A physicist loose among the liberal arts

Month: July 2017

Saruman 15-love

Gandalf probably has the most dedicated fan club of any character in LotR. But to an idiosopher, he has one moment of complete catastrophe. This is from Gandalf’s report to the Council of Elrond about his confrontation with Saruman:

“White!” he sneered. “It serves as a beginning. White cloth may be dyed. The white page can be overwritten; and the white light can be broken.”
“In which case it is no longer white,” said I. “And he that breaks a thing to find out what it is has left the path of wisdom.”

LotR, II, ii.

I’ve talked about this passage before, working from the possibility that Saruman was playing a clever joke. Lots of people, many of whom know more than I do, take that last sentence as a statement of JRR Tolkien’s own beliefs. Malcolm Guite‘s Signum Sessions lecture is an excellent example:

But there’s a problem with that: I agree with Saruman.  First, dyeing white cloth.  JRRT frequently mentions colors, and uses them as important signifiers in his texts.  Hobbits like to dress “in bright colours, being notably fond of yellow and green” (LotR, Prologue).  Bombadil’s jacket is bright blue (I, viii). Gandalf wears blue and grey. The dwarves in The Hobbit are even distinguished by the color of their hoods (I, i). Surely if wearing cloth of other colors than white were morally dubious, it would have been mentioned. If Gandalf is going to disagree with this, he’s going to have a lot of explaining to do.  JRRT provides no explanation.

Second, the white page can be overwritten. If it weren’t, a philologist would have nothing to do.  A twentieth-century author would not publish any books.  Writing on white pages can’t be a bad thing to Tolkien.  Something is going seriously wrong with the wise-Gandalf interpretation.

Third, breaking things to find out what they are is an essential part of learning.  In the specific case in the text, a group of photons that would have been annihilated in the electric field of earthly matter in a few nanoseconds was divided up to show its component colors and confirm the wave theory of light.  Lots of learning for no loss.  Here’s a sampling of other ways that life would be lessened, had we stayed on this so-called “path of wisdom”:

  • No one would ever have eaten an oyster or a walnut;
  • Musical harmonies might never have been discovered;
  • Doctors wouldn’t know about the circulation of the blood;
  • The beauty of the crystals that form inside geodes would never be seen.


(The dwarves of the Glittering Caves will back me up on the importance of that last one.)  None of these things is bad.  Gandalf is just wrong.

What’s going on, here?  It’s the power of the Voice of Saruman.  Even through the filter of Gandalf’s re-telling, the effect is still there.  Gandalf sounds like a fool.  Saruman’s voice has tricked him into a ridiculous position. JRRT has shown the effect, not just told us about it, by having it affect the reader as well.  As Théoden found out, “When others spoke they seemed harsh and uncouth by contrast…” (III,x.)

No worries, Grey Wanderer — it can happen to anyone.

Signed Graphs and Interesting Stories

Of all the types of graphs, signed graphs are probably the most interesting for looking at interactions among groups of people. Definition: a signed graph is a collection of nodes and links between them, just like a regular graph, but each link is flagged with a positive or negative sign. When we’re using the graph to describe a social network, those might be “loves” and “hates”, “admires” and “sneers at”, or any other dichotomy that comes to mind.

Some graphs have closed paths in them. Mathematicians call a closed path a “cycle”. If you go around a cycle and encounter an even number of negative signs, it’s a balanced cycle. A graph that contains only balanced cycles is a balanced graph. These are the simplest cycles:
three-node signed graphsHere’s where things get interesting: signed graphs apparently figure into human sociology. If a network of relationships forms a balanced graph, it’s a stable structure. Relationships that fall into unbalanced graphs aren’t stable, and lead to drama. (That last word can be taken either literally, or in the euphemistic sense that people give it these days.) I don’t think anybody knows why such a simple mathematical condition seems to be true; that’s just the kind of thing mathematics does every now and then. Some brilliant psychologist will figure it out someday.

In the unbalanced graph “a”, I colored the vertices pink and blue because my wife watches soap operas, and nearly as I can tell, there’s a cycle like that at the heart of every one of them. It never ends well, because it’s unbalanced. The balanced graph “b”, by contrast, is “you and me against the world”, which is a stable configuration. The all-negative graph “c” can go one of two ways. If the vertices represent people, two of them just go away and the network disintegrates. If the vertices represent countries, or something else that’s forced into interaction because it can’t quit the game, the network changes when two of the nodes look for an advantage by conspiring against the third. The fourth possibility, “d”, is that all the links are positive. It is balanced and kind of boring in its dramatic implications.

There’s a perfect example of three-party instability in Book IV of LotR among Frodo, Sam, and Gollum.  From the time they meet up, it’s graph “a”: Sam loves Frodo, Sméagol loves Frodo, Sam doesn’t like Sméagol.  Type “a” is unstable, so something’s got to give. The crisis comes in  Chapter 8, when Sméagol (possibly) tries to turn the graph into a stable all-positive triangle, but Sam intrudes, the opportunity is lost, and Gollum plots with Shelob to turn the graph into type “b”.

Of course, three-person networks are easy to understand without graph theory. The real advantage of mathematics is that it becomes possible to handle any size network. There’s a theorem about graph balance that applies in general: Any balanced graph can be re-drawn in a simple form. (Can I say “isomorphic”? Sure I can. Y’all are tough enough.) All balanced graphs are isomorphic to a graph that’s split into two parts, where there are only positive links within each part, and all the links between the parts are negative.  That’s called the Cartwright-Harary Theorem. Prof. Harary says that the theorem is unexpected and counter-intuitive, which I am half in agreement. The positive interpretation is easy to accept:  if the world consists of two parties, and every member of a party agrees with each other, and every member of each party disagrees with all members of the other party, the situation is stable.  (Then Romeo meets Juliet, and the stability is history.)  The counter-intuitive part is that this is the only way for a graph to be stable.  That’s it – the one way you can build a stable social system is for everybody on your side to agree and to hate the other side, and contrariwise on the other side.  In practice, I suppose you could allow disagreement on issues that were irrelevant to the structure, and thereby outside the graph model. But on any important issue, perfect party unity and perfect hatred of the other side is your only chance.

Interesting stories, whether they’re fictional or meta-fictional, don’t have balanced graphs.  One of the most intriguing things I scribbled down during Sørina’s lecture was that we might be able to define a new subset of graphs under the rubric of “interestingly-unbalanced”.

Illiterate Coda

Maintaining stable structures without fomenting partisan warfare is critically important in a society as complex as ours.  But math is math. So how do we handle the dilemma of the Cartwright-Harary Theorem?  We go around the horns. Almost every organization chart you’ll ever see has the same basic structure:  No cycles, so the theorem doesn’t apply.  That type of graph is called a tree.  It’s useful in all sorts of contexts, but until now it had never occurred to me that it means that management never has to choose between polarization and instability.

Graphing the Inklings

Sørina Higgins’s lecture at Mythmoot IV gave us a hint about where she’s going intellectually in the near future. She wants to apply network theory to create “meta-fictional narratives” about the interactions among the Inklings and how it affected their writing, and invited us to do the same.

The coolest figure from “Graph Theory as a Mathematical Model in Social Science”

This seemed like a good time to blow the dust off my command of graph theory. You can figure out lots of cool things from networks, if you know about graphs.   Frank Harary, writing from a period contemporary with The Lord of the Rings until well into this century, pushed the use of mathematical graph theory into the social sciences.  Here’s a short version.  Here’s what I think is his clearest explication of what can be done with graphs in the social sciences (which is what we are doing, now).

For instance, graphs are used a lot in management theory.  The fastest performing network structures were those in which the distance of all nodes from some central person (the “integrator”) was the shortest, say Borgatti, Stephen P., et al. “Network analysis in the social sciences.” science323.5916 (2009): 892-895. Now, if you’re looking for a paradigm of a stable, efficiently operating organization, the Inklings are not an obvious place to start.  I’m pretty sure that C.S. Lewis would turn out to be the integrator, but then what?  Here’s a chart from Borgatti et al. that might clarify the relevance:

Following Sørina’s Ansatz, we might begin with the box on the left to determine our set of writers (nodes). Next, we’d assign a numerical quantity to each node, probably derived from a lexomic analysis.  Then, we’d build links from the two boxes on the right, Interactions and Flows, based on accounts of how the writers interacted, to see how some attribute of the nodes changes over time.

The easiest thing to see would be something like the spread of Theosophy or Anthroposophy. Weird philosophies come with an idiosyncratic jargon that should be trivial to find in the writers’ texts. The mathematical tools we’d need to identify the influence of some *osophy have already been developed to model the spread of infectious disease.

Slightly more difficult would be to track down an agreement between the writers to split things up.  There was the famous wager between Tolkien and C.S. Lewis about writing a time-travel and a space-travel story, respectively.  We’d look for some lexemes they shared equally, which then split up mitotically into space on Lewis’s side and time on Tolkien’s. But a difficulty presents itself. It might be possible to find lexemes in Tolkien that correlate well with space travel, but I can’t think of them.  We’d have to find them via statistical correlations, which tend to make the final result less credible.  A better choice might be King Arthur.  In an old lecture on Youtube, Sørina mentions that Tolkien may have given up work on Arthurian legends because Charles Williams was doing so much in that area. It should be easy to find convincing Arthurian terms whose frequency evolves over time.

Caveat:  Sørina drops a hint that she’s dealing with a large network, which the Inklings are not.  We’ll have to wait and see.


Trying to love Modernism

Sørina Higgins’s plenary talk at Mythmoot IV, and the reaction it got from the high-octane scholars in the room, convinced me I should try to engage idiosophically with Modernism instead of treating all the Inklings’ works separately from it. But here’s the first hurdle: Modernism doesn’t appeal to me. What do I gain by putting my favorite book in a set with a lot of books I don’t like? How do I get over my distaste for most early-Twentieth-Century literature?

Maybe by skipping media. If I zoom ‘way out, I can find another modernist work I love. It’s a musical composition, not a book. “The Planets” by Gustav Holst might be the only “popular” piece in all of Modernist music. It’s older than all but the earliest things JRRT put on paper.

“The Planets” is a suite of seven movements, one for each planet except Earth. Holst doesn’t give the planets their Greco-Roman mythological significance; the subtitles are Theosophical instead. Though I don’t have any written evidence about JRRT ‘s opinion of Theosophy [1], I feel confident that it rose no higher than slight regard. Therefore, I’m not going to look for any congruence in the meanings of the pieces. I’d rather look at environmental effects. The parallels will more likely appear in the emotional responses the artists invoke, not their content.

“Mars, the Bringer of War” was written before World War I, so its depiction of the horrors of mechanized slaughter isn’t a mirror so much as a prophecy. This is an instantly-recognizable piece all over the world. David Bratman talks about it being echoed by Grond, the Hammer of the Underworld™, and also tosses in an allusion to the early drafts of the Quenta Silmarillion in which the dragons are described as mechanical, like tanks. To which I’d add the blaring trumpets that we hear when the Black Gate opens:

They came within cry of the Morannon, and unfurled the banner, and blew upon their trumpets; and the heralds stood out and sent their voices up over the battlement of Mordor. … even as the Captains were about to turn away, the silence was broken suddenly. There came a long rolling of great drums like thunder in the mountains, and then a braying of horns that shook the very stones and stunned men’s ears. And thereupon the door of the Black Gate was thrown open with a great clang, and out of it there came an embassy from the Dark Tower.

LotR V, x

“Venus, the Bringer of Peace” matches up well with the tone of JRRT’s prose that I hear in elvish lands, once I get past the things that my baroque ears still hear as weird dissonances. Here in Legolas’s speech about mallorn trees in LotR II,vi, the constantly-shifting rhythms match this piece well: “Not till the spring comes and the new green opens do they fall, and then the boughs are laden with yellow flowers, and the floor of the wood is golden, and golden is the roof, and its pillars are of silver, for the bark of the trees is smooth and grey.” Actually, now that I think of it, elvish music probably has all kinds of weird dissonances in it, by Western standards. After a thousand years or so, a single mode of composition might sound dull to even the most conservative audiences.

“Mercury, the Messenger” doesn’t have a good match in LotR. Its anti-gravity and velocity have a lot in common with Bilbo’s poem “Errantry”, but that mood is rare in the book proper.

“Jupiter, the Bringer of Jollity”, is the most fun, and it has hobbitry all over it. Bratman (op cit.) points out that Holst makes good use of English folk tunes in several of his compositions. [2] The Prancing Pony must have sounded like this in the years after the return of the King.

“Saturn, the Bringer of Old Age” was supposedly Holst’s favorite movement of the seven. That opinion points toward the reason I generally don’t like Modernism — slow, ponderous works of art are far less interesting to me than the liveliness of Jupiter or even the heavy-metal brutality of Mars. I was taught in English class that the morbid obsessions of the Modernists were a consequence of WWI, but this piece is evidence that they were already intensely focused on mortality before the war. It makes me wonder if we have the causality relationship backwards. I hear the passage through the Dead Marshes in this one.

“Uranus, the Magician” brings us into the full-scale theosophical rewriting of myth. “Magician” is quite a demotion from Uranus’s old job! This is a fun piece to listen to. I don’t quite get the processional feel to the music — what does that have to do with magicians? Perhaps Holst didn’t want me to be able to decide whether he meant a stage magician or Aleister Crowley. In any case, this works. Saruman might have told the musicians to play a piece like this as his army marched out of Isengard to make war on Rohan. He was probably conducting the band himself, using a wand as a baton.

“Neptune, the Mystic” is another Theosophical demotion. Amazing how a bunch of mystics set out to discover the nature of planetary intelligences, and one of the seven just happened to be a mystic. [3] It was almost half a century ago, but I remember the liner notes from my father’s recording saying this was “the pure, disembodied essence of sound.” Why that’s a good thing, the liner-noter didn’t say. They couldn’t have gotten further from my understanding of music if they’d tried. I suspect JRRT might have shared my opinion. His poetry begins with rhythm, and this piece has almost none. So even though it’s not so complimentary to the two artists, there’s a parallel here, too. Confession time: “Ainulindalë” bores me to the edge of coma. That’s not how the universe began; the universe began with a C-Major chord. (Some people say E-flat, but that sort is notoriously unreliable.) Tolkien and Holst made the same conceptual mistake (as I so humbly see it): because matter as we know it didn’t exist in their context, they went for slow, rhythmless modulations to represent something that’s as placid and introspective as the interior of a blast furnace. This is worse than wrong. It is French.


The parallels between Holst and Tolkien are there, and easy to see. Tolkien is a Modernist; Sørina isn’t crazy. [4] They have similar (6/7 cases) things in mind that they want their audiences to think about. Time to admit it; my favorite author is right smack in the middle of a bunch of artists I don’t like very much. Perhaps we should define a kind of “pop-modernism”, to go with all the other hyphenations of modernism that critics have created, to encompass those participants in the first half of the twentieth century who don’t owe future generations an apology.

[1] Theosophists have plenty of things to say about JRRT. I do not recommend searching “tolkien theosophy” until they make a search engine that filters out pages predominantly composed of deceased intestinal flora.

[2] Holst even wrote a suite of music for Morris dances. (!) They’re kind of tame. I don’t think they would protect against Elf invasions.

[3] Maybe they were using a reflecting telescope and installed the mirror backwards.

[4] Well, not in this case anyway. Trying to teach Idiosophers to dance weighs rather heavily against this conclusion.

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