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Won’t you be my neighbor?

On September 2, 2017

I’m playing with graphs again. Here’s a picture of my net-neighborhood out to two steps, i.e., the sites on my blogroll and the sites on their blogrolls.

Web Neighborhood

The funniest thing about this graph is that, despite the fact that it was designed to be my neighborhood, Idiosophy isn’t in the center. Olga’s Middle Earth Reflections is. (Fair enough; her blog has more than a thousand followers.) Science teaches humility, along with everything else.

Nobody else is interested in economics, so Grasping Reality is ‘way over in the corner. The rest of the network is easier to read if I cut that one link.

Zooming in on the non-economic network

J.R.R. Tolkien brings together some diverse parts of the world. There are priests and theologians along the south, language-inventors up in the northwest corner, medievalists in the northeast, and a little knot of modernists on the east side. Nobody who knows Tolkien’s curriculum vitae would be surprised to see that list (except perhaps for the economists and the physicist), but if there’s anything else in life that connects these communities, it doesn’t come immediately to mind.

Technical note

Drawing these graphs took ten minutes. The tools you can download freely from the Web are amazing. This was made by the “igraph” package in R. To make these plots, I used an algorithm that simulates a simplified physical system to place the nodes. It puts an electric charge on the nodes, so they want to be separated and legible. Then it pretends the links are rubber bands, so inter-linked nodes are pulled tighter together. I learned how to do this from an excellent tutorial by Katherine Ognyanova. (Who must be one of us; she posted the etymology of her name on her blog. I wonder if she’s related to the Vedic fire-god Agni.)

Twitter Voices

By Joe

On August 22, 2017

In trivial

I have just listened to two podcasts by people whom I know only from Twitter.

Elaine Treharne spoke with a Stanford University podcast on Anglo-Saxon literature, as I mentioned the other day. Sarah E. Bond talked to the New Books Network about Trade and Taboo: Disreputable Professions in the Roman Mediterranean, her study of professions that were excluded from polite society in Ancient Rome. (Seriously, U.Mich. Press? $80?)

Prof Treharne’s voice sounded just like I expected. Prof. Bond’s was a surprise. She sounded like my sister. In retrospect this makes sense; she grew up just a bit down the road. But why my different reaction? Why do I have an expectation of the sound of someone’s voice from reading their tweets?

Fan Art by Morticia the Cat

After careful examination (the unexamined Twitter feed is not worth following), I have come to the conclusion that I hear all tweets by women as if they were read by Kathleen Turner.

Prof. Treharne’s voice is similarly pitched, with allowances made for her outre-Atlantique accent, and therefore sounded right to me.

This post is of no importance to anyone.

Anglo-Saxons Weren’t Cynics

By Joe

On August 21, 2017

In scholarship

Elaine Treharne of Stanford University did a podcast interview recently. She gives a beautiful reading of the poem that she does not want to call “Wulf and Eadwacer” because it’s not really about those two guys. It’s about the woman who narrates it.

Titles are a problem in other ways, too. The podcast is unfortunately entitled “Reading After Trump”, as if the current president of the USA were in some way responsible for the thirty-year assault on the humanities, rather than just collecting its foul harvest. But let’s pass that by.

The interviewer asked an interesting question: What have we lost, that the Anglo-Saxons of a thousand years ago knew? Prof. Treharne’s response was “hope”, which I think any scholar of Tolkien would applaud. She contrasts that with the cynicism of our modern age. She finds no trace of anything like it in Anglo-Saxon manuscripts. That got me wondering about cynicism. Whence does it come? The Bosworth-Toller dictionary contains nothing about cynics.

Looking at the reasons for cynicism, it’s easy to see why it’s a relatively recent development. I studied with expert cynics in my youth, who taught me what to look for:

A government official who takes an oath of office, which he immediately abandons in favor of handing out money to his supporters. This doesn’t apply at all. An Anglo-Saxon expected this of his king. Any king who didn’t do that would get ditched for one who would. They would even flatter a king by calling him goldwine, “gold-friend”. There’s no ground for cynicism here.

A boss who’s several levels of management above me is clueless about what’s really happening, and will make foolish decisions because of his exalted distance. Not generally a factor, because the medieval orders were clearly distinct. The baron to whom I and my ox reported was the highest official who concerned himself with my job. The king was forbidden by custom to care how I did my job, just as I didn’t care how he did his. (Notwithstanding the continental practice of giving Charlemagne credit for figuring out how to grow wine grapes in Germany.) Cynical gossip around the village well wouldn’t happen as a result.

Advertisers who lie to me to get money from me. Not a factor, either. The Anglo-Saxon economy was largely based on gift-exchange. That’s an economics term; it doesn’t mean festive wrapping paper and bows. It means you’re dealing with people you know so they’ll give you seeds in the spring because you will still be around at harvest time to pay them back in the fall. Anglo-Saxon peasants worked that way because they didn’t have much money. (OK, this is disputed, but generally all the cash money got siphoned off as Danegeld.) In fact, one purpose of money is to make it possible to have economic interactions with people whom you do not trust. Kings have to do that all the time, but the general public did not. Money and cynicism go hand in hand. Without the former, it’s not surprising that we don’t see the latter.

People who pretend to love me to get their hands on something of mine. This seems like it should have been possible in a medieval society, even before they had French people running things. In fact, it’s possible that the narrator of “Wulf and Eadwacer” is running a scam like that. This is the one solid case where I’d expect to see hope failing and cynicism prevailing.

So of the top four reasons to be cynical, I find three that don’t apply to Anglo-Saxon England, but one that definitely does. The fact that we don’t see a cynical reaction to that last is some pretty solid evidence for Prof. Treharne’s idea.

Skin Color in Roman Britain

By Joe

On August 12, 2017

In Academy and Society, ardagraphy

There has been quite a stink over the past few weeks about what color skin the Romans in Britain had. The BBC put a dark-skinned Roman official in a children’s cartoon history program, and the denizens of social media were off to the races. [1] Mary Beard and Neville Morley picked up the standard for the classicists. Among the alt-right antagonists was the pop market-analyst N.N. Taleb, who got famous for coining the term “Black Swan”, but seems not to have the chops to back up his reputation. The noise from the racists got so loud that the Faculty of Classics at Cambridge felt obliged to weigh in. This is kind of amazing to me. I was sure everyone knew that the Roman Empire stretched well into Africa and Asia. They even had an emperor called “Philip the Arab“, for crying out loud! When the Roman generals chose troops to occupy a far-flung province, prudence dictated that their preferred troops not have any language in common with the subject population except Latin. So claiming that the Romans in Britain were all light-skinned seems unsupportable.

But let’s see what they’re saying. As nearly as the the alt-right are willing to be understood, they’re basing their objections on a map of genetic markers in the current British population. A 2015 study of the fine-scale genetic structure of the UK doesn’t show much sign of African genes. They think this “hard science” is much more important evidence than squishy, historically-based evidence, even when the historians have eyewitness accounts. The Guardian article I linked at the top lists some good reasons why genetic surveys might not be the best evidence for claims about ethnicity 2,000 years ago.

I’d like to add another reason: There resemblance between the genetic survey’s clusters and the patterns of family names in the UK is not strong. Leslie et al. tracked autosomal DNA, not mitochondrial, so there should be strong parallels. Surnames and genes are inherited from the same ancestors, after all. A map from the Nature article looks like this:

Clusters of genetic similarity.

In the course of tracking down hobbits, I found the work of James Cheshire and his collaborators, which shows a strong relationship between clusters of family names in the UK and the cultural/administrative regions of the country. Here’s a map published by Cheshire, Longley, and Singleton in 2010.

Clusters of family names

There are some general resemblances. The big homogeneous blob in the East and South East is there, though family names don’t let it extend all the way to Northumberland. I can see hints in the light-blue smear in the North West and the purple smear in the southern West Midlands. Below the coarsest level, though, the two distributions do not resemble each other very well. In particular, the genetics suggests that the people of Pembrokeshire (the southern peninsula of Wales) are affiliated with the Scotch-Irish borderlanders. Family names suggest they’re more like the West Midlanders. And if there’s a family resemblance between Yorkshiremen and Cornishmen, it doesn’t show up in their names.

The conclusion I draw from this is that the genetics is pointing us in a common direction with external markers of family ties. There really is something there, and a salute to the geneticists who have managed to tease it out. However, the signals are accompanied by a lot of noise. We can’t yet use genetic evidence with any precision. When we have a person standing next to an Ethiopian legionary on Hadrian’s Wall and writing about it, it would be foolish to try to contradict him with our rudimentary genetic surveys.

Post-scriptum: I really enjoyed the line, “History is written by the winners; genetics is written by the masses.”

[1] Sorry.

All that is gold does not glitter

By Joe

On August 12, 2017

In squibs & crackers

Over on Facebook, Arthur Harrow raises a point of logic:

“all that is gold does not glitter” means “nothing that is gold glitters” like the difference between “all refrigerators are not Frigidaires” and “not all refrigerators are Frigidaires.” It seems to me that JRRT would know the proper grammar; do you think there is significance to this?

The common proverb, of course, is “all that glitters is not gold”, which is a useful thing to remember. Tolkien twists it around for his narrative purposes. But I have learned that he thought about the roots of words as much as he thought about their current meanings, so I think this is JRRT having some fun with etymology. According to my go-to source on the Web,

c. 1300, glideren (late 14c. as gliteren), from an unrecorded Old English word or from a Scandinavian source such as Old Norse glitra “to glitter,” from Proto-Germanic *glit- “shining, bright” (source also of Old English glitenian “to glitter, shine; be distinguished,” Old High German glizzan, German glitzern, Gothic glitmunjan), from PIE *ghleid- (source also of Greek khlidon, khlidos “ornament”), from root *ghel- (2) “to shine,” with derivatives referring to bright materials and gold. … Other Middle English words for “to glitter” include glasteren and glateren.

Etymologically, everything that is gold glitters, by definition.

Does not glitter

But if we look at a modern dictionary, “glitter” means “sparkle”. The stuff that people throw around to celebrate is called glitter because of light sparkling off its cut edges, not because of the metallic sheen of the plastic it’s made from. The old meaning of shining like gold has passed over to “gleam”.

So, apart from its purpose in the story, “all that is gold does not glitter” is using the precise logical meaning that Arthur identified to make a wry comment on a change in the English language.

Anne Dufourmantelle

By Joe

On August 8, 2017

In Vive la France

Discovering an interesting philosopher by reading her obituary is a definitive case of mixed feelings. That’s where I am now with Anne Dufourmantelle, psychologist, theologian, and philosopher. Lately it seems that many projects in which I am interested are hobbled by an imbalanced perception of risk. All activities involve a tradeoff between the risks involved and the good that can be achieved, but lately safety and security have been elevated to pre-eminence over all other possible goods. This seems like a recipe for stagnation. I was pleased to learn that people are doing the intellectual heavy lifting to support or refute that apparent situation. Alas, the reason I heard about her in English-language media is that she lived up to her philosophical understanding of risk, and suffered a heart attack while rescuing two children caught in a rip tide.

Here’s what she said in an article in Libération, about her book In Praise of Risk. Interview by Anastasia Vécrin, 14 September 2015

Introduction

In the face of the terrorist threat and the migrant crisis, how can we continue to live without giving way to a security panic? Some want to close the borders, others advocate an increased armed presence on public transportation. But do these proposals reassure us? Or rather, do they remind us of imminent danger? The philosopher and psychoanalyst Anne Dufourmantelle, author of Eloge du risque (Payot 2011), explains that living necessarily involves taking risks. And today it is the migrants, victims of the wars in the Middle East, who need protection more than we do.

Q: In the context of permanent terrorist threat, must we over-protect ourselves?

AD: First, terrorist threats are always a political weapon for the control of individual freedom. Any security response is already political. The question is always phrased as “how, in addition to protecting people and preventing an attack, can we reinforce the means of control and make them more efficient?” Remember: all totalitarians end up using the terrorist threat to liquidate alternatives.

Moreover, in a more banal sense, “security” generates fear more than it assuages it. Under the media-pushed threat of random violence, the population becomes paranoid, even to the point of denouncing others to the authorities. Every terrorist act emphasizes a little more the idea of continuous danger. An opportunity for abuse of power exercised this way rests on the potentiality of a dangerous, even mortal, intrusion that can only be thwarted by maintaining a perpetual state of alert.

When there really is a danger that must be faced in order to survive, for example during the Blitz in London, there is a strong incentive for action, dedication, and becoming part of something larger than oneself. That doesn’t happen in the current case. In my opinion, if the threat of the attacks after the Charlie Hebdo massacre had lasted months, another relationship to the threat would have grown in the population, beyond any directives from the state. We’d have seen a form of active solidarity.

Faced with an external reality of anarchy and horror, people reorganize their lives, invents small rituals, tiny actions, magic words to protect a space of humanity. In a way, anxiety loses ground because people have recourse to an alternative. On the contrary, to imagine an enemy ready to attack from time to time induces a state of paralysis, a feeling of impotence which calls for a maternal body, supposedly all protective. “Big Brother” turns into “Big Mother” as the psychoanalyst Michel Schneider put it. Today, we desire this overprotection and are encouraged to remain in a condition of voluntary servitude.

Q: Nevertheless, the desire for security can’t be completely satisfied, because there’s always some risk…

AD: The idea of absolute security – “zero risk” – is a fantasy. It appeals to an archaic sense of impotence and the desire for remedies attached to it. You have to be wary of someone who offers you total security, because the shelter often works in a perverse way. The price of protection quickly becomes very high, as we see in mafia protection rackets. When we start from infantilization, we put ourselves under guardianship. Except that when you see police patrolling, it is more worrying than reassuring. Paradoxically, the signs of protection reactivate the feeling of insecurity. Security laws provoke transgressions that will themselves justify new security rules. It is a vicious circle. True protection includes confidence in the capacity that someone does or doesn’t have to experience their freedom. To live is to take risks by definition. A person with autonomy is less easy to influence than one who is governed by fear.

Faced with an unpredictable danger, the fear that overwhelms us is all the stronger because it traps us in the impossibility of anticipating and anticipating. We are paralyzed in the face of senseless cataclysm. To be a victim of a terrorist attack is to be a “generic” victim, that is to say, they have been targeted not individually but because they belong to a sex, a culture, a religion, or a function in society. Or they could just be in the wrong place at the wrong time. This fatal absurdity is unbearable in our modern age, where “destiny” has given way to everyday life, and where we’ve tried to make “chance” an endangered species.

Q: To refuse risk is to refuse to live?

AD: The usual expression is to say, “I risk my life”, but perhaps one should say, “I risk life”. To be entirely alive is a risk, and few people are. There are many zombies, undead, lives attenuated by the “disease of death” as Kierkegaard called it. This risk is what another philosopher who disappeared under torture, Jan Patocka, called “life in amplitude”.

Q: Why such a search for protection?

AD: One of the things that characterizes the human being is this first breath of a newborn baby. It is a suffering, and it can also be an ecstasy. In either case, it is a radical passage. Life is metamorphosis; it begins with this first risk. Man is neotenous, an unfinished being who needs to be protected for survival, unlike other animal species. If, initially, he is not surrounded by care and protection, he is in danger of death. These early stages of our being are marked by this association “ life = survival”, which are anchored in our memory, then repressed. When one invokes threat and fear, I believe that part of us regresses to this first period of life, to its fundamental vulnerability.

Q: How can we get free of this feeling of fear?

AD: I do not have a universal answer. From an analytical point of view, it may be possible to tame fear by welcoming it. When one admits his fear, his finitude, a confidence can be reborn from this vulnerability. If we make fear into something negative, we lock it in place. Like the mechanisms of anxiety or neurosis, fear is formed by one’s past, so we understand the future by means of that experience. Neurosis has a horror of the new. We can disarm fear if we identify this mechanism of referral to the past, of systematic repetition. Sometimes it is necessary to refuse a security initiative. Let there be a call to vigilance, fine, but let us still keep up our confidence. People who are not going to give up going about their business, even though there are bombs exploding on way, are people who are placing a heavy stone on the pan of the balance against terror.

Q: How to explain this paradox: that people want more security while wanting to preserve their freedoms?

This is not so much paradoxical as it is infantile. It brings us back to that age of life that wants both a protective cocoon and the thrill of transgressive experiences. The taste for freedom is widespread but the strength to bear the risk, much less so.

There is also an indirect answer to your question: those who really need protection are the victims of these unjust wars that have set fire to the Middle East, for which we are collectively responsible. We usually call them “migrants” (a term that leaves them perpetually wandering). The terrorist threat they live under is not fabricated by governments for control. They survive under terror, and try to escape from it. It is our duty to open our borders, for the law of unconditional hospitality is the first humanizing rule of a civilization. Let us not forget that one day it will be our turn to be the migrants, and we will be begging for hospitality and protection. What security procedures will be arrayed against us then?

Tales from the Attic

By Joe

On August 6, 2017

In trivial

There was an Old-Testament-grade thunderstorm this week. My shingles are apparently not among the righteous; the roof sprang a leak. We caught it before it could do any serious damage but I’ve been up in the attic this weekend, carrying boxes out to sit in the sunshine and replacing damp insulation.

One of the boxes contained a first edition of Unfinished Tales, purchased at the remainder price of $2.98. The glue on the fold-out map has come loose, but it’s otherwise in good condition. I’ve never seen it before. It must be part of my first wife’s estate, purchased before I met her. (That price is compatible with our net worth in those days.)

I was debating whether to purchase a copy of the book. Now I have my answer.

Saruman 15-love

By Joe

On July 28, 2017

In fantasy

Gandalf probably has the most dedicated fan club of any character in LotR. But to an idiosopher, he has one moment of complete catastrophe. This is from Gandalf’s report to the Council of Elrond about his confrontation with Saruman:

“White!” he sneered. “It serves as a beginning. White cloth may be dyed. The white page can be overwritten; and the white light can be broken.”
“In which case it is no longer white,” said I. “And he that breaks a thing to find out what it is has left the path of wisdom.”

LotR, II, ii.

I’ve talked about this passage before, working from the possibility that Saruman was playing a clever joke. Lots of people, many of whom know more than I do, take that last sentence as a statement of JRR Tolkien’s own beliefs. Malcolm Guite‘s Signum Sessions lecture is an excellent example:

But there’s a problem with that: I agree with Saruman. First, dyeing white cloth. JRRT frequently mentions colors, and uses them as important signifiers in his texts. Hobbits like to dress “in bright colours, being notably fond of yellow and green” (LotR, Prologue). Bombadil’s jacket is bright blue (I, viii). Gandalf wears blue and grey. The dwarves in The Hobbit are even distinguished by the color of their hoods (I, i). Surely if wearing cloth of other colors than white were morally dubious, it would have been mentioned. If Gandalf is going to disagree with this, he’s going to have a lot of explaining to do. JRRT provides no explanation.

Second, the white page can be overwritten. If it weren’t, a philologist would have nothing to do. A twentieth-century author would not publish any books. Writing on white pages can’t be a bad thing to Tolkien. Something is going seriously wrong with the wise-Gandalf interpretation.

Third, breaking things to find out what they are is an essential part of learning. In the specific case in the text, a group of photons that would have been annihilated in the electric field of earthly matter in a few nanoseconds was divided up to show its component colors and confirm the wave theory of light. Lots of learning for no loss. Here’s a sampling of other ways that life would be lessened, had we stayed on this so-called “path of wisdom”:

No one would ever have eaten an oyster or a walnut;
Musical harmonies might never have been discovered;
Doctors wouldn’t know about the circulation of the blood;
The beauty of the crystals that form inside geodes would never be seen.

(The dwarves of the Glittering Caves will back me up on the importance of that last one.) None of these things is bad. Gandalf is just wrong.

What’s going on, here? It’s the power of the Voice of Saruman. Even through the filter of Gandalf’s re-telling, the effect is still there. Gandalf sounds like a fool. Saruman’s voice has tricked him into a ridiculous position. JRRT has shown the effect, not just told us about it, by having it affect the reader as well. As Théoden found out, “When others spoke they seemed harsh and uncouth by contrast…” (III,x.)

No worries, Grey Wanderer — it can happen to anyone.

Signed Graphs and Interesting Stories

By Joe

On July 18, 2017

In graphs

Of all the types of graphs, signed graphs are probably the most interesting for looking at interactions among groups of people. Definition: a signed graph is a collection of nodes and links between them, just like a regular graph, but each link is flagged with a positive or negative sign. When we’re using the graph to describe a social network, those might be “loves” and “hates”, “admires” and “sneers at”, or any other dichotomy that comes to mind.

Some graphs have closed paths in them. Mathematicians call a closed path a “cycle”. If you go around a cycle and encounter an even number of negative signs, it’s a balanced cycle. A graph that contains only balanced cycles is a balanced graph. These are the simplest cycles:
Here’s where things get interesting: signed graphs apparently figure into human sociology. If a network of relationships forms a balanced graph, it’s a stable structure. Relationships that fall into unbalanced graphs aren’t stable, and lead to drama. (That last word can be taken either literally, or in the euphemistic sense that people give it these days.) I don’t think anybody knows why such a simple mathematical condition seems to be true; that’s just the kind of thing mathematics does every now and then. Some brilliant psychologist will figure it out someday.

In the unbalanced graph “a”, I colored the vertices pink and blue because my wife watches soap operas, and nearly as I can tell, there’s a cycle like that at the heart of every one of them. It never ends well, because it’s unbalanced. The balanced graph “b”, by contrast, is “you and me against the world”, which is a stable configuration. The all-negative graph “c” can go one of two ways. If the vertices represent people, two of them just go away and the network disintegrates. If the vertices represent countries, or something else that’s forced into interaction because it can’t quit the game, the network changes when two of the nodes look for an advantage by conspiring against the third. The fourth possibility, “d”, is that all the links are positive. It is balanced and kind of boring in its dramatic implications.

There’s a perfect example of three-party instability in Book IV of LotR among Frodo, Sam, and Gollum. From the time they meet up, it’s graph “a”: Sam loves Frodo, Sméagol loves Frodo, Sam doesn’t like Sméagol. Type “a” is unstable, so something’s got to give. The crisis comes in Chapter 8, when Sméagol (possibly) tries to turn the graph into a stable all-positive triangle, but Sam intrudes, the opportunity is lost, and Gollum plots with Shelob to turn the graph into type “b”.

Of course, three-person networks are easy to understand without graph theory. The real advantage of mathematics is that it becomes possible to handle any size network. There’s a theorem about graph balance that applies in general: Any balanced graph can be re-drawn in a simple form. (Can I say “isomorphic”? Sure I can. Y’all are tough enough.) All balanced graphs are isomorphic to a graph that’s split into two parts, where there are only positive links within each part, and all the links between the parts are negative. That’s called the Cartwright-Harary Theorem. Prof. Harary says that the theorem is unexpected and counter-intuitive, which I am half in agreement. The positive interpretation is easy to accept: if the world consists of two parties, and every member of a party agrees with each other, and every member of each party disagrees with all members of the other party, the situation is stable. (Then Romeo meets Juliet, and the stability is history.) The counter-intuitive part is that this is the only way for a graph to be stable. That’s it – the one way you can build a stable social system is for everybody on your side to agree and to hate the other side, and contrariwise on the other side. In practice, I suppose you could allow disagreement on issues that were irrelevant to the structure, and thereby outside the graph model. But on any important issue, perfect party unity and perfect hatred of the other side is your only chance.

Interesting stories, whether they’re fictional or meta-fictional, don’t have balanced graphs. One of the most intriguing things I scribbled down during Sørina’s lecture was that we might be able to define a new subset of graphs under the rubric of “interestingly-unbalanced”.

Illiterate Coda

Maintaining stable structures without fomenting partisan warfare is critically important in a society as complex as ours. But math is math. So how do we handle the dilemma of the Cartwright-Harary Theorem? We go around the horns. Almost every organization chart you’ll ever see has the same basic structure: No cycles, so the theorem doesn’t apply. That type of graph is called a tree. It’s useful in all sorts of contexts, but until now it had never occurred to me that it means that management never has to choose between polarization and instability.

Graphing the Inklings

By Joe

On July 14, 2017

In Digital Humanities, graphs

Sørina Higgins’s lecture at Mythmoot IV gave us a hint about where she’s going intellectually in the near future. She wants to apply network theory to create “meta-fictional narratives” about the interactions among the Inklings and how it affected their writing, and invited us to do the same.

The coolest figure from “Graph Theory as a Mathematical Model in Social Science”

This seemed like a good time to blow the dust off my command of graph theory. You can figure out lots of cool things from networks, if you know about graphs. Frank Harary, writing from a period contemporary with The Lord of the Rings until well into this century, pushed the use of mathematical graph theory into the social sciences. Here’s a short version. Here’s what I think is his clearest explication of what can be done with graphs in the social sciences (which is what we are doing, now).

For instance, graphs are used a lot in management theory. The fastest performing network structures were those in which the distance of all nodes from some central person (the “integrator”) was the shortest, say Borgatti, Stephen P., et al. “Network analysis in the social sciences.” science323.5916 (2009): 892-895. Now, if you’re looking for a paradigm of a stable, efficiently operating organization, the Inklings are not an obvious place to start. I’m pretty sure that C.S. Lewis would turn out to be the integrator, but then what? Here’s a chart from Borgatti et al. that might clarify the relevance:

Following Sørina’s Ansatz, we might begin with the box on the left to determine our set of writers (nodes). Next, we’d assign a numerical quantity to each node, probably derived from a lexomic analysis. Then, we’d build links from the two boxes on the right, Interactions and Flows, based on accounts of how the writers interacted, to see how some attribute of the nodes changes over time.

The easiest thing to see would be something like the spread of Theosophy or Anthroposophy. Weird philosophies come with an idiosyncratic jargon that should be trivial to find in the writers’ texts. The mathematical tools we’d need to identify the influence of some *osophy have already been developed to model the spread of infectious disease.

Slightly more difficult would be to track down an agreement between the writers to split things up. There was the famous wager between Tolkien and C.S. Lewis about writing a time-travel and a space-travel story, respectively. We’d look for some lexemes they shared equally, which then split up mitotically into space on Lewis’s side and time on Tolkien’s. But a difficulty presents itself. It might be possible to find lexemes in Tolkien that correlate well with space travel, but I can’t think of them. We’d have to find them via statistical correlations, which tend to make the final result less credible. A better choice might be King Arthur. In an old lecture on Youtube, Sørina mentions that Tolkien may have given up work on Arthurian legends because Charles Williams was doing so much in that area. It should be easy to find convincing Arthurian terms whose frequency evolves over time.

Caveat: Sørina drops a hint that she’s dealing with a large network, which the Inklings are not. We’ll have to wait and see.