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Proving a Thesis and its Limits

On May 20, 2016

Prof. Olsen’s Dracula Lecture 8 includes a special bonus rant on the wrong way to write papers about literature. It matches up marvelously with the next section of my paper. The issue, in a nutshell, is that if students think up a thesis and then look for evidence to support it, they can usually find some. Which is a good first step, but it doesn’t go far enough. Stopping there lets the writer get away with a thesis that’s not necessarily true. Ideally, the writer should also collect all the evidence that the thesis is wrong, and then decide which set is more convincing.

This is one of those cases where being a scientist helps. Standard methods for data analysis take contrary evidence into account on an equal footing with supporting evidence, so the subject of Prof. Olsen’s rant is one of “the blunders we didn’t quite commit” (in Piet Hein’s words).

Which brings us to the core of the paper: how do the regions of England that provide the names of hobbits relate to their role in the story?

Hypothesis: Family names from Birmingham or the West Midlands are close to the Narrator; names from other parts of England indicate families to be kept at arms length; and names that aren’t found in England indicate families that are liminal or distant from the Shire.

Administrative Regions of England

I’ve previously defined the categories of families. The regions of England are from Wikipedia. Birmingham, where J.R.R. Tolkien grew up, stretches from the “W” to the “a” in “West Midlands” now; it was much smaller a hundred years ago.

These are administrative regions, but I’ve checked with an English colleague, who confirms that the regions have cultural significance as well as political. If they were both in London, for example, a person from Warwickshire and a person from Shropshire would agree that they are almost neighbors, as if they came from the same place. (An example of the opposite case would be a Virginian and a Marylander. We don’t feel like we’re from the same place, even when we’re both in California.) So it makes sense to include everyone from the West Midlands in a single category, which is essential to this project because the heat-maps are only that precise.

Hobbit families, by region and role

When we count the number of hobbit families in each group and region, the relationship looks like this figure. Birmingham names are dominant among the “close” group and rare among the others. Names from other parts of England are almost as common among the close group, dominate the “arms-length” group, and drop off in the other groups. Names that do not appear commonly in England are steady across the four groups. Of the three clauses in the hypothesis, the first seems likely true, but the second and third are dubious. Not so good.

group vs. region, weighted by importance

Hobbit families by group and region

All names are not equally important, though. When the importance of each family to the story is included, the graph looks very different. Important characters with Birmingham names are overwhelmingly close to the narrator. Other English names dominate the “arms-length” group, as we expect. The high value of the red line in the “close” group is almost entirely due to Sam Gamgee, as we noted ‘way back at the beginning of this project. (If Sam were “close”, the red line would drop to 15 at “close” and the purple line would jump up above 35. More on that later.) The big spike of important, non-English names in the “liminal” category is mostly due to Merry Brandybuck. “Distant” families aren’t important at all.

So, to take us back to the top of this post, the preponderance of the evidence supports the hypothesis. The “Birmingham” line slopes sharply downward, the “Middle-Earth” line of names that sound strange slopes upward, and the “England” line of names that should sound like they’re from far away is in between the two. The causality runs only one way: if we’d tried to prove that families close to the Narrator were from the West Midlands, the first graph wouldn’t agree. (Only about half of the “close” families are from there.) Using a scientific approach tells more than one side of the story, and sets limits on the strength of the conclusion. With that I shall close, and amuse myself by imagining the look on the face of my high-school English teachers if I’d ever turned in a paper with graphs in it.

Seward’s Folly

By Joe

On May 1, 2016

In mythgard academy

Dr. Seward, the narrator of a large part of Dracula, sometimes seems like he’s there to make the reader feel relatively intelligent. His inability or unwillingness to comprehend things outside his experienced make him, despite his self-avowed erudition, the last person to understand what’s going on.

Dr. Seward refers to himself as a “sceptic” four times over the course of the novel. Old Pyrrho being unavailable, I’ll step in to say that’s not really what he is. Skeptics don’t believe absolute knowledge is possible, and that includes their own preconceptions. Seward has a solid base of things he knows, and anything contradicting it gets disregarded. Skeptics doubt their own working assumptions and even the framework in which they reason, the same as new information they receive. Dr. Seward isn’t doing that at all. In terms of Bayesian logic, he’s reasserting strong prior probabilities in the face of evidence to the contrary. There’s a word for that: the economist Noah Smith calls it “derp”.

Wait – what’s a “prior probability”? Bayes’s theorem is one of those amazing mathematical results that sits there for centuries before anyone really gets its significance. The basic idea (and you can look to Dr. Smith’s blogpost for a better explanation than mine) is that every thinker has a certain prior base of knowledge that she uses to interpret new information. As new information comes in, it modifies the odds of each thing in the base, leaving the thinker with a new “prior distribution” of (in this case) the likelihood that each possible cause gives rise to future observed effects. The mathematical operation that makes that happen is multiplication. One immediate result, therefore, is that if your prior distribution says the likelihood that thing X caused event Y is exactly zero, then the new information gets multiplied by zero. There’s no amount of new data that can make you think X is really going on. Dr. Seward has a prior distribution with zeroes assigned to everything he didn’t learn in school. A skeptic uses a prior distribution with no zeroes in it at all (like a bell curve), because those zeroes are awesomely powerful things, and they’re not to be trusted.

Perhaps I’m being too hard on the good Doctor, but I feel justified because there are examples right next to him of better ways to reason. Characters who use prior probabilities derived from literature seem to work much better. Mina Harker, for example; at times she seems to be the brains of the whole outfit. Why do I say her priors come from literature? Mina may have taken Corey Olsen’s Faërie and Fantasy class (or the 19th-century equivalent). She knows how to compose an oath so it doesn’t later cause trouble in an entirely-predictable way. Maybe this is why Prof. Olsen says she’s “awesome”. Mina reasons from stories. Here’s how she swears never to read her husband’s diary: “I would never open it unless it were for his own dear sake or for the sake of some stern duty.” (Chapter IX) When I read that, I said, “Brava!” [1] She drew the crucial lesson from Arthurian romances – be really careful how you swear oaths. That “unless” clause made the happy ending possible. (Oops – spoiler!) The sons of Fëanor should have been so wise.

Jonathan Harker has a similar skill at hedging his oaths, though I’m sure his prior probabilities come from law school. On the expedition to Dracula’s castle, Mina tries to make him understand that her life is secondary in importance to ridding the world of vampires. “’Jonathan, I want you to promise me something on your word of honour. A promise made to me, but made holily in God’s hearing, and not to be broken though I should go down on my knees and implore you with bitter tears. Quick, you must make it to me at once.’
“’Mina,’ I said, ‘a promise like that, I cannot make at once. I may have no right to make it.’” (Chapter XXIV) You have to love that “may have” — he won’t even commit to that, without consulting his books of precedents. Any knight of the Round Table would have sworn instantly and suffered for it for the rest of the poem.

The similarity of Mina’s and Jonathan’s thought processes raises a question. Instead of school, did Mina learn this mode of thought after meeting Jonathan, to be a better wife? Doing such a thing would be consistent with her character, since it’s not much more difficult than memorizing Transylvanian railroad schedules without speaking Romanian. But I prefer to think that it’s the way she was educated. Victorian girls were taught by literary example (I admit it: my own prior probability distribution is influenced most heavily by Alice’s Adventures in Wonderland). I’m sure that a mode of thinking so consistent with the British legal system was one of the salutary qualities that attracted Jonathan to her in the first place.

[1] Some people write in the margins of books. I talk to them.[back]

I’m in!

By Joe

On April 18, 2016

In ardagraphy, scholarship

The NY Tolkien Conference 2016 has accepted my paper. They’ve posted the first iteration of the program, and I’m on it.

They’ve extended the deadline for submissions to June 1st. This has happened with depressing frequency at aviation conferences in the last year – the paper I’m presenting Tuesday at I-CNS is one I submitted when I found out about their extension.

Surname Mapping

By Joe

On April 15, 2016

In ardagraphy, scholarship

An annotated bibliography of surname mapping. Research by James Cheshire and his collaborators underlies this ardagraphic study. Dr. Cheshire has a blog in addition to his university site linked above.

Oliver O’Brien, Suprageography

O’Brien’s data visualization blog post got this project started. The public-access web portal provided the qualitative data for classification of family names. If you don’t have an English name, the latter site hosts a world-wide version (at a much lower resolution).

Cheshire, James A., Paul A. Longley, and Alex D. Singleton. “The surname regions of Great Britain.” Journal of Maps 6.1 (2010): 401-409.

The map of surname regions in Great Britain shows that distributions of names track well with the administrative regions. The map itself, available for download at the link (17 MB) is gorgeous.

Paul A. Longley, James A. Cheshire, Pablo Mateos, “Creating a regional geography of Britain through the spatial analysis of surnames”, Geoforum, 42, 4, July 2011, Pages 506-516.

Mapping names in the 21st century is valid for this practice because Longley, Cheshire, and Mateos’s techniques make it possible to identify “combinations of location specific surnames that date back 700 or more years”. Figure 5 shows that the “Lasker distances” between Census Area Statistics Wards in a region cluster into a tight grouping, and each region is unlike other regions in England. In fact, some geographic resemblances are visible through the multidimensional clustering: wards in the West Midlands look like they feel a gravitational pull from Wales, as names originating in the Welsh language diffuse across the English border.

The Lasker Distance is elegantly simple. If we write the fraction of people in a small area i who have the name n as p(i,n), then the distance between areas i and j is -ln(Σ p(i,n)×p(j,n)) where the summation is over all names. Names that don’t exist in one of the areas don’t contribute to the sum.

Once the distance in “name-space” between population points is established, the next step is to cluster the points in that space, and set the cluster sizes so that the result is interpretable in geographic terms. The method used here is “k-means” clustering, and I hope I’m not being uncharitable if I describe it as “try every possibility and keep those that work”. That’s unfair, of course — independent consistency checks are applied at each step; the choice isn’t arbitrary.

Cheshire, James, Pablo Mateos, and Paul A. Longley. “Delineating Europe’s cultural regions: Population structure and surname clustering.” Human Biology 83.5 (2011): 573-598.

Figure 7 in this paper shows the relationship between physical distance and Lasker distance for the countries they studied in Europe. Culturally homogenous places like Poland and Luxembourg show a tight cluster of points, lying on a line that’s almost horizontal. That is, you find the same names, no matter where in the country you go.

Scatter plot of Lasker and Geographical distance

Some aspects of cultural history are visible in this figure copied from Cheshire, et al.

Countries unified by language, such as France, Italy, and Germany, show a slanted line (on a log-log plot), with a moderate upward slope. The further apart two villages are, the more likely you are to find different names in them. (France has a small Alsatian tail.) Norway and Denmark are fascinating exceptions: the line slopes downward! I’m just guessing here, but it could be due to the fact that until recently you didn’t get from one place to another by land. By sea, travel times depend on wind and currents as well, so genetics and patronymics can have a more complicated relationship with distance. (There might be a follow-on project, there, if I could only find family names in the Sagas.)

Spain has two distinct parts: One for the mainland and and one for the islands. They’re identical with respect to names. The mainland isn’t a long, thin shape, it’s an incoherent blob, caused by mixed Catalan, Spanish, Arabic, and possibly a Basque scattering off to the side.

The United Kingdom is a dense horizontal sprawl of English, with oddly-shaped protuberances of Welsh, Scottish, and Irish that make drawing a best-fit line through the points an exercise in graphical uniformity, not statistical rigor.

they
are always interested in technical
details when the main question is
whether the stuff is
literature or not
archy

Beyond Good and Evil

By Joe

On April 7, 2016

In ardagraphy, scholarship

The criticism of The Lord of the Rings that annoys me the most, and I think I share this opinion with most fans, is when people say the characters are black and white; bad guys are wholly bad and good guys are wholly good, and never the twain shall meet. These criticisms are made by people who’ve never tried to classify the characters into those groups.

In the post that started this ardagraphic quest, I used the term “bad guys” because I was joking. Now that I’m seriously trying to make something of that work, I need to replace it with something relevant to the text. The utility of the good guy/bad guy distinction fell apart for me when I tried to classify Lobelia. She’s built up as a villain all through the first three chapters, but you have to love an elderly lady, two feet tall, attacking a six-foot oppressor with her umbrella. In any case her repentance at the end, which leads her to give Bag End back to Frodo, ought to disqualify her from the “bad guy” label. “Bad guy” is only useful when talking about Uruk-hai or Bill Ferny. I hereby abandon it.

A better classification comes from my own experience living in Virginia.[1] It’s not so much good and bad people, as there are the people you keep close to you, and those about whom you always find yourself saying, “Bless his heart,” (if you’re a woman) or “That’s just Joe” (if you’re a man). They’re not bad guys, per se, but they frequently seem to act in a way that interferes with other folks getting on with their lives. It’s good practice to keep them at arm’s length.

Separation, then, is the classification I’ll use. The hobbits themselves talk in those terms, and the narrator reinforces it. I’ll use the terms “close” and “arms-length” to describe the two types of characters above. Bagginses, Tooks, and Gamgees are “close”; Sandymans and Sackville-Bagginses are “arms-length”.

I see two other kinds of hobbits, besides these Hobbiton types. First are the fringe elements, who are perceived as being a bit strange and often uncanny. “They still had many peculiar names and strange words not found elsewhere,” the narrator says about the Brandybucks. (Prologue, i) Likewise the Hornblowers, from ‘way off in the Southfarthing, who “had hardly ever been in Hobbiton before”. (I, i) Since this is a scholarly work, I won’t call them “fringe”. I’ll say “liminal”.

The last category are the “distant” hobbit-names. Hobbits in Bree have them. Frodo uses the name “Underhill” when he’s in Bree because Gandalf (who’s been everywhere) knows that someone who hears it won’t think of the bearer as living anywhere near the Shire.

Fig. 1. Classification of Hobbit family names

The counts work out to 13 Close families, 5 Arms-length families, 4 Liminal, and 5 Distant. These numbers are big enough to be just at the threshold where it doesn’t look silly to put them on a histogram. In Figure 1, the blue bars are the counts of families, and the red line is the sum of the importance of each family in the group. The distribution of importance is also reasonable; distant characters are less important to a hobbit (and to a story), and the weighting shows that effect. Families in the Liminal category are slightly more important to the story than those in the Arms-length category because of the presence in the former of Merry Brandybuck.

[1] This is not crazy, as the original post hints. My (English) ancestors, like other long-time Virginians, originated in the West Midlands near Tolkien’s boyhood home, but they left to come here between 1619 and 1750. They missed out on the birth of the Industrial Revolution in Birmingham, and kept an agrarian lifestyle until recently. It’s reasonable to conclude that they’re exactly the kind of peasants JRRT had in mind when he imagined the Shire.[back]

Brandy is too a Panacea

By Joe

On April 4, 2016

In mythgard academy, trivial

For anybody who’s laughing at the doctors in Bram Stoker’s Dracula who prescribe brandy for any illness: Remember that Elrond gave Gandalf a flask containing a cordial that was a sure-fire cure for hypothermia and squid attacks.

http://youtu.be/lPUAwwC_U8c&t=860

Taking the Plunge

By Joe

On March 26, 2016

In ardagraphy

The post on using a British GIS to learn things about hobbits attracted so much positive attention (42 inbound links!) that I’ve decided to turn it into a serious paper. I’m stunned – given the obscure topic, my expectations for the whole blog were more like “42 page views”.

One drawback is that I don’t yet know what the paper will be about. But Idiosophers are nothing if not data-driven, so I shall start collecting correlations, and we shall go where the numbers take us.

Things I’ll keep my eye on, in case one turns into the topic:

From the definition of “subcreation” [1], Middle-Earth is dependent on the real Earth. Therefore, studies of the created world can cast light on the subcreated world.
A teenager picking up LotR today bears the same chronological relationship to it that I bore to Sherlock Holmes. In 15 years, it’ll be like Alice’s Adventures in Wonderland. Some things that were obvious to JRRT’s intended readership are going to need footnotes, before long.
Did hobbit names convey meaning? Some of them are obvious short-jokes, and others are bragging about living in holes. What are the rest? Names are definitely important to JRRT. Can we tease out the implications this way?

To-do list:

Figure out how to assess the importance of a character to the story.
Separate the good guys from the bad guys. Or, rather, come up with a sensible categorization.
Define a relationship between the Shire and Britain.
Pick out from the data particular stories to tell.

Once that is done, we can identify the topic. Statistical methods will not be required, since I’m going to use every hobbit I can find. As statisticians say, “n=all”.

[1] Ordinarily I would include a link here, but none is available. Sub-sacroiliac pain from copyright law is Tolkien’s wyrd, even beyond the grave. [back]

Renfield ate beetles, right?

By Joe

On March 24, 2016

In mythgard academy, squibs & crackers

Bless that good, good woman who hung the crucifix round my neck! for it is a comfort and a strength to me whenever I touch it. It is odd that a thing which I have been taught to regard with disfavour and as idolatrous should in a time of loneliness and trouble be of help.

Bram Stoker, Dracula, ch. 3

To which I compare,

When I find myself in times of trouble,
Mother Mary comes to me, …

Paul McCartney, “Let It Be”

I’m going to assume that this is just a coincidence. I will keep it in mind, though, when I listen to experts in natural-language processing tout their skills at making connections between texts.

Relative Importance of Hobbit Families

By Joe

On March 20, 2016

In ardagraphy, scholarship

Since it got such a positive response, I’m trying to turn the GIS distribution of names in Britain into a piece of real scholarship. The first step is collecting and classifying Hobbit names.

Shortly after I started doing that, I was forcibly reminded that some characters just aren’t as important as others. Names that get mentioned a single time won’t be as carefully managed as those of more-important characters (even by JRRT), so they should carry less weight. I’ll need some kind of quantitative measure for the concept of “importance”. Searching about the Web for an hour produced nothing. I see plenty of syllabuses from digital-humanities courses that ought to use such a thing, but no explicit references. Perhaps it’s too trivial for them to mention. That’s an opportunity: What could be more appropriate for this blog than something too trivial for professors? Onward!

Principles for quantitative importance of a character:

A character must have a positive number of mentions in the story. In most books, this would be a trivial requirement, but not in LotR. There are lots of hobbits who are mentioned only in family trees in the Appendices. I don’t know enough about them to say anything, so they get dropped.
The difference between being mentioned on one page and being mentioned on ten is a big deal. The difference between being mentioned on 10 pages and 11 is not so big. The difference between 10 pages of mentions and 100 is a big deal, comparable to that between 1 and 10.

These two principles are just the definition of a multiplicative scale, like we use for sound. It would be funny to express importance of characters in units of dB_frodo, but a proper solemnity dictates that we use a more information-theoretic definition: the importance of a character will be the log₂ of the number of pages on which that character is mentioned. The page mentions are from the index of the 2002 single-volume edition of LotR from Houghton-Mifflin-Harcourt.

Hobbit families by importance: histogram

Fig. 1:Distribution of importance of hobbit families

For hobbit families in The Lord of the Rings, the distribution of importance looks like Figure 1. There are 28 family names mentioned in the story. Four are mentioned much more frequently than the others, which is reassuring.

There is a group of families that are mentioned only once. A larger group is mentioned thrice. This is due to the repetition for comic effect of the list of Bilbo’s relatives at the Long-Expected Party. Then there is a smaller group of hobbits who appear on dozens of pages. These can be good guys or bad guys. [1]

Fig. 2 Family names ranked by mentions

On the far right are Baggins, Gamgee, Took, and Brandybuck, as expected. Figure 2 is an attempt to reconcile my desire for a density graph like Figure 1 with the fact that logarithms don’t really mesh well with histograms. The left-right position is the number of pages, the vertical position of the name is that family’s position in the bin in Figure 1.

I think this measure of importance will work. It emphasizes the right things: Farmer Cotton is “the chief person around here”, and his family duly shows up near the top. It de-emphasizes the right things: Merry gets mentioned about 40% less than Pippin, but that washes out if importance is quoted with no fractional part. Hobbits who barely exist at all, such as a few families in Bree whose only significance is that there are similar names in the Shire, have zero importance.

[1] Sauron is mentioned on 273 pages, which makes him two notches worse than the Sackville-Bagginses.[back]

Dark Side of the Rainbow for Inklings Nerds

By Joe

On March 4, 2016

In mythgard academy

Just listened to Sørina’s lecture on little loosed dragons, and then played “Synchronicity” by the Police. The result was a fascinating experience in parallels.

Scientifically-dubious, early-twentieth-century Weltanschauung? Check.
A #1 hit single about co-inherence? Check.
Auto-intertextuality? Check.
A baffling hypotext? Check.
Dangerous giant reptiles? Check.

And, in a tour de force of seizing control of meaning from the author, I have always thought Miss Gradenko worked at the N.I.C.E., and C.S. Lewis left her out of That Hideous Strength because he didn’t have the chops to cover the electric guitar part properly.

P.S. For what it’s worth, I think Genette’s definition of “intertextuality” is useless. If I were going to define a sub-class of literature, I’d try to think of something that excluded at least one book. When anything that uses words is intertextual, why not just say “literary”?

P.P.S. The part where Prof. Higgins says the text isn’t really layered, but is actually woven of lots of threads — <dadjoke> you mean it’s a textile? </dadjoke>