Applying Math to Myth Helps Separate Fact from FictionApril 1, 2013
Pádraig Mac Carron and Ralph Kenna
Megalithic standing stones at Castlelack, County Cork, Ireland.
Megalithic standing stones at Castlelack, County Cork, Ireland.
Although the distinctions between them are not always sharp, myths differ from legends and folktales. Mythological epics frequently entail timeless narratives with abundant characters, outside documented history. Legends, on the other hand, are couched in a definite historical timeframe, and folktales are intentionally fictional.
A frequently asked question is whether some mythological narratives may contain traces of historicity. Despite layers of obfuscation added by distortive political and religious forces to epic tales as they were passed orally through the centuries, could remnants of reality still lurk within the pages of the ancient manuscripts in which they were eventually preserved?
In the absence of firm archaeological evidence for or against the existence of societies described by some mythological narratives, we turned to applied mathematics. In a recently published pioneering study, we looked at the social-network structures of three iconic mythological narratives and found indications that could point to elements of historicity.
Homer's Iliad and the Anglo-Saxon Beowulf are believed by many antiquarians to be partly historically based. The ancient Irish epic Táin Bó Cúailnge, by contrast, is often believed to be mostly fictional. By comparing the social-network structures underlying these three tales, we find that the apparent artificiality of the Táin is not pervasive; appropriately interpreted, the Irish narrative may hold a degree of historicity similar to that of the other two.
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Beowulf is an Old English heroic epic, set in Scandinavia. Estimated dates of the single surviving codex range from the 8th to the 11th centuries. The story tells of the coming of Beowulf, a Geatish hero, to assist Hrothgar, king of the Danes. After slaying two monsters, Beowulf returns to Sweden to become king of the Geats and, following another fabulous encounter many years later, is fatally wounded. Although the poem is embellished with obvious fictional elements and creatures, archaeological evidence in Denmark and Sweden offers support for historicity associated with some of the human characters. The character Beo-wulf himself is mostly believed not to have existed in reality.
The Iliad, an epic poem attributed to Homer, dates to the 8th century BC. It is set during the final year of the war between the Trojans and a coalition of besieging Greek forces. It relates a quarrel between Agamemnon, king of Mycenae and leader of the Greeks, and Achilles, their greatest hero. Although much debated through the years, evidence suggests that the story may be based on a historical conflict that occurred around the 12th century BC, interwoven with elements of fiction.
Táin Bó Cúailnge (Cattle Raid of Cooley), the most well known epic of Irish mythology, describes the invasion of Ulster by the armies of queen Medb of Connacht and the defence by Cúchulainn, Ireland's most famous hero. A number of related pre-tales and tangential tales (remscéla) give the backgrounds and exploits of the main characters of the Táin itself. The Táin has come down to us in three recensions. The first has been reconstructed from partial texts contained in Lebor na hUidre (the Book of the Dun Cow, dating from the 11th or 12th century) and Lebor Buide Lecáin (the Yellow Book of Lecan, a 14th-century manuscript) and other sources. The second, later recension is found in Lebor Laignech (the Book of Leinster, a 12th-century manuscript formerly known as Lebor na Nuachongbála, or the Book of Nuachongbáil). A third recension comes from fragments of later manuscripts and is incomplete.
Medieval scholars dated the Táin to the first centuries BC, but this may have been an attempt to artificially synchronise oral traditions with biblical and classical history. The historicity of the Táin is questioned. While some argue that such narratives corroborate Greek and Roman accounts of the Celts and offer us a window on the Iron Age, others object that such tales have no historical basis whatsoever.
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Social networks have been widely studied in recent years; researchers have looked at the interconnectedness of Hollywood actors, corporate directors, and scientific co-authors, amongst many other examples. These real-world networks all share certain properties. They are highly connected and small-world, a concept related to the famous six degrees of separation notion in sociology. They are also assortative, which means that people tend to associate with people similar to themselves. Their degree distributions (the pattern of links between nodes) are often scale-free, meaning that only a small number of people tend to know a very large number of people.
To construct the social networks underlying each of the mythological narratives, we created databases for the characters and their interactions (see Figure 1). Relationships between characters were categorised as hostile or friendly. The mythological networks were found to have characteristics of real-world social networks, including the small-world property and structural balance (related to the idea that the enemy of my enemy is my friend). The worlds of intentionally fictional narratives, such as Harry Potter and The Lord of the Rings, also exhibit these properties, as does the society underlying Marvel Comics.
Figure 1. The central clusters of the social network for Táin Bó Cúailnge. Green lines represent friendly links, red lines hostile links, where two characters meet only in combat.
The Iliad, however, is assortative, a feature lacking in these intentionally fictional networks. Beowulf is also assortative, but only if the eponymous character is removed from the network. The Táin is disassortative. These, and other social-network features, appear to corroborate antiquarians' interpretations of the historicity of the tales---the societies underlying the Iliad and Beowulf have traces of reality, whereas that of the Táin appears artificial.
To investigate the Táin's apparent artificiality, we looked further into the degree distributions of the social networks (Figure 2). This relates to the distribution of popularity amongst characters. Like real social networks, the networks in all three myths are scale-free. We observe a striking similarity between the Táin and Beowulf for all but the top six characters of the Irish myth (Figure 2, left). The degrees associated with these characters appear inflated, perhaps exaggerated. The beauty of the mathematical approach is that we can identify this anomaly as local---associated with only 6 of the 404 characters in the text. We can then correct for the anomaly by removing the weakest links (i.e., characters they encounter only once) from the six strongest characters. The resulting Táin network (Figure 2, right) is assortative, similar to the Iliad and to other real social networks and very different from The Lord of the Rings, Harry Potter, and other examples of fictional extremes, which also lack the scale-free property.
Figure 2. The degree distribution as a power law for (top) the entire, unadjusted Beowulf and Táin networks and (bottom) the adjusted networks. Here, k is the degree and P(k) is its cumulative frequency. Removal of the weakest links of only the six most strongly connected Táin characters renders the Irish network similar to that of Beowulf, which is believed to be based upon a real society.
This quantitative investigation is, of course, very different from traditional approaches to comparative mythology---it tells us nothing about qualitative aspects, only about how realistic, or otherwise, the societies appear when viewed as interconnected networks. However, the application of mathematics delivers new perspectives. In particular, it allows us to speculate that, if the Táin contains echoes of a bygone age, the six anomalous characters may be based on amalgams of a number of entities and proxies that became fused as the narrative was passed orally through the generations.
We thank Chris Budd for encouraging us to write this article for SIAM News.
The work described here is supported by The Leverhulme Trust under grant F/00 732/I.
P. Mac Carron and R. Kenna, Universal properties of mythological networks, EPL,
99:2 (2012), 28002; http://iopscience.iop.org/0295-5075/99/2/28002.
Pádraig Mac Carron is a PhD student, and Ralph Kenna is a professor of theoretical physics at Coventry University in England.