A physicist loose among the liberal arts

Category: ardagraphy (Page 1 of 2)

Publishing On Line

I’ve put the final version of the Ardagraphy paper on a couple of social networks.  The first is the Humanities Commons, which is brand new and looks encouraging.

The second is Academia, which gets a high page rank on Google. I’m not exactly sure of what that site is doing, though.  For example, it put the PDF I uploaded into Scribd.

Speculative Fiction: Fantasy : MidMoot 3.05

My notes from the second panel at MidMoot 3

Joe Hoffman: Fragments of a Geographical Approach to Fantasy Criticism

This paper is on line in its entirety,  by some strange chance.  Some of the symposium attendees looked disappointed when I mentioned I’d taken out the mathematical underpinning of the Tolkien section.  You guys are great!

A couple of interesting questions came up.

Q: Did I look for an alignment of Bree-hobbit names with Englishmen living overseas?  A: I don’t have an easy source for those, but it would be really cool if they were South Africans or Australians.

Q: Did you look along the coast of Cornwall, where Tolkien spent holidays as a child?  A: (Later) I found Chubbs there, but nobody else.

Prof. Flieger suggested the name “Trotter” might be interesting.


Distribution of Trotter in the UK, computed by Oliver O’Brien

That was Tolkien’s original name for “Strider”.  She suggested that it might be from the Scottish borderlands.

A: There is certainly a hotspot there, but the highest concentration is in Lincoln. Running through my associations with that city, I recall that Robin Hood’s band of Merry Men (aka rangers) dressed in Lincoln green. That is exactly the kind of thing I no longer dismiss as coincidence when I’m thinking about Tolkien’s writing.

David Gras: Harry Potter, C.S. Lewis & the Bridge between them

David describes himself as a Christian apologist. (I didn’t know that was still a job title.)

C.S. Lewis didn’t embrace paganism the way JRRT or J.K. Rowling did.  We shouldn’t resist the mythological resonances.  Lots of phoenix imagery in Harry Potter, for example.  Harry Potter and Aslan are bridges between the human world and the Forest. Making the self-sacrifice to save their worlds.

Q: Pre-christian myths have different status from a myth derived from Christianity. A: Lewis wrote a letter on that; you don’t have to abandon the things you learn from ancient myths when you convert to Christianity. We don’t have to avoid them, we should learn from them. The Phoenix was adopted as a symbol of Christ by medieval missionaries. Jesus was portrayed as a white stag; Harry’s patronus is a white stag.

Q: how do you deal with Christians who say that witchcraft is evil so christians must avoid it in books? A: It’s just brought in as a connection to mythology. The things in the book don’t have anything to do with actual Wicca. It’s there to communicate a moral about light, not inform about darkness.

Q: Nobody thinks they’re evil. Witches think they’re a force for good. A force within yourself (hereditary) isn’t what they think. A: When JKR was asked about that, she said that real Wiccans laugh at her books. The Navajo are kind of objecting to her latest work, by the way.

Michelle Markey Butler: Good People Doing Bad Things

A shared theme doesn’t require direct influence. It’s not a cage match, pitting authors against each other to see who did this better. Shared themes are handled very differently by Tolkien and Rowling.  Her examples are Boromir & Sam vs. Lupin, Dumbledore, & Harry.

Boromir accepts that Aragorn is the leader, which is a self-sacrifice. The fact that he’s a good guy is obvious to adults, but children don’t get it. Chesterton: children are innocent and love justice; adults are wicked and prefer mercy. One of the most psychologically-realized characters.  Sam is the hero, but he pushes Gollum past any chance of redemption. The most cynical observation in the book — that people frequently do real damage from just trying to help others.  Note:  It’s widely said that George R.R. Martin is a cynical reboot of Tolkien. This isn’t really true. JRRT has such a deep streak of cynicism that no such thing is needed.

Lupin taught most of the magic. But then he abandons his pregnant wife.  Dumbledore is kindness, patience, and wisdom. Until we learn about his past problems, like plotting to take over the world & rule through wizardry. How could the Dumbledore we thought we knew make those choices?  Harry makes choices that lead to the death of his godfather. He trusts his dreams too much, even when his friends urge him to wait. Harry can’t be a solitary hero. Without his friends, bad things happen.

Fragments of a Geographical Approach to Fantasy Criticism

My presentation from the Mythgard Mid-Atlantic Speculative Fiction Symposium 2016. It begins with the paper from this summer, drops the math, and investigates what happens if we try to apply the same methods to other fantasy works.

Primary Geography of Sub-created worlds


A subcreated world is derivative of the primary world, so fantastical geography is going to be derivative of primary-world geography.  This work began last winter when I stumbled across Oliver O’Brien’s public-access database that lets you type in a name and see where in the UK people are called that. Geographers have done extensive work on matching names with places all over Europe, it turns out. Like hobbits, English people move around only slowly, so names are strongly associated with places. When I was given the opportunity to map a family name in Great Britain, the second name I tried was “Baggins”. The distribution of that name is centered near Birmingham almost exactly over top of J.R.R. Tolkien’s boyhood home.

It turned out that this is not a coincidence.  Tom Hillman pointed out that the connection wasn’t dumb, and is worth pursuing. So let’s see what we can learn about fantasy novels by using real-world geography. This talk will tell you about three of them. The title has the word “fragments” because they don’t fit together into a solid piece of china.

The Lord of the Rings

Alone among the denizens of Middle Earth, hobbits have family names. They’re  conscious of their difference.  They effortlessly slide into “Peregrin son of Paladin” phrasing when they encounter Men.  As Tolkien wrote in letter 25, “[hobbit] family names remain for the most part as well known and justly respected in this island as they were in Hobbiton and Bywater.”

map of Baggins

There had always been a Baggins at Bag End. Computed by Oliver O’Brien.

I took this comment, along with another from Letter 211,  as explicit permission to look at The Lord of the Rings with real-world geography.  Hobbits are from different parts of England, according to their role in the story, and we know this is intentional because the story was stretched to fit them, if they didn’t match.


When we start looking at names, we can identify three categories of hobbits. Some people you keep close to you. They could be family, or they could be just friends.

JRRT was from the West Midlands; the close-by hobbits have names from that region. The Tooks and the Bagginses, despite their considerable differences in temperament, are quite close.

map of Took

The Tooks of Birmingham

This shows up on the map as surely as it does in the text. The Cottons are nearby, too, as is Hob Hayward, whom Sam picks out of the group of Shirrifs as being someone friendly. The readers Tolkien had in mind would have heard “Hayward” as going perfectly well with Cottons or Bagginses.


The second group of hobbits we find are neighbors who aren’t exactly bad, but they frequently seem to act in a way that interferes with others getting on with their lives. It’s good practice to keep them at arm’s length. They might be an unwisely-chosen in-law, or a cousin who borrows books and doesn’t return them. For example a Sackville-Baggins, rather distant from Birmingham to start with, can be led further from the fold by marriage to a Bracegirdle, who’s practically a foreigner in hobbitish terms.

The last category is the “liminal” hobbit-names. Hobbits in Buckland and the

Marish have them. Their family names in our world are either concentrated far from Birmingham, or they don’t appear in the UK at all,

underhill map

Underhills in the UK

like the Maggots or Brandybucks don’t. Frodo uses the name “Underhill” when he’s in Bree because Gandalf knows that someone who hears it won’t think of the bearer as living anywhere near the Shire. You can see here how well Gandalf knows his business. The Hornblowers are in this group, too. They’d “hardly ever set foot in Hobbiton before.” Although “Brandybuck” isn’t a name found in England, “Buckland” is. It’s on the extreme east outside Dover, that is, almost in France.


I mentioned that Tolkien would stretch the story, if a name didn’t fit.  Sam Gamgee is the conspicuous example. We know from Letters 72 & 144 that “Gaffer Gamgee” was a name Tolkien made up to amuse his children. It was a pun on “cotton”, like the Cotton family, and it occurred to him because there was a Dr. Gamgee at the University, but — it turns out that the name “Gamgee” doesn’t come from the West Midlands.

map of Gamgee

Serving the Bagginses may have involved commuting.

How then can Tolkien make Sam, whose presence in the story is essential, fit the pattern? The solution he found to this problem explains something I wondered about since the first time I read the Appendices.

Why is it worth half a page of Appendix F to write a lengthy discourse on the subject of how “Gamgee” isn’t really a family name, but more an epithet derived from the town of Gamwich whither their ancestors had decamped several generations back? This is why – Tolkien needed to get his hero within shouting distance of Birmingham. A London name wouldn’t do at all, but a nickname isn’t definitive.

Map of Gardner

Mayor Sam Gardner’s family

The final resolution of the story is in Appendix C. We learn that upon his accession to Mayor, Samwise changed his family name to “Gardner”.


That name has a much closer association with the West Midlands, though it’s not primarily in Birmingham. Evidently, three generations of residence plus saving the whole world from evil is almost sufficient to get one accepted into Hobbiton society.

The match of names isn’t perfect, but it works. As Tolkien says in the Prologue, “By the time of this history these names were no longer found only in their proper folklands.” Of course there will be some leakage across the boundaries for artistic purposes, and perhaps some because geographic information systems in the 1950s were less accessible.


At this point I went off looking for another novel I could subject to the same scrutiny. First consideration, I needed a world that was linguistically integrated. Most fantasy novelists don’t take the time to do that. They just pick names that sound cool. Unfortunately, this gives a geographical critic nothing to work with.

Tigana, by Guy Gavriel Kay, seemed ideal. First, most of the names sound Italian. Second, the author makes a grateful mention of the cartographer in the acknowledgements. He mentions that having clear maps guided him to fix some problems with the story. There are five maps in the TOR paperback edition, so it was reasonable to suppose that geography is important.

Tigana isn’t as famous as The Lord of the Rings, so here’s what it’s about in a few sentences. Two warlord/sorcerers are contending for the Peninsula of the Palm.

Frontispiece map from Tigana.

The Peninsula of the Palm

The Palm is divided into a small number of pseudo-feudal states. In the process of conquering the left side of the Palm, one warlord lost his son in battle. To punish the country that he was fighting at the time, he devised what may be the most absolute revenge ever conceived: The cities were razed, the populations were dispersed, and he cast a spell so that nobody can remember or even say the name of the country any more. Except, some of the people who were born there have formed a resistance movement, and when they induct another Tiganan (by birth) into their cell, they teach him or her the name. Covert action is only half of their subversion; the greater crime is memory. In the second part, a Tiganan woman has insinuated herself into the king’s seraglio to assassinate him, but ended up falling in love instead. Her love of her country gets opposed to her love of Brandin. In a nutshell, these are Kay’s two themes: love and memory.

So this is where I went looking for geographical significance in the text. What I found was several early mentions of the shape of the peninsula. Its shape is important to the characters in the first few chapters. After that, though, maps and geography are almost never mentioned. What’s going on?

Kay wants us to read this as an upside-down Italy. In case an inattentive reader didn’t notice the place names are all Italian (though the character names aren’t), he includes an epigraph from Dante. There are plenty of other inversions, once you start to look for them: Italy looks like a foot, the Palm looks like a hand. Italy points south towards a desert, the Palm points north towards a desert. Lower Corte, the new name given to the lost land of Tigana, is actually uphill from Corte. The queen of the empire to the east is named Dorotea, flipping the Byzantine Empress Theodora.

Putting the book in an inverted Italy has two purposes. First, this book is about memory. The former Tiganans, even if they don’t know that’s what they are, have a nagging feeling of uncertainty about their past. The spell isn’t perfect, so they have fleeting half-memories that leaked around its edges. I confess that’s a pretty good description for my own education in history – I never know if I’m remembering something correctly. For example, I had to hit up Wikipedia to see if there actually was a Queen Dorotea somewhere, to whom Kay was alluding. So this reader (at least) has the same sort of feeling about the past that the heroes do.

The second purpose is that, rarely among fantasy novels, Tigana fits into single volume. Using a mirror-image of our own world lets Kay focus his efforts on constructing his meticulously-crafted moral dilemmas. Kay uses this technique in many of his books. He invites us readers to use medieval Italy as a touchstone, any time we feel like we need a detail that didn’t interest the author. There’s no danger of taking us out of the story when he does this, because when we supply details from our own memory, they feel right automatically. But it’s not historical fiction, which brings us to the third book.

A Song of Ice and Fire

George R.R. Martin told January Magazine, “the only problem I have with historical fiction is that I know too much history. So I always know what’s going to happen. … With this sort of thing you can take people by surprise. It reads like historical fiction. It feels like historical fiction but you don’t know how it’s going to come out.”

It’s obvious that Martin isn’t interested in writing about anything but political history. He’s said as much, in fact. Perhaps out of respect for Tolkien’s precedent, there’s a map in the front of A Game of Thrones, but we can get an idea of its importance to the story by noticing that Chapter 2 takes place in a city that’s not on the map.

Westeros is the British Isles

Westeros, by KingofFairview, via  Brilliant Maps

When Martin does take the time to describe a landscape, in the very next sentence he’s back to politics. Here are two consecutive sentences. Catelyn is riding through the lands where she grew up. She hasn’t seen them in a long time.

North of here the Kingsroad ran along the Green Fork of the Trident, through fertile valleys and green woodlands, past thriving towns and stout holdfasts and the castles of the river lords. Catelyn knew them all: the Blackwoods and the Brackens ever enemies, whose quarrels her father was obliged to settle; Lady Whent …; Lord Frey ….

A Game of Thrones, P. 241

The first sentence jumped out at me because it’s almost a pastoral lyric, by GRRM standards. I’ve elided about 40 words of aristocratic political detail with those ellipses. It’s clear that the political actors are the important part.  Martin uses the land as a board to hold the pieces in his chess game, and that’s all. His text doesn’t encourage geographic analysis.

His fans, though, seem to have overruled him.  By now, twenty years after the first volume was published, Westeros has been invaded by amateur geographers like Adam Whitehead, professional demographers like Lyman Stone, and what appears to be a large detachment from the Stanford University Department of Geology.

The geologists support Martin fairly well. Mapping what must be happening in his world from beneath, they can find analogues to the earth’s crust. Nothing they found in the book is obviously absurd.

The geographers and demographers, on the other hand, are pretty brutal. They find only one way to make sense of the population densities, the city sizes, the number of ethnic groups, the patterns of dynasties, and so forth. They conclude that A Song of Ice and Fire has an unreliable narrator. If you assume that city populations are a factor of 10 too large, that all the distances are 5 to 10 times too broad, and that spans of time are 2 to 5 times too long, then Westeros at least is a self-consistent world. In a sense, Martin has reproduced a familiar problem – all the way back to Herodotus, sizes of armies and all the casualty figures are inflated by anyone’s-guess-how-much. Martin has actually expanded that mis-feature of ancient historiography into new areas.

At this point, I was all set to declare that my objective – using real-world geography as an approach to understand fantasy stories – must be limited to only a few, extremely thorough authors. But then I read a post by Adam Whitehead. Martin is listening to his fans, so these criticisms are feeding back into the series. In A Feast for Crows, Whitehead notes that the characters have begun mentioning that you can’t exactly trust things you hear from the maesters at the Citadel. The characters now know the lore is wrong.


I’ll conclude, therefore, by saying that Tolkien, and the writers who followed him, do to a large extent “keep their feet on their own mother-earth,” so this approach can be useful.

But subcreation is becoming a new and different thing.   World-building need not be an author’s solitary pursuit. It can be a collaborative effort, drawing on a range of knowledge that is limited only by the breadth of the author’s fan base. And not only “can be”, soon we may find that it must be. Once an author has a fan base, he may find that a world will be built whether he likes it or not. And literary criticism via the sciences is no longer a passive pursuit. In some cases, it appears to be able to affect the work it studies.


I can’t believe I just noticed this: Hobbits don’t like boats, right? The Shire is a fictional version of the West Midlands, right?

regions of England

Administrative Regions of England

Of the nine regions of England, eight are on the coast. I’d expect that from a country that’s (a) an island and (b) a maritime power. One of the regions doesn’t touch the sea. It’s only natural that, compared to the others, West Midlanders would get a reputation as incompetent mariners.

So is this the origin of the sidelong remarks in The Lord of the Rings about how incompetent hobbits are on the water? Even if it’s not, I’m perfectly happy to find another reason that the Brandybucks belong in the “liminal” category.

Next question – is this why mariners are exotic heroes from far away in LotR and The Silmarillion?

Ardagraphic Information Systems: the Paper

The second terrace in spring

My talk from the New York Tolkien Conference 2016, revised and improved by the comments of the audience, is now available for anyone to read.


First Solo Flight

It is done. Fertig. Au fait. About 10 people came to my talk, which was one of three in that time slot, so I got my fair share. The audience seemed to like it. The level of glassy-eyed stares in the audience was gratifyingly low. Maybe I’ve learned something about talking to non-scientists since I last taught intro physics.

There was a sardonic remark during the opening plenary session about scientists who stick their noses into areas where they have no expertise. (She meant Fred Hoyle.) Thanks, whoever you were, for setting the bar low for me.  Low bar = no pressure.  (Trust me, that kind of thing has physicists rolling in the aisles with laughter).

I have a bad habit. Over the years, I’ve drifted into a presentation mode of putting graphs up on the screen and improvising the interpretation based on reactions from the audience. That doesn’t work well in a context where (a) they’re expecting me to read from a carefully-written paper, and (b) they’re not waiting to pounce on the slightest error in my Ansatz.  Consequently, I said “um” a lot more than I should have. Next time, I’m just going to read the paper and see what happens.

In the question period, we had a pleasant discussion.  Almost everyone had something to contribute.  Kara Samborsky [1] pointed out that, while I’d been treating the parochialism of hobbits as a running joke through my talk, the Brexit vote seems to indicate that staying where you came from is a serious characteristic of the English. Her observation jibes awesomely well with James Cheshire’s results — the West Midlands (i.e., the trustworthy hobbits) had the highest percentage of “Leave” votes of any region in England. I thought I was giving a science/literature talk, not a current-events/literature talk!

One more “thank you” to everyone who came.  Based on their responses, I need to make some tweaks to the paper before I publish it.  The good thing about that is that I can give another presentation of the revised version.  (In conformance with Arrow’s Other Theorem.)

[1] The blog takes no responsibility for misspellings of Slavic names in the Latin alphabet.

Persistence of Family Names

If I still had any doubts about how much we can rely on the persistence of family names, Matt Yglesias just fixed them.  The article reports the results of a study of wealthy people in Florence, Italy in 1427 and 2011.  The richest people today have the same family names as the richest people in the fifteenth century.

The original paper is by Barone & Mocetti of the Bank of Italy.  More information is in a column from the Center for Economics and Policy Research.

Proving a Thesis and its Limits

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.

regions of England

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.

role vs. region.

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.

I’m in!

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

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.

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

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