined by Dragoslav Srejović, the archaeologist, who discovered and explored Lepenski Vir).

Figure 1.4:

The first sunrays on June 21st, 2017

(Photo by Stanko Kostić, from 44.557142° N 22.026590° E).

Elevation: E0 = 90.80m above sea level (ASL)

Thus, it became possible to draw the network of WGS/UTM coordinates onto the map of relocation,¹ created in 1969 by the team of surveyors of the Institute for the protection of cultural monuments of Serbia, and the geographical coordinates for each particular building in the original settlement were reconstructed. The data on the original elevations were preserved in the technical documentation on relocation. All these buildings were moved to 28.81 m higher position.²

2. On April 14th 2018, an astronomically referenced geodetic survey was performed, from the standpoint (Point no. 2) on the Danube bank, as close as possible to the original Mesolithic settlement, 6 m behind the house no. 72. The coordinates of the standpoint were surveyed by the same GNSS device, with the accuracy of ±15 cm:

Elevation: E2 =70 m ASL

(includes the theodolite’s height, 1.6 m)

Figure 1.5:

The map of relocation

The target horizon points are shown in Fig. 1.6.

Figure 1.6:

Distinctive points on Treskavac

The results are at the following table:

3. The hill named Treskavac is a very steep volcanic cliff on the opposite side of the Danube (in Romania), divided by nature onto several segments with several almost upright cracks. At the top, there is a narrow path which actually forms the horizon. During the course of astrogeodetic survey, Rejhan Zurapi, mathematician and alpinist, climbed the hill. While walking along its cliff with a GPS device (Garmin nuvi 2360) in his hand, he was observed through the theodolite’s telescope. As soon as he found himself at some of these distinctive points (marked A, B, C, D, E, F and G), he was asked by phone to record its coordinates:

Elevation: EA = 564.7 m ASL (calculated)

Elevation: EB = 652.28 m ASL (calculated)

Elevation: EC = 661 m ASL (calculated)

Elevation: ED = 662.34 m ASL (calculated)

Elevation: EE = 654.13 m ASL (calculated)

F. The southern notch wasn’t approachable, so it wasn’t positioned. Rajhan couldn’t get there, it was too dangerous.

Elevation EG = 645 m ASL(calculated)

4. Based on these data and on the coordinates and elevations recorded (reconstructed) on the map of relocation, we have calculated the azimuths³ and horizon altitudes of distinctive geological features of Treskavac, valid for an observer sitting at particular points (houses) in the original settlement. Since the horizon is less than 2500 m far, the correction for the Earth’s curvature was unnecessary.

5. Lepenski Vir was dated (Bonsall et al. 2000) to the period between 8250–7900 years before present (cal. BP). According to this dating, the Earth’s axial tilt was calculated using Laskar’s formula (Laskar, J. 1986), it was 24.217° – 24.208° and it was equivalent to the summer solstice Sun’s declination.

Now, the astronomical formula can be applied, to calculate the declination corresponding to any calculated azimuth as seen from any of the houses:

δ = arcsin(sin φ sin h + cos φ cos h cos A)

h = altitude of the horizon

(corrected for refraction, H – r) φ = geographical latitude of the standpoint (in the house)

A = Azimuth of the direction from the standpoint to the target point on the horizon

δ = declination

In calculating the declinations corresponding to azimuths, horizon altitudes were corrected for the values of atmospheric refraction, calculated by formulae given by Schaefer (1989–1993, 79) & Hawkins (1968, 53).

Thus, five houses in the original settlement were tested: the northernmost⁴ one (no. 28), the southernmost one (no. 65), the central house (no. 54), the house at the highest elevation (no. 60) and the lowest one (no. 63).

1.2.3 Results

As observed from any of the five houses tested, the summer solstice Sun rose on the flattened top of Treskavac, between its central crack (C) and the southern cliff (G).

The summer solstice sunrise as seen from the northernmost house (no. 28) 8,200 years ago:

Elevation: E28 = 62.9 m ASL

(includes +0.8 m for sitting observer)

Figure 1.7:

Summer solstice sunrise as seen from the house 28

The summer solstice sunrise as seen from the southernmost house (no. 65), 8,200 years ago:

Elevation: E = 63.41 m ASL

(includes +0.8 m for sitting observer)

Figure 1.8:

Summer solstice sunrise as seen from the house 65

If the observer moved only a couple of meters to the south of the house no. 65, he wouldn’t be able to observe the summer solstice sunrise on the volcanic rock, the Sun would rise somewhere out of the top. No. 65 (the southernmost one) was different from all other houses: it was the only one with a fence, and it was made of stone slabs. The fence gave it the additional impression of immutability and steadiness. The summer solstice sunrise as seen from the lowest house (no. 63) 8,200 years ago:

Elevation: E63 = 60.5 m ASL

(includes +0.8 m for sitting observer)

The summer solstice sunrise as seen from the central house (also the biggest one, no. 54) 8,200 years ago:

Elevation: E = 61.6m ASL

(includes +0.8 m for sitting observer)

The summer solstice sunrise as seen from the highest house (no. 60) 8,200 years ago:

Elevation: E = 67.8 m ASL

(includes +0.8 m for sitting observer)

Figure 1.9:

The map of Lepenski Vir, with the tested houses

As seen from any of the houses in the original settlement oriented towards Treskavac, (and this is the orientation of ca. 78% of those, according to the measurements of Lj. Babović (Babović, 2007, p. 245), the summer solstice Sun rose on the flattened top of the hill, between C and G.

As seen from any particular position inside the limits of the original Mesolithic settlement (out of the houses) the summer solstice Sun rose on the flattened top of the volcanic hill, there are no exceptions.

Our calculations demonstrated that the double summer solstice sunrise phenomenon, which inspired our research, was not visible from the original Mesolithic settlement itself. However, it was possible to observe it from several points (a row of points), some of which are now submerged. The closest accessible hypothetical observation point is at 72 m ASL, about 44 m north of the settlement. This area was not excavated. Therefore, any conclusion that a double solstice sunrise may have had cultural significance for the inhabitants of the Mesolithic Lepenski Vir remains an open question pending future archaeological investigation.

1.2.4 Observation

One might imagine an observer sitting at the back of his house, behind the hearth, watching Treskavac carefully. The hill is naturally divided into several segments by few almost upright cracks.

The observer who was sitting in the northernmost house was the first one to start observing, to see the sunrise on the flattened top of Treskavac. As soon as that happened, he would inform his neighbours. Every following day, more and more observers were able to see the sunrise at the top of the volcanic rock from their houses. Then comes the day, when the person sitting in the southernmost house (no. 65) could see the same. Everyone knows that day: The Sun has returned (home).

The trapezoidal shape of Treskavac is similar to the shape of houses in Lepenski Vir. Many archaeologists noticed that similarity, including D. Srejović. The House of the Sun (Treskavac) could be the model for people’s houses.

Figure 1.10:

Trapezoidal shape of the hill

When the sunrise at the top of the hill was visible from all over the settlement, a holiday (or a ritual) began. It lasted for several days, until the observer from the southernmost house announced that the Sun had begun to descend from the hill and made its way downstream to the south.

After the summer solstice, the Sun needs to change its declination for –0.327° (–190′37″) so that the centre of the disk emerges at the southern cliff (G). In that moment, it was at the last point where it is still at the top of the hill, as seen from the southernmost house in the original settlement. This is actually the difference between the Sun’s solstice declination and the declination of the southern cliff (G), observed from the house no. 65 (Fig. 1.8). It is only ca. 4′ more than the Sun’s radius. When the centre of the solar disk was on the southern cliff, the right-hand half would already be beyond the flattened top of the hill. Therefore the difference is reduced to just four arc minutes. We are aware that there are no solar ephemeris data for such a distant past. In 2018, the Sun’s declination decreased for four arch minutes in six or seven days after the solstice. We assume the holiday lasted that long.

Figure 1.11:

The idealized geometry of a house. The entrance provides a ca. 20° view for the observer

But the observation lasted longer, as long as it takes for the Sun’s declination to increase ca. 2°, which would roughly correspond to a period of a month before the summer solstice.

The entrances to the houses are wide enough to allow an observer to see ca. 20° of the horizon (±10° of the axial azimuth of the house). In a smaller house, the view can be even wider, because the entrance is closer to the observer.

This practically means that the axial azimuth of the house needs not be accurately hit during the construction to allow the observer to see the summer solstice sunrise at the top of Treskavac. A ± 10° error was tolerable.

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

According to Srejović, a total of 85 houses were discovered in Lepenski Vir. As seen from the tested ones, the summer solstice Sun rose at the azimuth of ca. 69.5°. It was possible to observe the event from any house with the axial azimuth of 69.5° ± 10 – 11°. There are 67 houses in the settlement (78.82%) fulfilling this condition.

The whole Mesolithic settlement was facing both the Danube and Treskavac. The direction of its transverse axis, as drawn by Dragoslav Srejović, is at the azimuth A = 68.5°, measured on the map (Fig. 1.9). With the correction for meridian convergence (+43′15″) it is very close to the summer solstice sunrise direction.

Deer antlers were found in all houses, and were also a frequent grave item in Lepenski Vir, pointing to certain ritual significance. Those are not made of keratin, but of bone and reach their maximal size in the second half of June, close to the summer solstice. In that period, the animals scratch their antlers on tree trunks, trying to take off the skin envelope which previously provided the nutrition and growth of the bone mass, leaving traces of such activity on the tree bark. The hunters search for trophy deer antlers at the end of June even in present times, knowing that those are fully developed and not yet damaged. Calendar significance of deer antlers has already been reported about (Gonzalez-Garcia et al. 2008).

There is some archaeological evidence that the inhabitants of Lepenski Vir were able to catch sturgeon (Srejović, 1969, p. 149), the giant fish, which used to come to this area seasonally, from Black Sea. It was travelling upstream in spring, spawning at the beginning of summer and then it was swimming downstream back to Black sea. The seasonal moving of the sunrise point on the eastern horizon is in a good correlation with the moving of sturgeon. When the giant fish was moving upstream in spring, the point of sunrise was also perceived to move upstream, and vice versa: when the giant fish was moving downstream in autumn, the point of sunrise was also moving downstream. Thus, the Sun could be perceived as a giant celestial fish, moving the same way as the giant Danube fresh water fish. Such a perception could explain the appearance of the monumental portrait sculptures, with the faces fishlike and humanlike at the same time. These are always rounded, being made of river boulders, associating to the round form of the Sun.

Srejović noticed the gradual movement of the settlement itself. During its flourishing time it was moving to the North and to the higher elevations (Srejović, 1969, p. 47). Now, when it is known that, as seen from the whole settlement, the summer solstice Sun rose on the top of Treskavac, such moving becomes logical: moving to the South was not possible if the inhabitants wanted to see this astronomical event on the top of the hill. Moving to the lower position was inadvisable; the lower positions were in danger to be seasonally flooded by the river. So, the only directions where the settlement could move were to the North and upwards, as there still was some space on the northern part of Treskavac to see the summer solstice sunrise on its top.

Some traces of cumulative symbolic records, as the term was understood by Alexander Marshak (1972), were found in Lepenski Vir. Few stone artefacts, named sceptres, were found, with carved notches on their surface, which could be counted.

Such a record on a stone artefact suggests a kind of important permanent document, produced to last throughout generations. Some daily notes, considered less important, could have been easily carved on the softer material, such as wood or clay.

One of these sceptres has 29 (14 + 14+1) notches carved on its upper surface, suggesting the number of days in a synodic lunar cycle. So, it can be concluded that the inhabitants of LepenskiVir were able to count the days between some (astronomical) events. Unfortunately, some of these artefacts were broken, so the number of notches on their surface can’t be counted with certainty.

Figure 1.12:

A sceptre with six carved notches on its lower surface, found in the house no. 50; the note could represent the number of lunar months between two solstices

(Srejović and Babović 1983, p. 186).

According to Dragoslav Srejović,

"… the dance of light and shadow in Lepenski Vir reaches sometimes the level of hierophany."

Figure 1.13:

The pyramid

(Photo by Stanko Kostić)

And he was right: The summer solstice sunrise on the top of Treskavac looks really magnificent: The hill produces a huge dark shadow, resembling a pyramid with the fire on its top, even when the sky is cloudy (Fig. 1.13).

1.2.6 Conclusions

The summer solstice appears to have been an important day in the culture of Lepenski Vir. Perhaps it was not one day only but few days, when the people celebrated the Sun’s returning. The holyday was the beginning of a new cycle. The community affirmed its cohesion by performing certain rituals. That day (or one of those few days) could have been the starting point for some sort of solar calendar.

Moreover, the presence of buildings that are not oriented to the sunrise behind Treskavac indicates the possibility that their inhabitants were interested in some other (lunar?) point(s) on the local horizon. Therefore, our archeoas-tronomical interpretation of the site remains preliminary pending future research to resolve the question of additional alignments.

1.2.7 References

BABOVIĆ, LJUBINKA: Svetilišta Lepenskog Vira – mesto, položaj i funkcja. Beograd: Narodni muzej 2007.

BONSALL, CLIVE; RADOVANOVIC, IVANA; ROKSANDIĆ, MIRJANA; COOK, GORDON T.; HIGHAM, THOMAS & CATRIONA PICKARD: ‘Dating burial practices and architecture at Lepenski Vir.’ In: BONSALL, C.; RADOVANOVIĆ, I. & V. BORONEAN (eds): The Iron Gates in Prehistory. Oxford: Bar International Series, Archaeopress 2008, pp. 175–204.

ČANAK-MEDIĆ, MILKA: ‘Projekat za spasavanje Lepenskog Vira.’ In: Saopštenje VIII, Glasilo Republičkog zavoda za zaštitu spomenika kulture. Beograd (The saving project for LepenskiVir) 1970.

GONZALEZ-GARCIA, ANTONIO C.; GARCIA QUINTELA, MARCO; BELMONTE, JUAN A. & MANUEL S. ESTEVEZ: ‘Calendrical deer, time reckoning and Landscape in the Iron-Age North-West Spain.’ In: Astronomy and cosmology in folk traditions and cultural heritage. Archaeologia Baltica [Klaipeda] 10 (2008), pp. 6–70.

HAWKINS, GERALD, S.: Astro-archaeology. In: Vistas in Astronomy 10 (1968), pp. 45–88.

LASKAR, JACQUES: ‘Secular terms of the classical planetary theories using the results of general theory.’ In: Astronomy and Astrophysics 157 (1986), pp. 59?70.

MARSHACK, ALEXANDER: The Roots of Civilization: The Cognitive Beginnings of Man’s First Art, Symbol and Notation. New York: McGraw-Hill 1972.

SCHAEFER, BRADLEY: ‘Astronomy and the limits of vision, Archaeoastronomy.’ In: The Journal of the Center for Archaeoastronomy 11 (1989–1993), 78–90.

SREJOVIĆ, DRAGOSLAV: Lepenskivir. Beograd: Srpska književna zadruga 1969.

SREJOVIĆ, DRAGOSLAV & LJUBINKA BABOVIĆ: Umetnost Lepenskog Vira. Beograd: Izdavački zavod Jugoslavia i Narodni muzej 1983.

1 The map of relocation was created by Martinović, Stanković and Janjić, engineers of geodesy, in the scale 1:200. It contains both, the position of houses in the original settlement and the position of relocation.

2 The available literature says that the new position was 29.5 m higher. Actually, it was the original elevation difference, but it decreased when the surface layer of soil was removed from the area where the settlement was to be transferred.

3 The azimuths were calculated from UTM coordinates of and corrected for grid (meridian) convergence.

4 Actually, the house no. 28 is not the northernmost one. At the end of the sonde, ca. 40 m to the north of it there are two houses more, no. 68 and no. 71. These houses were discovered in August 1968 and were not relocated. So, these were not drawn on the map of relocation (Fig. 1.5).

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

Alexey Stoev¹, Penka Maglova¹, Vassil Markov², Dimitriya Spasova² & Anton Genov²

1. Space Research and Technology Institute, Bulgarian Academy of Sciences, Stara Zagora Department,

2. South West University Neofit Rilski, Blagoevgrad

Email: [e-mail], [e-mail], [e-mail]

Abstract: In this paper we