Category: Digital Humanities Page 1 of 3

Mechanical Help Understanding Charles Williams

On April 22, 2024

I’m the first to admit that I don’t understand most of what Charles Williams wrote. I rely on Sørina Higgins to figure out the hard parts and explain them. So when even she has a puzzle, where is there to turn? This came up in Sørina’s blog yesterday. She asked for suggestions about mystical connections between Eidola and their Angeli, and if you have no idea what either of those words means, we’re even.

Since my ignorance is so near perfect, I decided that asking a Large Language Model would do no harm. We’ve set one up at work so we can test it and see what it’s good for. It’s based on Microsoft’s Azure. Usually, I make it read thick volumes of government regulations and see if it can answer questions about what’s in them. But the boss wants us to test it on as wide a range of topics as we can, and this one will definitely stretch its boundaries.

The query I gave the LLM was cribbed from the blog post:

This is a question about twentieth-century Christian mysticism. The novel “The Place of the Lion” by Charles Williams contains symbolic representations of Angelic Orders, their corresponding Platonic Virtues, and their symbolic earthly animal emanations. A scholar has created a table of the mapping among them, but some items are missing. The first column is the angelic order, the second column is the animal, and the third column is the Platonic Virtue. Elements of the table are separated with commas. Missing elements are denoted with “XXX”. What are the missing elements?
Angels,Lion,Strength
Archangels,Serpent,Subtlety
Powers,Butterfly,Beauty
Princes,Unicorn,Speed
Virtues,Eagle,Balance
Dominations,XXX,XXX
Thrones,XXX,XXX
Cherubim,Phoenix,XXX
Seraphim,Lamb,Innocence

This is a perfect question for an LLM: it needs to draw on a lot of literature, maybe including unexpected sources; it’s a complete-the-list format like the way the programmers tested early versions of the models; it doesn’t require thought, but can be derived just from associated words in other texts. I’m used to the LLM taking a few seconds to answer my questions, but this time the response came back immediately.

Dominations,Bull,Patience
Thrones,Elephant,Wisdom
Cherubim,Phoenix,Immortality

First off, even for a skeptic like me it’s impressive that an LLM can fill in the missing elements in a table. Tables are hard. But did it get it right? In my uninformed opinion, associating elephants with wisdom and assigning it to the Thrones is pretty good. There may be a pun in there (howdah you do?) messing up the answer, though.

bull icon by Dimitri Lupo. the bull is threatening to charge.

Patience is my most attractive feature.

Next: bulls, patience, and Dominations? Bulls and domination, OK. The conjunction makes me suspect a few Hemingway novels in the training set, which is perfectly plausible, but if there’s a word that appears less often in Hemingway than “patience” I don’t know what it is. Bulls are very patient when they’re hanging out with their cows, I suppose, but when they interact with humans patience is not their signal virtue. (Maybe it’s Bull from “Night Court”.)

The last one, now… is immortality even a virtue? The phoenix certainly doesn’t have it, or there would be no interesting story about the phoenix at all. Cherubim have a flaming sword and the phoenix is born in flames, so those go together, but I think the LLM is just guessing about immortality. Come to think of it, what’s a “platonic virtue”, anyway? Collecting a bunch of laudable qualities together and calling them collectively “virtues” sounds like it comes from at least 500 years after Plato.

Conclusion

English professors don’t have to give up and retire, just yet.

High-dimensional space is weird

By Joe

On May 8, 2022

In Digital Humanities, Slow learner

There was a mathematically unsatisfactory bit in the last post about measuring the relationships among mentions of color in The Lord of the Rings. When I used the Euclidean distance between the 62-dimensional vectors to calculate the relationship between color mentions, the dendrogram had some connections in it that don’t make much sense visually or textually, e.g., brown was clustered with black and red. The connections with a linear “Manhattan” distance measure made much more sense. I asked Digital Tolkien about it, as one does, and he assured me that the L1 metric was better. But why?

It turns out this is something that mathematicians know: in high-dimensional spaces, using the Pythagorean Theorem causes near neighbors and far-away neighbors to be all about the same distance apart! ¹ In fact, the choice of which of your neighbors is nearest isn’t even stable. The unavoidable numerical errors that come from using digital computers can dominate the real differences in the input data.²

Effect measured by L1 distance is more detectable at high dimension

Relative effect as a function of measure dimension

Of course, now that I’ve read a couple of papers about it, it’s obvious. Simplest possible case: suppose a book mentions one word once per chapter, and another word twice in one chapter and once in all the others. The relative difference between those two vectors, as a function of the number of chapters, looks like this.

62 dimensions counts as “high-dimensional”. Both ways of measuring distance have dropped a lot from our 3-dimensional experience, but the effect in our test case is twice as easy to compare when we use the Manhattan distance measure.

Notes

The Colors of the Forests

By Joe

On April 16, 2022

In Digital Humanities, fantasy

As previously discussed, black is the color mentioned most often in The Lord of the Rings, and white is right behind it. But grey is #3. Take that, Edwin Muir!

I fed the list of X11 color names into a text-processing program and collected all the color mentions I could find. With one exception: “tan” is a part of so many English words that it would be unfair to expect a computer to pick out which words containing that trigram were colors and which were not, so I deleted it from the list. This is what came out.

Figure 1. Frequency of color mentions

There are ten colors mentioned more than ten times in the text. Their relative frequency is in the pie chart in Figure 1. Oddly, none of the top-notch Tolkien illustrators has used this palette. I wonder why.

The places colors are most-often found are sometimes surprising. The chapter in which black is mentioned most is “The Siege of Gondor”. White, “The King of the Golden Hall”. Grey, “The Great River”. Red, “The Tower of Cirith Ungol”. Green and brown are mentioned in “Treebeard” more than any other chapter. Blue, yellow, and gold are mentioned most in “In the House of Tom Bombadil”; sometimes the place is not surprising at all.

Silver is most mentioned in “Lothlorien”. That chapter is #3 for “gold” instead of #1, because when a character has a color in her name, that tends to skew the distribution. Gold and silver are strongly present in all three chapters involving Lorien, though.

If we make a vector out of the fraction of each color’s mentions that happen in each chapter, we can test which colors tend to form clusters in the narrative. The dendrogram is in Figure 2. (I’ve inflicted dendrograms on you before.) As we trace a line from one color to another, the further left we have to go, the less-related the colors are in their occurrence in the text.

Figure 2. Which colors go together in the text

But what do we do with all these measurements? With an Idiosopher’s well-trained eye for the most significant thematic content of a work, I zeroed in on the disagreement between Celeborn and Treebeard. “Yet they should not go too far up that stream, nor risk becoming entangled in the Forest of Fangorn,” said Celeborn. “Do not risk getting entangled in the woods of Laurelindorinan!” said Treebeard. What’s the subject of their disagreement?

Figure 2 gives us an insight: brown is used to describe Fangorn more than any other place. Gold and silver are dominant in Lothlorien. The two forests agree on green, but to get from brown to gold and silver, we have to go all the way to the left edge of the diagram. These are the furthest-apart pair of colors in the text. So here is our answer: the source of the ancient enmity between the two forests is interior decorating. When Galadriel sang the woods of Lothlorien into existence³, she may have had an idea of the kind of forest she didn’t want, and Fangorn may have been it.

Coda: Boring Details

Sometimes a color word is also a noun. Olive dropped out of the analysis because it’s only mentioned twice, one of each. That was an easy one. I tried to separate mentions of gold and silver into the color and the metal, but quickly discovered any partition I could make would be arbitrary. Tolkien doesn’t clearly separate them. He rarely mentions the metals without the colors being important, so I left them all in.

The method: First, all the color words were pulled from the text. Then they were classified into a standard color-word. Usually that was straightforward. The exception was “scarlet”, which got absorbed into “red”. Then each instance of a color was collected into a histogram by chapter or whatever.

Instances of a color by chapter form a vector in a 62-dimensional space. Vectors were normalized so the elements of each color’s vector were the fraction of mentions that were in that chapter. The distance between two vectors was computed using the linear distance between elements. (This is not the Euclidean distance between unit vectors; I re-did the analysis with those and got similar results, but not as easy to interpret them in a way that made sense with respect to the text. Linear differences seem more relevant to text analysis, but it’s always good to check.) The vectors were clustered using the R hclust function with complete linkage.

Gimli’s Opium Dream

By Joe

On January 8, 2022

In Digital Humanities, fantasy, mythgard academy

I’m currently taking the mini-course “Tolkien’s Ents and the Environment” from Signum University’s SPACE program, taught by the unwiðmetenlic Sørina Higgins. We were discussing Gimli’s speech about the glories of the Glittering Caves (III, viii) and how it parallels the (more frequent) references to trees and plants as the object of environmentalist sympathies. Sørina challenged us to a close reading of Gimli’s speech.

by Massupa Kaewgahya

Surprising no one, I zoomed in on the extraordinary number of French-derived words in the passage. I’ve never counted them before. Time to fire up the OED Text Annotator! This analysis focused on Gimli’s direct speech, from “Strange are the ways of men…” to “It makes me weep to leave them.” This passage is 14% derived from French. As we have established, the threshold of madness in Tolkien is 7%. In this passage, Gimli leaves behind even the suicidal Denethor. It’s the second-highest French density I’ve identified so far, just behind Gollum’s pre-taming peak of 15%.

Then Sørina pointed out something fascinating: Gimli’s speech sounds a lot like Coleridge’s poem “Kubla Khan.” The speech and the poem are roughly the same length. (381 words to 349.) They share words like measureless caverns, underground rivers, domes, caves, towers, round, cover, hill, sea, music, deep, wall, war… (omitting the boring, common words). Of course the quantitative metrics kind of miss the point. The feeling is similar. Both are gushing over a beautiful place from which they’ve been untimely taken away.⁴ As Sørina put it, the caverns cause Gimli not just to switch languages, but also centuries.

“Kubla Khan” is famously the result of an opium dream. There’s only one conclusion to draw here. There’s some kind of narcotic in the Glittering Caves of Aglarond. Sauron missed a trick when he tried to snare Dwarves with Rings of Power. That kind of addiction⁵ doesn’t work on them. However, limestone caves apparently emit a gas that humans don’t notice, which acts like a drug on Dwarves. Even short-term exposure leads to monologuing, Romanticism, and French.

He got better

By Joe

On December 4, 2021

In Digital Humanities

A Mr. C. Hostetter (!) who is highly knowledgeable about these matters, points out an error in the post I derived from the Times Literary Supplement. Tolkien had nothing to do with Early English Lyrics: Amourous, Divine, Moral, and Trivial. I’ve fixed the old post.

Digitizing old magazines is a tricky business. In this case, the review was of two different books. The scanner put the two titles together up front and the authors’ names together at the end. This happens often enough in that database that I’ve been unable to do a graph analysis like I did with the London Review of Books, by the way.

While I was fixing that, I chased down all the other pre-Hobbit references. That brought me to a later review⁶ of what seems to be the same work. This reviewer was in a more eupeptic mood, I suppose, because “above average” has been superseded.

Mr Tolkien’s vocabulary affords an excellent handmaiden, not standing in the way, while decidedly more than an appendix. The scholar will enjoy the explication of, inter plurima, ‘knacke,’ ‘lay,’ ‘sentence.’

Now I find myself wanting to track down those explications.

Parenthesizing

By Joe

On November 18, 2021

In Digital Humanities, fantasy

Tom Hillman has joined the ranks of the digital humanists⁷ with three posts (I, II, III) at “Alas, not me” investigating parenthetical remarks in The Hobbit and The Lord of the Rings. These are good analyses. They’re not just counting; they contain fascinating insights about the deeper purpose Tolkien had in using that particular stylistic choice. Highly recommended.

Of course, that’s not what we do here at Idiosophy. Tom points out that there are two chapters that don’t fit the paradigm: “At the Sign of the Prancing Pony” and “Treebeard”. He calls them “aberrations”. That’s more like it. Aberrations, we can work with.

At the Sign of the Prancing Pony

The primary reason for thinking there’s an aberration at The Prancing Pony⁸ is the generally-accepted idea that Bilbo only wrote the first chapter of LotR. As he confessed to Frodo, “when I have time to write, I only really like writing poetry.” (VI,vii.) Taking Bilbo at his word, I note this chapter contains a two-page poem of Bilbo’s creation. Whoever wrote it did not omit a single stanza. Frodo’s fondness for his old cousin was immense, but even so stopping the narrative for such a long time might have been too much to ask. I’ve always suspected that this chapter was also written by Bilbo, because it’s a place he (probably) knew firsthand and it introduces his friend the Dunadan. The sudden up-surge in the use of parenthetical comments is a fourth item of supporting evidence.

Treebeard

The chapter “Treebeard” uses a lot of parentheses.⁹. As has been noted before, Treebeard talks like an old hobbit. There’s a reason. Let’s imagine Frodo, locked in a tower in Minas Tirith, getting briefed on all the things that happened in Books III, V, and VI that he wasn’t around to see. For most of the chapters, there’s one authoritative voice, or there are a lot of people who can remember for him what’s going on. But “Treebeard” is unique. For that one chapter, Frodo had both Merry and Pippin as sources, and no one else to straighten them out.

As we’ve noted in both LotR and The Hobbit, Bilbo is easily distracted. He uses parentheses to mention things that just crossed his mind, including things that just are amusing. What if Bilbo’s protegés picked up the same habit? Poor Frodo! He must have been getting the story from two different directions, both Merry and Pippin talking at once, saying different things as often as not. Bilbonian distractions were built into the source material. I can’t blame Frodo if he decided the best way to make sense of that chapter was to split the difference between the two versions, and preserve deviations in parenthetical asides. So what if that makes Treebeard sound like Gaffer Gamgee?

Coda

I can’t resist one small addition. Tom was sure to point out that he didn’t use a single logarithm in his analysis. (This has been a point of contention in the past.) But let’s look at a plot of the cumulative number of parentheses in the texts.

Fig. 1. The abrupt upward jumps are the chapters discussed above.

Those curves have an awfully familiar shape. Let’s take the logarithm of the horizontal axis.

parenthetical insertions vs. log of words into text

Fig. 2. I knew it!

Both Bilbo and Frodo pile up parentheses early in the text (when many explanations are needed) but let them fall by the wayside as the plot thickens. Those straight lines fit really well; the pattern is logarithmic. In fact, we can infer authorship from the slope of the count of parentheses on a log scale. See that blue dot above the red line in the lower left corner? That’s “A Long-expected Party”. We recognize the lion by its paw!

Notes

Tolkien’s Presence in the Publishing World

By Joe

On November 11, 2021

In Digital Humanities

The Times Literary Supplement has put on line a digitized archive of its content since 1902, with some basic search tools. So naturally I jumped in. Numerical analysis of such a database won’t tell us much about literature, but it has things to say about the reception of literature.

timeline of mentions of Tolkien in the TLS

Vertical lines indicate publication of The Hobbit, LotR, and The Silmarillion

This is the number of times articles mentioning “Tolkien” appear in the TLS by year. The blue line is the Loess¹⁰-smoothed trend. With this kind of smoothing important things are slopes as much as levels.

Professor Tolkien appears occasionally in his capacity as a scholar of ancient languages before the publication of The Hobbit. The publicity campaign for the book gives him a brief spike upwards (advertisements are digitized the same as editorial content), but the mentions drop back quickly. Children’s book, you know. After The Lord of the Rings appeared and sold a hundred million copies, the attitude at the TLS changed. In this period, Tolkien became a cultural touchstone. Most of the mentions come from people comparing other things to LotR, which got more common over time.

Then came a big change. 1977 was the year The Silmarillion was published, but that’s not what drives the bolus of Tolkien mentions. (The TLS reviewer didn’t like it.) The big push comes from the publicity for, reviews of, and references to Humphrey Carpenter’s biography. That’s the thing about counting words in a database: If you put Tolkien’s name in the title of your book, you get one count for the Table of Contents, one for the review itself, and one from the contributor index at the end of the year. I didn’t remove those as redundant because by this point I’d realized I was looking at popular reception, not scholarly. Popularity drives mentions in the TLS, and when publishers put a word in the title of a book, it’s because of popularity. Same impulse.

After the surge of publicity in the late 1970s, Tolkien stays in the pages. Now it’s not because of publication announcements. The History of Middle-earth hardly gets mentioned. The level of references is steady for a few decades. Almost always, it’s because reviewers are saying whether a new book is like LotR or not. Some years there are few mentions, some years over a dozen, but it’s a steady state.

Then at the turn of the millenium come two big changes in the world. First, Peter Jackson made movies that brought in six billion dollars. Second, Tolkien scholarship started getting noticed. The second-highest year for Tolkien mentions was 2004. This year included Tom Shippey’s review of the movie version of The Return of the King (he liked it), but also John Garth’s Tolkien and the Great War. According with the aforementioned principle, Garth gets a triple word score. Then there was a review of books by Jane Chance and Verlyn Flieger. That’s what “getting noticed” means. The number of mentions didn’t drop off from the peak as it has in the past.

For the last decade and a half, with no particular events to drive engagement, the level of mentions is 8-16 per year and slightly rising. For comparison, that’s 1/10 of Shakespeare’s level. In 2019, the chances were one in four that any given issue would mention Tolkien. He even shows up in clues for the crossword puzzle now.

Coda

The first mention of the Professor in the TLS is from October 5, 1922. Reviewing Fourteenth Century Verse and Prose by Kenneth Sisam, A. Blyth Webster says, “The glossary has been prepared by Mr Tolkien. So far as we have tested it it is above the average.” High praise!

Funny Names for Bureaucrats

By Joe

On July 10, 2021

In Digital Humanities, trivial

Brenton Dickieson posted the other day about a comic-book adaptation of The Screwtape Letters, by C.S. Lewis. I haven’t read that book in decades, but I did remember the wonderful names of demons. We’re in a digital world now, so I pulled out every such name from the text. The algorithm is nothing special: any word that begins with a capital letter and flunks spell-check is a candidate; delete a few dozen stragglers by hand.

Results: Scabtree, Screwtape, Slubgob, Slumtrimpet, Toadpipe, Wormwood.

What do we see here? They all come from the latter third of the alphabet. Lots of “s” words. (The Screwtape Letters is dedicated to Tolkien, who thought “s” was a sound for bad guys, too. Saruman, Sauron, Shelob, Sackville…). They’re mostly made from jamming two short English words together.

There’s another author who did that, at a much less elevated level. Keith Laumer wrote a ton of science-fiction stories about Jame Retief, a muscular, norm-busting diplomat in the “Corps Diplomatique Terrestrienne” a gender-busting arm of Earth’s hegemony over the galaxy. Wikipedia says they’re satirical, but I’d describe them more like broad, sophomoric humor. 21st-Century intellects will find them a bit crass. (Naturally, I love them.) Laumer was a diplomat himself before he became a writer. These stories seem to be settling scores with his old bosses. The bosses in these stories get names like:

Barnshingle, Clawhammer, Clayfoot, Crodfoller, Dimplick, Grossblunder, Hidebinder, Hipstinker, Lackluster, Longspoon, Nitworth, Otherday, Passwyn, Pennyfool, Proudfoot, Rumpwhistle, Shortfall, Sidesaddle, Sitzfleisch, Spradley, Sternwheeler, Straphanger, Thrashwelt, Thunderstroke, Underthrust, Whaffle, Wrothwax

Of course, my favorite of these come from proverbs: he who sups with the devil must use a long spoon”; “he who runs away lives to fight another day”. We see the same pattern — fully a quarter of the names begin with “S”. Almost half come from the last third of the alphabet. If we remove the names that explicitly come from such proverbs, the pattern gets more pronounced.

What is it that makes funny names bend that way alphabetically?

Gollum le Grand? Le Gollum!

By Joe

On December 30, 2020

In Digital Humanities, fantasy

This is another episode in my exploration of what we can see when we look at The Lord of the Rings through the lens of the frequency of French-derived words. Earlier posts are here and here, and the Silmarillion here. As always, kudos to the programmers of the OED Text Visualizer for providing the microscope.

We’ve seen that regular characters and situations use Germanic words. Like nuclear radiation, a low background level of French is unavoidable (viz., the louver on Meduseld), but as pomposity increases and sanity diminishes, the level of French in the text rises to double-digit percentages. This raises a question: does the craziest character use the most French words? The answer appears to be yes.

Gollum/Smeagol is almost certainly the least sane character in LotR. His dialogue needs quite a bit of editing before it can go to a computerized text analyser. The number of “s”s in a word needs to be standardized, sometimes “gollum” is an onomatopoeic punctuation mark not a proper noun, and so on. Also, his speech tends to be broken up in the text. The following computations are done on the closest dictionary-entry to Gollum’s words, aloud or internal.

There are seven blocks of dialogue long enough to support statistics between “The Taming of Smeagol” and “Shelob’s Lair”. One is a debate between Gollum’s two personalities; I’ve split that into its component parts. Depending on which of his personalities is dominant, the frequency of French words varies widely.

Frequency of French-derived words in Gollum’s speech

Tolkien gives us a brief flash of close reading from Sam that we can use as a guide: “[Sam] noted that Gollum used I, and that seemed usually to be a sign, on its rare appearances, that some remnants of old truth and sincerity were for the moment on top.” On each bar I’ve superposed the number of first-person singular pronouns in the passage. It correlates well, with the exception of one outlier.

The ring-maddened Gollum, as he talks to himself before he meets Frodo and Sam, reaches a level of French I’ve seen nowhere else in the text. If we recall our earlier estimate that something like 7% French is as far as a character can go without risking his health, Gollum’s 15.3% score is alarming. (Since much of that is his repetition of precious, maybe the computer isn’t telling us anything new.)

When Frodo uses his will, and the Ring, to dominate Gollum, Gollum’s word choices turn relatively normal for a chapter or two. Whether terrified or helpful, Smeagol’s French-level is healthy. But then, as the Gollum side recovers from the blow and he plots his revenge, he quickly blows past Feanorian levels into his record-level madness.

There’s one exception to this general rule. When Smeagol/Gollum gives us a short lecture on the history of Harad and Gondor, he briefly turns as normal as anyone in the book. He doesn’t use I, but he doesn’t sound much like himself either. And that’s a good thing. Later Frodo would say in another context, “his cure is beyond us; but I would still spare him, in the hope that he may find it.” There was no cure for Saruman, but Gollum could have been saved by an adjunct-lecturer position at the community college.

Case Study, Re-visualized

By Joe

On December 22, 2020

In Digital Humanities

Sara Waldorf’s master’s thesis at Signum University was built on a painstaking log of every use of the dative case in 2,000 lines of Beowulf. It’s entitled a “Case Study”, which is a joke so bad that Idiosophers have to salute. She gave a talk about this research in a “Thesis Theater” webcast at https://www.youtube.com/watch?v=VRhQHjIHSRQ.

Her thesis (available through the Signum U Library) contains the line, “The spreadsheet of dative categories could provide raw data for loading into a more sophisticated database.” Let’s take her up on that and see what we can do. Note: this post will contain no pie charts. They’re just empty calories.

It’s infuriating for the student but interesting for the philologist that grammatical cases are decaying during the Early Middle Ages. The obscure cases like locative and ablative were all collapsing into the dative case. The core of Sara’s work is unpacking these, leading to a classification of every dative into one of the 22 ways Old English used that case. Here’s what she found in these 2000 lines. Locative is on a line by itself because it’s by far the dominant function. The vestigial instrumental case, explicitly taught in the intro class, is almost completely gone from this sample.

		Locative	142
Dative of Means	68	State	20	Purpose	8
Object	53	Ablative	18	Impersonal	6
Dative of Reference	48	Reflexive	17	Measure	5
Indirect Object	47	Adverbial	13	Agency	3
Temporal	45	Cause	11	Inflected Infinitive	2
Possessive	32	Dative with Adjective	9	Modal	2
Accompaniment	26	Manner	9	Instrumental	1

Before and after the scribal change (click to embiggen).

Figures 4 & 5 in the thesis use pie charts to look at use of the dative in the 50 lines before and after the change of scribe. Here’s how I see them. As the thesis notes, there’s a huge difference. I’ve added the overall frequency chart for comparison. This enables us to see that the extraordinary case is the first scribe, who uses a lot of locatives. The second is much closer to the average for the whole selection.

The thing I liked best about Sara’s work (apart from the staggering labor of counting nouns and pronouns already being done for me) is how she split the selection up into separate stories. Beowulf is episodic. The way the poet talks changes with the material he’s talking about. This shows up in the dative-case usage. The stories in this sample are: the fight with Grendel’s Mother, the feast afterward, Beowulf’s departure from Heorot, Beowulf’s recap and prophecy about Freawaru’s marriage, presentation of gifts to Hygelac, the fight with the dragon, and Beowulf’s life in review. As good followers of Michael Drout, we should begin with a dendrogram: if we look at the fraction of all the datives in each episode that are of each type and cluster the episodes accordingly, they look like this. (complete-link cluster in 22 dimensions, four of which are boring)

Relationships of episodes by dative use

Among the seven episodes, there are three closely-related pairs. The gift-giving passage stands alone. Unlike the others, it’s loaded with indirect objects (without whom gift-giving is pointless).

The next step is to look at the density of various kinds of usage. Locatives are heavily concentrated in the first half of Beowulf’s departure. The scribal change is marked with a little orange dash in the middle of the departure episode. This is what we saw in the bar graphs above. The change appears to be due to the needs of the narrative more than the style of the scribe. The second scribe quickly returns to a locative pattern familiar from earlier episodes. Besides, had we used 100-line chunks instead of 50, the differences would have been minimal.

The dendrogram tells us that the Feast and Prophecy episodes are similar, but it doesn’t say how. Here we can see that they both start with some locative scene-setting, after which the need for locatives drops off. Grendel’s mother and Beowulf’s life in review trend the opposite way: few locatives at the beginning, but a double hump of them at the end. The gift section looks nothing like the others.

Density of locative datives

Indirect Object density

The deepest troughs of locatives correspond with peaks of two other common usages. (Naturally — you can’t have more than one or two datives per line, so when one type increases, the others must decrease.)

As we mentioned, the Gift-giving episode has lots of indirect objects. They fill in the trough around line 2175. The Departure and Dragon episodes, which didn’t look alike in the Locative graph, seem much more similar here.

The other low-locative part of the poem is at the beginning of the disagreement with Grendel’s mother. Those lines are full of Datives of Means. (A dative of means is like herebyrne hondum gebróden,”byrnie braided by hands” in line 1443.)

Density of means

There is a moderate surge in datives of means toward the end. I was expecting that to be inflated by pairs of nouns: wigum ond waépnum in line 2395, for example. (He supported the son of Ohtere with warriors and weapons.) But Sara knew that was coming, and only counted such doublets once. These peaks indicate many successive sentences using datives of means.

The densities of the other 19 uses of the Old English dative are less obvious in their meaning, but are available for consultation here: DativeDensity

Conclusion

I shall not pretend that the motivation of this study is anything other than, “Someone made a database — let’s look and see what’s in it!” Sara’s conclusion relates to the transition during the Anglo-Saxon period from inflection to preposition as a way to indicate the dative functions in an English sentence. My interests lie rather in seeing the ebb and flow of grammatical structures in response to the narrative. I would have expected each of the episodes to begin with a burst of locatives. (“In a hole in the ground there lived a hobbit.”) It’s interesting that most of these don’t. Though the poem as a whole begins with a burst of datives, they’re temporal and accompaniment; none are locative.

The “agglomerated dative” offers one way to quantify the presence of grammatical structures in the poem. Whether it can be expanded to yield new insights into the perennial questions about Beowulf remains to be seen.