Which you then claim is evidence the networks are real. Which is impossible if the characters residing at the nodes of the network didn’t exist. No characters, no nodes. No nodes, no network.

If your paper actually explored ways this could happen (fictional nodes wired up like real networks), then it would not have committed the fallacy of affirming the consequent that I document. That, indeed, would have been a much better paper.

And where exactly is that answer in your paper? Quote please.

(And not the paragraphs about possible amalgamation in the Tain; I’m asking for where you discuss this amalgamation theory for the Iliad, or Beowulf)

This of course would still be useless (“possible” does not get us to “probable”), and ignores the other ways a realistic network could be produced (some of which I discuss). But at least your paper would have been better, again, if it actually said the things you apparently wish it had said.

None of those facts contradicts what I said, or supports what you said. That you discuss the Tain’s peculiar traits does not make it the paper’s focus, nor does the paper ever say the other two epics were being explored only for the purpose of explaining the oddities of the Tain. At no point is that ever said to be the point of the paper. All three epics are treated as a unit, and compared with the four works of fiction as a unit. That the Tain was more complicated and had to be discussed a little more to cover its weirdness is presented as a consequence of your results, not your objectives.

Where in your paper is this stated of the Iliad or Beowulf? Quotes please.

A speculation that ignores other causes of the same phenomena. As I explain in my critique.

I did. That’s indeed one of the embarrassing things about it. Only three epics, none from the same culture, language, or historical period, are used to indicate “the universal properties of mythological networks.” That in and of itself is bad science. Imagine determining the universal properties of all mammals by looking at only three furry things.

And the “universal properties” you find for myth are that “myths” have realistic networks and that this is most likely explained by the characters in them being, at root, historical (you offer no other explanation).

That is what your paper actually argues. Maybe it’s not what you wish it had argued.

This is not science. Speculating what perhaps might be true is a non-conclusion.

Moreover, even the reasoning supporting the speculation is illogical. Archaeological evidence for a Trojan-Greek war combined with a realistic network of demigods in the Iliad written centuries later do not combine to equal “it is reasonable” to conclude those networks were as real as the war. For the very reasons I explain.

And by your own admission the realism in the Tain can only be restored by changing the data, which is a classic example of a retrofitting fallacy: any myth could be made realistic if we get to manipulate the network data in it however we need to make it fit a real pattern.

In short, you are only making your case worse here, by highlighting even more ways your paper is just bad science, and even worse history.

You are using disingenuous tactics to pursue your own agenda. Having exposed your opening sentence as rubbish, you respond by saying it was meant facetiously. You then take a few sentences out of context, highlight a few words here and there to alter meaning and use this to try to justify your initial critique, which, as you are forced to admit, is misrepresentative and misleading.

You quote
“the societies in the Iliad and Beowulf (without the eponymous protagonist) may be based on reality (p4)”.

In fact the full sentence reads
“This corroborates antiquarians’ interpretations of the historicity of these myths (obviously fabulous entities and interactions notwithstanding) – the societies in the Iliad and Beowulf (without the eponymous protagonist) may be based on reality while that of the Táin appears fictional.”

You miss again the concept of society as a social network. This means the collection of nodes together with the collection of links. It does not mean the collection of characters alone or the collection of events. The unique and pioneering feature of our work – which distinguishes it from previous analyses of mythology – is that we look at the collection of links between characters in a quantitative manner. This collection of links and nodes has similar features to many collections of links and nodes of real social networks.
You ask “If the characters aren’t real, why would their social network looking real support the historicity of anything in the story?” You also ask “How do you get real historical events from non-existent characters, and do that by proving that those non-existent characters have realistic relationships?” Our answer is that it is possible that groups of mythological characters – each of whom are not real – may actually be based on groups of sets of real characters and antecedents. Each of these sets may have become amalgamated into exaggerated, apparent individuals throughout the retelling of the tales. This would mean that the narrative contains traces of a real social network (real society) but that characters themselves have become exaggerated and distorted – are not real.

You say our paper does not single out the Táin any more than the other two. You also state “At no point in the article or its abstract is the Táin singled out as the focus of the article“. With these statements, you continue to misrepresent our work.

In the text, the Táin referred to over 25% more frequently than Beowulf and over 50% more than the Iliad. Over 30% of the abstract concerns the Táin alone, with the remainder concerning all three. The abstract states “This suggests that the perceived artificiality of the Irish narrative can be traced back to anomalous features associated with six characters. Speculating that these are amalgams of several entities or proxies, renders the plausibility of the Irish text comparable to the others from a network-theoretic point of view.”

You criticise that “your paper sets up a spectrum of real to fictional”. In fact we state that we attempt to place mythological networks on a spectrum from the real to the imaginary. Obviously we cannot give a precise coordinate on a one-dimensional line segment connecting some numerical representation of the entire corpus of world fiction to another numerical representation of the entire corpus of world fact. What we attempt to do is (i) show that (as others have done before us), some obvious fictional networks have strikingly dissimilar properties to some obviously real social networks (ii) the three myths we examine are more nebulous and lie somewhere in between the two extremes we have purposefully chosen (iii) in this framework, the Táin looks more like obvious fiction than either the Iliad or Beowulf (that is what we mean by its position on the spectrum) and (iv) we can tweak the Táin to make it more realistic (v) this tweaking underpins a speculation that we make at the end of the paper.
Regarding point (ii), obviously some works of fiction will be located at various points along a simplified spectrum and obviously a similar statement holds for some real social networks. Obviously also, it is rather a multi-dimensional construct (hence the various elements or dimensions in Table 2). Obviously ours serves as a simplified, highly approximate, first attempt to contextualise a pioneering concept – an attempt to introduce quantitative tools to a hitherto completely qualitative realm. But we are not interested in real social networks or fictitious ones per se (besides for this purpose of contextualisation). We are interested in universal properties of mythological networks. That is the reason for the title of our paper – I suggest you read that title.

We do not claim to have proved the historicity of individual characters or demi-gods as you continue to insist we do in the silly headline of your own article.

You repeat “The main thrust of the article is the comparison of those three myths with four works of modern fiction.” This is, again, _your_ misinterpretation of our paper. To summarise (again) the point of our paper (see again the last part of the abstract and the last sentence of the main text):

IF there is archaeological evidence for aspects of the Iliad AND the social network looks realistic from a network theoretic point of view, AND IF there is archaeological evidence for some aspects of Beowulf AND the social networks look realistic THEN, as the social network for the Táin looks similarly realistic (after a small degree of manipulation), it is reasonable to SPECULATE (not to claim to prove) that PERHAPS the Irish text has a level of plausibility similar to the other two which has been missed through other approaches.

Through reading into our paper statements which are not there, through omitting other statements which are there, you distort our message to suit your own agenda. In this, you do your readers a disservice and your article, with its crass, attention-seeking headline, is of a base level, worthy of gutter-press journalism. If you are not willing to read the paper properly, I suggest you to at least read the title and abstract.

Ralph Kenna

Kenna’s research speciality is statistical physics, so that would explain why he went to a physics journal. Not a defense from me, just FYI.

Facebook doesn’t strike me as a “real” network, though. Sure, it exists, but only for advertising and data mining purposes, and its structure is dictated by the limits of the technology and the wishes of its directors. It is constantly pushing and prodding for new members and new connections, in a sea of fake and doubled accounts, in a way that is no more “real” than the Marvel universe.

Plenty of “characters” in the Iliad who might have been major figures in their original locales are just a name and a brief eulogy in the epic. Why then assume that such tales are routinely preserved in their place of origin for hundreds of years out of local pride, with all foreign variants rejected?

That isn’t what I meant. I mean the Iliad and Odyssey as a whole were being regularly sung over hundreds of city-states across two continents. Homer cannot have been the first to compose those epics if they show signs of accumulation over centuries. Therefore they were well-known everywhere. His version of them cannot have deviated greatly from the popular versions and expected to eclipse them. Like the QWERTY keyboard, thousands of bards had already memorized the popular version, and audiences already craved its repetition. His would just lose.

I don’t know which discrepancies you have in mind. If it’s something like a hero driving a bronze age chariot in one episode, but later describing himself ruling a kingdom with iron age customs, what would this show? How would this be different from a character who is addressed with the post-Norman title “earl” but later swears by the classical deity Apollo?

Because the latter can be internally consistent (it’s just a mashup). The former is not, it varies by pericope. So a correct analogy would be a character addressed as “earl” in one section, but then addressed as “legate” in another, as if the author forgot which he was. Homer has characters fighting with bronze tools, weapons, and armor at one point, and iron at another. That indicates his material predates him, and was not composed by one author, or even in one century.

And again, the way lines and cliched phrases are used, assembled, and repeated throughout Homer demonstrates it was a bardic performance that was often subject to innovation in arrangement of familiar lines and phrases and designed to be easily memorized. A single author is much less likely to have anticipated this need and so successfully planned for it (by contrast, the Aeneid largely lacks this feature, being written by a single author, Virgil, it shows more variety of phrasing and attention to the written structure). Whereas a composition evolved over centuries by practicing bards would look just like it. Thus it’s more likely Homer was writing down a well-established performance piece, than recomposing it anew.

Dr. Ralph Kenna:

That’s true, I was being facetious in my opening line. And I misrepresented you on the matter of the Beowulf character. I have emended the first paragraph to make that clear, and in a later paragraph discussing Beowulf I now state your position correctly. I apologize if the opening line misled anyone, and for the error on Beowulf.

What the rest of the article takes to task was not that, of course, but attempting to prove the historicity of any characters in myths by this method. As you wrote:

the societies in the Iliad and Beowulf (without the eponymous protagonist) may be based on reality (p4)

and

In an attempt to place the three mythological networks on the spectrum from the real to the fictitious, we compared their properties to actual and imaginary social networks. … Of the three myths, the network of characters in the Iliad has properties most similar to those of real social networks. It has a power-law degree distribution (with an exponential cut-off), is small world, assortative, vulnerable to targeted attack and is structurally balanced. This similarity perhaps reflects the archaeological evidence supporting the historicity of some of the events of the Iliad. (p5)

Which of course only makes sense if you are saying your analysis supports the historicity of the characters in the Iliad (since that is the only data you analyzed, not separate data for the “events” without the characters). So when you now claim…

…I am really at a loss for how your paper’s conclusion can logically follow from its premises at all. If the characters aren’t real, why would their social network looking real support the historicity of anything in the story? By not even attempting to answer that question, your paper’s only identifiable argument is that the only way their social network looking real would support the historicity of anything in the story is by supporting the historicity of the characters. If that is not the paper’s argument, then what is it? How do you get real historical events from non-existent characters, and do that by proving that those non-existent characters have realistic relationships?

Your paper does not single that out any more than the other two. It was just one example of three. Which I didn’t mention because you could not find a realistic network in it and so concluded it was ahistorical (although as I point out in my article, that does not actually follow either). And even in this case you tried to suggest historicity could be supported by your method (emphasis mine):

We speculate that these characters may in fact be based on amalgams of a number of entities and proxies. … We therefore suggest that if the society in the Tain is to be believed, each of the top six characters is likely an amalgam that became fused as the narrative. (p6)

This is indeed pure speculation. Which in history is good for little. It is just as likely, if not more likely, that those characters are complete fabrications. Thus your method cannot support your speculation over the alternative. It is therefore of no use to historians.

No it isn’t. At no point in the article or its abstract is the Tain singled out as the focus of the article. The main thrust of the article is the comparison of those three myths with four works of modern fiction. If that isn’t the article you intended to write, then you should have written a different article.

Much of the rest of your reply, indeed, looks like that imaginary article you didn’t write: here you make an argument that isn’t in the published paper. Indeed, the argument you now present is better than the published paper. But it still doesn’t work, for all the reasons I enumerated in my critique.

This is nonsense historically. You evidently missed my point. The cultural context and aims and even economic and productive context of modern comic books does not resemble at all that of ancient and medieval myths. It’s a false comparison. Actual histories of actual people can also look the same, for the reasons I illustrated (thus the features of fiction are not indicative of fictional networks, when real networks can be described the same way by a historian selectively choosing which characters to discuss, and by ancient elite society being a smaller and more interconnected world than, for example, Facebook communities). Comic book “universes” are deliberately collusive for economic reasons and for reasons of collaborative play. Whereas myths are designed to allegorize social institutions and values and its characters are created and merged for specific reasons very unlike the reasons comic book characters are. These two genres therefore do not have enough causal similarity to be measured by your technique as if they were comparable.

Moreover, what you are now claiming above is false. Your paper says:

To facilitate comparison between our mythological networks and other real and imaginary networks, we also look here at four works of fiction. With these at our disposal, we seek to compare mythological narratives to other networks, ranging from the real to the imaginary. (p2)

First of all, your paper doesn’t do this. It doesn’t analyze any real historical narratives to establish the properties of how they describe networks (and just picking a few wouldn’t do it, since there are so many diverse ways a historical account can be written, as I explain). So it doesn’t compare “our mythological networks” with “other real” networks in the relevant way (by looking at written accounts of real networks, rather than the actual networks themselves).

But more importantly, your paper sets up a spectrum of “real” to “fictional” (your words, repeated throughout the paper) using just four works of fiction to establish what “fictional” networks look like (you use them to assign the “fictional” end of the spectrum). That is precisely the fallacy I call out. It’s simply bad science. And you don’t even do the same for the other end of the spectrum. Instead, you define the other end with actual data (real networks), and not with written accounts (thus the spectrum doesn’t even properly represent a spectrum of literature from true to fictional at all).

Thus when you say you “turn our attention to networks which are definitely fictional” (p4) you miss the point that works that are definitely factual could have exactly the same appearance, i.e. describe networks in ways that look just as artificial, even for the same reasons you speculate those modern works of fiction do. You also fail to suggest that works that are definitely fictional might also emulate real networks, for reasons other than being derived from real networks (a rather crucial point when questioning the historicity of texts that depict realistic networks). In other words, at no point in your paper do you ask what other causes there may be for that outcome. You simply assume “real networks” are the only things that can cause realistic networks in literature.

This is what your paper actually argues (emphasis mine):

The question arises whether these characteristics are properties of non-comic fictional literature in general or whether this may truly signal a degree of historicity underlying the three mythological narratives. To investigate this, we applied our network tools to four narratives from fictional literature. (p4)

That’s what your paper does. So you are not giving a correct account of your own paper here.

Your paper, as quoted, says that to answer the question of whether “historicity” (I repeat: historicity) underlies the “three mythological narratives” (so, again, your paper is talking about all three together, not Tain specifically) you need to determine the network properties of “four narratives from [modern] fictional literature.” That is bad science, on multiple levels, as my critique explains. This comparison cannot answer the question of historicity, four works of fiction is not sufficient to establish a baseline for what is “normal” for fiction, and modern fiction is too unlike ancient myth to be a relevant comparison point in the first place.

Koray objects that it is published in a physics journal.

For the record, I have no problem with where it was published. As long as the research was conducted in close consultation with historical experts on the materials tested (modern fiction, ancient myth, Homeric studies, etc.).

And I concur with your worry that the humanities community might have been too scared of the mathematical technique to publish it. I have met with the same fear in promoting Bayesian reasoning in the humanities.

I never suggested you would. It is others on the internet who have been touting your paper as a path to proving the historicity of Jesus, and my last paragraph makes that clear (that this is not your agenda, but theirs). I only mention it because this is the thing I study, and people want to know what my opinion is of the suggestion (made by others, not you) that this technique could be adapted to the question of Jesus.

(Although, BTW, the Iliad is a religious text. So you have indeed commented on a religious text. Just not a religion anyone follows anymore–unless you count neopagans. And I don’t think you should be any more averse to analyzing the texts of living religions.)

You are claiming something that didn’t happen.

What part of Scientists need to learn logic do you disagree with? If none, then how do we address those scientists which have failed to do so?

I imagine you are reading an accusation into this where there is none. All scientists need a refresher course in remedial logic because none show any sign that they understand it. This is not what was said.

If you are stuck on the road with some dangerous or inconsiderate jerks, and make the comment, People need to learn how to drive, is that an indictment against all people, or all motorists? I should think not.

Richard:

Maybe he is using complexity in that magical manner such as we have in the creationist term specified complexity. Or maybe it is all complete word salad without any particular meaning assigned to complexity at all. But Bible-believing engineers, mathematicians, and computer scientists like to concoct gibberish that looks like it might be real (and could probably be run through some sort of scientific textual analysis itself, for laughs), and that they may even believe, for purposes of propaganda.

But local variations of all sorts of things do get eclipsed all the time. If it hadn’t been for the particular efforts of anthropologists and folklorists, for example, pretty much the only version of Cinderella we’d have now would be the Disney version.

Unless you are saying that all the hundreds of local tales about all the hundreds of local heroes are preserved in the Iliad, as the local bards sang them, then it is indisputable that many such tales — one would imagine the great majority of them — were lost before they could be written down. Plenty of “characters” in the Iliad who might have been major figures in their original locales are just a name and a brief eulogy in the epic. Why then assume that such tales are routinely preserved in their place of origin for hundreds of years out of local pride, with all foreign variants rejected?

I don’t know which discrepancies you have in mind. If it’s something like a hero driving a bronze age chariot in one episode, but later describing himself ruling a kingdom with iron age customs, what would this show? How would this be different from a character who is addressed with the post-Norman title “earl” but later swears by the classical deity Apollo?