statistical approach on the orientation of prehistoric sardinian monuments: a comparative

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2014 45: 467Journal for the History of AstronomyA. César González García, Mauro Zedda and Juan Antonio Belmonte

Statistical ApproachOn the Orientation of Prehistoric Sardinian Monuments: A Comparative

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Copyright © The Author(s) 2014

JHA, Vol 45(4), 2014

ON THE ORIENTATION OF PREHISTORIC SARDINIAN MONUMENTS: A COMPARATIVE STATISTICAL APPROACH

A. CÉSAR GONZÁLEZ GARCÍA, Instituto de Ciencias de Patrimonio, CSIC,MAURO ZEDDA, Isili, Sardinia, and

JUAN ANTONIO BELMONTE, Instituto de Astrofísica de Canarias & Universidad de La Laguna

Abstract

On the basis of a recently updated data base of Sardinian Megalithic monuments, we perform two independent statistical analyses on several groups of these structures and confirm the existence of differences between the southern and northern halves of Sardinia, indicating that there seem to be different traditions of orientation in these two parts of the island. We then compare the orientation of these groups with other groups of contemporaneous sacred monuments in the central Mediterranean basin. The differences observed in Sardinia could be related to differences in the orientation customs between the north and south shores of the Western Mediterranean.

Keywords

Megalithic monuments. Cluster analysis. Mediterranean prehistory. Domus de Janas. Nuraghe.

Sardinia is in effect an open-air museum housing some of the most impressive megalithic and cyclopean monuments in the western Mediterranean, if not in the world. The majority of these monuments have already been investigated from the point of view of archaeoastronomy with varying results.1 A number of associations with different astronomical objects have been pointed out in these studies.2 It is interesting and intriguing to note that previous results indicate that there seems to be an invisible dividing line across the central part of the island (more or less at the 40º parallel), indicating different orientation traditions, in some of the monument typologies, notably with regard to the tombe di giganti.

In this paper, a reappraisal of these studies will be presented together with new data collected in recent years for new monuments of diverse typologies, including a nearly complete sample of Domus de Janas.3 In total, more than 1500 megalithic structures in the island will be analysed. Two different statistical cluster analyses of the data will be performed: on the one hand, we have used a grouping analysis to search for similar groups of orientation by means of a dendrogram; on the other hand, we have clustered the orien-tations according to the shape of their distribution by a k-means test.4 As we will show, the existence of differences between the southern and northern halves of Sardinia will be confirmed. We have then compared the orientation of this Sardinian group of monu-ments with other groups of contemporaneous, or nearly contemporaneous, megalithic and cyclopean monuments in the central Mediterranean region. Groups from the other western

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A. César González García, Mauro Zedda and Juan Antonio Belmonte468

Mediterranean islands, southern France, northeast and southern Spain, as well as from the north of Africa, have been included. The dolmens of ancient Thracia have also been considered as a testing interloper. The results of these analyses suggest that the differences observed between the north and the south of Sardinia could be related to differences in the orientation customs in the northern and southern shores of the western Mediterranean. In this sense we have envisaged Sardinia as a probable carrefour for orientation customs.

1. Introduction: The Data

The landscape of Sardinia is characterized by virtually thousands of prehistoric monuments built between the fourth and the second millennia b.c. Over the past 25 years, a series of archaeoastronomical research works have been dedicated to the study of the orientation of these monuments, including Domus de Janas (monumental hypogeic tombs), dolmens, dolmenic corridors, tombe de giganti (‘tombs of giants’), nuraghi and megara (temple-like structures).5 Those works have resulted in a huge corpus of measurements which has been recently updated with the orientation data of 643 Domus de Janas (see Figure 1) and 15 new megara, also extending the data to the sacred wells (templi a pozzo or simply pozi). These measurements, together with the data of 27 dolmens, 21 dolmenic corridors, 305 tombe de giganti (some of them recently measured) and 541 nuraghi will be used — to a total of 1573 monuments of diverse typologies (see Figure 2) — to implement the statistical analysis. This has three main objectives: (i) to refine, when possible, the interpretation of the orientation of each typology of monuments; (ii) to try to understand the evolution of orientation customs within the geography of the island, including a diachronic analysis; and finally (iii) to compare customs of prehistoric construction orientation in Sardinia with those of neighbouring areas in order to ascertain mutual influences or to investigate the possibility that they aim at similar astronomical targets.

The Domus de Janas are monumental burial tombs carved — actually, almost sculp-ted — in the cliffs and rocky outcrops of the island, although it is likely that larger ones also had a role as sanctuaries. Domus de Janas means ‘Fairy Houses’ in the Sardinian language, a Latin tongue still widely spoken, beside Italian, in most of Sardinia. Many legends have been created involving these monuments and, although less noticeable than the ubiquitous nuraghi, they are crucial for Sardinian prehistory. The island was a very important crossroads in the western Mediterranean at the moment when Domus de Janas were built and used. For example, the obsidian of Monte Arci was widely exported and has been found at archaeological sites in Corsica, the Italian Peninsula and even the southern French coast. The first Domus (such as Cuccuru s’Arriu) could have been developed in the late phases of the Bonuighinu Culture (c. 5800−3800 b.c.), but the wide majority of them were sculpted during the late Neolithic period (3800−2900 b.c.) within the context of the so-called Ozieri Culture,8 although they continued to be built even at sub-Ozieri (2900−2700 b.c.) and in the Copper Age (2700−2300 b.c.). New Domus de Janas were seldom built during the Bronze Age, although the tombs already built in the Late Neolithic continued to be in use for several centuries.

Dolmens were built during the Ozieri culture, but only in the northern half of the island. In contrast, dolmenic corridors are more widespread throughout the island, dating back to the period between the sub-Ozieri and the early Bronze Age (2300−1900 b.c.). They



On the Orientation of Prehistoric Sardinian Monuments 469

are not very common. However, it is highly probable that many of them were turned into tombs of giants in the Middle Bronze Age. The tombe de giganti date back to the period between the Middle Bronze Age (1900−1350 b.c.) and the Late Bronze Age (1350−1150 b.c.) and can be considered as dolmenic corridors built on a monumental scale to which an exedra and a frontis have been added. Nuraghi are towering cyclopean structures of different sizes and complexities, contemporaneous with the giants’ tombs. In our analysis,

Fig. 1. An example of the data used in the analysis: orientation histograms of 435 northern and 208 southern Domus de Janas — divided by the 40º N parallel — from data recently completed by the second author.6 Notice the similarities between both plots with few monuments orientated in the northern half of the horizon. The discrepancy of this outcome with previous ones on the nuraghi7 was the origin of the idea behind this work.




Fig. 2. A series of images of the six most characteristic and exclusive typologies of Sardinian monuments included in the analysis: (a) a nice example of Domus de Janas at Montessu, (b) tomba de giganti of Sarbogadas, (c) the simple nuraghe Ruiu at Chiaramonti, (d) nuraghe Santa Barbara di Macomer, an example of a complex monument, (e) Su Tempiesu di Orune, an impressive example of a sacred well, and (f) the megaron of Gremanu near Fonni. Images by the authors.

the orientation of the entrance to the single-tower of simple nuraghi and to the central towers of complex nuraghi have been taken into account.

A simple nuraghe consists of a single tower in the form of a truncated cone (see Figure 2). The tower can include one, two or three chambers located one above the other. A complex nuraghe consists of an entire conjunct of different monuments (further towers, cyclopean walls, etc.) placed around a central tower which is often identical to a simple nuraghe. These central towers were probably the first elements to be built.9 The name of the people who built them is still unknown and the nuraghi have determined the origin of the name of the culture of this ancient society, the Nuraghic civilization. The




towers and ruins of the nuraghi dominate the Sardinian landscape, where the remains of some 7000 monuments have been identified on an island of only 24,090 km2. Of these, a number close to 500 are in a relatively good state of preservation (our data include ~540 of them).

The megara date back to the Bronze Age and extend especially to the Final Bronze Age (1150−900 b.c.). The sacred wells are probably contemporaries to the megara. Both types of cyclopean structures (see Figure 2) certainly had a strong ritual and religious component. It is worth noticing that most of these monuments (and especially the Domus de Janas, nuraghi and tombe de giganti) remained in use even for many centuries after the epoch in which they ceased to be built. Curiously, material culture shows substan-tial differences between the two halves of the island only during the Late Bronze Age (1350−1150 b.c.), according to archaeological findings.10 This fact is also manifested in the architectural styles for both the nuraghi and the tombe de giganti.11 The differences are self-evident in the cyclopean and megalithic monuments since the very beginning of their construction, but there are also suggestive differences in the way that the Domus de Janas were structured.12

2. Statistical Methods and Multivariate Techniques

In the following we will be using an appropriate smoothing of the azimuth histogram by a function called the kernel to produce the azimuth ‘probability density function’ (PDF, see Figure 1). At each entry in azimuth, we multiply the value of the number of occurrences of a given azimuth by the kernel function with a given pass band or width. For this process, an Epanechnikov kernel is employed13 with a bandwidth of twice the estimated error in azimuth.14

To be able to say whether a measurement is significant, we use a normalized relative frequency to scale our PDFs or histograms. To do so, we divide the number of occur-rences of a given azimuth by the mean number of occurrences for that sample; this is equivalent to dividing or comparing with the results of a uniform distribution of the same size as our data sample, and with a value equal to the mean of our data.

Multivariate techniques are commonly used in archaeology and have been used in the recent past for archaeoastronomical data.15 These techniques produce some kind of graphi-cal output and statistics that are descriptive, because they simplify the data and present possible patterns within them.16 In this particular case, two techniques will be applied to the Sardinian data: the cluster analysis and a representation called the dendrogram on the one hand, and k-means clustering on the other.

As part of a multivariate analysis, cluster analysis tries to search for regularities in the data that may allow the finding of groups or clusters among them. Using a given distance-measuring algorithm, cluster analysis finds groups among the data and then finds distances among those clusters, finally building a hierarchy of distances. A plotting procedure of such a hierarchy is known as dendrogram.

We have followed the same procedure as in previous works of our research team to characterize the different groups under study.17 The team has come to the conclusion that the kernel density distributions of each group are well represented by the following seven




numbers (see Table 1) which we have named ‘genetic markers’: the mean azimuth, the median azimuth, the standard deviation of the azimuthal distribution, the maximum and minimum azimuths of the distribution, and the azimuth of the first and second (if exist-ent) maxima in the azimuth PDF diagrams of the group. In the rare case that the second maximum is non-existent, this is taken to be equal to the first one.

We have used IDL software to produce first the cluster analysis data and then the distances among groups, besides the plotting procedures included in the package. In the present study, we have used a weighted pairwise average where the distance between two clusters is defined as the average distance for all pairs of objects between each cluster, weighted by the number of objects in each of the clusters. We have done tests with a nearest-neighbour algorithm and no significant changes resulted. The relative distance is given on the left side of the diagrams. This quantity will be used to find correlations between the different groups.

Finally, the k-means clustering links the groups of monuments into clusters by compar-ing the shape of the kernel density distribution of each data group with a given seed.18 In each step, the method computes the distance of each distribution to the seeds and then does the grouping. The groups define a new seed by calculating the one in that cluster which is closer to the mean of the cluster, and the process is iterated until it reaches convergence.

3. Results of the Comparative Statistical Analysis

3.1. Sardinia

We first concentrate our analysis on the Sardinian data alone. For each of the 12 groups of monuments considered (see the first twelve rows of Table 1), the seven ‘genetic markers’ as defined above have been calculated. The first five markers are the basic statistical values for a population and the last two are obtained from the histogram for each of them. In Figure 1 we present as an example the histogram for 435 and 208 Domus de Janas to the north and south of 40° N latitude. The similarities are clear, especially in the range of azimuths where it is more frequent to have orientations.19 However, a number of characteristics seem also to make the distributions dissimilar. For instance, the two most prominent maxima are not located at the same azimuths; in fact there can be as much as 30° difference, something not explicable by the change of latitude. As we want to test whether the alleged difference between north and south is common to all the megalithic monuments in the island and perhaps find when it appeared, we have carried out the multivariate tests described above.

Figure 3 presents the result of using the ‘genetic markers’ to find the distances between the 12 groups of monuments and plots them in a dendrogram. There is a first division into two groups, with six elements in each of them, and they are clearly divided between north and south (with the pozi in an intermediate position), with the notable exception of the Domus de Janas. The two groups, north and south, of Domus de Janas appear very close indeed in these computations despite the apparent differences, while the geographic divi-sion seems certain for the nuraghi (in both typologies) and the tombe de giganti. Dolmens, typical in the north, lie in the correct group accordingly.

Figure 4 shows the results for the k-means analysis. We have used three seeds for this computation, the corridoi, the southern Domus (Domus S) and the southern simple nuraghi



On the Orientation of Prehistoric Sardinian Monuments 473T

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(N mono S). The results do not depend critically on the selected seed, as these change throughout the computation until convergence is reached. The results again present a cluster of mostly northern monuments (tombe de giganti North, dolmens, megaron, cor-ridoi, and the two groups of northern nuraghi), a second cluster with the Domus of the north and the south (in agreement with the dendrogram) in the same group, plus some other southern monuments (pozi and the southern tombe de giganti), and a third one with the southern nuraghi of both typologies.

The analyses are independent and both produce similar results with a clear-cut division between the north and the south of the island, with the single exception of the Domus de Janas. The results are therefore robust. What could have caused this ‘geographic’ differ-ence during the Nuraghic phase that was not present in the earlier period when Domus de Janas started to be built? Seeking an answer to this question, we must go a step further in our analysis.

3.2. Comparison with the western Mediterranean: Sardinia as a cradle of cultures?

We have extended the analysis to include other megalithic monuments from the Western Mediterranean. First, we have included the monuments from neighbouring Corsica. These are divided into 13 megalithic cists and 28 dolmens. We have also included the

Fig. 3. Dendrogram of Sardinian monuments. Note that, with the exception of the Domus de Janas, most of the island megalithic and cyclopean monuments clearly divide into northern and southern groups. The vast majority of the dolmens are located in the north of the island.




megalithic monuments of the Balearic Islands and Malta, often typologically connected with the Sardinian ones in the literature. We have also considered the monuments close to the ancient Gaul Mediterranean coast, such as the Languedoc L-dolmens and the BR-dolmens of Provence, or the megalithic monuments of the French departments of Herault and Aude, beside the ones at the department of Pyrénées Orientales. These have already been reported to present very similar orientations to those in the northeast of the Iberian Peninsula, such as the groups of the Spanish provinces of Barcelona and Gerona, and certain regions of the Pyrenees (Cerdagna and ‘Pirineos Este’).20 For completeness, we have also included monuments from the southeast of the Iberian Peninsula, such as Los Millares and Montefrío.21

Finally, we have considered the megalithic monuments measured from the north of Africa divided into three groups (Tunisia, Algeria, and Foum al Rjam in Morocco) together with the Tunisian Hawanat. Thracian dolmens are included in the analysis as

Fig. 4. The k-means of Sardinian monuments. Three seeds have been used in the analysis. Two of them are at both sides of the 40º N parallel (with the single exception of Domus de Janas). A third characterizes the nuraghi of the south of the island.




a clear geographic and cultural interloper.22 In total we consider 1444 monuments in those areas, to add to those already considered for Sardinia (a sample of more than 3000 monuments!). The details for each zone can be found in the respective publications, while the corresponding ‘genetic markers’ are presented in Table 1.

Figure 5 presents the results of the k-means computation. We have used five seeds. Three of them are from Sardinia: the Domus North group, the tombe de giganti South group plus the dolmens. The other two seeds are the taulas in the Balearic Islands and the BR-dolmens of southern France.

We find a first similarity among the monuments of Provence and Languedoc and those of the Balearic Islands,23 and among those of the northeast of the Iberian Peninsula and nearby areas of France.24 It is interesting to note that the results show that the Sardinian north–south division still appears after the inclusion of the other neighbouring areas, again indicating that such a division must be real. If we inspect this figure closely, we find that the northern nuraghi present orientations similar to those of some monuments in the northeast of Spain and the Balearics. Of particular interest is the similarity with the square talayots of Majorca. The similarity is broken for the southern nuraghi, which

Fig. 5. The k-means of Western Mediterranean ‘megalithic’ monuments. See the inset for a legend of the different groups and Table 1 for their identification. Thracian dolmens (number 32) are not presented in the map for the sake of clarity and resolution, but they are included in the analysis and form part of the group rendered by an inverse triangle. Sardinia once more presents a subtle difference between north and south monuments, especially in the nuraghi and tombe di giganti. These last support the idea that the north of the island is more related to the northern shores of the Mediterranean while the south part is more closely related to the north of Africa (see also Fig. 6). See the text for further discussion.




seem to have orientations more similar to the megalithic monuments of Algeria, but also with the taulas of Menorca.

The Domus de Janas again appear in a common family, this time together with the tombe de giganti from the south of Sardinia. Curiously, they appear related to the monu-ments of the northeast of Iberia and the south of France, but, most important, they are also related with those from Tunisia (notably the similarly constructed hawanat) and Malta. A final cluster groups together the monuments of southern Iberia with those of Morocco and, interestingly, the cists of Corsica and the northern tombe de giganti. The results of this particular analysis are at once puzzling and elucidating.

Figure 6 presents the results of our cluster analysis which clarifies the situation. The dendrogram presents a first complete separate section (branch 4) which includes the Balearic monuments (megalithic monuments and navetas) plus those of southeast France, the Thracian dolmens — a clear geographic interloper — and the pozi. All of them are predominantly orientated towards the setting part of the horizon.

The next division (branch 3) groups monuments from the Pyrenees (Spanish and French), the Corsican dolmens (3(a) sub-branch), and those in the north of Africa (Algeria, Tunisia, hawanat) with those in the southern sector of the island of Sardinia, including all the Domus de Janas. A similar outcome to the k-means computation resulted. A further division (branch 1) groups the rest of the island monuments (except the Corsican cists) with the related monuments of the Iberian NE and the south of France. Branch 2 finally groups the monuments of the northern part of Sardinia (sub-branch 2(b)) with those from the south of the Iberian Peninsula and Morocco; certainly a curious outcome.

Broadly speaking, these results could indicate the presence of two or three tradi-tions or orientation customs in the western Mediterranean. A first one would be those

Fig. 6. Dendrogram of the comparative statistical analysis of monuments in the western Mediterranean region. Four different groups can be identified, with Sardinian monuments located — with just a single exception — in two of them, showing that the island could be interpreted as a sort of carrefour of orientating customs. See the text for further discussion.




monuments with orientations mostly towards the setting part of the horizon, basically including those of southern France and the Balearic Islands. The Sardinian pozi would be surprisingly connected with this tradition. A second family would include those groups with orientations mostly towards the SE quadrant of the horizon. This includes the monuments from the Iberian Peninsula and the south of France close to the Pyrenees. The northern tombe de giganti present orientations compatible with this family and in general those from the northern sector of Sardinia. We could be talking of a ‘northern group’ custom. Finally, there are constructions mostly orientated towards the southern part of the horizon, which contain the monuments of Tunisia and southern Sardinia, including the Domus de Janas and the hawanat. Indeed, we are not arguing that these families are culturally related, at least not all the members of each group, but rather that the orientations of those monuments were possibly connected with similar astronomical events on the horizon.25

4. Conclusions

As a final result of our experiment, the following preliminary conclusions can be arrived at.During the Bonuighinu Culture, from the late fifth millennium b.c. onwards, Domus de

Janas started to be built, or — better — sculpted, in Sardinia with an orientation custom that possibly favoured the ‘illuminated’ southern half of the horizon. This tradition had certain parallels with the monuments later built or sculpted in other islands of the western Mediterranean Sea — such as Maltese temples and the taulas of Menorca — and the north of Africa — notably the hawanat. This custom spread throughout the insular territory with minor differences between the north and the south of the island.

The situation remained so during the period of maximum construction during the Ozieri Culture (c. 3800−2700 b.c.), but a new tradition of megalithic tombs (predominantly dol-mens but also dolmenic corridors) came, possibly from the sea, and was established in the north of the island. These new burial buildings came with an orientation custom (southeast quadrant of the horizon: related to either the sun or the moon) that was loosely related to those present in other areas of the western Mediterranean region such as the Iberian Peninsula where the megalithic phenomena had been developed earlier. Curiously, the tradition was also present in neighbouring Corsica but had no parallel with the megalithic monuments built in the nearby coast of southern France.

During the Bronze Age, the Nuraghic civilization was born, presumably in the north of Sardinia, bringing the construction of literally hundreds of cyclopean monuments both for the living (nuraghi or megara) and the dead (tombe de giganti). The orientation custom was apparently copied from the earlier megalithic tradition. However, when the nuraghe builders spread to the south of the island, the custom relaxed, perhaps influenced by the original ‘southern’ tradition expressed in the orientation of the Domus de Janas. Only the sacred wells (pozi) do not fit the proposed simple scheme and this could be related to an actual difference in the cult performed in those sacred structures —possibly related to the new crescent moon26 — or to a more prosaic statistical problem due to the small size of the sample. Indeed our analysis identifies Sardinia as a formidable crossroads of different traditions in the middle of the western Mediterranean region.




ACKNOWLEDGEMENTS

This work has been partially financed within the framework of the projects P/309307 Arqueoastronomía of the Instituto de Astrofísica de Canarias, and Orientatio ad sidera III (AYA2011-26759) of the Spanish MINECO. ACGG is Ramón y Cajal researcher of the MINECO.

NOTES ON CONTRIBUTORS

A. César González García ([email protected]) is a Ramón y Cajal Fellow at the Heritage Sciences Institute (Incipit-CSIC, Santiago de Compostela, Spain) where he develops research lines on archaeoastronomy, ranging from the orientation of megaliths and landscape to the orientation of Roman cities or medieval churches. He currently is Vice-president of SEAC.

Mauro P. Zedda ([email protected]) is a student of archaeology and heritage at the University of Sassari. For the last decades he has been measuring the orientation of numerous buildings of the Nuraghic civilization of his island, Sardinia, including tombe de giganti, Domus de Janas, sacred wells, and the fascinating nuraghi. He is now studying the orientation of pre-Romanesque and Romanesque churches in Sardinia, Corsica and Tuscany.

Juan Antonio Belmonte Avilés ([email protected]) is an astronomer at the Instituto de Astrofísica de Canarias (Tenerife, Spain) where he researches in exoplanets and cultural astronomy. In the last decade he has been investigating the astronomical traditions of ancient civilizations, concentrating on the ancient Mediterranean cultures.

REFERENCES

1. See for example, M. Zedda, M. Hoskin, R. Gralewski and G. Manca, “Orientations of 230 tombe di giganti”, Archaeoastronomy, no. 21 (1996), S33–54, for the tombe di giganti; M. Zedda and M. Hoskin, “Orientations of Sardinian dolmens”, Archaeoastronomy, no. 22 (1997), S1–16, for the dolmens; M. Zedda and J. A. Belmonte, “On the orientation of Sardinian nuraghes: Some clues to their interpretation”, Journal for the history of astronomy, xxxv (2004), 85–107, for the nuraghi; and J. A. Belmonte and M. Zedda, “From Domus de Janas to Hawanat: On the orientations of rock carved tombs in Western Mediterranean”, in M. P. Zedda and J. A. Belmonte (eds), Light and shadows in cultural astronomy (Cagliari, 2007), 39–46, for a preliminary study of the Domus de Janas (2005).

2. Such as the sun, the moon, the Southern Cross area of the sky, etc. Also relevant would be: A. C. González-García, L. Costa Ferrer and J. A. Belmonte, “Solarist vs. Lunatics: Modelling patterns in megalithic astronomy”, in Zedda and Belmonte (eds), Light and shadows in cultural astronomy (ref. 1), 23–30.

3. M. P. Zedda, Astronomia nella Sardegna preistorica (Cagliari, 2013). Actually, the review and later publi-cation of this book, with its huge series of new data, has been the trigger initiating the work presented in this paper. The data of these, and other, Sardinian monuments are available on request from the second author.

4. For similar approaches, see: A. C. González-García and J. A. Belmonte, “Statistical analysis of mega-lithic tomb orientations in the Iberian Peninsula and neighbouring regions”, Journal for the history of astronomy, xli (2010), 225–38; and A. C. González-García, “Profiting from models of astronomical alignments to unveil ancient cosmologies in Europe and the Mediterranean”, in I. Sprajc and P. Pehari




(eds), Ancient cosmologies and modern prophets (Anthropological notebooks, xix (2013), supple-ment), 49–66.

5. Each of these typologies is extensively analysed and discussed in Zedda, op. cit. (ref. 3). 6. The data come from Zedda, op. cit. (ref. 3), Tables 3.3 and 3.4. 7. As shown in Zedda and Belmonte, op. cit. (ref. 1, 2004). 8. G. Tanda, “L’ipogeismo in Sardegna: Arte, simbologia, religione”, in Atti del Congresso Internazionale

L’ipogeismo nel Mediterraneo Orogini, sviluppo, quadri culturali (Sassari, 2000), 399–426. Also rel-evant, although somewhat outdated, is G. Lilliu, La civiltà dei Sardi, dal paelolitico all’età dei nuraghi (Turino, 1988).

9. Analysis of the orientation of the tangent lines of the peripheral towers of complex nuraghi showed a sta-tistically significant preference towards the points from which the sun and the moon rise and set at the solstices and the lunistices. See Zedda and Belmonte, op. cit. (ref. 1), and M. P. Zedda, “When astro-nomical meaning goes beyond orientation and becomes architectural design”, in Zedda and Belmonte (eds), Light and shadows in cultural astronomy (ref. 1), 31–8. It is also important to note that in the more sophisticated nuraghi, there are seldom additional windows in the upper levels of the nuraghe (and the central tower in the complex ones) that keep the same orientation of the gate at groundfloor.

10. See A. Depalmas, “Il Bronzo medio della Sardegna”, “Il Bronzo recente della Sardegna”, and “Il Bronzo finale della Sardegna”, in Atti della XLIV Riunione Scientifica Istituto Italiano di Preistoria e Protostoria: La preistoria e la protostoria della Sardegna (Florence, 2009), 123–30, 131–40 and 141–60.

11. See Zedda, op. cit. (ref. 3). Also relevant would be also M. P. Zedda, Archeologia del paesaggio nuragico (Cagliari, 2009).

12. See Zedda, op. cit. (ref. 11), and Zedda and Belmonte, op. cit. (ref. 1). Surprisingly, the geographical distri-bution of the two dialectal versions of Sardinian (Campidanese and Lugudorese) coincides with the geographic boundary of the two styles of nuraghe, despite both being descendents of the Latin spoken on the island after the Roman conquest in the third century b.c.

13. The Epanechnikov kernel is optimal given that it does not have tails towards infinity like a Gaussian, where part of the estimate would be diffused. V. A. Epanechnikov, “Non-parametric estimation of a multivariate probability density”, Theory of probability and its applications, xiv (1969), 153–8.

14. A key choice is that of the bandwidth of the kernel function. Depending on the number of monuments, the spread in azimuths and the errors implied in the data acquisition process, one may use larger or smaller values for the pass-band. It is important to note that for other kernels there are theoretical or practical prescriptions, but for the Epanechnikov kernel this is based mostly on a trial and error method.

15. González-García and Belmonte, op. cit. (ref. 4). See also J. A. Belmonte and A. C. González-García, “The ‘genetic’ analysis of Iberian dolmens: A test of the idea in the central Pyrenees”, Journal for the history of astronomy, xliii (2012), 227–32. Also relevant will be: A. C. González-García and J. A. Belmonte, “Temple orientation across the Mediterranean: A comparative statistical analysis”, Mediterraean archaeology and archaeometry, in press.

16. M. Fletcher and G. Lock, Digging numbers (Oxford, 2005), 139.17. González-García and Belmonte, op. cit. (ref. 4).18. E.g. B. S. Everitt, Cluster analysis (London, 1995). See also: González-García, op. cit. (ref. 4).19. In our statistical analysis we consider only azimuths and not declinations. In principle such a choice

seems surprising when considering orientations at different latitudes, such as the northern and south-ern shores of the Mediterranean. However, the choice is justified by the intention to include the effect of the rising and setting directions, which is lost when using declinations. Besides, it should be noted that, for instance, the most extreme positions of the sun at winter solstice would differ by as much as 3½° between latitudes 36° and 43°. The variance is of course larger at latitudes further north, but these lie outside the geographical scope of this paper.

20. Data on all these series of monuments can be found in M. Hoskin, Temples, tombs and orientations: A new perspective on Mediterranean prehistory (Bognor Regis, 2001), and references therein. Two excep-tions are the Corsican dolmens and the square talayots of Majorca, for these, see: G. Thury-Bouvet, J.-F. Santucci, E. H. Khoumeri and A. Ottavi, “Orientations of Corsican dolmens”, Journal for the history of astronomy, xxxvii (2006), 299–306; and J. Aramburu-Zabala and J. A. Belmonte, “On the orientation of the square talayots of Mallorca”, Archaeoastronomy, no. 27 (2002), S67–74. See also




the relevant chapters in J. A. Belmonte and M. Hoskin, Reflejo del cosmos: Atlas de arqueoastronomía en el Mediterráneo antiguo (Madrid, 2002).

21. For data on southeastern Iberian dolmens, see Hoskin, op. cit. (ref. 20).22. For data on megalithic monuments and hawanat in the north of Africa, see: J. A. Belmonte, C. Esteban and

J. J. Jiménez, “Mediterranean archaeoastronomy and archaeotopography: Pre-Roman tombs of Africa Procunsularis”, Archaeoastronomy, no. 23 (1998), S7–24; J. A. Belmonte, C. Esteban, L. Cuesta, M. A. Perera Betancort, J. J. Jímenez González, “Pre-islamic burial monuments in Northern and Saharan Morocco”, Archaeoastronomy, no. 24 (1999), S21–34; J. A. Belmonte, M. A. Perera, R. Marrero and A. Tejera Gaspar, “The dolmens and hawanat of Africa proconsularis revisited”, Journal for the history of astronomy, xxxiv (2003), 305–20; and J-F. Santucci, E. H. Khoumeri, “Orientations of megalithic tombs in Algeria (1): Djebel Mazela and Rocknia Necropolises, and the Kabylian ‘Allées couvertes’”, Journal for the history of astronomy, xxxix (2008), 65–76. For data on the Thracian dolmens, see: A. C. González-García, D. Z. Kolev, J. A. Belmonte, V. P. Koleva and L.V. Tsonev, “On the orientation of Thracian dolmens”, Archaeoastronomy, the journal of astronomy in culture, xxii (2009), 21–33.

23. As noted by González-García and Belmonte, op. cit. (ref. 4).24. Something already suggested by González-García, op. cit. (ref. 4).25. Broadly speaking, we could be talking of a sun-decending/sunsetting, sun-ascending/sunrising and sun-

at-the-meridian — or ‘Southern Cross’ — customs, respectively, in agreement with Hoskin’s earlier proposals, op. cit. (ref. 20). Indeed, the actual situation will certainly be much more complicated with the moon possibly playing a role. See González-García et al., op. cit. (ref. 2).

26. It has been reasonably argued that the moon played a relevant role in the planning — and the related water cult — of certain important sacred wells. See A. Lebeuf, Il pozzo di Santa Cristina, un osservatorio lunare (Cracow, 2011).



statistical approach on the orientation of prehistoric sardinian monuments: a comparative

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