Idiosophy

A physicist loose among the liberal arts

Tolkien’s Macaroni

Dan Stride has purchased a copy of The Bovadium Fragments by J.R.R. Tolkien, and saved me $26.99. I won’t be buying one, even though I love that kind of humor, which I now know is called “macaronic”. When I encountered Godley’s poem “The Motor Bus” about 50 years ago, I laughed my fool head off. But this poem will always be my favorite, not least because it proves that sort of erudition isn’t the sole possession of the English: Malum Opus
 

Letter-mention worthiness

A friend is working on a talk about the relationships Charles Williams had with C.S. Lewis and T.S. Eliot. He noticed that Eliot gets mentioned more in Williams’s letters than Lewis does, which might not be expected since Lewis and Williams were good friends. He counted 46 letters in Letters to Michal from Serge mentioning Eliot and 33 for Lewis. Is that a big difference, I wondered, or could it be due to chance? That’s the sort of question we use statistics for, if we can think of a way that we’re talking about a random process. The mechanical computation part of statistics is amazingly easy these days, but before I can let the computer tools loose, I have to figure out what question I’m really asking. Fortunately, that’s the fun part.

Let’s begin with a model of mentioning writers in letters. Suppose there’s some underlying thing about writers that’s generally “how important they are to Charles Williams”, which causes him to mention them in a letter or not. For statistics, we don’t need to know the precise definition of what the importance factor is in literary terms (or general-human terms). All we need is that the higher that factor is, the more letters they’ll be mentioned in.

Second assumption: Whether CW wrote a letter to his wife is determined by other parts of life than the literary-importance parameter. (Money, for instance, is a frequent topic.) If we believe that CW wasn’t motivated by his admiration for another writer to dash off a letter, then those circumstances are effectively random for our purposes.1 Now, let’s imagine an ensemble of parallel universes in which different letter-worthy events happen and spare time comes on different days. In each of those worlds, CW writes different letters from the ones he wrote in our world, but the number of times alt-CW mentions another writer is based on that same importance factor. 2 Then the mentions in each universe will fall on a curve whose shape we can calculate. From that posterior distribution, we can estimate how likely one writer is to be mentioned more than another.

Under this model, the number of letters mentioning a writer will have a binomial distribution. For a fixed set of 320 letters (like LtoMfromS), a binomial distribution has one unknown parameter in it; counting mentions in the book tells us information about that parameter.

The blurb on the flyleaf of Letters to Michal from Serge mentions six contemporary writers: Eliot, Lewis, Dorothy L. Sayers, W.H. Auden, Christopher Fry, and Edith Sitwell. Let’s run them all through the model. (It’s only one line of code apiece.) The peak of each author’s probability density is the most likely number of letters, which matches the figure in the book. What we get from these distributions is the spread — could things have been otherwise? How different are parallel universes likely to be?

The first thing we see is that the more likely a writer is to be mentioned, the more spread around their observed value there is. For example, Dame Edith gets mentioned 3 times; maybe that could have been 4 but it wasn’t going to be 10. Eliot, on the other extreme, might have been mentioned anything from 30 to 60 times under this model.

line graph of density of six binomial distributions

Binomial distributions for the six authors.

Eliot’s curve is definitely to the right of Lewis’s, but there’s some overlap. How likely is it that Lewis could have been mentioned more? These curves have analytic forms so we could compute it exactly, but these days it’s easier to run a simulation. I drew 10,000 numbers from each of their distributions, and Lewis’s number was higher than Eliot’s in just under 5% of them. That’s pretty solid evidence. The less-mentioned writers overlap more. Lewis was mentioned more than Sayers 99.98% of the time. Sayers is mentioned more times than Auden in 92% of our parallel universes. Auden is mentioned more often than Fry in 68% of them, which is in the range where the difference could have been just by chance.

The basic observation that started me down this path is confirmed: To Charles Williams, Eliot was almost certainly more letter-worthy than Lewis. Might be something to do with that Swedish thingy (as Paul Krugman calls his).

The importance of being Samwise

I have just made the acquaintance of the Old Icelandic Hávamál. Among other things, it’s a source of wisdom-verses. The originator of the wisdom related here is Odin himself. Here’s W.H. Auden’s translation in alliterative verse.

Carolyne Larrington points us to stanzas 54-56:

drawing of Odin in a horned helmet with a raven on his shoulder.

Not trusting this guy until I know where the other raven is.

It is best for man to be middle-wise,
Not over cunning and clever:
The learned man whose lore is deep
Is seldom happy at heart.

It is best for man to be middle-wise,
Not over cunning and clever:
The fairest life is led by those
Who are deft at all they do.

It is best for man to be middle-wise,
Not over cunning and clever:
No man is able to know his future,
So let him sleep in peace.

The three verses all start with the same two lines, which are a maxim. 3 The third and fourth lines explicate the maxim, slightly.

I know someone these might apply to. Let’s match these up with our friend Samwise Gamgee. We know from his name that he’s one of the middle-wise. How does that work out for him? His lore is not deep — he knows just enough to write silly songs about trolls. [LR 1.12.069] He is certainly deft at all he does. He’s a good cook, even by hobbit standards [LR4.04.027]  and the restoration of the Shire after Sharkey’s depredations is largely his work.  [LR 6.09.021]  He’s not good at thinking, but he knows that. “Think, if you can!” is good practice for the half-wise. [LR 2.10.097] Can he sleep in peace? Like a log. [LR1.07.037]

So this supernatural being who looks like an old man in shabby grey robes drafts a medium-wise person to accompany Frodo. That’s the beginning of Sam’s relationship with Gandalf. He can be forgiven for wondering who this old guy actually is. Though by the time they get to Moria, Sam is sure Gandalf isn’t Odin. [LR 2.04.039] The role of Anglo-Saxon Merlin is still open, of course.4.

I searched all kinds of places around the World-Wide Web for someone who’s noticed this before, but came up blank. I guess it’s either too obvious or not significant enough to be included in a journal paper. Which means it ought to be perfect for a blog post.


 

Wisdom Poetry on Broadway

line drawing of a bird. maybe a bluebird, if it weren't black and white.When Old English maxims appear in poetic usage, as opposed to collections, they frequently take the form of an indisputably true observation about nature, followed by a statement about the current situation, from which we are to infer an analogy that will guide the character’s choice. That sounded familiar, but it took me days to figure out what I was remembering. It was a song by Jerome Kern & Oscar Hammerstein from “Showboat“: 

Fish gotta swim, birds gotta fly,
I gotta love one man till I die.
Can’t help lovin’ that man of mine

line drawing of a shark. He looks happy. His teeth are not threatening at all.

Or, just maybe, it was Tom Lehrer. Either way, I love seeing thousand-year callbacks in popular culture.

In Defense of Aldarion

It’s fun hearing Alan Sisto and Sara Brown on the Prancing Pony Podcast judge Aldarion and Erendis by the standards of a 21st-century two-career couple. It’s not surprising that pre-modern Númenoreans fall short, especially since Aldarion is in line to be a king, and Sara has told us before how little she thinks of kings. But we ought to be a little bit fair to Aldarion, and try to infer how he’s doing by his own standards.

How good was Aldarion at being a crown prince? The duties of a crown prince are almost the same as the duties of a king, except doing them as an apprentice. I can think of six big ones. There could be more, but they’d just be guesswork, given how few details we know about what was going on on the island.

1. Secure the succession

This is the top priority for any royal heir. Alan and Sara haven’t really talked bout this, as of Episode 388, but to be fair, J.R.R. Tolkien didn’t pay much attention to it, either. (cf. Boromir, Faramir, Théodred, Éomer…) Aldarion doesn’t have a leg to stand on here. It’s a shameful dereliction of duty to trust the grace of the Valar to keep you alive until some century when you feel like having a child.

2. Manage the royal bureaucracy

To the extent that Númenor is like an ancient kingdom (probably Egypt), Aldarion is guilty here, too. Except that there are few things Tolkien thought less of than bureaucracies (Letter 52), so Númenor may not have had one for Aldarion to master. 

But now we get to the things Aldarion was paying attention to.  Setting up the Guild of Venturers was a very clever thing for the crown prince to do. It covers four things I could think of that he ought to be doing.

3. Lead large groups

Leadership is the sine qua non of a king. It’s essential for the heir apparent to practice it before it becomes a matter of survival. If the crown prince doesn’t spend his time doing something like a Guild of Venturers, you get Henry the 8th, and nobody but tour guides wants that. Tar-Meneldur makes a fair point that Aldarion needs to learn to lead the women of Númenor too, but the skills aren’t very different.  Besides, this seems to imply that Meneldur wasn’t expecting war.

4. Secure resources for the country

People always want more than they have. We’re humans. That’s what we do. A country with a growing population will need more stuff, and a good king finds ways to provide it. Of course, if everyone in Númenor is like Aldarion they won’t have a growing population, but then they just die out and nobody sings songs about them in the Third Age.

4. Expand the country’s power (or “splendour” in Tolkien’s word)

We have to look into the future to see why this is important. At the time of the story, though Meneldur doesn’t find out until the end, Sauron is threatening Middle-earth and Gil-Galad is worried. Without Aldarion’s focus on building naval power, what use would Númenor be in a fight? 

6. Keep the population of unemployed young men manageably small

Bored young men are bad for a country’s stability, as a glance at the newspapers might suggest. Historically, people have tried all kinds of things to keep them out of mischief.  The Guild of Venturers must have been a good safety valve. Aldarion deserves credit for finding a productive use for whatever surplus manpower was loafing around the docks.

I’d say a record of 4 wins, 1 loss, and 1 unknown is pretty good for a prince, so maybe we should lighten up on Aldarion just a bit. 

The Marxists present us with an opportunity

Just read a paper by Dennis Wilson Wise 5, in which he talks about the way Peter Jackson’s Hobbit movies flatten and trivialize the historical depths of Tolkien’s fiction. It’s always gratifying when someone who thinks deeply about things comes close to my reflexive response. In this case, twenty-five years ago, I walked out of “The Fellowship of the Ring” thinking that (a) If Peter Jackson understands what the Ring is, he didn’t put that in the film, and (b) that could be because the evil of the Ring might strike a bit too close to home for a movie-maker to be comfortable. DWW shows the whole iceberg of which I’d just seen the top.

An icon that's supposed to represent "movement", but ends up being the Chaos symbol from Moorcock's Elric novels, which is perfectly appropriate.In the process, he lands some well-deserved punches on Marxist literary critics. I’m always up for that. But he points us to a quotation from Fredric Jameson from 1991 that got me thinking:

…this whole global, yet American, postmodern culture is the internal and superstructural expression of a whole new wave of American military and economic domination throughout the world…

Right now, we have a natural experiment to test Jameson’s theory. The USA is backing away from military and economic domination, so if Jameson is right, a new literary and cultural movement is about to emerge. Authors, sharpen your pencils and get to work!


 

Subconscious Influence

As I mentioned the other day, I’m reading about Old English wisdom poetry. What with the all the references to winter in the examples there, I suddenly realized that Bilbo’s little quatrain in Rivendell is just such a seasonal wisdom poem:

When winter first begins to bite,
and stones crack in the frosty night,
When pools are black and trees are bare,
‘Tis evil in the wild to fare.   [LR 2.o3.o14]

As always when I think I’ve discovered something, I go check what Tom Shippey had to say about it. In Chapter 6 of The Road to Middle-earth6 Shippey makes the connection with the coda of Shakespeare’s Love’s Labours Lost and notes that both contain only words “… rooted in Old English. Both poems would require little change to make sense at any time between AD 600 and now.” So the idea of a wisdom poem is kind of there, but not explicitly stated. Scull and Hammond, in The Collected Poems7, bundle this poem in with “I Sit beside the Fire and Think”, but don’t make any further reference.

Bilbo’s quatrain supports my reading of the Exeter Maxim so well, I have to suspect that remembering it is what gave me that reading in the first place. 


 

The sceal/bið problem? No problem!

I’m six pages into A Store of Common Sense: Gnomic Theme and Style in Old Icelandic and Old English Wisdom Poetry by Carolyne Larrington8, and I’ve run into a swamp. Scholars from 50 years ago got themselves wrapped around the axle, trying to figure out the difference between maxims that have “bið” in them and those that have “sceal” in them. “Bið” is a fancy word for “is”. “Sceal” is our modern word “shall”, among other things. Those other things are making a mess as the scholars try to figure out when maxim-makers chose to use one or the other. 

“Winter bið cealdost” means “winter is [the] coldest [season]”. That’s fine. It’s in a list of seasons, the next of which is “lencten hrimigost (he byð lengest ceald)”, which is the punchline (spring is frostiest, it’s cold for the longest time). Everyone who’s planted a garden knows the temptation to plant as soon as it feels like spring, and then watch your plants die when the temperature drops below freezing two weeks later. Even scholars understand “bið” here. 

But then we come to “sceal”. Among its meanings are “oughta be”,  “has to be”, and so forth. A parallel maxim to the winter one from Maxims II is in the Exeter Maxims: “forst sceal freosan”. One of the snottors cited on page 7 translates that as “It is appropriate that frost should freeze.” I am unable to understand why. Nobody would ever say that! That sentence means, “Frost is gonna freeze you”! The whole point of Wise Sayings is to warn people about what’s going to happen, and Old English doesn’t have a future tense, so this is what’s available to the writer. 

What is it about scholaring that makes people miss things that are obvious?


OK; now I’m up to page 18. Prof. Larrington is no longer quoting distinguished greybeards, but speaking for herself: “I contend there was a body of folk-wisdom, not yet in metrical form, a body which can be sensed…” Exactly. When a writer puts a Wise Saying into the text, they’re not springing some new insight on the reader. The reader already knows it. If a character in a story says a contemporary maxim like, “Never sign anything by neon light,” the expected reaction is “damn right,” not “gee, I never thought of that before.”

New Perspectives in Alliteration (well, half, anyway)

On September 1st I participated in a conference on New Perspectives on Alliteration in Poetry and Cultural History. It was organized by Tim Anderson, a postdoctoral researcher at the University of East Anglia. It was a fascinating experience — a topic like “alliteration” doesn’t have a tight connection to any particular academic discipline, so people can come at it from any direction. And did we! It was a great opportunity to meet people I only knew from reading their poems, like Paul Deane, Adam Bolivar, and Rahul Gupta. I couldn’t attend all the talks, but here’s what I saw in my half of the parallel sessions.

Modern and Contemporary Alliteration

Harriet Truscott, “Type-setting, Poem-making, Pattern-shaping: Alliteration and the poem as a print object”

This was an eye-opener. To Harriet, poems are something different from what I’d thought. She painted us a picture of a typesetter loading type into a frame. To the typesetter, alliteration is a motion, as they reach to the same box for a letter — or even a space! From this point of view, the printed poem on the page is an adaptation, made by the typesetter. Her example was Ezra Pound’s poem “In a Station of the Metro“. If you click on that link, you’ll see something quite different from what Pound sent to the printer, and what the printer put in the magazine. That’s because HTML doesn’t care about how many spaces you put into the text. Pound and his typesetter did, though. The original had several spaces in the middle of the lines. So… what’s the actual poem? I think she wants us to treat everything as an adaptation — even the typewritten page the poet sent to the publisher, which would have been my guess.

Paul Deane, “The Late Twentieth- and Early Twenty-First-Century Alliterative Revival”

Paul traced the history of alliterative poetry over the past 150 years, from the discovery of ancient manuscripts by the Victorians to the science-fiction and fantasy fans who have been writing under the cultural radar. That latter group has been well documented by Dennis Wise in his book and in a series of blog posts at Tales after Tolkien. My favorite line: “Gerard Manley Hopkins doesn’t count!” Without Paul’s work, my own paper wouldn’t have happened, so it was good to meet him and hear the story of his decades of work to publicize modern alliterative verse. 

Jacob Edmond, “Bad Bad Beat: The Alliterative Alignments of Revolutionary Rhythm”

Scholars have a tendency to focus on poetic alliteration that’s derived from Old English. (guilty!) To this body, Jacob wants to add the Barbadian poet Edward Kamau Brathwaite. Iambic pentameter doesn’t go well with Caribbean speech-rhythms, so his poems are quite different. He uses short lines, usually with two stresses, which makes alliteration really stand out. He likes to alliterate on “b” and “d”, to give his verses a feel like drums accompanying them.

Alliteration in Numbers

Maria Hartman, “Alliteration in Edgar Allan Poe’s ‘The Masque of the Red Death’ in Swedish Translation: A Mixed-Methods Study”

Edgar Allan Poe loved alliteration. This talk was about the tradeoffs you have to make when translating him into Swedish. Lots of S-words in English are P-words in Swedish, so which do you want to keep: onomatopoeia or alliteration? And when a character is Prince Prospero, do you try to keep the P’s? Or do you change him to Duke Prospero, so everyone will get the reference to The Tempest?

Joe Hoffman, “The Hunt for Alliterative Melody”

We’ve already read this one

Rafael Pascual, “Alliterative Metrics and Digital Methods: A new Index and Database for Classical Old English Verse”

Rafael told us about his work in the trenches of digital humanities. This is the kind of thing that makes life so easy for numerically-oriented investigators into how poems work. (In case I should ever run into one.) He calls it a database in the title, but when he’s talking he says it’s an Excel spreadsheet. (Not everything has to be Big Data!) Each half-line of Old English poetry gets a row, in which it is labelled by scansion, alliterative pattern, and position of the caesura. It’s going to be online under the title “The Scansion of Old English Verse”. It’s intended as a replacement for Hutcheson’s “Old English Poetic Metre”. Rafael noted, as an example application, how to use it to find what he calls “clichés of alliteration”, which may help with attribution of anonymous works (is my guess).

Alliteration in Translation

Selene Genovesi, “Finding Phonetic Fidelity: Alliteration in English Translation of Trilussa’s Poetry”

I’d never heard of Trilussa before. As Selene introduced him to us, he was a 19th-century Romantic poet, with extra Roman. The Italian language was just getting standardized back then; Trilussa wrote in the Roman dialect. He wrote a lot of political satires that, as translated for us, were pretty brutal. Selene has a gorgeous reading voice, which made a funny contrast with the subject matter. The main point of the talk was about a recent translation by Lawrence Hooper of his poems into Cockney, which some scholars say is insulting but I accept Selene’s argument that it keeps the disrespectful tone intact. Trilussa’s alliteration was (fittingly) three-fold: for reinforcement, playful manipulation of words; and as a mnemonic aid. The talk was followed by a spirited discussion of whether it was legitimate to alliterate on the apostrophe at the beginning of a word, so that e.g. “here” and “there” alliterate in Cockney. I think the consensus was “yes”.

Margaret Ann Noodin, “Naanabweginiwewe gaye Nanaabikidowinan (Folded Phonemes and Waves of Words): Anishinaabe Alliteration in Songs and Stories”

Margaret is a poet in the Ojibwemowin language. The language is agglutinative. It makes different parts of speech out of the same concept by adding suffixes. As you can see in the title, the suffixes can pile up pretty deep. Ojibwemowin poetry, therefore, has an alliterative pattern that’s tightly bound up with the subject matter. She sang us a song that illustrates it well: the root for “opening” applies to springtime, flowers, river mouths, and being bitten by mosquitoes. All those ideas begin with “zaag” so the poem is highly alliterative, four letters deep. Presumably, a poem that talked about two contrasting ideas would find itself falling into an ABAB alliterative pattern.

Carlos Fernandez, “Cayeron … como caían los cuerpos muertos del Dante”: José Martí’s Alliterative Adaptation of Dante’s Inferno in “El presidio político en Cuba”

This talk zoomed in tightly on the line in the title of the talk. The Inferno, which is an unimpeachable choice of source material for a poem about being sentenced to hard labor in a pre-revolutionary Cuban prison camp. All those “k” sounds give the feeling of dead bodies piling up. 

Jean Martinely Iata, “It’s Not a Broken Record: The Dynamics of British and Malagasy Battle Raps’ Poetic Sounds”

Few things in our sublunary existence approach the perfection of a Platonic ideal, but one of them was, until this talk, my ignorance of Malagasy battle rap. The genre is derived from US hip-hop culture, but the rappers on Madagascar have given it their own twist. They write with a two-line structure: the first is an image to be taken literally; the second is the figurative application to the person who needs to be taken down a peg. The narrative images get fricative sounds (f, v, θ, ð, s, z, ʃ, ʒ) and the punchlines get plosives (p, t, k, b, d g). In a way, this means that Malagasy rappers use slant alliteration the same way US and British rappers use slant rhyme.

Plenary Talks

Joseph Phelan, “Made to Match: Alliteration in the Poetry of Robert Browning”

Robert Browning had a long career, during which fashions changed tremendously. His use of alliteration rose and fell over time. “The Ring and the Book” is the peak, after which he seems to have gotten the feeling that he was getting too “mannered” (a word I had to look up). There’s a correlation between lines that include alliteration and lines where Browning deviates from strict iambic pentameter and some other way to flag the end of a line was evidently needed. Best throwaway line: ” ‘Browning’s macabre poems’ is practically a pleonasm.” For a contemporary critical source, Prof Phelan referred us to the marvelously-named Coventry Patmore’s “Essay on English Metrical Law“, whither I shall proceed directly.

Chris Jones, “Over all Nations: Alliteration and Indigeneity in the Work of Carter Revard”

Birch Canoe” by Carter Revard is only six lines long, but Prof. Jones spent an hour on a close reading of it. Electron microscopes don’t read so closely. Carter Revard was a half Osage scholar of Old English poetry. This poem is a perfect fusion of those two things. The “indigeneity” in the title refers to the unfortunate infestation of the fields that study early-medieval England by anti-immigrant racists, and forces us to use circumlocutions like “early-medieval England” after they crufted up the term “Anglo-Saxon”. They’re very proud of being the spirit of their homeland, but if you want to talk about being indigenous, the descendants of immigrants from Germany don’t have a leg to stand on, compared to the Osage. By the time Prof Jones got done, we could see that almost every word in the poem, which on the surface is about paddling on a stream in America, harked back to something in Old English literature. For example, “the lightfoot deer” has a web of semantic and contextual relations to the “hæðstapa” in Beowulf. A real tour de force.

The Hunt for Alliterative Melody

As presented at “New Perspectives on Alliteration in Poetry and Cultural History”, University of East Anglia, 1 September 2025

1. Introduction

What’s the purpose of alliteration in modern poetry? The oldest answer I could find to that question is from 1902. Talking about Shakespeare’s sonnets, Thomas R. Price said, “As the result of the caesura was to cut the verse into two halves, he felt, like older poets, the need of linking the two parts by most ingenious harmonies of sound.” (Price) I like this: As poetic structures got longer and more complex, poets needed a technique to keep the listener’s ears connected to what they were doing. So they reached back into the history of English, where alliteration linked two halves of a longline, and gave it a new job: jumping across a caesura wherever one might show up. Or in a rhymed poem, alliteration can pole-vault line endings, connecting verses orthogonally to the rhythmic structure. In a sense, it might even form a separate melody, like a baroque concerto over the continuo, or a jazz solo over the rhythm section.

If this is truly what’s happening, it will take some proving. This is going to be harder to hear than the structures of formal verse. It’s just at the limit of what I can hear. Well, when confronted with a phenomenon that’s just beyond sensory perception, physicists immediately start thinking of a way to augment our senses with some sort of technology. And that’s exactly what I did.

As Paul Deane argued this morning, and as Dennis Wilson Wise demonstrated by collecting 400 pages of it (Wise), the language is currently experiencing a revival of alliterative verse. Are modern alliterative poets using it for the same function? Is this a recreation of the old forms, or are they doing something new? I can’t think of anything more 21st Century than to apply natural-language processing to that question. A caution, though, from Richard Bailey in 1971: “some of the questions of greatest concern to critics are amenable to mathematical treatment. Yet work of this kind is historically troubled by literary fatuity or statistical ineptness…”. (Bailey) I’ll have to be careful.

2. History

Literary scholars have been extracting everything they can from Shakespeare for a few hundred years, including detailed maps of which sounds are used where in his sonnets. They found all sorts of interesting things, like Price’s observation.

Around 1939, B.F. Skinner (the famous psychologist and rat-tormentor) decided that their scholarly claims were nice, but they needed quantitative validation, and he began with Shakespeare’s alliteration.(Skinner) He identified the positions of common letters at the start of stressed syllables, tested them according to a binomial distribution of the expected frequency of repetition, and concluded that you could produce a similar distribution “by drawing words out of a hat.” I have tremendous respect for anyone with the perseverance to do a binomial regression by hand, but unfortunately Skinner began from some flawed premises. He was immediately smacked down in the literature for (a) not understanding how alliteration is defined and (b) ignoring the fact that alliteration has an ancient tradition in English verse and poets have said they’re using alliteration for centuries. His antagonists, such as Elizabeth Jackson (Jackson) and Ulrich Goldsmith (Goldsmith), used the old qualitative methods, augmented by knowing that alliteration resides mostly in nouns and verbs and never in function words, and combinations of consonants aren’t the same as a consonant in isolation, to set the record straight, and there it lay for a few decades.

In the 1970s, digital computation became cheap enough that a new generation of non-poets was inspired to turn computers loose on the question of poetic alliteration. (Leavitt), (Greenberg) They created a variety of clever algorithms to do simple statistical tests and make contour maps of sound density of a selection of poems. They were hampered a bit, though, by the unavailability of a large corpus of phonetically-coded digital texts and, once again, their unfamiliarity with the traditions of alliterative verse. Their algorithms tended to zero in on very simple structures and miss some features that would jump out immediately at a human reader. As a result, when they ranked poems by the importance of alliteration within them, they would get odd results. For example, Ezra Pound’s translation of “The Seafarer”, (Pound) which explicitly echoes Old English alliterative patterns, comes out in the middle of the pack. Jay Leavitt et al. in particular knew this wasn’t working well, because their papers provide several different algorithms that give different results, and the reader is invited to choose among them. (Machine-learning researchers do this, today.)

Then there was another lull until the 21st Century, when natural-language processing and digital archives of verse became available. Text-to-speech systems could finally reproduce the patterns of stressed syllables and their associated phonemes in a way that matches how humans hear poetry. These spoken-equivalent texts get tested with graph theory, time-series analysis, and geolocation. I’m a particular fan of a group called “Plotting Poetry” dedicated to pushing the boundaries of “mechanically-enhanced reading”. But I haven’t seen modern statistics applied to alliteration yet, and that’s where I’m going to go.

3. Method

Three-box process diagram as described in the text.

Figure 1. Analytical process.

The Carnegie-Mellon University has put on line an open-source English dictionary for the text-to-speech step.(Rudnicky) Open source is important, because poets don’t use the same kind of English that telephone-answering robots use, so every new poem I investigate requires a few words to be added to the dictionary. I also needed to tweak the database to account for the convention that not all words participate in alliteration, so words like “the” and “she” and “if” don’t have a stressed syllable. The next step is a Perl program to read the poem and throw out everything except the sound at the beginning of the stressed syllables. (This role was played by two young women in Skinner’s work.) These sounds, the skeleton if you will of the audible part of the poem, are fed to a notebook in the R statistical software. A function in R counts, for each sound, the number of non-alliterating stresses that come before the next occurrence of the same sound, generates histograms of intervals, and compares them to the theoretical distribution we should get if the choice of sounds were truly random.

a histogram with high peaks at 0 and 1 (about 25) and low, random bars (about 2-3) elsewhere.

Figure 2. Intervals in strict Old English form

For the most-alliterative end of the bench, I chose J.R.R. Tolkien’s “Song of the Mounds of Mundburg”(Tolkien, Poems 1235), which he said in Letter 187 was “the strictest form of Anglo-Saxon verse”. (Tolkien, Letters) The spike in the left figure is what the rules require: 0 means two consecutive stresses alliterate; 1 means the half-line skipped one syllable. So that’s what the left-hand side of these histograms means: a high bar means a lot of old-school alliteration.

A bar graph that slopes gradually downward from 15.

Figure 3. Intervals in Wikipedia sample

The graph in Figure 3 might be unexpected, though. As we’d expect, it’s a lot more spread out and there’s no distinctive spike. Its maximum is 2 however, and zero is the second most-common interval. English speakers like to alliterate even when there’s no poetic intent at all.

4. Experiments

Now that we’ve got the machinery built, we can conduct experiments. The frequency of letters in English, etaoin shrdlu, is not the same as the frequency of alliterative sounds: all the vowels are lumped together; “T” gets split into T and TH; “S” gets split apart into S, SH, ST, and SK. When we get done, there are 28 possible things on which to alliterate. But the chance of getting an alliterating syllable on the next stress isn’t 1/28th – English speakers love to alliterate, so the best-fit chance is closer to 1 in 6.

4.1. Inside you there are three Beowulves

3 bar graphs with the same red reference line. They're described in the text.

Figure 4. Frequency graphs of three Beowulf poems.

Here are the first 200 lines of “Beowulf” translated by Seamus Heaney (Heaney), the same very freely translated by Maria Dahvana Headley (Headley), and “The Lay of Beowulf” by Tolkien (Tolkien, Poems 815). The red line I’ve put on the histograms is the best-fit parameter to a negative-binomial model of “K” in the Wikipedia selection. Headley, on the left, makes heavy use of alliteration but she’s not being poetic about it. She’s more like cramming alliterating words together for fun. You can see that the normally-expected intervals between consonants of 3-8 stressed syllables has been depleted after each alliteration binge.

Heaney, in the middle, looks pretty random. This is close to the reference line, and wherever there’s a peak, there’s a valley next to it. Tolkien’s “Lay” on the right doesn’t really have alliteration beyond the typical English rate, but since it’s a lay, every stanza ends with the word “Heorot”. The poem is in iambic tetrameter, so the end repetition causes the bump up at 15. The bump up at 8 is also not very alliterative, because that happens every time an H-syllable appears in the middle of a stanza. It breaks the 15 into two halves. So now we know what the right-hand side of those histograms means: it’s where large-scale poetic forms can make an appearance.

4.2. A-LotR-ation

The alliterating consonants are colored. D is orange and W is green., there are S and ST as well.

Figure 5. Last stanza of the poem.

Gimli’s song about Khazad-dum from The Fellowship of the Ring (LR 2.04.188) is the poem that got me started. This all began with Corey Olsen’s talk at Mythmoot XI. The poem’s form is rhymed quatrains of iambic tetrameter, but some people see an irregular pattern of alliteration in it. Other people aren’t convinced, so out come the computer programs. Measuring the alliterative structure of a Tolkien poem is tough, though, because Tolkien used alliteration much more than your typical trafficker in text. If we feed the entire Lord of the Rings to the program, zero is prominently above the curve. If we’re going to ask about “Khazad-dum”, we need to take this into account. If we compare Gimli‘s song to some random victorian tetrameters it might or might not look alliterative, but what happens if we compare it to the 300 words of prose that come right before it?

Two histograms. The one for the poem has lower frequencies and less structure than the one on the right.

Figure 6. Frequency graphs for Gimli’s song and preceding prose.

Gimli’s song has a spike at 4 that might be important – 4 beats is the distance from the middle of one line to the next, which is what you’d see if alliteration was working vertically, tying lines together, but overall it’s much less alliterative than the prose section. It’s also less alliterative than the other dwarf song we get, “Far over the Misty Mountains Cold”. Now, an absence of tight alliteration goes along with the idea of tying large-scale structures together. If people are constantly hearing ram-rum-ruf, it’s harder to hear an interleaved sparse alliteration, so a poet will want to exclude that. It’s possible that Tolkien was making what he thought of as a kind of blank verse, leaving out alliteration for poetic effect, just like the way a blank-verse poet avoids rhymes.

4.3. Sparse Alliteration

Leaving out the close alliteration is a feature I’ve found in another genre. Here are four classic hip-hop songs, “C.R.E.A.M.” from the Wu-Tang Clan, “Express Yourself” from N.W.A., “Lose Yourself” from Eminem, and “Make Tracks” from US3. West Coast, East Coast, Detroit, and the U.K. The reference line in red is the same as before, scaled for the size of each sample. All of these songs have a deficit at 0, and 1. The Americans continue the deficit up to 4 or 5 syllables, but the Brits hit the curve at 3. I’m disappointed that US3 didn’t turn out to have a stronger Old English influence. That would have been fun, but numbers are merciless.

Four bar graphs with the same red reference line. For small intervals, the bars are all below the line.

Figure 7. Frequency graphs for four hip-hop songs.

North Atlantic hip-hop basically doesn’t alliterate. It happens, but less often than standard English prose. Like Dwarves, rappers de-emphasize close alliteration. Their verses are short, dominated by rhymes crammed tightly together. There’s no need to bind together a long alexandrine or anything, so they don’t use alliteration for that purpose. Besides, when a rhyme comes every four or five syllables, it’s hard to alliterate on top of it without just saying the same word again. After Jacob Edmond’s talk this morning, highlighting repetition as a form of alliteration in Caribbean verse, I wonder if this might not be an explicit intention of the rap poets.

4.4. Ranking poems by median interval

I’ve been saying the word “compare” a lot, but I haven’t given a direct standard yet. These histograms are important when we’re dealing with small sample sizes like a poem, but it’s hard to compare them directly. For that, we need a single metric. I propose to use the median of the distribution of intervals. Medians are good because they don’t depend on the exact value of long intervals that I’ve cut off of these histograms. And because my poet friends said they wanted a graph that showed how alliterative a poem is, this graph shows the inverse of the median.

Horizontal bar graph. The bars increase smoothly from 0.09 to 0.2 in length. Then there's a jump up to 0.4 - 0.5 for the Old English verses.

Figure 8. Alliterative density of a set of poems.

This shows a sampling of verse that has already been identified as alliterative and some that isn’t. Paul Deane’s alliteration.net website has a great selection of poetry, some of which is more faithful to the Old English and Old Norse forms and some which is more modern and free-form. From this archive, I selected some poems that Paul has previously flagged if they’re faithful to an old form. Then I picked a few others that aren’t and a few non-alliterative Tolkien poems. The prose samples are in green and the rappers are in red. Last, in keeping with my conviction that literary theory should always be tested with literary experiments, I’ve included a poem by Rio Wulfmare, a fellow member on the “Forgotten Ground Regained” listserv, written precisely for the purpose of superposing an alliterative melody over metered rhymes.

The first thing to see is that when we rank the more-or-less poetic samples by density, they fall into natural groupings. At the bottom we have the Old English forms. Just above them are the Middle and Modern English poetic forms, with our Norse example mixed in because formal Old Norse poetry has other things going on besides the alliteration. Higher up are Tolkien’s non-alliterative poems. Prose is near the top, but not at it. The rappers have the lowest alliterative density. I spent quite a while looking around Ireland and anglophone Africa for writers who are unaffected by Anglo-Saxon traditions, without great success, but there was one right under my nose all along. The West-African/Celtic fusion from which American pop music sprang turns out to be the counterweight to Anglo-Saxon poetics.

A ranking that makes intuitive sense is further than my 20th-century predecessors in feeding poems to computers usually get. Their rankings are all mixed together, and they’ll often have something like Vachel Lindsay’s “The Congo” at the top.
The second thing to notice is that there’s not a clean break between poems that alliterate and those that don’t, with one exception: none of these poems has a median of 3 or 4 syllables, which would put them between .25 and .33 on the graph.

a similar bar graph, as described, with the 3, 6, and 9 called out.

Figure 9. Frequency graph for “Children of Dusk”.

“Children of Dusk”, our literary experiment, is sitting between the old-school alliterative poems and the modern revival poems. Mr. Wulfmare set out with the intention of writing a two-level poem that exactly matches the melody-plus-continuo hypothesis. On its graph we can see more structure than most poems show: The usual spike at zero & 1 that says we’re in Old English alliteration, but then there’s a deficit at 2 and a spike at 3, a deficit at 5 and a spike at 6, and a deficit at 8 and a (tiny) spike at 9. Then we run up against the limits because we run out of poem.

4.5. The “Main Sequence”

Here’s one last graph, of an unexpected result. I asked, How many of the possible alliterative sounds does a poem use? These samples are all pretty much the same length. There’s a general trend – the tighter the alliteration, the fewer consonants of the set of 28 get used by the text. The two outliers are Tolkien rhymed poems. It’s almost like alliteration is draining attention away from some other, less fortunate sound.

This scatter plot has the names of the poems arrayed according to the two variables. They cluster around a straight line upward to the right.

Figure 10. Scatter plot of sounds used vs alliterative interval.

5. Conclusion

In conclusion, this work has built upon a long tradition of numerical analysis of poetry. The tools we have now for language processing make it easy to investigate the distribution of alliteration within a poem, whether the poet has foregrounded it or not. This method is very simple; looking at histograms and picking out the median is as basic as you can get. I did some high-powered Bayesian analysis using Stan; it gave me better uncertainty estimates, but the story was the same. Apart from that, calibrating the baseline was the most statistically difficult part. Despite the lack of sophistication, the method can rank texts according to how they use alliteration, and the results seem correct: Different kinds of alliterative verse are stratified as we’d expect. Prose on one end, strict Old English on the other, middle-english in between Old and Modern. Spurious alliteration that comes from structural repetition in formal metered verse has a clear signal in the histogram, which resolves the weakest part of Skinner’s original treatment.

That horizontal bar graph was a surprise. I was expecting the analysis to show me that some poems are alliterative and some are not, but that’s not what came out. Instead, it shows that some poems are strict Old English, but those that aren’t have a lot of variety. Modern alliterative-revival verse lies on a continuum. We’re trying everything. With one exception – that gap at 3 or 4 syllables might present an opportunity. Maybe a hexametric expanded version of Old English longlines? I’ll leave that to a poet.

So what?

This is a method that works on small samples, where parametric statistics are overwhelmed by “noise” as scientists call it, or “technique” as poets think of it. The ideas are 50 years old; the difference here is that combining the statistics with natural-language processing, incorporating the rules of English stress, removes a lot of the noise that interfered with the letter-based methods a couple of generations ago.

When I started my project of quantitative analysis of literature, my goal was to find ways that graphs and numbers and maps can increase readers’ enjoyment of whatever they’re reading. Now, the world contains quite a few nerds who are delighted just to see things in graphs, and for … us … this is already an interesting contribution. But it’s really just the first few steps. The more I’ve learned about Old English, the more I’ve come to see that its old music is still with us today. If Price is right, though they can be hard to see and hear, they’re what makes modern poetry possible. I hope to extend this method to find out how to alert readers when an ancient tradition is still alive and playing a new role in a modernized form.

The “Main Sequence” is intriguing: There’s no reason in principle that alliterative poems couldn’t use the same range of consonants as any other sample of similar size, but they don’t. Next up is to figure out if this is true in general, or just for the poems I happened to choose. It’s possibility that alliterative verse might be as much about the sounds poets omit, as about the ones they use. Richard Bailey stated in his 1971 review that “readers can’t hear the sounds that aren’t there.”(Bailey) It will be fun to put that to the test.


Works Cited

Bailey, Richard W. “Statistics and the Sounds of Poetry.” Poetics, vol. 1, no. 1, Jan. 1971, pp. 16–37. DOI.org (Crossref), https://doi.org/10.1016/0304-422X(71)90003-9.
Goldhahn, D., et al. “Building Large Monolingual Dictionaries at the Leipzig Corpora Collection: From 100 to 200 Languages.” Proceedings of the 8th International Language Resources and Evaluation, 2012.
Goldsmith, Ulrich K. “Words out of a Hat? ‘Alliteration and Assonance in Shakespeare’s Sonnets.’” The Journal of English and Germanic Philology, vol. 49, no. 1, 1950, pp. 33–48. JSTOR.
Greenberg, Nathan A. “Aspects of Alliteration: A Statistical Study.” Latomus, vol. 39, no. 3, 1980, pp. 585–611.
Headley, Maria Dahvana. Beowulf : A New Translation. Farrar, Straus and Giroux, 2020.
Heaney, Seamus, editor. Beowulf: A New Verse Translation. 1st bilingual ed, Farrar, Straus, and Giroux, 2000.
Jackson, Elizabeth. “The Quantitative Measurement of Assonance and Alliteration in Swinburne.” The American Journal of Psychology, vol. 55, no. 1, 1942, pp. 115–23, https://doi.org/10.2307/1417038. JSTOR.
Leavitt, Jay A. “On the Measurement of Alliteration in Poetry.” Computers and the Humanities, vol. 10, no. 6, 1976, pp. 333–42.
Pound, Ezra. “The Seafarer.” The Poetry Foundation, https://www.poetryfoundation.org/poems/44917/the-seafarer. Accessed 16 June 2025.
Price, Thomas R. “The Technic of Shakespere’s Sonnets.” Studies in Honor of Basil L. Gildersleeve, Johns Hopkins Press, 1902, pp. 363–75.
Rudnicky, Alex. CMU Pronouncing Dictionary. 0.7b, http://www.speech.cs.cmu.edu/cgi-bin/cmudict.
Skinner, B. F. “Alliteration in Shakespeare’s Sonnets: A Study in Literary Behavior.” The Psychological Record, vol. 3, 1939, p. 185.
Tolkien, J. R. R. The Collected Poems of J.R.R. Tolkien. Edited by Christina Scull and Wayne G. Hammond, William Morrow, an imprint of HarperCollins Publishers, 2024.
—. The Letters of J.R.R. Tolkien. Edited by Humphrey Carpenter and Christopher Tolkien, Revised and Expanded edition, William Morrow, an imprint of HarperCollins Publishers, 2023.
Wise, Dennis Wilson, editor. Speculative Poetry and the Modern Alliterative Revival: A Critical Anthology. Fairleigh Dickinson University Press, 2024.

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