Update to the 'Origin of the Greek constellations' paper

The manuscript below has been updated and resubmitted to the journal. It is provided here with permission of the journal.

Origin of the ancient Greek constellations via analysis of Pillar 43 at Göbekli Tepe  

 

Martin B. Sweatman and Dimitrios Gerogiorgis

 

School of Engineering, The University of Edinburgh, The King's Buildings, Sanderson Building, Mayfield Road, Edinburgh EH9 3JL, United Kingdom.

email: martin.sweatman@ed.ac.uk

 

key words: Greek constellations, Göbekli Tepe, Pillar 43, digital image analysis

 

ABSTRACT

Göbekli Tepe is an Epipalaeolithic/Neolithic hill-top archaeological site in southern Turkey featuring several large enclosures formed of megalithic pillars, many of which are covered with intricately carved symbols. We re-evaluate an astronomical interpretation of Pillar 43 at Göbekli Tepe using digital image analysis to quantitatively evaluate pattern matches between animal symbols on this pillar and Greek constellations. Our statistical analysis of the results supports earlier conclusions that at least some of the animal symbols on this pillar almost certainly represent constellations genetically related to those of the ancient Greeks.

1.      Introduction

This work investigates the origin of the ancient Greek constellations that we continue to use in modern astronomy. They are similar to some of those used by ancient Mesopotamian cultures. Their origin is largely unknown, despite great interest in this problem. Here, we explore the possibility that precursors to some of the Greek constellations appear at Göbekli Tepe, an early Neolithic archaeological site in southern Turkey, circa 10,800 BCE.

Although the constellations are human inventions, the brightest stars form obvious patterns that are likely to be highly conserved for many millennia. Indeed, widely dispersed myths related to the Pleiades, Orion and Ursa Major constellations are thought to be over 50,000 year old (Frank and Bengoa, 2001; d’Huy, 2016; d’Huy and Berezkin 2017; Norris and Norris, 2021). There are likely to be many reasons for this early interest in astronomy, including navigation (especially in a maritime setting), time-keeping, and optimisation of seasonal resources so that family and tribal life can be planned.

Specifically, regarding the Greek constellations, Ptolemy’s Almagest (2^nd century CE) is the earliest surviving catalogue of these constellations, described with sufficient detail that we can identify from his tables the specific stars and the likely patterns they formed (Toomer, 1984). In case of doubt, the Farnese Atlas (also 2^nd century CE) and other ancient globes provide useful hints about how these constellation patterns were viewed at this time. Stellarium and other modern astronomical software provide modern interpretations of these constellation patterns (Stellarium, 2022).

Going backwards in time, details recorded in Aratus’ poetic version of Eudoxus’ Phenomena suggest the Greek constellations were known as a complete set already by the mid-4^th century BCE (Rogers, 1998b). But before this, the trail of evidence for their invention becomes vague and difficult to interpret.

For example, references to a few of the non-zodiacal Greek constellations are found in ancient works by Homer and Hesiod (Rogers, 1998b). In particular they allude to Orion, Bootes, Ursa Major and the Pleiades and Hyades, as well as specific stars. Although the earliest versions of these epics are thought to date to the 8^th Century BCE, they are thought to describe events from the preceding millennium. Therefore, it is likely that some of these non-zodiacal constellations also existed during the 2^nd millennium BCE. As already stated, some of these constellations, like the Pleiades, Orion and Ursa Major, could be extremely ancient with origins in the middle Palaeolithic.

Regarding the zodiacal constellations, the earliest written accounts of them are found in Babylonian texts, such as the MUL.APIN, also from the mid-1^st millennium BCE (Rogers, 1998a). These texts list descriptive names for these constellations as well as ancient names for some of their stars, providing convincing evidence these constellations were known at this time, even if they are not described with the same level of detail as in Ptolemy’s Almagest. However, it is thought by some scholars that these surviving cuneiform texts are probably copies of older ones from the end of the 2^nd millennium BCE.

Therefore, it is often suggested that the Greeks combined the Babylonian zodiacal constellations with disparate non-zodiacal constellations, including a few of great antiquity, to create the complete set of ancient Greek constellations around the middle of the 1^st millennium BCE (Rogers, 1998a, 1998b).

While this is an attractive story, there is no clear evidence it is correct. In fact, it is contradicted by Pseudo-Eratosthenes who recounts a myth recorded in a lost work by Hesiod (which therefore might have originated in the 2nd millennium BCE) about the deity Orion (Condos (1997));

“Orion went away to Crete and spent his time hunting in company with Artemis and Leto. It seems that he threatened to kill every beast there was on earth; whereupon, in her anger, Earth sent up against him a scorpion of very great size by which he was stung and so perished. After this Zeus, at one prayer of Artemis and Leto, put him among the stars, because of his manliness, and the scorpion also as a memorial of him and of what had occurred.”

This suggests the Greeks already knew of the zodiacal Scorpius constellation by the 2^nd millennium BCE. It is for reasons such as this that Kechagias and Hoffman (2022) state,

“… the origin of the 48 ancient constellations of the Almagest remain largely enigmatic in contrast to the modern southern constellations, … There has been much speculation about possible origins in ancient Mesopotamia and ancient Egypt (Boll 1903) with the first hypothesis being more popular due to the panbabylonism in the first half of the 20th century. … Nevertheless, evidence for the conjectures about the constellations is hardly to be found.”

Despite this uncertainty, there is strong evidence for the existence of constellations similar to several of the Greek zodiacal constellations already in ancient Sumer and Egypt by the mid-4^th millennium BCE (Sweatman, 2023; Rogers, 1998a; Hartner, 1965). This evidence is in the form of artistic works rather than texts. In several cases, these zodiac-like animal symbols are accompanied by sunset-like symbols which are interpreted to indicate their zodiacal function (see Figure 1). They can be interpreted as displaying dates using precession of the equinoxes (Sweatman, 2023). Hartner (1965) argues that many bull and lion symbols from this time clearly represent constellations, i.e. Taurus and Leo respectively, since they are covered with star-like inclusions or are placed against a starry background or are exaggerated in a way consistent with a zodiacal interpretation. Moreover, Sweatman (2023) shows that early Sumerian pictographs for units of time also resemble sunsets (see Figure 1). They are practically identical to the early Sumerian pictograph for the sun (Puhvel, 2023). Thus, it is clear that for prehistoric Sumer at least, a sunset symbol was used to denote both the sun and units of time, and similar symbols are often found in the same context as zodiac-like animal symbols, some of which clearly represent constellations.

Figure 1. Ancient Iranian Jiroft stone weight in the shape of a sunset symbol, circa 2,500 BCE (a, from Wikipedia, CC-BY-4.0) showing zodiac-like animal symbols and a Master-of-Animals symbol. Uruk Vase, Mesopotamia, circa 3500 – 3000 BCE (b, from Wikipedia, CC-BY-4.0) showing zodiac-like animal symbols above sunset-like symbols. Copy of the inscription at the Gebel Djauti rock shelter site discovered by Darnell and Darnell (2002) showing zodiac-like animal symbols and a sunset-like symbol. The ‘akhet’ Egyptian hieroglyph for ‘horizon’ (d). Bottom of Figure 2.9 from Woods (2010) showing proto-cuneiform time-keeping symbols that resemble a sunset symbol turned on its side (e), which are practically identical to the proto-cuneiform sunset-like symbol for ‘sun’.

 

The origin of these 4^th millennium BCE zodiac-like animal symbols and sunset-like symbols is unknown, but their dispersion across a wide region and the common appearance of animal symbols on even earlier Neolithic artefacts in Mesopotamia, Iran and Egypt leaves open the possibility of a much earlier Neolithic, or even Palaeolithic, origin.

For example, Marshack (1972) suggested that animals painted inside European Upper Palaeolithic caves might represent constellations. This artistic tradition endured in Palaeolithic Europe almost unchanged for 30,000 years, which suggests it might be linked with a long-lasting mythical tradition. Given that some widely dispersed myths are associated with constellations represented by animal symbols, we have a consistent set of assumptions. Namely, that Palaeolithic Europeans observed the stars, associated constellations with animals and mythical stories, and painted their symbols on cave walls.

Later, Rappengluck (2004) suggested that some of these paintings might even be associated with some familiar Greek constellations, citing the bull as Taurus, or specifically the Hyades cluster. Moreover, Jegues-Wolkiewicz (2007) found that most of these Upper Palaeolithic painted cave entrances appear to have significant solsticial or equinoctial orientations. The Lascaux cave entrance known as the ‘Hall of Bulls’, for example, faces towards the setting sun on the summer solstice, to within a few degrees, such that paintings of bulls on its walls are illuminated only for a few days or weeks around this auspicious time.

More recently, Sweatman and Coombs (2019) compared radiocarbon dates for many of these animal cave paintings with their expected ‘zodiacal date’, based on an assumed ancient zodiac deduced largely from early Neolithic sites like Göbekli Tepe (Sweatman and Tsikritsis, 2017a), and found such a strong correlation that they concluded that most of the animal paintings almost certainly do represent constellations. Apparently, ancient people painted these symbols to mark the observation of solstices and equinoxes.

Hayden and Villeneuve (2011) performed an ethnographic survey of extant hunter-gather cultures and found that many of the more complex groups maintained an interest in astronomy, including observation of the solstices and equinoxes. Therefore, an interest in observing the solstices and equinoxes among Upper Palaeolithic hunter-gather groups is plausible. Once this practice is established, we can expect the discovery and recording of the obvious astronomical phenomenon of precession will likely soon follow (Hughes, 2005). De Santillana and von Dechend (1969) argue that precession is also likely to be encoded in many widespread, and therefore ancient, myths, and Magli (2004) provides good evidence of its knowledge in early Bronze Age Indus Valley, Egyptian and Mesopotamian cultures.

Thus, it appears the origins of several of the ancient Greek constellations, along with knowledge of precession, might be traced far back into Upper Palaeolithic Europe. Given that Sweatman and Coombs’ (2019) observations drew on earlier work by Sweatman and Tsikritsis (2017a) concerning animal symbols on the broad sides of T-shaped pillars at Göbekli Tepe, it appears that this site might represent a bridge in time and place between European Upper Palaeolithic symbolism and similar astronomically-related symbolism observed across late Neolithic Near Eastern cultures. Peters and Schmidt (2004) also suggest Göbekli Tepe could feature symbolism from the Palaeolithic era.

Sweatman (2023) describes a more detailed astronomical interpretation of Göbekli Tepe’s symbolism and its importance in the debate concerning the Palaeolithic-Neolithic cultural transition, a.k.a. the Neolithic revolution, in the Fertile Crescent. In particular, he finds evidence for use of a lunisolar calendar system at Göbekli Tepe that supports the earlier interpretation of Sweatman and Tsikritsis (2017a). He also describes several other examples of potential symbolic links between Göbekli Tepe and much later Neolithic and Bronze Age cultures, which provide further support for Sweatman and Tsikritsis’ (2017a) ideas.

In Sweatman’s work, a key line of evidence is a statistical argument devised to support the view that animal symbols on the broad sides of Göbekli Tepe’s T-shaped pillars, especially Pillar 43, can be associated with ancient Greek constellations. This view was challenged by Notroff et al. (2017) for several reasons, including that they considered this possibility “extremely far-fetched”. However, they did not challenge Sweatman and Tsikritsis’ (2017a) statistical method directly. Instead, they simply ignored it. Sweatman and Tsikritsis’ (2017b) response dealt adequately with each objection raised by Notroff et al. (2017), with additional arguments given by Sweatman (2023). Especially, they pointed out that Notroff et al’s (2017) opinion on the origin of the Greek constellations was unsubstantiated, i.e. it was unsupported by any evidence. As we have already seen, the origin of the Greek constellations in unknown, although a Neolithic, or even a Palaeolithic origin, is plausible.

Nevertheless, by challenging Sweatman and Tsikritsis’ (2017a) conclusions, Notroff et al. (2017) effectively called their statistical method into doubt. The aim of this present work, therefore, is to re-evaluate Sweatman and Tsikritsis’ (2017a) statistical method. Digital image analysis and Bayesian statistics are used to support this analysis.

The rest of this paper is as follows. In the next section we first briefly introduce Göbekli Tepe and Pillar 43. We then summarise the statistical method used by Sweatman and Tsikritsis (2017a) to analyse Pillar 43 before describing some if its shortcomings. We then describe how some of those issues can be overcome, including through the use of digital image analysis and Bayesian statistical arguments. By performing this analysis, we arrive at a more robust conclusion for the symbolism for Pillar 43. We conclude with a summary of this work and a view of its implications.

 

2.      Göbekli Tepe and Pillar 43

 

Sweatman (2023) provides an account of the archaeological site of Göbekli Tepe, Pillar 43, the related Taş Tepeler complex, and their importance in understanding the Neolithic revolution. Therefore, only brief details about Göbekli Tepe and the Taş Tepeler complex are given here. Pillar 43, which is the focus of this work, is described in detail later.

 

2.1 Göbekli Tepe and other Taş Tepeler sites

Göbekli Tepe is an Epipalaeolithic or early Neolithic archaeological site only 12 km north-east of Sanliurfa, southern Turkey (Schmidt 2000; Schmidt, 2011). It is a hill-top site with excellent views to the south over the Harran plain, and is therefore ideally located for naked-eye astronomical observations. Excavations on the main archaeological site began in 1994 led by Klauss Schmidt of the German Archaeological Institute. They revealed a system of four sub-circular enclosures, labelled enclosures A-D (see Figure 2), formed of rough stone walls embedded with many T-shaped megalithic pillars. Another enclosure, labelled E, sits outside the main excavation area, but its walls and pillars are missing; only its smoothed bedrock floor complete with a central pair of pillar sockets remains. The stone pillars embedded in the walls of enclosures A-D feature remarkably intricate symbols, including many animals and more abstract symbols, thought by Schmidt (2011) to be an early form of proto-writing. Like the inner ring of enclosure C, enclosure D is formed by 11 T-shaped megalithic pillars, roughly evenly spaced around the enclosure wall.

Figure 2. Plan of enclosures A-D at the main excavation site of Göbekli Tepe.

 

The earliest radiocarbon dates reported so far for Göbekli Tepe are (Dietrich, 2013);

         I.            A measurement (KIA-44149) on charcoal particles from within mortar that binds the wall of enclosure D, from between pillars 41 and 42 in north-west of the wall, with a (95.4%) calibrated radiocarbon age of 9,530 ± 200 BCE.

       II.            A measurement (UGAMS-10796) from a hearth just outside and north-east of enclosure D close to the bedrock, also with a radiocarbon age (95.4%) of 9,530 ± 200 BCE.

We have re-calibrated both of these radiocarbon measurements using the latest radiocarbon calibration curve (Reimer et al., 2020). Clearly, they are in excellent agreement. However, according to Kinzel and Clare (2020), the earliest phase of construction (phase 1) of Enclosure D corresponds to a section of the southern wall, and the north-west part of the wall that has been radiocarbon dated (KIA-44149) seems to belong to a later phase (see Figure 3.12 of Kinzel and Clare (2020)). Regarding the earlier phase 1 construction, they state,

“Although radiocarbon dates are lacking for this phase, it likely belongs to the second half of the 10th millennium cal BC (PPNA), though an earlier (Younger Dryas) age cannot be ruled out.”

This appears to contradict the above radiocarbon dates, since phase 1 apparently precedes that part of the wall dated to 9,530 ± 200 BCE. Since the date of this wall is supported by an identical date from a hearth close to bedrock from outside of the enclosure, we can conclude that the earliest phase of construction of enclosure D is unknown, but it is likely to be somewhat older than 9,530 BCE. Since Göbekli Tepe itself likely has an origin that pre-dates Enclosure D (Sweatman, 2023), and Enclosure D’s origin is likely significantly older than 9,530 BCE, a Younger Dryas origin (i.e. between 10,800 and 9,600 BCE) for Göbekli Tepe is quite reasonable.

Since excavations at Göbekli Tepe began, other neighbouring sites with some similar features, such as T-shaped megaliths, have been discovered. Along with Göbekli Tepe, these twelve sites are excavated under the Taş Tepeler project and are thought to be contemporaneous. Included among them are Karahan Tepe, which is closest in terms of scale and symbolism to Göbekli Tepe, Şayburc where an interesting wall carving similar to a Master-of-Animals symbol has been found, and Balikligöl In the centre of modern Sanliurfa where the Urfa Man statue was found. Excavations at Karahan Tepe, which only began within the last few years, have uncovered a ‘pool’ structure, also formed of 11 pillars sculpted from the bedrock. Thus, it appears the number 11 has a special significance for the Göbekli Tepe culture. Sweatman (2023) suggests this number relates to a lunisolar calendar system used by this culture, where 11 is the number of epagomenal days added to 11 + 1 lunar months to make a solar year of 365 days.

 

2.1 Pillar 43

The main subject of this work, Pillar 43, is embedded into the northwest side of enclosure D at Göbekli Tepe (see Figure 3). Its astronomical interpretation is described in detail by Sweatman (2023). Briefly, notice the circular disk symbol at the visual centre of this pillar. Given a similar symbol is adjacent to a moon-like crescent symbol on Pillar 18, and that the front of Pillar 18 resembles the Nebra sky-disc (a bronze-Age artefact generally recognised to encode astronomical data), it likely represents the sun. Surrounding a similar disk on the main panel of Pillar 43 are carved several animals in various poses (see Figure 3). At the bottom of Pillar 43 we find what appears to be a headless man, probably indicating death. If the disk at the centre of the main panel represents the sun, then it follows that the animal symbols might represent constellations.  

The disk symbol rests just above the outstretched wing of a bird-of-prey, probably an eagle or vulture. If the disk represents the sun and the animal symbols represent constellations, then the head and wings of this bird symbol must represent a constellation very close to the path of the sun. Using Stellarium (2022) with the Western constellation set, we find that the only Greek constellation along the ecliptic with this geometry is the ‘bow’ of Sagittarius, also known as the ‘teapot’, viewed at sunset. The apparent fit of this constellation to the head and wings of the vulture, including the relative positions of the disk and the sun, appears to be very good.

This choice orients the main panel and suggests that if the animal symbols represent constellations, they might be ancestral to some of the ancient Greek ones. In this case, and given this orientation, we expect to find a symbol similar to the Scorpius constellation directly below the eagle/vulture. This is exactly what is found, although the scorpion’s vertical orientation is reversed. Likewise, we expect to find a symbol similar to the constellation Lupus directly to the lower left-hand side of the scorpion. And indeed, quite remarkably, we find exactly the symbol expected in this position on the pillar – likely a dog or wolf with snout and paws in precisely the direction expected. This is highly significant, and unlikely to be a coincidence. To the right of the scorpion and eagle/vulture we expect to find symbols similar to the Ophiuchus and Serpens constellations, and indeed we find what appears to be a flamingo with a wriggling fish or snake grasped in its beak, with overall shape similar to Ophiuchus, although its position is slightly out. Moreover, underneath the Scorpion we expect to find a symbol similar to the Libra constellation. Interestingly, we find a duck or goose symbol that can be viewed as representing Libra, which at sunset is reminiscent of the classic ‘rubber duck’ shape.

Figure 3. Pillar 43 at Göbekli Tepe embedded in enclosure D’s wall (right, image courtesy of Alistair Coombs). Line drawing of Pillar 43 revealing more of its symbolism (middle). A scene in the sky around Scorpius, 10,950 BC, from Stellarium with the teapot constellation within Sagittarius highlighted in yellow (left).

 

Already, given our expectation that these animal symbols might represent constellations, the strong correlation observed suggests they are very likely to be ancestral to the ancient Greek constellations. But what might this scene on its main panel represent? One obvious possibility is that it represents a date using precession of the summer solstice, with the position of the sun-disk relative to the wings and head of the eagle/vulture (hypothesised to represent the teapot asterism), providing a date roughly 10,950 ± 250 BCE. This date is consistent with the Younger Dryas impact (Firestone et al., 2007; Kennett et al., 2015; Sweatman, 2021; Powell, 2022), which then provides an interpretation for the headless man symbol at the bottom of the pillar. That is, this pillar is possibly a memorial to the Younger Dryas impact event. This interpretation is reinforced by the V-symbol present at the vulture/eagle’s neck, which indicates it symbolises a special day (since V-symbols are thought to represent the counting of days; see Sweatman (2023)), i.e. the summer solstice.

Now let’s move up to consider the three animal symbols in the top panel of Pillar 43 (see Figure 4) adjacent to semi-circular symbols. Sweatman (2023) argues the semi-circular symbols likely represent sunsets. As already mentioned, this is because similar semi-circular symbols adjacent to other animal symbols found on 3^rd and 4^th millennium BCE artefacts from Iran, Mesopotamia and Egypt can also be interpreted as representing a system of zodiacal dating using symbols similar to Greek zodiacal constellations (see Figure 1).

If the semi-circular shapes in the top panel do represent sunsets, then each small animal very likely represents the three other solsticial and equinoctial constellations corresponding to the summer solstice constellation on the main panel. Gurshtein (2005) predicted a system of zodiacal dating using all four solsticial and equinoctial constellations should have developed by the 6^th millennium BCE to support a farming calendar. But his arguments about the importance of observing the solstices and equinoxes should also apply to hunter-gatherers. Thus, it should not be a surprise to find a system of zodiacal dating existed already in the early Neolithic period.

In this case, and again taking the ancient Greek constellations as a basis, the corresponding equinoctial constellations are Pisces (spring equinox) and Virgo (autumn equinox). Pisces is the spring equinox constellation until around 10,200 BCE, whereupon it transfers to Aquarius, and Virgo is the Autumn equinox constellation until also around 10,200 BCE, whereupon it transfers to Leo. The winter solstice constellation, on the other hand, is less clear. Gemini is the winter solstice constellation until around 10,800 BCE, whereupon it transitions to Taurus. Therefore, both Gemini and Taurus are consistent winter solstice constellations corresponding to the position of the sun-disk on the vulture/eagle’s wing on the summer solstice.

Looking from left to right along the top panel, we see first a bending bird which has a remarkably similar shape to Pisces. The middle animal symbol can be viewed as either a charging long-legged quadruped (facing left) or a crouching short-legged quadruped (facing right). Either way, it is clearly a quadruped viewed from the side with legs vertically beneath a slightly inclined torso. Gemini can easily be interpreted in this way, but Taurus is less clear in this context. It was for this reason that this central animal was associated with Gemini by Sweatman and Tsikritsis (2017a). Finally, the right-most animal symbol appears to be a quadruped, this time viewed from above with legs splayed out at each corner and crawling downwards. Again, this symbol is a reasonably good match to Virgo.

If these associations are correct, we can obtain a refined date range for the date represented by Pillar 43. On the one hand, we can estimate a lower date based on the position of the sun relative to the eagle/vulture’s head and wing. Since the midpoint between the head and wing, which we assume to be the top and spout of the teapot constellation respectively, corresponds to 10,950 BCE, and since the disc is much closer to the eagle/vulture’s wing than head, a lower bound of 10,900 BCE can be set. If the winter solstice constellation corresponds to Gemini, as expected, then an upper bound of 10,800 BCE can be set. This produces a more refined date of 10,850 ± 50 BCE. However, if the winter solstice constellation corresponds to Taurus, then the upper bound of 10,700 BCE is unchanged. In this case, a more refined date of 10,750 ± 50 BCE is obtained. Taking both possibilities into consideration, we have a refined estimate of 10,800 ± 100 BCE. The Younger Dryas impact is dated to 10,835 ± 50 BCE (Kennett et al., 2015).

 

3.      The statistical shape correlation method (Sweatman and Tsikritsis, 2017a)

Given this very remarkable series of correlations between symbols on Pillar 43 and the Western constellation set in Stellarium, earlier work tried to estimate the probability that this correlation is purely a coincidence. This is a difficult problem, but Sweatman and Tsikritsis (2017a) approached it as follows. Assuming the null hypothesis, which is that animal symbols do not represent constellations, they estimated the probability that a set of animal symbols can be selected at random from those seen at Göbekli Tepe and placed on Pillar 43 and yet be mistaken for Greek constellations representing a date using precession of the equinoxes with as strong a correlation, or better, as those that actually appear on Pillar 43. The probability of obtaining this level of correlation, they assumed, is a reasonable estimate for the probability the animal symbols do not represent constellations.

Figure 4. The upper panel of Pillar 43 that displays three small animal symbols next to three handbag-like ‘sunset’ symbols, compared with expected constellations: Pisces (left), Gemini (middle) and Virgo (right). Image courtesy of Alistair Coombs.

To understand this statistical method, consider some simpler problems first that elaborate the key ideas.

i)                    Suppose a pill is given to a random group of 50 people while a placebo is given to another random group of 50 people. If all the people that took the tablet are dead by the following day, while all of those that took the placebo are alive and well, it is fair to assume the tablet is deadly. No prior knowledge of the mechanism leading to death is needed, nor is any hypothesis about the properties of the pill needed a priori. We can conclude that taking the pill is almost certainly deadly solely on the basis of the statistics a posteriori. This is the scientific method in action.

ii)                   Now consider a different situation, where in a room of 100 people all of them are stood on caricatures painted on the floor that look just like them. Again, using basic probability, i.e. logic, it is safe to assume this situation did not occur by chance because the probability of it happening by chance is tiny. However, for this example prior knowledge might influence our estimate of this chance. For example, suppose it is known that this situation occurs by design, i.e. it is arranged, only on Mondays. Then, if we did not know which day it was, our estimate of the probability that this situation occurred by chance would be influenced, or biased, by this prior knowledge. We could also know with high confidence that the day on which this observation was made was a Monday. Clearly, our estimate of the probability that events happen by chance or not can be affected by prior knowledge. This is the principle of Bayesian statistics.

iii)                 Now suppose the same situation as ii), but instead it is not so clear that each person is stood on a caricature that looks the most like them. Nevertheless, the likeness between the caricatures and people can still be ranked. In this case, it is still possible to reach a conclusion with confidence about whether the situation occurred by chance or design using a statistical estimate of the correlation. Again, this probability estimate can be influenced by prior knowledge. This method follows basic scientific principles.

This last problem is identical to the statistical test devised by Sweatman and Tsikritsis (2017a) for Pillar 43. They assumed no prior knowledge of the probability of whether astronomical symbolism could appear at Göbekli Tepe. Their statistical test is therefore unbiased in this respect.

In more detail, they took a combinatorial approach where any animal symbol associated with a constellation on Pillar 43 can be replaced with any of the 12 main ones found to date at Göbekli Tepe with uniform probability. As there are 8 animal symbols linked with constellations on Pillar 43, and around 12 animal symbols on the broad sides of Pillars at Göbekli Tepe known so far to choose from, there are a total of 12⁸ = 430 million distinct and equally likely combinations of animal symbols on Pillar 43, if we allow the same symbol to occur multiple times. Let’s call this number, the number of allowed combinations, x. Considering that some pillars at Göbekli Tepe display the same animal symbol more than once, this seems to be a fair way of counting x.

They then estimated how many of these combinations were as good as the one that already appears on the pillar for representing a date. To answer this, they first ranked each animal symbol against each constellation associated with that position on Pillar 43. In this way, a score, Z, can be associated with each distinct combination by summing the ranks for each animal symbol in that position. By counting how many other combinations, y, there are with the same or better score as the animal symbols that actually appear on the pillar, an estimate of the probability that the overall pattern match on Pillar 43 is a coincidence is obtained as y/x.

In principle, this is a fair and scientific approach provided the ranked lists for each animal symbol are obtained objectively. Note, however, that it does not take into account any prior knowledge about the possibility of astronomical symbolism at Göbekli Tepe. It is therefore an unbiased test.

Clearly, the ranked lists that compare animal symbols with constellations are crucial in this test. Preferably, these rankings should be obtained objectively. However, Sweatman and Tsikritsis (2017a) instead created their ranked lists by eye, resulting in a subjective result. Note, however, that visual inspection and judgement of artifacts is commonplace in archaeology. Pieces of pottery, bone, stone, and many other materials are routinely inspected visually by archaeologists. Often, this process is deemed sufficient to confidently decide to which category each object belongs, provided the context of the find is also respected. Sweatman and Tsikritsis’ (2017a) study, therefore, follows similar rules to the bulk of archaeological research.

Nevertheless, they obtained an estimate of 1 in 100 million. This means that, according to their view of the pattern matches and ignoring any other biases, the correlation almost certainly did not occur by pure chance. They therefore concluded the arrangement of animal symbols on Pillar 43 was not a fluke, and that the animal symbols almost certainly are related to Greek constellations.

However, there are a few more problems with their statistical estimate. First, the scorpion was used to locate and orient the scene in the sky (despite being upside-down), and it was also included in their statistical estimate. This generates a bias, which should be avoided. Second, their estimate for the number of combinations as good as or better than the one that actually appears on Pillar 43, y, was incorrect since it did not fully account for the multiplicity of possible outcomes. Taking both these errors into account, their result should be adjusted to a probability of 1 in 2.2 million, which is still a highly significant result.

In later work, Sweatman and Coombs (2019) took account of another degree-of-freedom on Pillar 43 not considered by Sweatman and Tsikritsis (2017a). That is, they provided an estimate for the probability of the placement, i.e. the precise location, of animal symbols around the scorpion on the main panel. Ultimately, a statistical estimate of 1 in 7 was obtained for this placement correlation which reduces the probability of the overall pattern match to around 1 in 15 million.

In summary, Sweatman and Tsikritsis’ (2017a) statistical method for evaluating Pillar 43 suffers from several problems, listed as follows;

1.       The ranked lists that compare animal symbols with constellations were generated by eye, which potentially introduces some subjectivity and bias.

2.       They used the scorpion symbol to pin the scene in the sky and included it in their statistical estimate.

3.       y was counted incorrectly due to a multiplicity error.

4.       No prior knowledge about the possibility of astronomical symbolism being present at Göbekli Tepe was taken into account.

Our aim here is to address all of these issues. To improve confidence in the first issue we use an alternative statistical test supported by digital image analysis (DIA). Correction of the second issue is trivial, and we use a simple Monte Carlo (MC) method to correct the third issue. Sweatman (2023) provides arguments that affect the fourth issue, and this is discussed in detail in section 6.2.

The revised statistical test and DIA method is described next.

 

4.      A robust statistical test of shape correlation for Pillar 43

If the animal symbols on Pillar 43 represent constellations, then the people who carved Pillar 43 must have had a view of which stars formed recognisable groups and how they were connected by imaginary lines. Unfortunately, we don’t have any direct knowledge of this information; we only have the animal symbols on Pillar 43. Our task, then, is to design an improved method for comparing animal symbols on Pillar 43 with the Western constellation set in Stellarium.

The term ‘constellation’ has several meanings. Sometimes it is used to refer to a constellation symbol, like a great bear. Fortunately, in some cases, such as the scorpion for example, the animal symbols on Pillar 43 and the expected Greek constellation symbols match perfectly, in terms of both the correct species, pose and viewpoint.

However, the term ‘constellation’ usually refers to a specific combination of stars, i.e. an asterism, and lines that join these stars to form a 2-dimensional pattern. If the constellation symbol is an animal, which is always the case in this work, then the connecting lines can be viewed as behaving like a skeleton, creating a framework which constrains the animal’s torso and appendages.

Any given constellation in Stellarium is just one instance of the multitude of ways that an asterism can be joined by lines. If the lines are absent, as in Ptolemy’s Almagest, an asterism can be accompanied by a constellation symbol which indicates how the points should be joined. In this case, the constellation symbol is like a powerful clue in a dot-to-dot puzzle; given an asterism and a constellation symbol, similar constellation patterns (points and lines) should be produced by different people attempting to solve the puzzle. The fact that this procedure works is evidenced by the very existence of asterisms and their symbols, such as those given by Ptolemy. If this information was insufficient to reliably construct a constellation, we can expect Ptolemy would have provided additional information to encode a constellation instead.

As a good example, consider Pisces whose points form two roughly straight lines along two sides of a triangle, and whose Greek symbol consists of two fish lying along these two sides. Anyone solving this puzzle, given the points and symbol, will form almost identical constellations.

Sometimes, though, the term ‘constellation’ is used simply to refer to a group of stars without any lines. Here, this is called an asterism. In fact, it is a pointless exercise to try to match an asterism without any lines with a 2-dimensional animal symbol. This is because an asterism without lines will fit a vast number of different patterns equally well, and this number increases exponentially with the number of stars in it. Any match of an asterism to a 2-d symbol is therefore statistically meaningless.

Our main problem, then, is to assess the similarity of the Western constellation patterns (the stars and lines) in Stellarium with the animal symbols on Pillar 43 when the corresponding symbols don’t match conceptually in terms of species. In this work, for each animal symbol on Pillar 43 we create a short-list of candidate constellation patterns in Stellarium that fit the morphology of the symbol well, and then use a DIA method to rank the constellations in this short list.

We can see two potential methods for achieving this digital comparison. In either case, the aim is to convert one kind of representation into the other, i.e. animal symbols to dots and lines, or vice-versa. We choose the latter route, i.e. we attempt to convert the constellations in Stellarium to animal symbols. To achieve this, we essentially ‘fatten’ each constellation line and then perform a pixel-by-pixel cross-correlation with an animal symbol on Pillar 43 to produce an ‘overlap’ score. In performing this translation and the subsequent scoring there are several issues to consider, discussed next.

 

4.1 Selection of animal symbols and constellations

Since the animal symbols on Pillar 43 appear to be similar to the Western constellations in Stellarium as they set on the western horizon, we use every Greek constellation in Stellarium’s Western constellation set except those that do not set. This means those southerly constellations that could not be seen from Göbekli Tepe, or were mostly obscured, at the time of the Younger Dryas impact event (taken to be 10,835 BCE) are eliminated, i.e. Canis Major, Lepus, Eridanus, Orion and the constellations that form Argo Navis. Furthermore, it also means those circumpolar constellations that do not set at this time are also eliminated, i.e. Corona Borealis, Lyra, Sagitta and Hercules. Serpens is also eliminated, since it is cut into two distinct halves in Stellarium. As explained later, for the digital representation each constellation is viewed anatomically in terms of a single torso section connecting one or more limbs or appendages. Since Canis Minor consists of a single line it cannot satisfy this imposed anatomical rule and is therefore also rejected. This leaves 37 constellations in total.

In the statistical test described later we compare these constellations with animal symbols on Pillar 43, except for the odd-looking squat bird symbol to the right of the scorpion since there is no corresponding Greek constellation in that region to the right of Scorpius.

 

4.2 Digital image analysis comparison strategy

To compare a set of ‘fattened’ joined lines with an animal symbol digitally, we need to take a view about what is important in this comparison. Since all the animal symbols carved on the broad sides of Göbekli Tepe’s pillars that we need to analyse are large vertebrates in various poses, consisting of specific arrangements of an animal’s torso and connected appendages, we consider this to be an important detail. We therefore need to specify which parts of the animal symbols and constellations consist of a ‘torso’ and which are an ‘appendage’, so that they can be matched. Our digital matching algorithm is therefore much more detailed than a simple comparison of outlines or silhouettes.

Deciding and labelling which part of an animal symbol corresponds to torso or appendage is relatively intuitive and straightforward. Torso sections are coloured black while appendages are coloured red. However, deciding and labelling the corresponding lines of a constellation is less straightforward. To help with this process, we use a basic rule of anatomy; a vertebrate consists of a single, large, relatively straight and central torso that connects one or more, typically smaller, more distant appendages. We therefore require every constellation to have at most one continuous section labelled as ‘torso’. This will either consist of a relatively straight set of connected lines, or a closed loop, near the centre of the constellation. All other lines are labelled as appendages.

Since for some constellations there can be several ways in which the torso and appendages are labelled, we create variants for each constellation to allow for this variation. Therefore, although there are only 37 constellations in the set to be considered, we create a total of 72 variants. Every variant of a specific constellation is included in the digital comparison process, with the score for the best matching variant retained.

 

4.3 Establishing a digital reference set of animal symbols and constellations

Photographs for each animal pattern on Pillar 43 are coloured-in digitally with black ink to create a silhouette. Appendage sections are then coloured over in red. This is a trivial exercise, except for the animal symbol at the top-middle of Pillar 43. As stated earlier, it can be viewed as either facing left or right, which affects which parts are viewed as ‘torso’ or ‘appendage’. The animal symbols are shown in Figure 5.

Each constellation in Stellarium under consideration is exported digitally and defined in terms of a list of pairs of Cartesian coordinates. When drawn, these coordinate pairs are joined by fattened lines. These coordinates correspond to a constellation in Stellarium as it sets on the western horizon on the spring equinox on a date representative of the Younger Dryas impact, taken to be 10,835 BCE. To ensure a consistent comparison between the different constellation variants, each constellation is scaled with fixed aspect ratio such that its maximum vertical or horizontal extent is exactly 600 pixels. Each constellation variant under consideration is shown in Figure 6.

Figure 5. The animal symbols on Pillar 43 considered in our statistical method. Black regions are torso sections, red regions are appendages. Two variants are created for the middle symbol on the top panel, one ‘charging’ animal facing left and the other ‘crouching’ animal facing right. The fish/snake next to the flamingo is treated as an appendage for this exercise.

Figure 6. The 72 constellation variants used in this work, derived from the Western constellation set in Stellarium. Thick lines indicate torso sections, thin lines are appendages. 0 degrees is straight up.

 

4.4 Digital comparison of the animal symbols and constellations

In order to digitally compare a fattened constellation variant with an animal symbol, each constellation is manipulated to optimise its overlap score. Each constellation can be shifted vertically and horizontally relative to the animal symbol, and also stretched or shrunk by a scale factor while preserving its aspect ratio. Two more parameters account for the ‘fattening’ of torso and appendage sections respectively, constrained as follows. All appendage sections of a constellation have the same fatness, which is constrained to be between one quarter and one half that of the torso section. These constraints seem to be anatomically sensible. We also introduce an upper limit on the allowed fatness of torso sections. This is introduced to prevent the torso section obscuring the details of the constellation and the appendages. For example, in the limit of infinite fatness, all constellations become circular torsos with no appendages, since the torso sections are drawn over the top of appendage sections. An upper limit for torso thickness of 200 pixels appears to achieve the desired effect. Both fatness parameters are scaled by the ‘scale’ parameter, i.e. the fatness of constellation lines scale directly in proportion with the constellation’s size.

In addition, we cannot expect each animal symbol to perfectly preserve the orientation of a constellation as it sets on the western horizon on the spring equinox at 10,835 BCE, as reported by Stellarium. We therefore allow each constellation to be rotated by an angle of no more than 20 degrees in each direction to allow for this uncertainty. We expect that constellations would have been viewed as other animals entirely, or in different poses, at greater orientational deviations. However, we do not know in which epoch a constellation was defined. Over the course of a precessional cycle the angle at which constellations set on the horizon at Göbekli Tepe’s latitude can vary by, approximately, between 0 and 60 degrees in the clockwise direction, relative to the orientation already defined (see Figure 7). Therefore, we actually allow the orientation of each constellation, relative to that already defined, to vary by between -20 and + 80 degrees, with a positive value corresponding to a clockwise rotation. This provides another reason why circumpolar constellations are not included in the set to be considered. Allowing a circumpolar constellation to adopt any orientation within the optimisation process would unfairly bias results towards it, relative to those with a pre-defined orientation. In total, therefore, each constellation is adjusted by six parameters; scale, x-shift, y-shift, torso thickness, appendage thickness, and orientation.

Figure 7. Comparison of Virgo setting on the western horizon in two different epochs, from Stellarium. Its orientation differs by around 60 degrees over half a precessional period, around 13,000 years.

 

4.5 Digital optimisation method

Our aim with the DIA method is to find the global optimum of the fit between a fattened constellation variant and an animal symbol from Pillar 43. Trials showed that the most important parameter in this process is the orientation, since its variation creates several deep local minima as the torso and appendages rotate. Fortunately, for a given orientation, the parameter landscape is relatively smooth once the torso sections overlap and are of a similar size. This means an effective optimisation method consists of stepping through the orientation parameter in steps of 5 degrees, with local downhill optimisation of the other parameters at each step with the orientation fixed. Then, once a preferred orientation is found, a final optimisation is performed, this time without the orientational constraint, initialised from the preceding best solution.

Our downhill optimisation method consists of moving downhill to the local minimum along each parameter in turn, and repeating this cyclic process until no further significant downhill movement is obtained. However, to ensure the torso sections of the animal symbol and constellation overlap initially, the first two parameters in this cycle should be the horizontal and vertical shift parameters together with a good initial estimate of the scale parameter. This ensures a relatively smooth optimisation path towards the global optimum.

Nevertheless, even with these refinements, the parameter landscape near the global optimum is not perfectly smooth. Therefore, the whole procedure above is performed three times with different initial conditions. Our final result using the DIA method is the average of these three trials. Fortunately, it is typically found that for a given animal symbol the standard deviation of these three trials is significantly less than the difference between constellation variants.

 

4.6 Objective function

Both the animal symbol and fattened constellation variants are drawn as black or red sections on a white background; torso sections are black, appendage sections are red. They are compared pixel-by-pixel. A simple objective function (OF) that compares their similarity digitally is: OF = S(2c – (a + 2b)), where;

·       a = 1 if both pixels are black (and 0 otherwise),

·       b = 1 if both pixels are red (and 0 otherwise),

·       c = 1 if the constellation pixel is black or red and the animal pixel is white (and 0 otherwise).

The sum is over all pixels.

We aim to minimise this OF, which means the optimisation method encourages torso sections to overlap, and appendage sections to overlap, but penalises situations where the constellation lines ‘protrude’ outside the animal symbol. Overlap of torso sections with appendage sections is neither encouraged nor penalised.

This OF is aligned with the view that the constellation lines should behave somewhat like a skeleton, such that the skeleton should preferably remain inside the animal’s body. Since appendage sections are at most half the thickness of torso sections, their weight in the OF is doubled so that appendage sections can contribute equally as much as torso sections to the OF. Moreover, the penalty for constellation sections straying outside of the animal bodies is also doubled to limit this occurrence.

 

5.    Results of the digital image analysis method               

Sweatman and Tsikritsis (2017a) asked: what is the probability of randomly selecting animal symbols available at Göbekli Tepe and placing them in fixed positions on Pillar 43 such that they could be viewed as Greek constellations representing a date using precession of the equinoxes as well as the set that actually appears on the pillar. This requires comparison of all animal symbols available on the broad sides of Göbekli Tepe’s pillars, which is taken to be 12, with each constellation thought to be represented on Pillar 43, of which there are 8, or 7 not including the one that locates and orients, or pins, the scene on the main panel.

Here, we take the opposite approach instead. That is, we ask: what is the probability of randomly selecting constellations from a specific constellation set that match the animal symbols on Pillar 43 as well as those that can be interpreted as representing a date using precession of the equinoxes. This requires us to compare all available constellations from a constellation set, numbering 37 in our case, with each animal symbol on Pillar 43, which is 7 (not including the pinned one).

Both tests are valid, but the one use here has the potential for greater statistical significance because the pool of constellations (37) is greater than the pool of animal symbols at Göbekli Tepe (12). In addition, Sweatman and Coombs (2019) analysed the continuous degrees-of-freedom for placement of the animals on the main panel. They asked: what is the probability the animals on the main panel of Pillar 43 could be placed with such good accuracy relative to the scorpion when compared with the corresponding scene in the sky. We also include these degrees-of-freedom in our analysis by simply carrying-over their result, which is a probability of around 1 in 7.

Our main task here, then, is to compare each available constellation from a given constellation set with each non-pinned animal symbol on Pillar 43. Since in this work we choose to pin the head and wings of eagle/vulture to the teapot asterism of Sagittarius, we are left with the other 7 animal symbols. We go through each animal symbol in turn next. Remember, we expect to find Scorpius, Lupus, Libra, and Ophiuchus on the main panel of Pillar 43, with Pisces, Gemini or Taurus, and Virgo in the top row in the correct order.

 

5.1 Scorpion

Beginning with the scorpion, it is a conceptual match to the expected constellation in this position, Scorpius. Although the scorpion’s orientation is reversed by around 180 degrees relative to Scorpius, both are viewed from above with legs splayed. Therefore, we rank Scorpius 1^st out of 37. We consider this an objective result.

 

5.2 Canid

Next consider the symbol, likely a canid, to the left of the scorpion on Pillar 43 where we expect to find Lupus. We can see its head and front paws facing to the right, with possibly its hind paws lower down on the pillar. This canid symbol is a conceptual match to three Greek constellations; Lupus, Canis Major and Canis Minor. However, Canis Major and Canis Minor are both eliminated from our constellation set (see above), leaving just Lupus. Indeed, the head and front paws of the Lupus constellation are an excellent match to the features of the animal symbol on Pillar 43. This strong correlation, which is unlikely to occur simply by pure chance, means we should strongly favour Lupus, which we therefore also rank 1^st out of 37. Again, we consider this an objective result.

 

5.3 Bending bird

Next, consider the bending bird at the top left of Pillar 43. Pisces is expected in this position, which according to the Greek tradition is represented by two fish instead. We therefore have a symbol mis-match. If we consider all the Greek constellations in our set of 37, only two have the overall shape of this bending bird, namely Pisces and Aquarius. None of the other 37 constellations have a morphology consistent with a right-angle. Therefore, our short-list for use with the DIA method consists of only these two constellations.

Results from using our DIA method are shown in Figure 8a. Thus, Pisces is ranked 1^st out of 37. Again, we consider this an objective result.

Figure 8a. Comparison of DIA results for the bending bird symbol in ranked order from left-to-right showing only the best variant of each constellation. Black regions correspond to torso overlaps. Pisces, on the left, is ranked 1^st on this basis. Table 1a displays the corresponding numerical scores.

 

5.4 Down-crawling quadruped

Next consider the down-crawling quadruped at the top-right of Pillar 43. It is not clear from this photograph to which class of animal this creature belongs. Nevertheless, it is clearly a quadruped with its large rounded body perpendicular to the viewpoint and with legs splayed downwards at the corners.

Note that evidence from Çatalhöyuk suggests it might represent a bear (Sweatman and Coombs, 2019). Çatalhöyuk is an early Neolithic town in Central Anatolia, circa 7,100 – 6,000 BCE, near the Konya plain. Excavations over many decades there have revealed four types of large zoomorphic installations within rooms from its lower levels, before around 6,400 BCE. After this time, it seems interest switched to painting animals on walls rather than the construction of large installations, or shrines. Other zoomorphic wall inclusions are also found at Çatalhöyuk, but according to Hodder (2011) there are only four types of large zoomorphic wall installation. These are bovine, feline, ovid, and ursine. Although the ursine-type shrines were initially thought to symbolise an anthropomorphic goddess, discovery of seal stamps with a similar shape and ursine features now indicate otherwise.

Clearly, with four types of major zoomorphic shrine, Çatalhöyuk displays symbolism expected of a solar cult with a focus on observing the four solstices and equinoxes, where the animal symbols represent constellations. This is consistent with Gobekli Tepe. It is also worth noting that a ‘Mistress-of-animals’, or Potnia Theron, statuette has been found at Çatalhöyuk. In this example, she displays a circular disk symbol on her abdomen and on each knee. Next to each knee is a feline, which she grasps by the neck. Sweatman (2023) suggests the Çatalhöyuk Potnia Theron likely symbolises the fertility of the spring equinox sun. This is because the Çatalhöyuk felines are thought by Sweatman and Coombs (2019) to symbolise the spring equinox constellation at the time, thought to be similar to Cancer, while Potnia Theron symbols are typically thought to symbolise fertility. A similar ‘Master-of-animals’ wall carving has been found at the Taş Tepeler site of Şayburc, near Gobekli Tepe. Thus, there are clear symbolic similarities between Çatalhöyuk and the Taş Tepeler sites, which are separated by only around 500 km and around 1000 years.

The ursine symbols from Çatalhöyuk and Göbekli Tepe are compared in Figure 8b. Typical Çatalhöyuk bear shrine symbols display a circular disk on their abdomens and are thus thought by Sweatman and Coombs (2019) to signify the summer solstice constellation at the time, similar to Virgo. Four millennia earlier, at the time of the Younger Dryas impact, Virgo is the spring equinox constellation. We therefore expect to see this symbol at the top-right of Pillar 43, which is confirmed in Figure 4. This correlation is highly unlikely to occur by pure chance and is therefore very significant.

Figure 8b. Down-crawling quadruped from the top-right of Pillar 43 (a), stone carving in Sanliurfa museum recovered from Gobekli Tepe (b), bear-like wall installation from Catalhoyuk, (c, image courtesy of James Melaart), bear seal stamp recovered from Catalhoyuk (d, image courtesy of Ian Hodder).

 

Returning to Pillar 43, it is clear that the symbol at top-right is a quadruped viewed from above, crawling downward with its legs splayed at each corner. This pose is similar to that of Virgo, although the down-crawling creature here is clearly not a human female, the Greek symbol for Virgo. Again, we have a symbol mismatch.

We therefore use our digital image analysis method to compare the down-crawling quadruped symbol with a short-list of constellations. Considering the animal symbols in Figure 8b, our short-list of constellation patterns should ideally feature large, rounded torsos with relatively short appendages splayed at each corner. Six constellations are considered to have these features, namely Leo, Lupus, Pegasus, Sagittarius, Ursa Major and Virgo.

Results from using our DIA method are shown in Figure 8c. Virgo is therefore ranked 3^rd out of 37. We consider this an accurate result with only a small error.

 

5.5 Bird with fish

Next, consider the bending bird with wriggling fish or snake, which we expect represents Ophiuchus. Although there is a partial conceptual match of the wriggling fish or snake with Serpens, we consider this insufficient to rank this animal symbol by itself. We therefore use our DIA method with a short-list of constellations.

Considering the shape of this symbol, we should favour constellation patterns consisting of large, loops with minimal dangling appendages that tend to be narrower at the top than bottom. Greek constellations in Stellarium that satisfy these criteria are; Ara, Auriga, Capricornus, Cepheus, Corvus, Crater, Equualus, Leo, Libra, and Ophiuchus.

Results from using our DIA method are shown in Figure 8d. Ophiuchus is therefore ranked 3rd out of 37. We consider this an accurate result with only a small error.

 

5.6 Duck/goose

Now let’s consider the duck/goose at the bottom of Pillar 43, which we expect represents Libra. Again, there is a symbol mismatch with Libra which is symbolised by the Scales in Stellarium. And, since only the head of the duck/goose is showing on Pillar 43, we cannot attempt to use our DIA method either. We therefore exclude it from the statistical analysis.

 

5.7 Horizontal quadruped

Finally, let’s consider the small animal symbol in the middle of the top panel of Pillar 43. As stated earlier, it is not clear what animal family is depicted, making a symbolic match with a Greek constellation symbol impossible. However, suggestions include a charging ibex facing left, or a crouching feline or crocodile facing right. Whatever animal is depicted, it is clear that it is a standing quadruped viewed from the side with either long horns or a long tail over its back anchored at the left of the torso. We therefore consider both cases separately using our DIA method.

Our short-list of constellations should ideally feature long horizontal bodies with 2 to 4 leg-like appendages projecting downwards. Ideally, they should also have a short appendage at the left or right representing the head as well as another long roughly horizontal tail or horn appendage anchored at the left of the torso. Considering the Greek constellation patterns in Stellarium, we find the following patterns are the closest matches to this morphology; Aquarius, Cancer, Capricornus, Cetus, Gemini, Lupus, Sagittarius and Ursa Major. Taurus is not included, meaning its morphology clearly does not fit this description.

Results from using our DIA method are shown in Figures 8e and 8f. Gemini is therefore ranked 1^st out of 37 if facing right, and 3^rd out of 37 if facing left. We consider this an accurate result with only a small error.

Figure 8c. Comparison of DIA results for the down-crawling quadruped symbol in ranked order from left-to-right and top-to-bottom showing only the best variant of each constellation. Black regions correspond to torso overlaps. Virgo at top-right is ranked 3^rd on this basis. Table 1a displays the corresponding numerical scores.

Figure 8d. As for Figure 8c, except the bird with fish symbol is analysed. Ophiuchus is ranked 3rd at top-middle.

Figure 8e. As for Figure 8c, except the horizontal quadruped facing right symbol is analysed. Gemini is ranked 1^st at top-left.

Figure 8f. As for Figure 8c, except the horizontal quadruped facing left symbol is analysed. Gemini is ranked 3^rd, top row 3^rd from left.

 

5.8 Statistical analysis of the correlation between animal patterns on Pillar 43 and Greek constellations

Our statistical estimate is a probability of p x 2/7 that the correlation of Pillar 43 with the Greek constellations in Stellarium occurred by pure chance, where p is the probability of randomly choosing 6 symbols from a set of 37 whose ranks when summed give Z or less. The pre-factor of 2 in this calculation arises because of the symmetry of the top row of Pillar 43, i.e. the order of the animal symbols in the top panel could be reversed and yet still be read as the same zodiacal date. Therefore, the probability of success must be doubled. Division by 7 reflects the spatial correlation of the animal symbols on the main panel, discussed earlier.

Using the results of the DIA listed above, Z is 10 or 12 depending on whether the middle animal symbol at the top of Pillar 43 is facing right or left, respectively. We use a Monte Carlo method to calculate p corresponding to this value of Z. That is, we draw six random integers between 1 and 37, sum them to obtain Z’, and then find the probability that Z’ is less than or equal to the values of Z above, i.e. 8 or 10, by repeating this process one billion times.

The dependence of this probability on Z is plotted in Figure 9. Reading from this plot for Z = 10 gives p = 1.1x10^-7. For Z = 12 we find p = 3.5x10^-7. Therefore, a final estimate of 1 in 30 million, or 1 in 10 million, is obtained when the middle-top animal symbol is facing right or left, respectively. 

Figure 9. Dependence of p on Z.

 

This result corresponds to the choice of objective function described in Section 4.6, OF = S(2c – (a + 2b)). If we instead consider the objective function OF = S(3c – (a + 3b)), which gives more weight to the overlap of appendages, b, as well as to the penalty for any part of the constellation straying outside the animal symbol, c, then the results are as shown in Table 2. It is seen that the rankings of the expected constellations improve overall. The probability estimate now is p = 4.5x10^-8 which equates to a probability of less than 1 in 80 million. Thus, the above probability estimate is stable to small changes in the objective function.

Table 1. Results of the DIA method. For each symbol analysed, the three columns record the variant name, the score (i.e. the negative of the optimised objective function described in section 4.6) and the standard error (1 sigma) calculated from three optimisation attempts.

Table 2. Results of the DIA method for the alternative OF discussed in the text. For each symbol analysed, the two columns record the variant name and the score (i.e. the negative of the optimised objective function). Only one optimisation attempt is made.

 

6.      Discussion and Bayes theorem

The above statistical analysis has addressed issues 1, 2 and 3 listed in Section 3. We find that the unbiased probability that the correlation between Pillar 43 and the Greek constellations in Stellarium could occur by chance is estimated to be extremely small (< 1 in 10 million). Even though there is some uncertainty in this result and there remain some choices in our comparison method that cannot be made perfectly objective, we consider this result to indicate an extremely strong correlation between Pillar 43 and the constellations in Stellarium that deserves an explanation beyond pure chance.

To be clear, this statistic does not apply to any individual animal symbol. Rather, it applies to the whole group. Thus, we cannot say that every animal symbol on Pillar 43 almost certainly is related to a Greek constellation. Instead, we conclude that it is extremely likely that at least some of them are. 

However, prior knowledge of whether astronomical symbolism occurs at Göbekli Tepe could bias this estimate. Therefore, a discussion of Bayes’ theorem and its implications for this statistical estimate are discussed in section 6.2.

 

6.2 Bayes theorem and its influence on interpretation of Pillar 43

Bayes’ theorem is,

P(A|B) = P(B|A) x P(A)/P(B)           (1)

where P(A) is the probability of A being true and P(A|B) is the probability of A being true if B is true. We signify that A is false with ~A. Thus, by definition we have P(A) + P(~A) = 1 and P(B|A) + P(~B|A) = 1. We can therefore write,

P(B|A) = 1 - P(~B|A)          (2)

Using (1) gives,

P(B|A) = 1 - P(A|~B) x P(~B)/P(A)         (3)

For the statistical test of section 5, we make the following definitions;

A = “the correlation between symbols on Pillar 43 and constellations in Stellarium is better than 1 in 10 million”

B = “Pillar 43 expresses a zodiacal date using precursors of the Greek constellations”

Thus, the statistical test of section 5 corresponds to P(A|~B), i.e. “the probability of observing a correlation better than 1 in 10 million if Pillar 43 does not express a zodiacal date using pre-Greek constellations.” However, we want to know P(B|A), i.e. “the probability that Pillar 43 expresses a zodiacal date using precursors to the Greek constellations if we observe a correlation with Stellarium better than 1 in 10 million.”

Equation (3) shows that we can use P(A|~B) to calculate P(B|A). However, we also need to know P(~B) and P(A). What do we know about these latter probabilities? By definition, P(~B) = 1 – P(B). Also, P(A) = P(A|B)P(B) + P(A|~B)P(~B). Therefore, we finally have,

P(B|A) = 1 - a P(A|~B)                         (4)

where a = (P(A|B)P(B)/(1-P(B))+P(A|~B))^-1.

Equation (4) is our key result. It shows how we can use the statistical result of section 5, P(A|~B), to obtain the probability that Pillar 43 expresses a zodiacal date given the very strong correlation with Stellarium observed, P(B|A).

To understand how to use equation (4), let’s first consider the example from Section 3 involving 100 people who are stood on caricatures that look a lot like them, and suppose that the unbiased probability for this situation to occur by chance is found to be 1 in 1 million. In this case we make the following definitions;

A = “the correlation between people stood on caricatures is better than 1 in 1 million”

B = “This situation has been deliberately arranged”

For this example, we can take P(A|B) = 0.5. Since we only have this single example as evidence, we should conclude this level of correlation is no more likely than not. Furthermore, if P(B) >> P(A|~B), then a is dominated by the first term, and therefore a ~ 2(1-P(B))/P(B). In this case, a can take on a wide range of values. If P(B) is small, then a ~ 2/P(B), which is large. On the other hand, as P(B) approaches 1, a approaches 2(1-P(B)), which is small.

Thus, provided P(B) >> P(A|~B), a behaves like a slider; it is large if P(B) is small and vice-versa. Nevertheless, without any prior knowledge we should take P(B) to be 0.5, which gives a = 2. Then, using (4) we find that P(B|A) = 1 – 2 x 10^-6 = 0.999998. We therefore conclude the situation has almost certainly been arranged.

Now, let’s suppose that we do have some prior knowledge. Suppose we know that this situation is always arranged on Monday’s, but is never arranged on any other day. Suppose also that we don’t know what day it is. In this case, we should take P(B) = 1/7. Then, we find a = 12, and P(B|A) = 1 – 12 x 10^-6 = 0.999988. This shows how prior knowledge can bias this kind of statistical test.

Now let’s consider the case of Pillar 43. We see that as P(A|~B) reduces, i.e. as the strength of the correlation increases, the probability the pillar expresses a zodiacal date moves closer to 1. This makes perfect sense. However, the pre-factor a is important. It expresses the bias caused by prior knowledge of three things;

i) the probability that the pillar expresses a zodiacal date, P(B).

ii) the probability of observing such a strong correlation between the pillar’s symbols and Stellarium if the pillar does express a zodiacal date using precursors to the Greek constellations, P(A|B) (as discussed for the example case, since Pillar 43 is our only example we should take P(A|B) = 0.5).

iii) the probability of observing such a strong correlation between the pillar’s symbols and Stellarium if the pillar does not express a zodiacal date using precursors to the Greek constellations, P(A|~B) (as already shown, this has an extremely small value).

As discussed above, provided P(B) >> P(A|~B), a behaves like a slider; it is large if P(B) is small and vice-versa. Essentially, a scales the influence of the correlation P(A|~B) depending on prior knowledge of P(B).

This means the rate that P(B|A) converges to 1 as P(A|~B) reduces is strongly influenced by evidence that Pillar 43 expresses a zodiacal date using precursors to the Greek constellations, P(B). In other words, the more evidence that supports the view that Pillar 43 expresses a zodiacal date using pre-Greek constellations, in addition to the strength of the observed correlation, then the more likely it is that it actually does express a zodiacal date (and vice-versa). Of course, this makes perfect sense too. When viewed this way, equation (4) simply expresses the principle of Occam’s razor.

Therefore, in the remainder of this section we describe further evidence, beyond the strong correlation estimated in Section 5, that Pillar 43 expresses a zodiacal date using precursors of the Greek constellations. In fact, this evidence has already been presented by Sweatman (2023). He lists many different lines of evidence that support the view that Göbekli Tepe’s symbolism is mainly astronomical. We summarize some key points next (see Sweatman (2023) for details).

1.       Sweatman (2023) shows that the front of Pillar 18 is very similar to the Nebra sky-disc which is generally acknowledged to display astronomical information. Therefore, the circular disc symbol likely symbolises the sun. In fact, the circular disc symbol and crescent symbol seen on Pillar 18 represent the sun and moon, respectively, in Egyptian hieroglyphics. On Pillar 43 we see a circular disc symbol surrounded by animal symbols, which is exactly what we would expect to see if Pillar 43 represented a zodiacal date using constellations.

2.       The top panel of Pillar 43 shows animal symbols next to sunset-like symbols. Sweatman (2023) shows that similar symbols are observed on 3^rd and 4^th millennium BCE artefacts that are also consistent with expressing zodiacal dates. These include, but are not limited to, a 3^rd millennium BCE Jiroft stone weight from ancient Iran, the 4^th millennium BCE Uruk Vase from ancient Mesopotamia, and 4^th millennium BCE rock graffiti found in the Theban desert (see Figure 1). The animal symbols on these artefacts are generally recognised as being possible precursors of the Greek constellations (Rogers, 1998a).  They also appear to be strongly correlated with the earliest dynastic Egyptian deities. The sunset-like symbols, on the other hand, are very similar to early Sumerian pictographs for the sun and for measures of time (see Figure 1).

3.    Gurshtein (2005) predicted a system of zodiacal dating involving all four solsticial/equinoctial constellations likely developed by 6,000 BCE to support a farming calendar. However, his arguments should also apply to hunter-gatherers.

4.     A likely ‘Master-of-animals’ symbol has been found nearby at Şayburc and a ‘Mistress-of animals’ symbol was found at Çatalhöyuk, central Turkey, circa 7,100 – 6,000 BCE. Both these symbols support an astronomical interpretation for Göbekli Tepe’s and Çatalhöyuk’s symbolism. Similar symbols are found on 4^th and 3^rd millennium BCE artefacts across a wide region that can also be interpreted astronomically. More importantly, they indicate that astronomically-related symbolism from the time of Göbekli Tepe can endure until the Bronze Age. This supports the identification of animal and sunset-like symbols at Göbekli Tepe with similar 3^rd and 4^th millennium BCE symbols.

5.    This astronomical theory perfectly explains why a similar symbol, i.e. the splayed quadruped viewed from above, is observed at the top-right of Pillar 43 at Göbekli Tepe and is also one of the four main kinds of wall installation at Çatalhöyuk (see Figure 8). The explanation involves the constellation Virgo, which was the summer solstice constellation at the time Çatalhöyuk was occupied and the spring equinox constellation at the time of the Younger Dryas impact. It also explains perfectly why circles are seen on the bellies of these symbols at Çatalhöyuk and next to the eagle/vulture on Pillar 43, where they likely symbolise the summer solstice sun, and only three semi-circles are seen at the top of Pillar 43, where they likely symbolise the other three solstices and equinoxes. This correlation is a natural consequence only of the astronomical interpretation.

6.    Hayden and Villeneuve (2011) show that extant hunter-gatherer tribes are often interested in astronomy and the solstices/equinoxes in particular for the purpose of arranging tribal meetings. Moreover, this interest occurred more often for so-called ‘complex’ hunter-gatherer tribes. Göbekli Tepe appears to have been built by a complex hunter-gather tribe. Later cultures in the region are known to have strongly astronomically-related religions where animal symbols are used to represent both deities and constellations.

7.     Pillar 43 appears to display a lunisolar system for counting the days of the year using V-symbols and box-symbols. The final day of the year appears to be signified by the V-symbol at the neck of the vulture/eagle. This is consistent with the view that it symbolises the summer solstice constellation. Symbols at the neck appear to be important in Göbekli Tepe iconography. Enclosure D, the inner ring of enclosure C and a special pool structure at Karahan Tepe all feature 11 pillars, which reinforces the notion that the Göbekli Tepe culture used a lunisolar calendar system (Sweatman, 2023).

8.    If Pillar 43 does symbolise a date, then it is close to the date of the Younger Dryas impact event. This can explain the presence of the headless man at the bottom of the pillar, i.e. the pillar can be viewed as a memorial to this great event. Other pillars at Göbekli Tepe can be viewed as expressing the path of the radiant of the Taurid meteor stream, which is thought to be the culprit for the Younger Dryas impact event (Sweatman, 2023).

9.     Göbekli Tepe’s accomplished design and symbolism indicate the beginning of a new religion requiring much more effort than earlier forms. This can also be explained in terms of the Younger Dryas impact event (Sweatman, 2023). We can expect this religion to have evolved over the course of millennia. This can explain the prevalence of many catastrophic myths involving cosmic serpents, cosmic bovids and solar deities in neighbouring regions.

10.    A zodiac derived mainly from Göbekli Tepe can be used to analyse European Palaeolithic cave art (Sweatman and Coombs, 2019). The extremely strong correlation observed between radiocarbon dates and zodiacal dates for these painted animals, along with a strong correlation in the direction of these painted cave entrances towards solstice/equinox sunrises/sunsets (Jegues-Wolkiewiez, 2007), strongly suggests a system of zodiacal dating already existed in Palaeolithic Europe.

All of the above evidence increases the value of P(B), and therefore reduces the value of a. In turn, using a Bayesian statistical argument expressed by equation (4), which is simply a form of Occam’s razor, they each increase the probability that the extremely strong correlation observed on Pillar 43 implies the pillar expresses a zodiacal date using constellations.

This methodology and result is useful because, to our knowledge, it is the only interpretation of Pillar 43 that is supported by a statistical analysis. We recommend that any other theory for interpretation of Pillar 43 is analysed in a similar way. Our results would then provide a useful benchmark for comparison. It should be noted that Gresky et al.’s (2017) hypothesis that Pillar 43 symbolises a skull cult cannot be analysed this way, since it only provides an explanation for a couple of the symbols on the pillar and no statistical case can be created from them, i.e. the idea is very speculative. The astronomical interpretation, on the other hand, provides an efficient explanation for all the symbols on this face of the pillar, except the H-symbols, as well as many other symbols across the Göbekli Tepe culture and in later neighbouring regions.

 

7.      Summary and conclusions

Our conclusion that many of the animal symbols on the broad sides of pillars at Göbekli Tepe almost certainly represent constellations genetically related to the much later Greek constellations is based on the Bayesian statistical argument presented in section 6.

It is worth considering how this strong correlation between the animal symbols on Pillar 43 and the Western constellations in Stellarium could have arisen. Clearly, the main link must be through the ancient Greek constellations, since Stellarium’s Western constellation set incorporates the Greek set.

Therefore, we propose that the constellations apparent at Göbekli Tepe, represented in terms of animal symbols, continued to be used in the regions around southern Turkey for several thousand years during the early Neolithic period. Çatalhöyuk circa 7,000 – 6,000 BCE, only a few hundred kilometres from Göbekli Tepe, provides a likely example of this, as earlier work indicates animal symbolism there is consistent with a zodiacal interpretation (Sweatman and Coombs, 2019). This view is reinforced by the many circular disk symbols embossed on Çatalhöyuk’s prominent bear shrines, which indicate this animal symbol signifies the summer solstice constellation at this time (see Figure 8b). On Pillar 43, we see a very similar animal symbol next to a sunset-like symbol at the top-right of the pillar, consistent with this constellation representing the spring equinox constellation at this time. This work shows these symbols could be precursors to the Greek Virgo constellation. We also see a Mistress-of-animals symbol, or Potnia Theron, at Çatalhöyuk that indicates continuity of the symbolism observed at Şayburc, near Göbekli Tepe (Sweatman, 2023).

Unfortunately, there has been no systematic study of the potential astronomical significance of animal symbols in the late Neolithic era of the Fertile Crescent, but it is well-known that animal symbols are prevalent on pottery and other artefacts from archaeological sites across this region at this time. We also see a strong correlation between the animal symbols on Pillar 43 and the oldest Egyptian deities, which indicates they might have evolved from this early constellation set. This view is consistent with the known importance of astronomy in the earliest Egyptian writing, such as the so-called Pyramid Texts (Magli, 2004; Brady, 2015). It is also known that early Babylonian deities were often symbolised by animals that also represented constellations with mostly Sumerian names (Kurtik, 2019).

Eventually, probably with some changes, we suggest these astronomical symbols were adapted and formed the basis of the late Neolithic and Bronze-Age inter-cultural style of zodiacal symbolism apparent on artefacts recovered from ancient Iran, the Indus Valley, Mesopotamia and Egypt. We suggest these symbols were used in some of the earliest hieroglyphic writing systems in Egypt and Sumer. The animal symbols on these artefacts are generally regarded as potential precursors to Greek constellations.

Later, we suggest this symbolism evolved such that constellations observed by cultures in different regions of the Near East diverged somewhat, although there remained considerable similarities in the most visible constellations, such as Ursa Major and Orion. One set was known to the early Greek poets circa 700 BCE at the latest, and another by Babylonians as expressed in the MUL.APIN, by 600 BCE. It is not clear to what extent the Greeks updated their zodiacal constellations with those known by the Babylonians circa 500 BCE.

Later still, we suggest small refinements to these symbols and constellations were made by the classical Greek astronomers, culminating with Ptolemy’s Almagest. Finally, the makers of Stellarium, based their Western constellations on the ancient Greek and Babylonian ones, especially those described by Ptolemy.

The possibility that constellations and their symbols can be culturally transmitted over such long timescales, relatively unchanged, is supported by the long timescale continuity of European Palaeolithic cave art. This artistic style, with few changes, endured for around 30,000 years, from the time when hunter-gatherers first migrated into Western Europe. It follows that if an artistic tradition can endure for this long, then astronomical information in the form of constellations and symbols can also endure for such long timescales. As already mentioned, Sweatman and Coombs (2019) showed that most of the animals depicted in this cave art very likely also represent constellations observed at the solstices and equinoxes. Therefore, it might be the case that the nearly-fixed starry sky helped to preserve this artistic tradition. Thus, the possibility that some Epipaleolithic constellation symbols can be recognised in modern astronomical software is plausible.

 

Competing interests

The authors report there are no competing interests to declare.

 

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