1. Introduction

The use of symbols is probably an early kind of abstract thought dating almost 50,000 years. Bone and stone carvings from more than 30,000 years ago, including "The Venus of Laussel" already involve some degree of data recording, marking for example, what may be the phases of the moon (Joseph 2010). The Venus of Laussel is 1.5 foot high limestone bas-relief of a pregnant female with swollen distended breasts, painted with red ochre. She holds what some believe to be a bison horn with 13 cuts. Joseph (2010) believes the "horn" might instead represent the crescent moon, and the 13 cuts a symbol of the relationship between the lunar cycle and the menstrual cycle. Yet others believe some of the symbolism deep within the recesses of ancient Paleolithic underground caves and caverns may represent the stars and constellations (Belmonte 2010). Together with other substantial evidence this clearly seems to document an early observational and registration stage of the intellectual analysis of nature and astronomy.

The Neolithic may be the first intellectual revolution from which we may aspire to have glimpses of the earlier cosmic views of the universe (i.e. of the sky and of the celestial bodies), possibly embedded in the large stone monuments that we can still see today. That landscape includes symbols of the celestial bodies (Ruggles 1998) created 5000 to 10,000 years ago. Analysis of these creations, suggest that the humans of that period, in their magic religious ritualization of time and space, tried to incorporate the surrounding cosmic order in their stone monuments. Possibly these behaviors reflect the belief that this appropriation would confer them some control over the celestial bodies or the forces of nature.

The Neolithic humans view of the surrounding cosmos may have been composed of their territory, loosely limited by the "distant" horizon, and of the sky above. This distant horizon would separate their world where they could walk, from the sky where they could not, but where some powerful heavenly bodies seemed to move in some kind of order. The celestial bodies would emerge and disappear in that unreachable line separating their territory from the celestial realm. They could not fail to have noticed, long before the Neolithic, that the activity of these bodies repeats in cycles that seem to find counterparts in their territory (Joseph 2010).

Continued observation of the celestial regularities, over centuries, would have provided an intimate perception of the cycles of the most prominent astral bodies, the Sun and the Moon. Surviving detailed registration of such regularities by the Babylonians circa 2500BC lead us into the modern views of the sky.

The geographical orientation of dolmens over vast regions seems to have been made with reference to the sky (Hoskin 1998), and as based on orientation, the occurrence of eclipses, the Moon seems to be favored (Clausen et al. 2008). Thus, we speculate that some of this symbolism and monumental architecture represents the Equinox about the middle of the up and down swing of the sunrise on the horizon in a close and intimate relation with Spring.

The present paper is a speculative discussion on the symbolic value of the ritual practice related to the spring equinox, and on its possible association to the distribution of the major megalithic sites, from the Sahara to the Artic Circle. The terms, Equinox and Spring are almost interchangeable in this paper, the first relating to our present day knowledge and the second to Neolithic ritual symbolic practice. We suggest that intelligent perceptions of nature, in the Neolithic, may involve second order concepts. In this case, the equinox would not be a result of a direct observation, e.g. of the sun against the horizon, but rather a method using, for instance, the count of days or the sunmoon cross over, etc. Also, an imaginary entity in the center seems to provide a consistent view of the observed cosmos.

1.1. The Equinox

As opposed to the solstices, which are marked by very clear indications in the sky (provided by the standstills at the extremes of the Sunrise and Moonrise sweep of the horizon) the equinoxes are not marked by such a simple and direct observation methodology. Very early in the 1960’s Alexander Thom introduced the concept of the Megalithic Equinox (Thom 1967, p. 107). He supported it with data on particular solar orientations, with declinations close to zero, observed in some megalithic sites. Thom based this concept on the very simple technique of counting days and on the possible registration of those counts in the monuments or artifacts. Increased plausibility was derived from the observation that these data clustered around 0.5ºN from the East-West direction; a consequence of Earth's slightly elliptical orbit which causes the true equinoxes to separate the orbit in two halves of unequal length. Therefore the division of the year in two halves with the same number of sunrises results in the indicated azimuth offset. This view highlights both the mid-swing ritual importance and the need to resort to a second order concept to materialize it. Nevertheless the lack of objective and consistent evidence on equinoctial markers has always been controversial (Ruggles, 1997).

An alternative indication of the equinox might have been employed by humans of the megalithic period. This is based on the observation that, close to the solstices, the full Moon and Sun, rise in opposite extremes of the swing on the horizon. When the sun is close to the winter solstice the full Moon rises close to the direction of the summer solstice sunrise, and vice versa. However, as the sunrise departs from the winter solstice moving north, the full Moon rise moves south, until they cross close to the equinox. The awareness of the cross over and of its observation was the basis of the "Spring Full Moon" concept of Megalithic Equinox in southwest Iberia (da Silva 2004) and is evident based on data from M. Hoskin (1998). The variability of the azimuth of the Spring Full Moon rise, i.e. of the first fullmoonrise to pass over the sunrise, exhibits a bell shaped distribution centered about 9º south of true east. This has been found to be remarkably compatible with the orientation of the megalithic dolmens in this region, but it can also be observed in Hoskin (2001) data for other parts of the Mediterranean and Brittany. This analysis reinforced previous observations of astronomical directions between isolated megalithic monuments and conspicuous hills in the eastern horizon (da Silva & Calado 2003a), i.e, as based on particular directions of stones in the internal architecture of some stone circles in this region, and by the fact that these stone enclosures are generally set on top of a hill on a slope facing east toward the rising sun and moon (da Silva & Calado 2003b). Some of these astronomical alignment provide equinoctial markers within 0.5º.

The major monument in southwest Iberia exhibiting these features is the Almendres enclosure near Évora, which is clearly oriented due east. Since it is set on a gentle slope (6º), facing east, the observation of the sunset on a truncated monolith situated on the western apex, can not be made from the axis but rather from a station located at the eastern end of the northern wing. This is a very accurate alignment (less than 0.5º) for the observation of the spring equinoctial passage of the sun, and the features of this station suggest that this passage could be anticipated by two to three weeks and followed day by day. These findings indicate that people of that period placed great importance on the ritual observation of the passage of the Sun and of the Moon close to the direction that we now call the equinox (Oliveira & da Silva 2010) and with the average azimuth of the Spring Full Moon rise (Fig. 5). Figures 5 and 8 are two examples of these orientations about 9º south of east, the first coinciding within 0.5º with the symmetry axis of the horseshoe monument and the second using a prominent hill in the landscape to be sighted in that direction from an isolated menhir.

We may speculate that the neolithic early view of the cosmic order was mostly related to the passage of these celestial bodies in the horizon rather than the diurnal arch in the sky. Lack of permanent references would not imprint in the human mind much more than the variation of the length of the shadows of the sun during the day, i.e. long shadows at the beginning and end of the day, changing fast, and a shortest shadow around the "middle" of the day when the sun is at its highest.

The natural cycles of the horizon crossing by the celestial bodies would have been very clear and prominent in the case of the Sun, occurring in a fixed interval of the horizon. The Moon (particularly the Full Moon) would display a similar pattern, sometimes overshooting the Sun limits, sometimes not quite reaching those limits. Their observations that the astral bodies most influential in their territory were confined to a narrow strip of the horizon, associated with the fact that, as the sun approached those limits, life in his territory seemed to become increasing hard (freezing cold in one of the limits, and boiling hot in the other extreme), might have imprinted in their minds that life was more comfortable during the periods in which the sun was closer to the "center" of his swing in the horizon. We can even speculate that they may have attributed a magical power to this "centrality" perception that would retard progressively the sun as it approached the limits. In their minds this central region in the horizon could possibly be the home of a mighty force that kept their world stable and under control. They may then have felt inclined to praise and pray, or even rejoice, when the effect of this "force" was seen to to bring the sun back to a more comfortable situation. These events may have been the beginning of the summer and winter festivities close to the solstices followed by the spring rebirth of nature, or the welcoming of the autumn close to the equinoxes.

2. The Monument

The Almendres Cromlech near Évora, Portugal (Fig. 6) is a megalithic enclosure discovered by H. Pina in the 1960’s (Pina 1971, p. 151). It consists of about 95 stones, many very large and weighing a few tons, distributed in a layout roughly elliptical. The monument sits on top of a small hill and the 60m major axis develops along a gentle slope facing East. Since its discovery several measurements have been performed that confirmed the East-West alignment of the long axis. This is also clearly a symmetry axis, and no one questions its possible importance as a place of ritual cult involving the observation of Sunrise or Moonrise close to the Equinox. It is a very large version of smaller enclosures in the surrounding 100Km region, of a type designated as "horseshoe" from its layout. In the case of Almendres the two long arms of the horseshoe almost touch and seem to embrace the rising sun near the equinox. Detailed analysis of the layout has identified precise features that may have been dedicated to the the equinoctial transit of the Sun, as seems common in the surrounding area. A few very precise solstice alignments (within 1º, in some cases 0.5º) have been identified and measured, as well as lunar major and minor standstills (da Silva 2000).

From the Almendres enclosure it is possible to observe a conspicuous hill (Évoramonte) in the far distant horizon (≈20Km), very sharply close to the winter major standstill lunar rise. A hill that due to its prominence and conspicuous nature seems also to be a precise target to see the summer solstice sunrise from nearby megalithic sites marked by menhirs (e.g. Caieira) and enclosures (e.g. P. Mogos). The internal analysis of the layout of stones in the Almendres enclosure has also suggested that some other internal alignments may be supported, particularly by the identification of some distribution of stones that seem to materialize purpose built corridors to provide observation lines of sight, in particular to the Spring Full Moon.

Although the monument was constructed to be used facing East, it should be mentioned that, facing west, from the top of the monument (and of the hill) it is possible to identify features in the horizon that seem relevant to identify the passage of the sun through the equinox, and also the major and minor winter standstills of the setting Moon. Altogether, it looks like that the whole layout indicates that the monument was erected in such a place as to satisfy multiple celestial alignments.

2.1. The (Latitude) Speculative Conjecture

The lunar major standstill elongation observed over the Évoramonte hill in the winter standstill moonrise indicates an association between the value computed for the major lunar standstill elongation (ex. ±38º 36´, 2000BC) and the value of the latitude of the implantation of the Almendres enclosure (38º 33.5´N). This coincidence is within minutes of arc and can be made exact if very small elevations of the horizon (e.g. <1º) were taken, or by changing the date used in the calculations. We all know that there is no practical way in which we may invoke human knowledge of the Earth curvature in that period that could suggest a deliberate choice of placing the monument at such latitude, and therefore the capability to measure it. These observations have led to the question: given a value ∂ for the declination, at what latitudes can the corresponding elongation E equals the latitude value λ?

The spherical trigonometry regularly used to compute the azimuths provided the following equation,

2.1

This, when solvable, has two solutions E1 and E2 that complement i.e. E1+E2=π/2. Using a declination close to the major lunar standstill we find one solution at the latitude of Almendres, and the other at the complement latitude, which is very close to those of Stonehenge (51º 10.5´N) and Goseck (51º 12’N). The small differences, in the order of minutes of arc, are again subject to the same comments given above.

The detailed trigonometric treatment shows that there are no solutions for declinations greater than 30º. We can see in Fig. 7 that for the northern hemisphere there are two solutions far apart as ∂ is increased from zero, but the two solutions approach each other until they coincide both at 45º for ∂=30º. Note that –E is a solution for –∂. Fig. 7 shows the two solutions for declinations close to the cases of the sun standstill and of the moon minor and major standstills, representative of an epoch around 2000BC.

This interesting coincidence acquired, in this way, the status of an astronomical conjecture in search for a megalithic explanation, and was reported in earlier publications (da Silva 2000; da Silva & Calado 2003a). With our modern understanding of the world we seem to be able to speculate on and relate the latitude values of some megalithic monuments, using the consequences of the spherical model of the earth, and wonder if this may have been fortuitous.

3. Discussion

The observation and associated importance of the equinox may have provided Neolithic and even earlier cultures with a cosmology which helped them to understand nature and the universe. We can only speculate and there are a variety of models which purport to explain the underlying belief system, including, perhaps attempts at controlling the movements of the sun and of the moon, and the corresponding events on Earth. The agent of that force being situated in the horizon close to what we now call the direction of the Equinoxes, i.e. the East-West line. This view requires no more than just one intellectual concept: that of centrality, in the sense of Mircea Eliade(1964). Man is always in the center of his territory and this may be divided in two halves: the one where the sun, the moon and the stars rise, and the other where they set. These two halves are separated by the smallest shadow of a vertical pole (a representation of his "axis-mundi").

The concept of spring (equinox), with its prominent anthropological importance, might have produced an important artifact, "the staff" (or pole). We know that when placed vertical at noon, during the equinox, the geometry of its shadow (i.e. of the right-angled triangle whose legs are the staff and its shadow) incorporates the latitude. If this was understood 6000 years ago is unknown. However, this vertical triangle when placed on the ground, by letting the staff point in the direction of the equinox, would encompass the ranges of sunrises and moonrises in the horizon (i.e. the hypotenuse would provide a limit to the elongation of the sunrise/moonrise). This observation might have added to the anthropological value of the equinox for it provided a method for them to measure, and thus keep control over the observed cosmological order. As they perceive cycles in time, as the sun rises in the horizon, the axis of the observers becomes horizontal and the middle point of the swing is just another form of "center". This model becomes dynamical (i.e. non geometrical) as the "influence" in the center seems to control the swing. Other particular horizontal directions become important in this ritual. From the dynamical point of view, i.e. from the perception of a central direction, the axis in the direction of the equinox may have played the role of a geographical orientation. Also, the displacement of the sun and of the moon, as they rise in the horizon, could be viewed as displacements left or right of that direction, sweeping the small range of the horizon where they occur. It may well have bordered on a mystical experience to see the full Moon rise when the sun is setting straight opposite relative to the center where the observer stands.

This preference for a direction close to the center of the swing, seems well represented in the geographical orientation of various groups of funerary megalithic monuments, as a result of the observation that the full Moon rise and the Sunrise cross over on the horizon close to the equinoxes, as discussed above. The cross over assumes the role of a Megalithic Equinox and seems to be very frequent in regions of Brittany, Iberia and parts of the Mediterranean. We have observed also in the region around Almendres several examples of such orientation, for instance in the alignment of the horseshoe axis of the Vale d’El Rey enclosure (Fig. 5) and in alignments defined by menhirs and prominent hills in the landscape (Fig. 8). Other horseshoe enclosures are not sufficiently preserved, and therefore not so clear, but they seem to align in the same general direction.

The above analysis assumes that Neolithic monument builders had at best only a rudimentary understanding of the solstice and equinox, and could not possibly have conceived of a round Earth or the 365 day periodicity of Earth's orbit around the Sun. It is easy to assume that the monument builders were not scientists, technicians, or astronomers, but may have based their beliefs on ritualistic magic and rudimentary observations and perceived coincidences without any real understanding of the underlying celestial dynamics. Certainly this may have been true of Neolithic people in general. Yet, at the same time it must be recognized that those who built these monuments had in fact studied, observed, analyzed, understood these celestial events, and were able to make extremely precise scientific predictions. They were also able to mobilize the local population to undertake massive engineering projects resulting in the creation of monoliths whose orientations have obvious celestial significance. These were not the creations of a primitive mind, but were the product of very precise scientific observation. Certainly, it can be said that the monument builders need only walk up or down along the general direction of the mid day shadow until a match is found and then proceed to build. However, they had to know what to look for and why.

As demonstrated in Figure 7 we can walk Iberia and France until reaching Brittany always with values of the major lunar standstill elongation smaller than those provided by the shadow of the pole. However, to find a clear departure to values of the elongation greater than the latitude it would have been necessary to come as far south as M’soura in the Sahara, marked by a cromelech with a large central menhir (Belmonte 1999), or to go as far north as Lituania where a flourishing community worshiped the sun and the moon in times past (Straižys & Klimka 1997). These two sites, however seem to satisfy the requirements of Eq. 2.1 for a declination of the moon closer to 28º in the major standstill, which could possibly place them later in time than the previous sites.

It is also interesting to note that the equinoctial marker in Gran Canaria (Esteban et al. 1996) may satisfactorily share with the Kings Tombs in Sahara (Belmonte et al. 2002) the solution where the elongation of the sun standstill equals the latitude, as may the Finland structures of Kastelli and Raahe (Ridderstad 2009) at the same latitude of the Faroe Is. It is however true that it may be possible to find a megalithic monument at any designated latitude.

At the latitudes derived from Eq. 2.1 we seem to find large Neolithic structures, either constituted by single monuments of reasonable size, or by large aggregations of smaller structures in a short geographical area. Also, it is interesting to note that no structures close to 20º and to 70º (the lunar minor standstill solutions) have been discovered. But, if the anthropological interpretation is correct then, symbolically, we speculate that it might be sufficient to contain (or control) the major deviations and, particularly, those of the mighty astral bodies, i.e. those that most influence the events in the territory. This may even be applicable to other prominent celestial bodies since man is now in the possession of a "yardstick" that can measure the cosmos and relate it to his own territory. Sirius might have been an example because this star had an elongation close to the latitude of Abu Simbel for a few centuries around 2000BC, before the precession of the ecliptic has thrown it out of alignment.

Translating into magic-symbolic language this might have appeared as a means of appropriation of the cosmological order. Or, a few Neolithic geniuses may have in fact understood what they had observed.

If this speculative conjecture finds any support in the role of the equinox then we may envisage the Neolithic man as master of the universe for he is able to contain the variations of the sun and of the moon within limits derived from the centre of the celestial swing where the Spring full Moon rises (Figs. 5 and 8). The maximum elongation at the solstice standstill, for the sun in particular, never exceeded the limit given by the equinox mid-day shadow from the level of Morocco and Tenerife to the level of the Faroe Is. north of Scotland. Beyond those limits life again was not very comfortable.

Although admittedly the above discussion is highly speculative, and controversial, we consider that the observed data seem to reveal an interesting conjecture suggesting further analysis.