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An interpretation of the Nebra disc
Em´
ılia P´
asztor1&CurtRoslund
2
The Nebra disc is one of the most sensational European discoveries of the decade. It appears to
carry symbols of the sun, moon and stars wrought in gold on a flat bronze disc just over a foot
across (320mm). It is not only very strange, but, famously, appears to be winking, initially raising
the suspicion that it may be a hoax. Scholars have, however, claimed it firmly for the Bronze
Age, and the debate now moves to the matter of its meaning. Here the authors offer a subtle
interpretation that sees it as the shamanistic device of a local warrior society.
Keywords: Europe, Bronze Age, Germany, Sachsen-Anhalt, Nebra, shield, religion, shaman
Discovery, description and authenticity
As is often the case nowadays, the Nebra disc was not found by archaeologists but by two
treasure hunters in the summer of 1999. The disc was retrieved by Swiss police in 2002 and
returned to Germany, where it is now on display in the Landesmuseum f¨
ur Vorgeschichte in
Halle. When the treasure hunters were apprehended, they were persuaded to reveal the spot
where they had found the disc, and pointed out the 252m-high hilltop called Mittelberg
in Ziegelrodaer Forst near the small village of Nebra in Sachsen-Anhalt. With the help of
other datable objects that the treasure hunters had found at the same place, the disc has
been dated to c.1600 BC or the Middle Bronze Age.
The bronze disc (Figure 1a-c) weighs 2kg and has a diameter of 320mm, a thickness of
4.5mm at its centre but thins out to 1.5mm at the rim of the disc. The centre of the disc is
dominated by two gold plates, each about 100mm across. One describes a full circle while
the other forms a crescent (lune). The surface of the disc is further adorned with small,
round, thin gold spots (measuring 10mm in diameter) of which there were originally 32.
Two of these have been removed and one slightly adjusted to give room for two arcs of thin
gold strips lining the rim of the disc. One of these arcs is now missing. A third, shorter
and curved gold strip is placed along the rim between the two long gold arcs. The thin arcs
lining the rim of the disc subtend nearly 90 degrees each or a quarter of a circle with a radius
of 160mm. The remaining shorter gold strip on the rim between them measures about 120
degrees or a third of a full circle with a radius of 90mm. The profile of the disc is almost flat
(Figure 1c) and the back of the disc shows no trace of an attachment (Figure 1b). However
the rim of the disc is punctuated by 38 (?) pin-holes which may indicate that it was sewn
onto fabric or nailed onto wood.
The authenticity of an important archaeological find must be established beyond all
doubt, especially for a find with a somewhat obscure provenance. The Nebra disc has
1Matrica Museum, HU-2440 Szazhalombatta, Hungary (Email: pasztore@enternet.hu)
2Department of Astronomy, Gothenburg University, SE-41296 Gothenburg, Sweden
Received: 16 June 2006; Accepted: 6 September 2006; Revised: 9 October 2006
antiquity 81 (2007): 267–278
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An interpretation of the Nebra disc
Figure 1. a. The Nebra disc adorned with gold plates that might represent the sun, the moon and stars. b. Back view.
c. Profile.
therefore gone through a series of rigorous laboratory tests to prove that it is genuinely
ancient (Pernicka 2004), although in spite of this, the object still attracts some sceptical
comments (Schauer 2005). According to the metallurgical investigation, the relationship
between different isotopes of lead points to the eastern Alps as a possible source for the
copper used in making the bronze. The bronze of the disc contains an unusually low tin
content of 2.5 per cent (Pernicka 2004). The high silver content of more than 20 per cent
in the gold strips indicates that the gold was mined in Transylvania, except for the shorter
peripheral curved gold strip which has a comparatively low silver content of 13 per cent.
The source for this gold has not been identified.
The eastern Alps and Transylvania provided copper and gold, respectively, not only for
central but for northern Europe as well (Liversage & Northover 1998: 137-8). According to
the metallurgical examination of early Danish Bronze Age craftwork, similar bronze-making
processes were used in both regions, although neither imports nor influences from the central
European Aunjetitz culture (2300-1600 BC) can be traced in Denmark in the metalwork
of Bronze Age Period IA (1700-1600 BC; Vandkilde 1998: 128, 131-2.). Vandkilde even
argues that ‘in this period the [metal producing]central area around Halle disappears, locally
leaving a social and cultural vacuum that re-echoes up the northern peripheries’ (Vandkilde
1998: 133).
While the ornament is not itself very characteristic, the short strokes and the parallel
bands on the curved strip are rather characteristic features on Danish metal finds from the
Bronze Age (Kaul 1998). This provides some support for the idea that the Nebra disc might
have been produced in the cultural region of the Nordic Bronze Age or by smiths from that
area.
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Sun, moon and stars?
Almost immediately after the disc had been returned to Germany, it was suggested that
the round gold images that embellished the green corroded bronze disc represented stars,
the sun and the moon (Meller 2002; Schlosser 2002). If this interpretation is correct, it
would place the disc among the most important finds from Bronze Age Europe, making a
close investigation of the basis for an astronomical explanation imperative. Intuitively, one
identifies the full circle in the centre of the disc with the sun or the full moon and the
semicircular lune with the lunar crescent of the new moon or old moon. By coincidence,
the angular size of the sun and the moon in the sky is the same. On the disc, however,
it is clearly noticeable that the radius of the outer arc of the lune is greater than that for
the ‘sun’. The goldsmith may here have been misled to exaggerate the radius of the lunar
crescent due to a well-known optical illusion causing the angular length of the outer arc of
alune to appear longer than in reality and the radius to be overestimated (Minnaert 1940:
105).
If the circular object represents the sun, its style is unusually plain. On archaeological
finds of the Aunjetitz and other contemporary cultures or from the areas of the eastern Alps
and Transylvania, the sun is always richly decorated with concentric circles, and spirals and
often displays radial rays (Neugebauer 1987: Abb. 51, 54; Probst 1996: 101, 210, Figures
24-5; Kaul 2004: 56-7; Kov´
acs 1991; Schwarz 2004: 179; Zipf 2004: 75-6). Some of the
symbols on archaeological finds believed to be the sun might actually have been of the full
moon; this could be the case for the Nebra disc as well. Unfortunately, the portrayal of the
lunar crescent like the one on the disc seems to be rather rare. A single depiction of it is
known on a golden bowl but from the later period of the Bronze Age (Green 1993: Figure
438), although jewellery in the unique shape of a crescent (lunulae) was produced during
this period or near it. The most prominent arm rings ending with lunulae were produced
from Transylvanian gold (Schumacher-Matth¨
aus 1985: Taf. 24; Kov´
acs 1999: Figures 26-7).
If the larger central objects represent the sun and the moon, they are not astronomically
correct. Although both the sun and the moon can be seen at the same time in the daytime
sky, the convex, illuminated, part of the moon is always turned towards the sun and not away
from it as on the disc, where the sun faces the concave side of the moon. The scene might be
suggested as representing an eclipse, but this is highly unlikely, since there is not the slightest
hint in the archaeological record that Bronze Age people understood the underlying cause
for an eclipse of the sun or the moon.
The small round gold spots on the disc have generally been thought of as stars, and one
cluster of seven spots lying between the ‘sun’ and the ‘moon’ has naturally been associated
with the Pleiades (Schlosser 2002; 2003).However, the other spots are spaced too regularly
on the disc to represent the stars of the firmament (Schlosser 2004: 44). Figure 2 shows
that, with the exception of the ‘Pleiades’, the spots are evenly spaced with respect to a grid
(in this case of 51mm). Such regular spacing implies that they were set out freehand to
make an aesthetically pleasing picture. Figure 3 shows the position of the same number of
real stars centred on the Pleiades, all brighter than visual magnitude 3.0 which is usually
the brightness limit used for delineating constellations. The stellar chart shows the uneven
distribution of real stars in the sky. If the goldsmith intended to produce an accurate chart
269
An interpretation of the Nebra disc
Figure 2. Drawing of the Nebra disc overlaid by a
network of squares with sides measuring 51mm.
Figure 3. Chart of a field centred on the Pleiades con-
taining all stars brighter than visual magnitude 3. 0.
The field measures 105 degrees in right ascension and
70 degrees in declination. The dashed line marks the
celestial equator and the open circle the vernal equinox
in 1600 BC.
of the region around the Pleiades, he would
hardly have omitted the conspicuous Orion
constellation to the bottom left and the square
of Pegasus to the right.
Bright stars have a distinctive radiating ray
pattern (Navarro & Losada 1997), which may
feature on symbols for stars from the first part
of the Bronze Age, although these are difficult
to distinguish from symbols for the sun (Ko´
os
1988: 1. kep; Kovacs 1991: Abb. 2, Abb. 5;
Probst 1996: 148, 197, 221). However, the
plain style of the round gold plates (the single
big one and the small spots) recalls cup-marks
and circles in rock carvings of the Nordic
Bronze Age. The plain circles and the cup
marks predominate on rock–carving sites in
Denmark, while they decline in number when
one goes further north (Malmer 1981: 68-9,
75). Depicting the stars as round objects
might therefore have been intentional.
Horizons, rainbows or boats?
According to Schlosser (2002) the two arcs of
gold framing the rim of the disc may show
how far the sunrise and the sunset move along
the horizon from one solstice to the next.
Their length of 82-3 degrees is just right
for the latitude of the Mittelberg which he
argues cannot be by chance. His view is given
some support by the unique position of the
Mittelberg in the landscape. From here the
sunset reaches its most northerly point behind
Brocken, the legendary 1142m-high summit
of the 75km-distant Hartz Mountain, at the summer solstice on 22 June. Supported also
by Meller, Schlosser goes so far as interpreting the disc as an instrument for measuring
the sun’s azimuth at sunrise or sunset in order to obtain a calendar date (Meller 2004: 31;
Schlosser 2004: 44). The horizon itself at the site however, offers a simple and completely
adequate reference for calendrical use without the need for a precise device. The origin
for the peripheral arcs is not marked and there are no sights for establishing a sightline
to the sun. There is no other feature on the disc that shows any aspiration towards exact
representation. The close agreement of the length of the peripheral arcs with the movement
of the sun‘s rising or setting might be a pure coincidence. The two arcs on the disc may
alternatively symbolise the arcs of the golden sunset and the blush of dawn at the horizon,
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asztor & Curt Roslund
two meteorological phenomena that have always made a deep impression on observers
who considered them to be independent and separate celestial objects as seen on the Skidi
Pawnee star chart (Chamberlain 1982: 189). Equally the purpose of these arcs may have
been a simple geometric attempt to divide the circumference of the disc into four equal parts
to fit into the general concept of cosmos as displayed in rock art and many other Bronze
Age decorations (Malmer 1981: 66-76; Larsson 1996: 45, Figures 21-2).
The shorter gold curved strip at the rim of the Nebra disc, with its three parallel incised
arcs, has been suggested as a depiction of the rainbow, showing the bands of colour (British
Archaeology 2004: 16-7). The rainbow would be a natural feature of Bronze Age mythology.
In the old Scandinavian belief system, it was imagined as a burning bridge (Davidson 1988:
171) created to connect the sky and the earth. It consisted of three colours of which the
middle one was made of hot iron.
A more usual explanation for the arc is that it portrays the mythical boat that brought
the sun across the sky from the east to the west in daytime and back to the east through
the underworld at night. The sun boat myth is well-known from ancient Egypt but it could
just as well have been created in Scandinavia as seafaring there was an everyday experience
in the Bronze Age, as witnessed by the numerous ships rendered on rock carvings. It would
likewise have been natural for the sun to travel by boat as depicted clearly on rock carvings
and razors from the Bronze Age (Kaul 1998). However, these boats are flat-bottomed with
rising stems and sterns. No boat with a semi-circular profile has yet been seen depicted in
prehistoric Europe.
In any case, in landlocked central Europe, the boat can never have been as important for
transportation as in Scandinavia. This is attested by the almost total absence of boats on rock
carvings in inland Europe from this period. No ships have yet been found on rock carvings
in north Germany (Malmer 1981: 18). In Val Camonica, only five ships have so far been
reported on rock carvings (Kaul 2005: 56). In contrast, there are frequent finds of models of
wagons with sun symbols and wheels. It would have been completely natural if the sun was
here believed to travel on a wagon across the sky instead of by ship. There are ‘sun-chariot’
finds even from Scandinavia (Larsson 1996: 45, Figures 12, 14; Kaul 2004.). This shows
the complexity of the role the sun might have played in the Bronze Age mythology. From
1500 BC onward the custom of placing miniature wheels representing the sun as ornament
in graves can also be observed in Europe (Green 1993: 301-3).
Astronomical inheritance
A strong connection is supposed to have existed between the Nebra people and the earlier
or contemporary people of western Asia, both of them using celestial symbols which might
have included the Pleiades (Meller 2004; Kristiansen & Larsson 2005). The Pleiades were
recognised in Mesopotamia at the time the Nebra disc was made. They are mentioned in a
text called Prayer to the Gods of the Night from Babylon around 1830-1530 BC (Rogers 1998:
15). They are also mentioned on circular tablets (astrolabes) from about 1100 BC, giving
their rising and setting and their implication for agriculture and mythology (Rogers 1998:
16-7). The lay-out of the closely-knit group of seven gold plates on the disc is, however,
rather different from the depictions of the Pleiades in the Near East. There they have a
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An interpretation of the Nebra disc
more realistic long-shaped form (Lindsay 1972: Figure 17; Collon 1990: Figure 16; Black
& Green1992: 162-3, Figures 49, 55) in sharp contrast to the round clustering on the disc.
Some 3600 years ago, the Pleiades lay close to the vernal equinox, a point in the sky
where the sun crosses the celestial equator from the southern to the northern hemisphere.
This means the star group was just opposite the sun in autumn: when the sun rose they
set and when the sun set they rose. During the Bronze Age that would have made the
Pleiades a prominent astronomical object in the autumnal night sky, so prominent that
nobody could have missed it. The dashed line in Figure 3 marks the celestial equator with
the vernal equinox for the year 1600 BC set out as an open circle. Schlosser (2003) has called
attention to the dates of the appearance of the Pleiades in the Bronze Age. Their heliacal
setting in March (the last day in the year they were seen setting in the evening twilight)
and acronychian setting in October (the first day in the year they were seen setting in the
morning dawn) could have been used by the farmers to define their working year. He cited
the Greek poet Hesiod from around 700 BC in support of this idea: ‘When the Pleiades rise
it is the time to use the sickle, but the plough when they are setting’ (Hesiod Works and Days,
line 382; Pannekoek 1961: 95). The Roman scholar Varro mentioned the Pleiades by the
name of the Vergiliai in his now lost books as a heliacal rising that took place between 22
April and 10 May marked the beginning of spring (Lat. ver, spring; Lindsay 1972: 224).
The harvest in Greece actually takes place in May, while in central Europe it is in August,
leaving the association between the Pleiades and the sickle in question. However, as recently
as the nineteenth century, farmers in central Europe started their fieldwork in late February,
with one or two weeks either way depending on the local weather. It is not excluded therefore
that in both regions the Pleiades were used to mark turning points of the farming year.
Some researchers suppose that the major part of European Bronze Age iconography can
be explained by the assumption of a complex pantheon of gods which had spread with the
migration of proto-Indo-Europeans. They argue that the worship of the Divine Twins, who
were multifunctional gods from this pantheon and broke open the daylight for their sister,
the sun-goddess, is indicated by references to twins in Bronze Age hoards. Especially in
northern Europe, the increase in the deposition of double axes can be seen in this light. The
Nebra hoard might have been such a sacrifice, demonstrating a close connection with the
course of the sun, the moon and the stars. For this reason the disc has clear Near Eastern
roots as these motifs (that is the sun, the moon and a bright star as symbols of the sky
divinities) often appear on Syrian and Mesopotamian seals (Kristiansen & Larsson 2005:
264-7).
However, the Nebra disc cannot be said to make any direct reference to this iconography,
because on the seals the third member beside the sun and the lunar crescent was a star,
presumably Ishtar, the morning star (which in reality is not a star at all, but the planet Venus)
but not the Pleiades. Moreover on the cylinder seals of the third and second millennia, the
crescent is almost always depicted below the sun disc and quite close to it (Collon 1990: 52,
Figures 8, 13, 17, 23, 31, 34-5, 42). They detach themselves from each other as on the disc,
on the boundary stones but these royal charters are from a later period (1350-1000 BC)
than the Nebra disc. On the gold Mycenaean rings (1500 BC) they are also depicted
independently from each other (Goodison: 1989: Figures 129, 130) and are supposed to
represent rituals which were performed on certain days of the year when they were seen
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simultaneously in the sky (Nagy & Valavanis 1993: Figures 401-2). These gold rings,
however, represent the sun and the moon without a star.
Stellar patterns can have carried many millennia of local meanings. The creation of
zodiacal constellations in Mesopotamia took several millennia according to the archaeo-
logical finds and written sources. It is logical to assume the same for non-Mesopotamian
peoples, so one should avoid theories which suppose a single place and time for developing
sky lore (Maunder 1913; Ovenden 1966; Roy 1984). From prehistoric Europe there are
no written sources dealing with this process as in Mesopotamia or Egypt; but it seems
likely that early Europeans were equally interested in the starry sky. Their sky lore can
be detected in the use of celestial symbols on finds and the orientations of archaeological
features such as houses, megalithic monuments and Neolithic enclosures. The investigations
of these monuments has shown how important it is to survey the location and the design of
monuments in relation to the surrounding landscape and the celestial bodies (Ruggles 1988;
1999). However, no orientation with the Pleiades has yet been detected in a monument or
structure from Bronze Age Europe.
Ethnographic analogy
Evidently sun, moon and stars are widely recorded in the folk traditions of many countries,
and some specifically cite the seven stars. For example, the Skidi Pawnee Indians in North
America also used the Pleiades together with other signs from nature to mark the time
for starting the preparations for the planting ceremonies, when the priest sitting by the
fireside inside the lodge could see the Seven Stars directly above, through the smoke hole
(Chamberlain 1982: 134-5). The Skidi Pawnee buckskin star chart now in the Field Museum
of Natural History in Chicago (Figure 4) depicts stars according to their different mythical
powers on the earth. The pronounced groupings roughly follow the virtual clustering of the
starsintheskybuttheiridentificationswiththerealskywereonlypossiblewiththehelpof
written texts (Chamberlain 1982: 184-205).
The depictions on the disc also bear a striking resemblance to the portrayal of shamans’
drums which symbolise, by their material and decoration, a strong relationship with the
cosmos and the supernatural world. The shaman, as a mediatory person between the spirits
of the other worlds and the community, was active for the welfare of the people and helped
them with controlling their relations with natural and supernatural forces. They used the
drums to evoke the spirits and ‘travelled’ on it as a magic steed between different worlds.
Several stations of these quests and their cosmos were portrayed on the surface of their
drums. Symbols include the sun, the moon, stars, the Milky Way, the rainbow, the World
Tree and animals. Being a model of the universe they always show the most important
elements of the owners’ mythology (Jankovics 1984). Figure 6a-b shows examples from
Siberia and from Nepal, both of which show the sun and moon. As with the Nebra disc, in
each case the moon is turned the wrong way, so as to face the sun rather than be lit by its
light.
Field research among the Inuit Eskimos in the early 1950s and 1990s proved that astro-
nomical knowledge meant great power to shamans or/and their leaders, their close friends
and families (MacDonald 2000: 6, 32). Even today those people who are still under the
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An interpretation of the Nebra disc
Figure 4. The Skidi Pawnee buckskin chart of the heavens. The size of a star on the skin depends not only on its brightness
in the sky, but also on its assumed power (by courtesy of the Field Museum of Natural History in Chicago).
influence of shamanism keep their heritage alive in creating artwork. Figure 5 shows an Inuit
Nunavut in 1993, depicting the sun moon and stars. The sun and moon are again shown as
facing each other.
The role of the disc
The holes around the perimeter suggest it was attached to a support of some kind, but at 2kg
the disc is perhaps too heavy to be worn. It could, however, have been nailed to a shield or
standard made of wood. In song XVIII, lines 478-89 of the Iliad, Homer describes in detail
how Hephaestus makes a shield for the great hero Achilles: ‘First fashioned he a shield, great
and sturdy, adorning it cunningly in every part, and round about it set a bright rim, threefold and
glittering, and therefrom made fast a silver baldric. Five were the layers of the shield itself; and on
it he wrought many curious devices with cunning skill. Therein he wrought the earth, therein
the heavens, therein the sea, and the unwearied sun, and the moon at the full, and therein all the
constellations wherewith heaven is crowned – the Pleiades, and the Hyades and the mighty Orion,
and the Bear, that men call also the Wain, that circleth ever in her place, and watcheth Orion, and
alone hath no part in the baths of Ocean’.
It does seem that Achilles’ shield and the Nebra disc have several traits in common. It was
not unusual in the Bronze Age to attach solar amulets to armour, to decorate shields with sym-
bols which might have been believed to be protective or endowed with supernatural power.
The round shields of central and northern Europe are often decorated with concentric circles,
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Figure 5. Modern Inuit artistic work. Nunavut, by Kenojuak Ashevak. Cape Dorset, 1993. Note the similarity in relative
size, position and orientation of the centre objects with those on the 3600 year old Nebra disc (by courtesy of the West Baffin
Eskimo Co-operative and Indian and Northern Affairs, Canada).
Figure 6. a, Shaman’s drum of the Kets people in Siberia with the depiction of the sun and the moon and the accesses to
the Upper and Lower Worlds. Note that the lunar crescent is erroneously turned away from the sun (from Yenisei Ostyak,
Philadelphia, University of Pennsylvania Museum. After Ivanov 1954: 94). b, Shaman’s drum of the Magar people in Nepal
with the depiction of the cosmos (after Oppitz 1992: 75).
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An interpretation of the Nebra disc
solar or star images with ray patterns, or wheel-cross signs, from the second half of the Bronze
Age, a time when warfare had become general according to the increased number of deposits
of weapons (Sprockhoff 1930: Tafel 1-2; Coles 1962: Plates 28, 30, 31; Jensen 1999: 97).
As the disc was possibly found together with swords and other war items, it is conceivable
that it once embellished a ceremonial shield belonging to a person of a high rank, the
representative of a mythical hero or the image of a god in a ritual combat. As many hoards
containing swords are assumed to be offered to the gods as a gratitude for victory after a
combat (Kristiansen 2002: 329-30), the disc, like the armour found with it, might have
been offered for the same purpose. The cut on the upper left top of the disc might be the
mark of a stroke from a sharp object during combat (Meller 2004: 24-5).
Conclusions
The Nebra disc seems to have carried a mythical representation of the cosmos featuring
the sun, moon and stars. Mounted on a shield or standard, it may have participated in a
ceremony for a man of rank and position in society, or as a ritual object empowered with
supernatural forces by portraying shamanistic symbols of the Upper World.
There is little support for a connection with western Asia so close that the iconography
of the divine triad was adopted. The iconographic arrangement of the symbols on the disc
does not seem to follow any foreign influence, but just to express a basic but aesthetically
organised laying out of the elements of the cosmos. The sun and the moon must have always
played an important part in the life of European people because of their presumed impact on
the fertility and wealth of the community, and once agriculture began to spread they became
essential. The investigation of sites and monuments in relation to the local landscape and the
movement of celestial bodies has enriched our awareness of cognitive responses in prehistory.
Interest in the starry sky might at first have been raised by rituals such as initiation rites
or rites connected with belief in shamans’ journeys into the Upper world. In initiation
ceremonies, stories about the deeds of heroes might have been projected onto the starry sky
so that star groups with patterns that are easy to remember stored their memory (Frank
& Bengoa 2001). There might have been as many different stories about different heroic
deeds, creating as many different prehistoric ‘constellations’, as there were different peoples
living in prehistoric Europe.
Current scientific knowledge may tend to direct us towards astronomical explanations,
but we cannot expect to encounter a coherent knowledge of celestial phenomena among the
peoples of prehistoric Europe. In general the purpose of their observations might have been
ritual and the ritual rules of one community was likely to be different from another. Even
the elements of the calendar referring to star positions in the sky were likely to have been
influenced by the local climate and landscape. The sky lore necessary for communal needs
was orally transmitted and not necessarily shared among the members of the community.
Ethnographical accounts suggest that the chiefs and/or the shamans of a community were
the only people privileged to have access to it.
Thus there is no compelling evidence that the Nebra disc ever served as a precision
instrument for astronomical observations or was intended to depict celestial objects or
events with any accuracy, or that it shows iconographical links to western Asia. It is more
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likely that the disc was a symbolic expression of the cosmos with some reference to the
iconographical system of the Nordic Bronze Age. It even might have been produced there
or by Nordic smiths. Although the disc may be of limited value to astronomers, it still has
considerable interest to prehistorians and historians of religion. If we accept that Bronze Age
Europeans people could produce works of art as beautiful as the Nebra disc, their creative
genius is worth our deepest and most sincere admiration.
Acknowledgements
The authors would like to acknowledge Roselyn Frank, Clive Ruggles, Michael Rappengl¨
uck and Stanislaw
Iwaniszewski for their valuable comments on the preliminary versions of the paper and Alad´
ar G´
asp´
ar for
drawing the profile.
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