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Monty Python cribs from Aristotle

On September 7, 2024

According to Monty Python¹ King Arthur, when asked how he could have coconuts in a temperate climate like England’s, replied “The swallow may fly south with the sun, or the house martin or the plover seek hot lands in winter, yet these are not strangers to our land.” (page 2) In my copy of the screenplay, which is a facsimile, lots of lines are scratched out, hand-written, or otherwise edited in production. Not this speech. It is unchanged from the first typewritten copy.

Eleanor Parker (the scholar, not Lenore from Scaramouche) on the approach of autumn, directs us to the Secreta Secretorum²:

In herust fallyth the contrary. In this tyme the eeyre wixeth colde and dry, the wynde of the Northe oftymes turnyth, Wellis wythdrawen ham, grene thynges fadyth, Frutes fallyth, the Eeyre lesyth his beute, the byrdys shechyn hote regions, the bestis desyryth hare receptis, Serpentes gone to hare dichis. (P. 245)

This is an odd book. Wikipedia refers to it as a pseudo-Aristotelian treatise, which implies there are more things like it in the world. Let’s see how rusty my Middle English is: “In harvest the contrary happens. In this time the year grows cold and dry, the wind often comes from the north, water levels in the rivers drop, green things fade, fruits fall, the year loses its beauty, the birds seek hot regions, the beasts desire their burrows, serpents go to their holes.”

Monty Python’s line about birds “seeking hot lands in winter” clearly came from here.³ The more I learn about history, the more I wonder if Monty Python actually made up anything at all.

Un Changeable

By Joe

On August 30, 2024

In fantasy, scholarship

Tom Hillman is taking on another of the big questions. This time it’s Fate, and how Turin relates to it.⁴ He calls out the line from “Beowulf”: “Fate often keeps an unfey man safe when his courage avails.”

I’ve taken a couple of courses from Tom Shippey in which he brought up that line. Usually with a comment like, “That’s not much of a fate, if you can avoid it with a bit of courage.” When he’s being more formal⁵, he says

… people are not under the domination of wyrd, which is why “fate” is not a good translation of it. People can “change their luck”, and can in a way say “No” to divine Providence, though of course if they do they have to stand by the consequences of their decision.

The Road to Middle-Earth, Chapter 5

I suspect that wyrd isn’t the only word here whose meaning has slipped over the last thousand years. The word unfaege, produced from the word for “fey”, also has the prefix “un-“. When I first learned Old English, it jumped out at me that “un-” isn’t quite what it used to be. In most words, it means what modern speakers expect, but there are plenty of words where it doesn’t. Unweder, “un-weather”,is a storm. Unweod, “un-grass”, is a weed, as is unwyrt. Uncræft, “un-craft”, is an evil art. Unbletsung, “un-blessing” is not the absence of a blessing, but a curse.

The “un-” prefix seems also to have meant “wrong” or “the opposite of what you wanted”. Is it possible that unfaege, “un-fey”, might have meant something like “doomed to something else”? Then the Beowulf poet would have meant, “If wyrd has something else in mind for a man, he’ll come through this one safely as long as he keeps his courage.” With the implication that a coward can screw up even the fate of the world, so don’t be one.

Lagrangian Theory of Science Fiction

By Joe

On August 14, 2024

In science fiction

Sørina Higgins gave a talk recently at the Brazilian Mythopoeic Society about how time flows in fantasy. This is something that has interested me ever since I read Umberto Eco’s essay “The Woods of Loisy”⁶. One of the techniques Eco used there to describe the temporal flow in a story was to make a graph of the “in-world time”, what the calendar on the wall says, versus the reader’s progression through the narrative. I’ll use “page number” to stand in for that. Eco uses it for The Odyssey, and Sylvie by Gerard de Nerval, and a limerick about a man from Peru.⁷ I want to use it for stories about literal time-travel, instead of a narrative that shifts about in time while the characters all go forward.

Figure 1.

For experimental purposes, let’s construct a trivial time-travel story: A mad scientist in Texas invents a time machine. He uses it to go back to last February in Brazil. While he’s sight-seeing there, a butterfly lands on his shoulder and he brushes it off. Then he climbs back into his time machine and returns to the time he left. Well, we all know about the awesome power of butterflies in Brazil. When he returns, his lab has been blown apart by a tornado, the infrastructure for time-travel is wrecked, and so he sets about the job of rebuilding, one day at a time like the rest of us have to. The End.

Figure 1 is what that story looks like when it’s drawn as one of Eco’s diagrams. An upward-sloping line is what we all do all the time. A big jump straight up or down is when the time machine causes a change of the in-world time on a single page for the reader. These parts are the pure science fiction.

Among Sørina’s citations are Ted Chiang’s “The Story of Your Life”⁸ and Richard Feynman’s Nobel lecture. Though she didn’t mention it, these two texts share a deep structural element. Chiang’s protagonist learns an alien linguistic form from creatures who perceive language as a kind of variational principle, and ends up seeing her daughter’s life in that way, instead of via pedestrian linear time. Chiang, according to the end-notes in my copy of the book, is fascinated by Lagrangian dynamics, so he wrote them into a story.

Feynman earned his Nobel Prize for applying Lagrangian variational principles to Quantum Electrodynamics, and in the process inventing a way to compute preposterously-complex integrals⁹ without making your head explode. That method is now called a “Feynman diagram”. A Feynman diagram has solid lines with arrows for electrons, quarks, etc. There are wavy lines for photons and curlicue lines for gluons. Other bosons are represented by dashed lines. (E.g. the famous Higgs boson, but there are lots of smaller ones.) There are rules about how different lines connect at vertices, and if you follow all the rules, you can read the function you need to integrate off the diagram, and you’re sure to be doing a calculation that makes sense.

One of the key insights that made diagrams possible was that we can think of a particle of anti-matter as a particle of regular matter traveling backward in time. That’s because the critical parameter describing motion is the product of energy and time, so, mathematically, there’s no difference between something with positive energy going forwards and something with negative energy going backwards. -iEt = i(-E)t = iE(-t), right? But the corners of the red zigzag in Figure 1 all have one arrow coming in and one going out, which means they obey the most important rule of Feynman diagrams.

Figure 2.

In Figure 2, let’s fix the diagram in Figure 1 so that it obeys the rest of the rules, too. Those blue dashed lines are some kind of boson. They represent a force coming into the story from outside, which causes the time machine to turn on or off.

The upper left corner, when the time machine is first turned on if we read from left to right, has a forward-in-time arrow and an backward-in-time arrow if we read from bottom to top. That’s particle anti-particle annihilation. The bottom left corner is the reverse, called pair production. The third and fourth corners are good old scattering, as a particle gets kicked so it moves differently but doesn’t change into antimatter or anything. Another fun thing is that the internal lines don’t have to obey one law of physics (E=mc²); breaking one law of physics is very useful for someone in a science fiction story.

Now, if I were a French philosopher, I’d say something like we’ve drawn the role of the author into the story. And the next step is to add up the contributions from all the possible locations of the vertices and all possible trajectories of the internal lines, which means that all stories involving turning a time-machine on and off twice will be added together. Most of them will cancel each other out, but the ones that reinforce each other will be the enduring Ur-myth of the Time Machine. Good thing I’m not a French philosopher!

But that means that I don’ t know what is represented by those blue dashed lines. I know they aren’t eternal; the number of them isn’t conserved. They can be created or destroyed by interaction with a plot. What do you think they are?

Appendix

Here are Feynman diagrams for two simple scattering events.

on the left, scattering of matter, on the right, matter and antimatter.

time flows left to right

Meticulous etymology

By Joe

On July 29, 2024

In squibs & crackers

It just occurred to me, and the Digital Tolkien project confirms, that in all the books Tolkien wrote about war, he never once used the word “martial”. Which makes perfect sense — Mars would be as out of place in Middle-earth as Father Christmas in Narnia. There is one use of the word in an appendix near the back of Unfinished Tales, discussing the Marshals of the Riddermark. But those are drafts, for which I do not hold J.R.R. Tolkien responsible. The word “Marshal” must have exerted a gravitational force, which would surely have been corrected before publication.

Separating us from all the good things

By Joe

On June 16, 2024

In fantasy

Tom Hillman ponders the relationship between humans and Faërie over on his blog. I think he’s right that Tolkien thinks it’s our fëa that doesn’t belong in Faërie. But there’s another conclusion we can draw from the literature that says something Tolkien would have liked a lot less. It’s not The Fall, or positivism, or statistical analysis, or the industrial revolution that separated us from the Fair Folk.

I’ve mentioned before that, according to Rudyard Kipling, the Protestant Reformation chased the fairies out of England:

This Reformatories tarrified the Pharisees same as the reaper goin’ round a last stand o’ wheat tarrifies rabbits. They packed into the Marsh from all parts, and they says, “Fair or foul, we must flit out o’ this, for Merry England’s done with, an’ we’re reckoned among the Images.” (p.242)

Of course, the Faërie creatures of the Continent had been chased out much earlier. The faun in Poul Anderson’s The Broken Sword¹⁰, whom Skafloc meets in his elf foster-father’s lands, says:

The new god whose name I cannot speak was come to Hellas. There was no more place for the old gods and the old beings who haunted the land. (p.21)

The faun is fleeing West, like Tolkien’s elves. But it doesn’t stop in England. I heard a familiar echo when I was reading the introduction to Alan Lomax’s collection of American folk s0ngs.¹¹

With most of the Southern Negro ministers and teachers urging their followers to abandon the old songs, a flood of jazz and of tawdry gospel hymns comes in. A black giant in the Nashville penitentiary resolutely refused to sing an entirely innocuous levee camp work song since he was a Hardshell Baptist and his church regarded such melodies as “Devil’s songs” or “sinful songs.” (p. xxxi)

They never stop! Fortunately, the world is round, so the Fair Folk, and now the Singing Folk, can’t be cornered. They can always keep going west. I recommend Japan, where the anime industry would welcome them.

Time-traveling pronunciation

By Joe

On May 30, 2024

In Alliterative Verse, Slow learner

While thinking about alliterative verse, I came across an interesting case. Alliteration, in the traditional Old English form, doesn’t have to be on the first consonant in the words — it’s on the first consonant in the stressed syllables. A thousand years later, in Modern English it’s not rare to have more than one syllable in a word that gets stress, though the others are less emphasized. (24% of the words in the CMU Pronouncing Dictionary have a secondary stress in them.) We still alliterate on the stressed syllable, in principle. Which brings me to the word “technological”. The way I say it, the primary stress is on “log”, and the Wise Clerks of Pittsburgh agree with me. Let’s try to alliterate with it:

“Technological Language” sounds like alliteration, and it matches the Old English form.
“Technological Treatise” sounds like alliteration, too.

It’s like the second word causes a change in how we hear the first. The secondary stress on “tech” gets promoted. The presence of “Treatise” seems to move the primary accent from the third syllable “log” to the first syllable “tech”. But I’ve already read the first word — This is time travel!

Light cone, showing the accessible past an future of any event where the speed of light is the limit.

By: K. Aainsqatsi at Wikipedia, CC BY-SA 3.0.

Maybe I can see a physical mechanism here. When I read, I “hear” the words in my head, but I sight-read the words much faster than that. Reading is different from systems described by the Theory of Relativity, because signals are primarily at the speed of (thinking about) sound, but there are also light signals that can exceed that maximum speed. Which makes the “sound cone” permeable, unlike the light cone we know about from Relativity.

So my eyes see the next word before I read the line into memory, and therefore later words in a line can affect the earlier ones. I’m sure every theater director already knew this.

Post Scriptum

The same thing happens with “proctological”, but in this case the dilemma can be resolved easily by never using that word in a poem.

What kind of tree is Treebeard?

By Joe

On May 11, 2024

In fantasy, graphs

J.R.R. Tolkien spends so much time talking about trees, telling us details of their species and their growth, that it’s curious there’s one omission. What kind of tree is Treebeard?

A few seemed more or less related to Treebeard, and reminded them of beech-trees or oaks. But there were other kinds. Some recalled the chestnut: brown-skinned Ents with large splayfingered hands, and short thick legs. Some recalled the ash: tall straight grey Ents with many-fingered hands and long legs; some the fir (the tallest Ents), and others the birch, the rowan, and the linden. [LR 3.04.142]

We get a hint here that Treebeard sort-of looks like an oak (400 species) or a beech (13 species), but it’s never explicitly stated and that doesn’t narrow it down much. Can we use external information to figure out what Tolkien might have been thinking? Of course we can!

Since Treebeard can get most of the Ents of Fangorn to a moot with one morning’s work, he must be a central figure in the Ent community. If we had a graph of relationships between trees, then we could look for centrally-positioned tree species. Treebeard is probably one of those.

The European Commission has funded research into forest types and the species that make them up, all available on line.¹² With a lot of transcription¹³ and a little bit of matrix algebra, we can turn their tree species matrix into a species adjacency matrix, and thence into a graph.¹⁴ All matrix algebra and graph metrics were computed with the R statistical software, version 4.2.2.

I have omitted the species that only live by themselves, most conspicuously the junipers. (See the Canary Island pine, all off by its lonesome? Some species are even more isolated than that.) The introduced species are also removed,¹⁵ because Treebeard is nothing if not native to his forest. There are 112 species in the graph, after we remove the singletons. There are 92 types/subtypes of forest.

The graph is a dense cluster in the middle, with a halo of sub-graphs for Turkey, Portugal, Scandinavia, and the Canaries.

The European Forest Matrix converted to a graph. Hardwoods are in orange and softwoods in blue. Click to embiggen.

Even blown up to full size, that graph is too tightly connected to analyze with just eyeballs, so we need mathematical measures of centrality. I used four:

Degree just counts how many species can live next to the tree of interest, because they exist in the same kinds of forest. The Ent with the most friends has the highest degree.
Page Rank is how the Google search engine works. If your species is around other species that are themselves around lots of species, your centrality is higher. If organizing an Entmoot involves recruiting highly-connected Ents to help you out, the tree with the highest page rank would be a good one to do it.
Closeness is a measure of how many steps through the graph (friend-of-a-friend) a species needs to get to every other species. This would be useful for organizing an Entmoot by yourself.
Betweenness (that’s really the word) looks at the shortest paths through the graph connecting each pair of species. The species that’s on the most of those paths is the most between — this is the tree that would know all the news in the forest.

We don’t know how Treebeard did it; it might have been any of them, so I looked at these measures to find species that are near the top on all of them. Here are the candidates.

Ash: The European ash tree has the highest degree centrality. 65 other species connected to it. That’s because the range map on Wikipedia says it grows basically anywhere with water. Definite possibility! Except the text says that other Ents look like ashes, and they’re not Treebeard. Also, Gandalf’s staff was made of ash, so I doubt an ash-ent would think he’s such a good friend. So the ash is out.

Black elder: Besides elderberries being tasty, the Black elder has the highest page rank. Unfortunately, it looks more like a bush than a tree. I’m sad that this one didn’t work out because Celeborn addressing an elder as “Eldest” would have been a great joke.

Field maple: This tree isn’t number one on any metric, but it’s #3 or #4 on all of them so it’s a contender. It loses out because it doesn’t have any textual support. It doesn’t look anything like an oak or a beech. (No beech ranks above #8 on any metric.)

Pedunculate oak: This is the good old English oak. It’s a very long-lived tree, and very tall. The Wikipedia article says there are more ancient oaks in England than any other country in Europe. It also cites old myths saying oaks were the “thunderstorm trees”, with which Saruman might agree. Merry said “The Forest had felt as tense as if a thunderstorm was brewing inside it”. [LR 3.09.059] Though it’s not higher than #3 on any metric, this is almost certainly the species Tolkien was thinking of. But… the graph suggests a dark-horse candidate.

These trees have branches that look like arms. They're totally Ents.

Turkey oaks in New York’s Central Park

Turkey oak: It’s got a funny name (OK, maybe not as funny as “pedunculate”), but it’s #1 on the betweenness metric. Turkey oaks have an interesting history. Wikipedia says, “The species’ range extended to northern Europe and the British Isles before the previous ice age, about 120,000 years ago.” I can’t help remembering Elrond saying the Old Forest once stretched all the way from the Shire to Dunland, but had shrunk since. Almost like Treebeard could have walked among Turkey oaks from Wellinghall to England, but now there’s just empty lands between them.

So I liked Turkey oaks, but on top of that, searching for Turkey oaks on line took me to the website for Central Park. They have Turkey oaks there, and look at them! The one on the left is absolutely an Ent, caught in mid-pandiculation.

Credit where credit is due

About a quarter of the way through this exercise, I realized I was tracing the steps of Kieran Healy of Duke University, whose essay on how British intelligence might have caught Paul Revere if only they’d known some math is one of the funniest things ever written about graph analysis. Note for his most-obscure joke: “eigenvector centrality” is the same as what I called “page rank” here.

Mechanical Help Understanding Charles Williams

By Joe

On April 22, 2024

In Digital Humanities

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.

Swallow the bones and choke

By Joe

On February 11, 2024

In fantasy

File Under: The things you find out while wasting time on a Sunday morning.

Eleanor Parker’s excellent newsletter this morning is about Old English people gearing up for Lent by eating everything they can. ¹⁶ She points us to Kate Thomas’s “For the Wynn” essay on cheese. That essay is wonderful for many reasons, but one that jumped out at me was the part about the use of cheese in jurisprudence:

Some early medieval liturgical books contain an ordeal using barley bread and cheese – a way of ascertaining a person’s guilt or innocence via the eating of small pieces of food. It operates upon the same rationale as ducking witches – nature rejects someone who has done wrong, so a guilty person will choke on the bread or cheese.

Of course, my mind went immediately to the pool beneath Henneth Annun, where Frodo compels Smeagol with force majeure: “I shall take Precious, and I shall say: make him swallow the bones and choke. Never taste fish again.” [LR 4.06.047] ¹⁷

This is the second time we’ve seen little asides in LotR that come straight from Anglo-Saxon law. I don’t imagine it’s the last.

Notes

The First Temptation of Sam

By Joe

On January 29, 2024

In fantasy

When Sam took the Ring and entered Mordor, we get the famous passage that lots of people take for Sam’s test versus the Ring:

Already the Ring tempted him, gnawing at his will and reason. Wild fantasies arose in his mind; and he saw Samwise the Strong, Hero of the Age, striding with a flaming sword across the darkened land, and armies flocking to his call as he marched to the overthrow of Barad-dur. [LR 6.01.018]

I don’t agree that this is the test. This attempt to suborn the faithful Samwise is risible. If that’s the best the Ring can do, it wouldn’t have been a problem for anybody, let alone Boromir, Gandalf, or Galadriel. Tolkien gives us a hint that this idea isn’t quite right, though. The previous sentence takes us into Sam’s thoughts: “He felt that he had from now on only two choices: to forbear the Ring, though it would torment him; or to claim it, and challenge the Power that sat in its dark hold beyond the valley of shadows.” Sam is thinking, which is not his strong point. We shouldn’t expect him to comprehend such an important and subtle matter on the first try.

Tom Hillman points out that the Ring is exploiting the way Sam loves old fairy-stories.¹⁸ Sam is a romantic. In that passage, the Ring is using Sam’s romanticism against him. That’s what the Ring does, as we know. It attacks your virtues. It uses your strengths against you. But a fondness for old stories and songs is more of an endearing trait than a great virtue.¹⁹ It’s not where the Ring would try Sam, when we know that he has a great virtue to work with. That’s where we should expect the Ring to attack first.

Sam’s great virtue is his loyalty to Frodo. That’s where the Ring ought to start to work on him, and sure enough, it did. Back in “The Choices of Master Samwise” we saw the real attack.

He flung the Quest and all his decisions away, and fear and doubt with them. He knew now where his place was and had been: at his master’s side, though what he could do there was not clear. [LR 4.10.057]

Right there, Sam lost the contest of wills with Sauron’s Ring. Fortunately, being Sam, he botches the attempt to rescue Frodo, loses the orcs in the tunnel, and concusses himself on the door. The Ring fails to get back to Sauron, and Middle-earth survives for another day.

People who like to find the hand of the Valar in any lucky break will be disappointed, but Sam’s failure to make a heroic stand over Frodo’s body isn’t a eucatastrophe. It was predictable. Indeed, it was predicted back at the beginning of the story! I knew not that Pippin, of all people, was a hobbit foresighted, but he’s the one who said, “Sam is an excellent fellow, and would jump down a dragon’s throat to save you, if he did not trip over his own feet,” and he was almost exactly right. [LR 1.05.060]

It’s only fair. If Sauron can turn people’s strengths into vulnerabilities, some Vala or other ought to be able to turn klutziness into a world-saving virtue. There may be hope for me yet.