Idiosophy

A physicist loose among the liberal arts

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The more things change

This is a funny line from the beginning of The Tale of King Arthur:

And the thyrd syster, Morgan le Fey, was put to scole in a nonnery, and ther she lerned so moche that she was a grete clerke of nygromancye.  (p.5, lines 28-9.)

The Mythgard Academy class broke a number of staves of wit on the abbess of Morgan’s convent. (about 40:00)

It’s hard not to hear an echo of parents who send their children off to college, and then lament that they’ve come back with their heads full of funny ideas.  To a modern-day capitalist father, Marxism might be an exact parallel to black magic in medieval times.

Friday and Saturday Papers at Mythmoot

Commentary on some talks I heard at Mythmoot V. They were recorded; when the recordings are posted I’ll add a link here.

Lee Smith – Getting sick of it

Lee looks at sickness in two sagas: Egils Saga Skallagrímssonar and Laxdæla Saga, and there is no way I could have spelled those correctly without looking it up in her abstract.

Illness is housekeeping, as she puts it. It’s a way to get characters off stage, if the author is denying them death in battle. The only three ways to die are battle, sickness, and old age. This is something I’d never noticed before: no accidents? Nobody gets kicked by a horse, or gets caught in an avalanche? Maybe vikings thought those were comedy, not fit for a saga. 3 characters who die of illness pair certainty that their illness will be fatal with noting they’ve never been sick before. People in real life do this, too, but these days they’re frequently wrong. These guys want to establish houses, and keep watch over them after they die. They’re aiming for “post-mortem agency” (another gem from Lee’s unique idiom), an naturally their descendants go mad from the haunting.

This was a funny talk about illness and death, which I think is probably the right attitude to take when reading sagas.

Jennifer Ewing – The bitter watches of the night

Jennifer’s point is that there are a lot of parallels between Anne Elliot in Jane Austen’s Persuasion to Éowyn of Rohan in The Lord of the Rings.

To begin with, both women are stuck in similar environments. Home is where tradition and memory are kept. Going out to work makes you forgetful. What Aragorn says about Éowyn in the Houses of Healing lines up nicely. Both women feel walls closing in. Both women are neglected by the men around them. It’s not Éomer who takes Éowyn’s side, it’s Gandalf and Háma. Anne is isolated by her family and others, and spends her time taking care of an aging uncle. Sounds familiar. Éowyn leaves her people to live in Ithilien, in the same way Anne wants a mariner husband who will take her far away. Captain Wentworth’s letter is parallel with Faramir’s speech in the Houses. The two do disagree about duty. Éowyn sees it as a cage; Anne sees it as a source of strength.

Jennifer’s conclusion is that JRRT can write as good a female character as writers of mainstream fiction.

Well, that started a lively discussion! John Garth noted that Jennifer carefully avoided claiming that Anne Elliot was an influence on Tolkien’s character, but the idea ought to be pursued. The context of 19th century society informed JRRT, who actually mentioned William Morris’s The Roots of the Mountains as an influence. That book contains the transitional character of a woman who goes to war. Jennifer replied that women actually were going to war by 1944, and dressing in men’s clothes while they did that.

Kay Ben-Avraham wasn’t having that last conclusion. She says you can’t put JRRT on a level with Austen, without addressing the Smurfette Principle. Jennifer’s reply was that most of the male characters in LotR are just cannon-fodder; only a few are fleshed out as fully as Éowyn. She’s better drawn than Éomer, for example.

Alicia Fox-Lenz says the centrality of the female characters is what makes the legendarium separate. The true sign of a hero in LotR is that a character can heal, and sing, and cook, and garden. Not masculine attributes. Kate Neville backed her up, pointing out that the entire concept of hobbits is a sort of feminine embodiment.

Then John Garth made a brilliant observation: LotR is a story about men going to war, not a story about women. But there’s Éowyn in the middle of it, a female hero in a men’s story exactly the way Dernhelm is concealed among the host of the Rohirrim. Applause.

Jennifer said her talk was drastically abridged from its original form. The audience clamored for her to publish the whole thing.

Tom Hillman – Lame Sovereignty in Melkor and Man in The Children of Hurin

This paper is already on line (yes, of course starting with Plutarch) so I’ll talk about the Q&A. The first question was that lameness doesn’t mean the same thing to us as it meant to the ancients, where “ancient” means “before antibiotics, X-rays, and other effective medical care”. In the ancient world, everybody knew someone who was lame. Does that affect the meanings of how these stories should be read? (I was wondering this myself.) The answer is best found in textual history – which character gets lamed by the author? The first one to appear in the development of the story, or is the lame character a foil for someone else?

Kate asked another good question – who would want to be compared to Turin? The story of Turin is the only story about Men that Elves tell each other. Alan Sisto followed up on that by pointing out that Elves can’t escape fate, and they kind of envy Men their apparent ability to change the course of the world. Turin is interesting to them because he’s more like them; he doesn’t have the human talent for wriggling out of fate. Tom wrapped it up by saying that it was a nice complement to our human fascination with Elvish immortality.

Alyssa House-Thomas – Planet of Exile and the Frontiers of the Human

planet iconPlanet of Exile is the novel that begins Ursula K. LeGuin’s Hainish cycle. She was trying out new concepts, and we can see themes partially developed here that will appear in their full form in the later novels in the series. Here, there is a conflict between a humanoid race and some marooned Earthlings, which has to be set aside as an invading force comes into view. This sets up a Romeo-and-Juliet situation. The two humanoid races can’t interbreed, which is only the most biological level of the exploration of the boundaries of what is human. There’s a development of touching, at the physical level. The top level is etiquette. Alyssa worked from the taboo on looking another person straight in the eye for a big chunk of her talk.

What interested me was the way Alyssa called out the use of light. The skins of the two humanoid races are different colors, and the light-dark contrast is a launching point for LeGuin’s Taoist inspiration in the book. As Alyssa put it, “light means building connections”. That’s definitely a way to get an old physicist to prick up his ears. Exchanging light signals is the core of special relativity. The Hainish cycle will lead us to the physicist Shevek in The Dispossessed, who overthrows Einstein’s relativity in favor of simultaneity. And touching is an electromagnetic interaction, accomplished by the exchange of virtual photons between two extended bodies. Could this have been intentional? Like Alyssa, I’m inclined to doubt it, but the commonality of language is intriguing.

Tom Shippey – The Hero and the Zeitgeist

Heroic Fantasy, as a genre, has never been more popular. By absolute numbers this is unquestionable. I suspect that even as a fraction of the total audience of readers and viewers, it is true as well.  Tom Shippey gave a plenary address at Mythmoot V to tell us what that might signify.  (And let us pause for a moment to marvel at the fact that Prof. Shippey, whose adversarial relationship with computer technology is famous, skyped from England into a conference in Virginia which was streamed via Twitch in the cloud and watched as far away as Japan. Kudos to Ed Powell, Ringmaster!)

So: Is heroic fantasy the spirit of our age?  Because Prof. Shippey knew to whom he was talking, he started with Tolkien. In The Hobbit and The Lord of the Rings, Tolkien doesn’t use “hero” without some kind of modifier. There’s only one sincere use.  In The Silmarillion, he doesn’t use the word at all.

Here’s what the Encyclopedia Galactica Oxford English Dictionary has to say about heroes.  The various definitions align with Northrop Frye’s literary modes, once Prof. Shippey adds a line referring to current popular usage.  The examples are mine.

Mode Earliest Use Meaning Example
Myth 1387 demigod Hercules
Romance 1586 warrior hero Horatius
High Mimesis 1661 great soul Nelson Mandela
Low Mimesis 1697 the chief male personage in a story Candide
Irony current any military veteran Norman Schwarzkopf

scruffy batmanIf we accept the historical Western idea that military glory is greater than any other, this is a clear downward trajectory. “Hero” has had its meaning lowered as the idea becomes more widespread.  Of course, the true historical progression might be a circle, as pushing through irony puts you back at the top. (cf James Joyce’s Ulysses) LotR has each kind of hero, and it’s an entertaining way to pass a long drive, thinking of which ones are which.

Why has heroic fantasy become the spirit of the age?  Prof. Shippey has been around long enough that he’s personally experienced another descending scale:

  1. Leadership
  2. Management
  3. Administration

So where once we had leaders out front, we now have administrators who are invisible.  As the old man who taught me how to be a system engineer loved to say, “You lead people. You manage resources. You administer punishment.”  (Come to think of it, he was born not far from Prof. Shippey,  a decade earlier.)

Heroic fantasy is not an escapist genre any more. It’s a response to the things we are losing. We’re pushing back up the Frye scale because we miss leadership.

Best line of the talk: “Tyrion Lannister is someone you can look up to.”

Worst scholarly reference of the talk:  Hietikko, H. Power, Leadership, Doom, and Hope. “Management by Sauron”.  Because it’s in Finnish so nobody had read it.


Question period:

Q: is the dwindling of the Elves like the dwindling of heroes? A: An intriguing idea, but no.  (JH: That sounds like a story idea.)

Q: haven’t people always thought the past was more heroic? A: If we could call back a viking hero from the past, and ask him to do what the Atlantic convoys did in WW2, he’d say hell, no. The ancient models were more personal.   We have different requirements for heroism these days. Ancient heroes wouldn’t fare any better today than ours would fare in a fight with battle-axes.


BTW: the cartoon of a hero on a downward trajectory is by Ian Ransley.

Inklings and Arthur and Imagery

Sørina Higgins ran a photo contest for pictures of her book The Inklings and King Arthur at Mythmoot.  I almost won.  Apparently visual interest and well-thought-out composition count more towards photographic artistry than bad puns.  Congratulations, Tom!

Sunday Papers at Mythmoot

A lot of Mythmoot V was recorded on video and will be posted to the Signum University channels on Twitch or YouTube, so I’m not going to do a full recapitulation this year.  I’m just going to mention some talks where I have something to say.  The Sunday morning paper session is one such.

Luke Shelton – Young Readers’ Receptions

Luke walked us through one of the survey methods he’s using in his dissertation research.  He’s studying how young readers respond to The Lord of the Rings. One example of his methods is called “diamond-ranking”. You can see a diagram in the video, but essentially it’s a way of measuring readers’ reactions that takes account of the fact that people are generally pretty clear about the best and worst of a group, but don’t make such big differentiation in the middle.  His example question was “Which members of the Fellowship do you feel positive about, and which negative?”

He passed out cards with the names of the Fellowship of the Ring on them, and split us into two groups to do the ranking. Interesting debates ensued, where “interesting” is defined as in the apocryphal Chinese curse. Judging from the decibel level, I suspect these groups were rather more opinionated than average.  Both put Sam at the top.  Luke noted that children never put Sam at the top. It’ll be interesting to see what conclusions come out of this.

Arthur Harrow – Isaac Asimov and the rise of the Nerd Hero

Arthur began by surveying the dismal landscape of his childhood. Tom Swift books were just about the only good books for boys before Asimov came along. Then the Nerd became the target for science fiction. Not only are the heroes of Foundation mathematicians, psychologists, and disruptive students who are too smart for their teachers, but the whole trilogy assumes that the reader is widely read in history, math, physics, and psychology. Which is to say, us.

Then the talk veered away from nerdhood to talk about the role of women in SF. As far back as the 1930’s, Doc Smith’s Lensman series took tantalizing steps toward making women real characters, but they fall short – the only woman who could become a Lensman was “some kind of freak”. But mostly, space-opera sopranos spend their time screaming and being rescued. Doc Smith elevated them a bit.

Then came Asimov to the portrayal of women as heroes, just as he did for male nerds.  In I, Robot, the hero is Dr. Susan Calvin, inventor of the positronic brain. She drives the plots of the stories, in the mid-1940s, ahead of the rest of SF, and far ahead of less forward-thinking genres.

Dom Nardi – How game theory solves the paradox of foreknowledge in Dune

If a writer is going to put knowledge of the future into a book, it’s going to be necessary to take a stand on the question of free will vs determinism.  Frank Herbert put the sentence “Dreams are predictions” right up front in Dune.  Do the characters still have free will, if someone can predict the future?

Usually, the author dodges.  The Oracle at Delphi got around this by being incomprehensible.  Hari Seldon resolves the problem by not telling people what he foresaw.  Herbert’s characters grab the bull by the horns.  Dom says this works because of game theory.

Towards the end, Paul sees branching possible futures in some cases, but in others its definite.

Other critics haven’t quite understood this. Lawrence Luton (“The Political Philosophy of Dune.” [1979]) applies a type of Heisenberg principle, saying that seeing the future makes it change.  There’s no such thing as “The” future.  This is only correct in Dune itself. In the sequels, characters can use their foreknowledge.  Sam Gates-Scovelle (Nicholas, J. [2011], Dune and Philosophy: Weirding Way of the Mentat) says there’s a difference between knowledge and prediction. But we don’t see the difference in application.

In Dom’s view, prescience is a form of computation. The paths in the future that Paul sees are the same thing as the outcomes of a game in mathematical game theory.  He gave us an example of a very simple game: Paul vs the Emperor.  If everyone has all the information and both make rational choices, we see the emperor abdicate.  But of course, Herbert was writing an interesting book, not a dull one.  Imperfect information and bounded rationality are at the core of the difference between Dom’s simple model and the actual plot.

In this view, where any actor can make any move with some (unknown) probability, prescience is a power Paul can use to torque the game’s outcome because he has better knowledge of the probabilities than someone who’s not able to see the future.  When Paul sees a single path, it’s because there’s a clear choice for both players.  When he sees branching futures, it’s because the payoff is indifferent among some of the choices.

David Maddock’s comment got at the core of how clever this is. In computer jargon, he noted, prediction is an NP-hard problem.  Translating into human language, that means that if you’re trying to test out possible futures, you do it by building a simulation, changing the inputs according to a model you’ve thought of, and running the simulation to see how it comes out.  For a complicated system, though, the computation gets so big that it takes more time to run the simulation than it does to just wait and see how things come out.  So prediction is impossible, and you can have free will and determinism at the same time, if you’d like.

Here’s the best thing about David’s observation:  it means that the power of the Mentats can be thought of as a way to address NP-hard problems such that they’re solvable in a reasonable time.  I’ve never been comfortable with the Butlerian Jihad, because if a science-fiction story is going to have a high-tech world with no computers, it should explain how a human mind by itself can be faster than a human mind plus a computer.  This is a good way to do that.

(And congratulations on your new degree, David!)

Contra-Economics

Stephen Winter says a lot of nice things about Idiosophy over at Wisdom from the Lord of the Rings this week.

One thing I’d like to clarify: In case anyone concluded that the disjunctions in time in Middle-earth are a weakness in the story, I think they’re intentional. When Tolkien wanted his creation to resemble our world, he was careful to make sure his facts were correct. We have seen this in astronomy, botany, cosmology, ecology, and even in quantum physics.

But if there’s one discipline Tolkien didn’t respect, it’s economics. He went out of his way to break economic laws. The logic of economics is the logic of the Industrial Revolution, and Middle-earth was going to have none of it. So The Shire and Bree have money, but no government that coins it. The places with the most advanced technology are the ones with the lowest population density. Fast technological development in Isengard is the product of one single mind, not a collaborative community. All of these things contradict well-established economic theorems.

The one place I can think of where economic logic applies is in Lake Town. The stories people tell about the King Under the Mountain are a good application of Keynesian macroeconomics, but we readers are not encouraged to think of the Master and his guild-inspired community leaders as heroes.

That, I think, is the purpose of the steep time-gradients on the map of Middle-earth — to renounce Adam Smith and all his works. Faërie and Economics are natural enemies.

The Friendship of Kings

I love Shawn and Alan, The Prancing Pony Podcasters, but they’re such Americans sometimes. In last week’s episode, they heaped derision on Thorin Oakenshield for telling Bard, Gandalf, and the Elven-King, “Take him, if you wish him to live; and no friendship of mine goes with him.” “Him” meaning Bilbo, of course.

To our intrepid Digressors, this was childish. It sounded like a grade-schooler wielding his meaningless social connections as if they were punishments and rewards. That’s what living in America will do to you. But J.R.R. Tolkien was thinking of an older form of government. Here’s a story:

Caesar Augustus as Jove

You wouldn’t like him when he’s angry

Imperator Caesar Augustus ruled Rome though his personal network. He was the patron of millions of clients (including the entire army and navy). He didn’t have much statutory power, just a few honorary titles. But when he said something should be done, it got done, because everyone wanted to be on his good side.

One day, he learned that the Governor of Africa had “appropriated” a golden statue from a temple in his province, which Augustus had forbidden. Augustus’s response? There was no indictment, or prosecution, or sentence. All that happened was that Augustus was disappointed and sad, and told the people in attendance, “That man is no longer my friend.” When word of it got to Africa, the governor committed suicide rather than bear the shame, and the disrespect from his followers that was soon to come. That’s power.

The same attitude applied up north. For example, look at how many Anglo-Saxon kennings for “king” have the word for friend in them. There’s Folcwine, Fréawine, Goldwine, and we haven’t even gotten to England yet. So when Thorin said he had “no friendship” for Bilbo, “friend” should be read this way. Those words are not empty.

Just for fun, let’s flash forward to the Scouring of the Shire, when Pippin gets fed up with the gangsters. Pippin makes a good warrior’s boast, but that’s not the scary part.

‘I am a messenger of the King,’ he said. ‘You are speaking to the King’s friend, and one of the most renowned in all the lands of the West. You are a ruffian and a fool. Down on your knees in the road and ask pardon, or I will set this troll’s bane in you!’

The King’s friend, huh? Is it any wonder that the ruffians turned and fled?

Defining Science Fiction

Have you ever wondered how exactly to define “science fiction”? I’ve seen lots of opinions, none of which sounded right.  In an article in PMLA, though, Eric Rabkin pointed me in an interesting direction.  He said “Carl Freedman wrote that his ‘thesis about critical theory and science fiction is that each is a version of the other’.”  Intriguing — they certainly have lots of things in common, since critical theory is constitutionally incapable of staying in one lane, and so wanders from literature to politics to economics to sociology to linguistics and back again.  SF started out that way on purpose.  Maybe there’s something there.

Via inter-library loan, Carl Freedman tells me that Darko Suvin defines science fiction as “the literature of cognitive estrangement.”  Whoa!  Assessing the analytical validity of that assertion will take some thought, but my immediate reaction was that it’s a perfect description of science-fiction fans. Suvin has got to be onto something.  SF fans are not only cognitively estranged from the mundane world, they positively embrace that status. (I say “they” as if I’m not one of them, but I doubt anyone will be fooled.) We’re proud of how differently we think, and judge our ways superior.  Somewhere in a box around here is a button that says “Reality is a crutch for people who can’t handle science fiction.”  We give non-fans scornful names like “mundanes” or “muggles”.

That last word brought me up short. Though SF fans use it, it’s from fantasy. I’m looking for a way to distinguish SF from fantasy.  Fortunately, Darko Suvin actually said something rather different.

SF is, then, a literary genre whose necessary and sufficient conditions are the presence and interaction of estrangement and cognition, and whose main formal device is an imaginative framework alternative to the author’s empirical environment.

“Estrangement” is easy, and obviously correct.  SF is set in a world that is not our own (though it may look just like ours, at the start).

The word “cognition”, once you work through the jungle of academic prose, isn’t quite right. As Suvin eventually explains, it means that the writer isn’t trying to give authoritative statements about characters, relationships, or phenomena. The writer is trying to pose them as problems to be solved, to expose them to inquiry.

The reader’s response is equally important.  The reader of SF is expected to think about the story in the same way as a scientist approaches an experiment: “How does this work? What processes are happening here? What can I learn from this?”  Fantasy is read completely differently.  “What a wonderful/terrifying world! Can I go there?”  This distinction in reader response is what distinguishes SF from fantasy, and from all other genres of estrangement.  In fact, it may be what gives SF the right to have the word “science” in its name.  Science fiction is not “fiction about science”. When I look at Robert Heinlein, for example, it’s hard to find any science in any book he wrote.  All the characters are engineers, solving engineering problems.  But they are solving problems, and the readers are right there working alongside them.

(As an aside, it’s interesting that when C.S. Lewis invented reader-response criticism, he talked for a whole page about SF [p.110], and said things that make it clear that he knew all this, but he never actually said it explicitly.)

So this is useful, and I shall use it.  But now I’m wondering why the terminology shifted.  The term that grabbed me was “cognitive estrangement”, not “estrangement and cognition”.  And I’m not the only one. Here’s how the two terms have fared so far:

So I conclude that the road to scholarly fame runs through steps:

  1. Think an intriguing and useful thought.
  2. Give it a clunky name that uses the same words as a good bumper-sticker.
  3. Wait for somebody else to slip up and say the bumper-sticker version.
  4. Watch the citations roll in.
Obligatory Quantitative Appendix
  • My citation of Rabkin is at the top of a blog post.
  • Rabkin’s citation to Freedman is on Page 2 of his 18-page paper.
  • Freedman’s citation to Suvin is on page xv of his book.
  • Suvin’s concise statement is on page 7 of his book.

We don’t have to read far into a work of literary criticism to get all the good stuff!


Works Cited

Freedman, Carl. Critical theory and science fiction. Wesleyan University Press, 2000.

Lewis, Clive Staples. An experiment in criticism. Cambridge University Press, 1992.

Rabkin, Eric S. “Science fiction and the future of criticism.” PMLA 119.3 (2004): 457-473.

Suvin, Darko. “Estrangement and Cognition“, in Metamorphoses of science fiction: On the poetics and history of a literary genre. Yale University Press, 1979.

They Call it Humanistic Mathematics

In which the Idiosopher discovers a lot of new friends.

Antediluvian Friend-of-the-Blog Steve Devine points us to a paper in the Journal of Humanistic Mathematics entitled “Franz and Georg: Cantor’s Mathematics of the Infinite in the Work of Kafka“. If this paper is not idiosophical, then idiosophy has no meaning.

Knudson is discussing a posthumously-published story by Franz Kafka entitled “The Great Wall of China“. I had never heard of it before; getting to read a new Kafka fantasy means it’s already a good day. (The story is depressingly relevant in a few places.) Knudson’s paper talks mostly about the curious method of constructing the Great Wall, and notes its similarity to the “Cantor Set“. (Please go look at the pictures in that Wikipedia article — there’s a wonderfully unexpected one in there.) It doesn’t mention the messenger finding his way through the crowd, which appears to be a two-dimensional analogue of the same fractal process.

Illustration of the Cantor set to five levels

Cantor Set

If necessary, it’s possible to read Knudson’s paper like a moviegoer, skipping the theorems the way a Peter Jackson fan skips the poems in The Lord of the Rings. He always returns to plain English before long.

This kind of mathematics is related to graph theory in a way I hadn’t appreciated before, and graph theory is no stranger to Idiosophy. (Do you suppose the editors at JHM would be interested in hearing about calling people fools?) Anyway, at the end of Shi Wen’s post, there’s a link to a wonderful video, made by the kind of student I always wished I had.


Work Cited

Knudson, K. P., “Franz and Georg: Cantor’s Mathematics of the Infinite in the Work of Kafka,” Journal of Humanistic Mathematics, Volume 7 Issue 1 (January 2017), pages 147-154. DOI: 10.5642/jhummath.201701.12 . Available at: http://scholarship.claremont.edu/jhm/vol7/iss1/12

Science Fiction vs. Theater

Mythmoot V is coming up, and the theme is “Fantastic Frontiers”. That’s got me looking at all kinds of boundaries, frontiers, and demarcations in speculative fiction.

Isaac Asimov once wrote this about how to write a science-fiction detective story (which his editor said couldn’t be done):

The writer must carefully explain to the reader all their boundary conditions of the imaginary society. It must be perfectly clear what can be done and what can’t be done and with those boundaries fixed, the reader must then see and hear everything the investigator sees and hears, and he must be aware of every clue the investigator comes across.

From the hundred-or-so Asimov stories I’ve read, I infer that this is a good rule for all SF stories if you replace “investigator” with “protagonist”. Readers are willing to make great leaps of faith to enjoy a story, as long as the boundaries are fixed [1] and we know how far the author wants us to jump.

There is one side, though, on which the boundary is fuzzy and permeable. That’s the side that faces the reader. Anything that’s familiar to us in our mundane world can be in a science fiction story. In fact, it’s almost essential to include a bunch of things from our world to keep from weirding the readers out.Fuzzy boundaries of SF and theater

It amused me to notice that the theater works the exact opposite way. The wall that faces the audience is the only fixed one, there. The other three walls are almost infinitely mutable. From one minute to the next they can be DUKE ORSINO’s palace, The sea-coast, OLIVIA’S house, A street, and Before OLIVIA’s house. The fourth wall can be broken, sure. When it is, the playwright is doing it consciously, in exactly the same way that a science-fiction writer might deliberately minimize the connections between the fictional world and the mundane to build a sense of alienation.

The theatrical version of boundaries seems to apply to television and movies, too. So when the subject of a movie is science-fictional, which one wins? Interestingly, it seems that all the rigid boundaries apply. A science-fiction movie is truly in a box.


[1] This is not to say the boundary is finite. Borrowing from complex analysis [2][3], I consider a boundary at infinity to be fixed.

[2] This concept is also useful in real analysis, but this is a humanities blog where the phrase “real analysis” can easily be misinterpreted, so I bumped it up a level.

[3] I’ve read so many Terry Pratchett stories that nested footnotes don’t look odd to me any more.

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