Saalon Muyo

This is the second article in a series inspired by Paul Lockhart’s essay “A Mathematician’s Lament.” It is a meditation on Art, Mathematics and Education. The first part, “Why Them Kids Don’t Learn Nothing,” is primarily about education. This second part talks about art as a process of discovery, and the third part, “How I Learned to Stop Caring and Love the Verse” is a story of my first experiences with poetry.

One of the things that always fascinated me about J.R.R. Tolkien’s work on Lord of the Rings was his attitude that he was not the creator of his stories, but the discoverer of them. He often attributed inaccuracies and inconsistencies in his works to this fact. The story was not inconsistent, he had just misunderstood what he was unearthing. This isn’t an uncommon view amongst artists. “The greatest artist has no single concept which a rough marble block does not contain already in its core,” Michelangelo wrote above sculpture, and J. Michael Straczynski has compared his writing to unearthing artifacts.

The idea that the artist’s work is more about discovering and communicating patterns and ideas already out there, somewhere, in the ether is one I share. Writing, to me, has always involved two major steps. The first is abstract, a sort of reaching out blindly and feeling out the overall shape of the story. When I describe this part I talk a lot about themes and scope and pace, but it’s really not that technical. By the end, the most I have is closer to a probability cloud than an outline. I can see the shape, and I can sense the feeling it gives me, but that’s about it. From there, it feels a lot like passing questions and ideas through the cloud and seeing how they fit. If they fit. If I’ve “created” anything at all, it was the initial cloud. After that, the only things I can take credit for are discovering the correct pieces. The things I create whole-cloth from that point are the ideas that are dead wrong and have no place in the story.

Trust me, I get that this is a hokey, dippy way of discussing the creative process, and it likely sounds as if I’m wearing a tin hat, waiting for the otherworldly transmissions to get through. That’s not what I mean, and this is exactly why talking about a creative process - any creative process - is either superficial and incorrect, or slightly less incorrect but sounds batshit insane.

I do believe that there’s an important, powerful process of discovery present in any artistic creation. It’s about finding something that vibrates at that perfect frequency. The one that, when someone else reads or views what you’ve made, comes across as more true than truth. Doing that is, I think, more alchemical than just making things up and slapping them down on the page.

But if art is just discovery, why are some people successful at it and others not? Are they just worse archaeologists? No, because it’s not just discovery. It’s only part of the process. The other part is communicating that idea. That’s where things get ugly.

The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant.

- Paul Lockhart, “A Mathematician’s Lament”

Before Paul Lockhart starts talking about how poorly we teach mathematics, he talks passionately about what mathematics is. It’s not, he states, about adding numbers together. It’s about finding patterns, the communicating them. As he says, the art of mathematics is not the fact itself, but how that fact is expressed. Two equations can express the same fact, but one can be superior by expressing it more beautifully.

The first thing I wrote about after taking in “Lockhart’s Lament” was a bunch of stuff about education, but it wasn’t the first thing that grabbed me while reading. What hit me like one of those Japanese war clubs you see Oni carrying in woodblock carvings was how similar Lockhart’s description of mathematics was to my own creative process. Is mathematics a purer art than the others? Maybe. For the moment, I don’t care. Better, purer, whatever - I finally got why people became mathematicians. The art of mathematics holds the same lure as the art of writing or painting: The siren call of bringing into the world a unique and beautiful argument about the very nature of the world.

This is a major theme in mathematics: things are what you want them to be. You have endless choices; there is no reality to get in your way.

- Paul Lockhart, “A Mathematician’s Lament”

When I look with skepticism upon stories whose primary objective is realism, I do so partly because I can’t understand why someone would part with the freedom the form has given them. Much as Lockhart decries the boiling of mathematics education down to a series of complicated but rote “proofs” of obvious things (like the angles of symmetrically crossed lines being equal), I chafe at the notion of writing’s primary function to be journalistic. While the chronicling of actual things is a noble pursuit, in writing - like mathematics - you have endless choices. As Lockhart points out about math classes: there are cases where 1 + 1 != 2.

And yet, even with complete freedom, there are rules. The trick with art, any art, is twofold. You must be boldly creative while conforming to the physics of your chosen playground. The real beauty of creating something is the duality of the process. Your imagination must run wild while your express the fruits of your imagination in a way that rings true. At its core, mathematics plays by sets of rules that cannot be ignored. Writing is the same way. So is painting. But those physics, those rules, change depending on where your imagination takes you. “Everything is relative and relational,” is how Lockhart puts it. Indeed.

Look at Michelangelo. Within his art, the art of creating images, his choices were limitless. All that mattered was the intended effect it would have on its audience. The hard work begins once he took his first step. Deciding to communicate through sculpture put certain boundaries, certain rules on how he could work. Everything is possible in art, perhaps, but stone carries certain, immutable properties. So does fresco, but those properties are almost entirely different than those of stone. Everything is relative and relational.

Doing mathematics should always mean discovering patterns and crafting beautiful and meaningful explanations.

-Paul Lockhart, “A Mathematician’s Lament”

I wish I could have described my own art form as beautifully as Lockhart describes his. The best I can do is take his statement and change “doing mathematics” to “writing.” The patterns we find as writers are different than those found by mathematicians, but no less important. They serve a different purpose to their audiences, but are no less in need of people to craft beautiful and meaningful explanations for them.

Until reading Lockhart’s essay, I never truly understood mathematics. It seemed to me a powerful and important scientific tool. I was wrong. Mathematics is no mere tool to express scientific fact just as writing is not simply a means of transmitting factual information. These are applications of wide and versatile art forms. That a writer can use his craft to record history as easily as he tells a faerie tale is a testament to its power. For the first time, I understand that math’s role in physics and chemistry is no different. We’re both finding our own patterns and struggling to master the means of expressing them.

Grasping a little of what makes math an art, I’m looking back to my own playground and understanding it a little better. As Lockhart and Tolkien and Michelangelo and Straczynski have explained in their own words, art is exploration and creation and discovery and communication all at once. If we talk about it like archaeologists unearthing artifacts, it’s not only because we’re crazy. It’s because we’re looking for a way to make you believe triangles can fly.

This is the first article in a series inspired by Paul Lockhart’s essay “A Mathematician’s Lament.” It is a meditation on Art, Mathematics and Education. This first part is primarily about education. The second part, “If Triangles Could Fly” talks about art as a process of discovery and the third part, “How I Learned to Stop Caring and Love the Verse” is a story of my first experiences with poetry.

I’m not sure if you noticed, but there are a lot of people who think our system of education is fundamentally broken. In fact, gallons of ink and billions of pixels have been conscripted to communicate how much danger we think we’re in and solutions we will never implement. It helps that every one of these thinkers and nearly everyone in the audience went through some version of the same story, giving us all common ground on which to debate. If nothing else proves the theory that we have educational problems, that everyone can read an article damning our system and nod their heads for most of it should do the trick. Unfortunately, a lot of those people nodding will suggest or support solutions that only escalate the problem. So it goes.

I’m one of the many who look back on my trip through school with cynicism, not just because of my own experienced, but because of what I watched the system do to my friends. I was lucky, too. I attended a well funded, middle-class public school. We didn’t have serious problems with violence to deal with, and we had enough money in the budget to keep our textbooks less than 10 years behind the times. I was able to join a marching band that provided school-owned instruments to the students going without, and the students in art class had, you know, art supplies. I could have had it a lot worse, yet most of the problems endemic in my school system were the same as those both above and below my school’s means. The blow was softened by economic factors, but we still got bludgeoned a bit.

Paul Lockhart’s excellent essay “Lockhart’s Lament” goes into (25 page) detail on the problem of our mathematics education in our school system, and he gets everything right except his assertion that our mathematics curriculum is more onerous than the rest. I understand why he thinks this; I would have said the same about my own art of choice while saying that at least in math, there’s occasionally a verifiable right or wrong answer to keep mean spirited teachers at bay. As Lockhart notes, though, the facade of absolute correctness in mathematics makes it that much easier to teach incorrectly. So it seems we’re both right; our subjects of interest are taught in the wrong way. The logical conclusion can only lead to depression: we aren’t teaching much of anything correctly.

What other subject shuns its primary sources— beautiful works of art by some of the most creative minds in history— in favor of third-rate textbook bastardizations?

-Paul Lockhart, “A Mathematician’s Lament”

The answer is: all of them. Much as I thought that forcing the Pythagorean Theorum on kids at least taught a true thing, Lockhart believes forcing every high school student to progress through the same three Shakespeare plays (Romeo and Juliet, Julius Caesar, and Hamlet) at least does not shun some of the most important literature written. He’s correct in a way, but much as requiring the memorization of the Pythagorean Theorum is inferior to allowing children to explore why triangles work the way they do, memorizing facts about a work they must agree is good before they’ve read it is inferior to allowing children to discover what makes art great - and to define greatness on their own terms.

The same can be said for every discipline we teach, save for, perhaps, graphic arts and music. These subjects are not on a standardized test and have not been reduced to a series of educational milestones, and so the teachers of them have more latitude. The flip side is that these are the first subjects to lose their funding for precisely the same reasons. The people who went through band or chorus or art got something out of it. It’s just not available to kids in every school.

English teachers know that spelling and pronunciation are best learned in a context of reading and writing. History teachers know that names and dates are uninteresting when removed from the unfolding backstory of events. Why does mathematics education remain stuck in the nineteenth century?

-Paul Lockhart, “A Mathematician’s Lament”

I wish to God Lockhart was right. The problems in our curriculum run as deep as they can, corrupting every subject the demons of standardization can get their hands on. If teachers knew that spelling and pronunciation were learned in the context of reading and writing, multiple years would not have been spent diagramming sentences. If history teachers knew that names and dates were uninteresting when removed from their narrative context, there would have been something on my history tests beyond names and dates. If social studies teachers cared about producing civil-minded students, we would have discussed the Declaration of Independence and not memorized it. Our entire educational system is stuck in the 19th century, and shows no sign of getting out.

When the No Child Left Behind act was passed, in all its Orwellian name-reversing glory, it calcified a system that puts plain facts above context, creativity and analysis. Encoding a silly, memorized equation within a poorly written word problem actually makes it more insidious than the initial trauma of memorization because it pretends to be about something other than rote fact-cramming. Beyond all arguments about how best to make students interested in subjects, and how to build context for them, fact-cramming simply does not work. Years ago on Saturday Night live, Father Guido Sarducci advertised his Five Minute University that would teach only the things you’re going to remember: Supply and Demand, “¿Como está usted?” and “Where is God?”. That’s it. And that’s about all people remember from a curriculum composed of fact-cramming.

No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a “mixed number,” while 5/2 is an “improper fraction.” They’re equal for crying out loud. They are the same exact numbers, and have the same exact properties. Who uses such words outside of fourth grade?

-Paul Lockhart, “A Mathematician’s Lament”

I’m reminded of my middle-school English classes, where we were tested on the definition of words like “gerund”, “participle” and “transitive verb” on a weekly basis. Outside of school - hell, outside of middle-school - no one proofreads a friend or colleague’s work and writes about their use of a dangling participle. They comment on words and punctuation that decrease its readability. That’s how we approach writing: how well does it express what it means to say? No one diagrams a sentence during proofreading, and the time spent diagramming sentences in fifth grade does not produce more readable work. The word “gerund” will likely never pass the lips of 90% of the people out of school.

Much as Lockhart is disturbed by the redundant nomenclature in math curriculum, I look back at my time in English classes and shudder at how they nearly destroyed the curiosity and love I had for language. 2 1/2 and 5/2 are equal in the same way “John watched as his soup boiled over.” and “John watched the pot as soup boiled over the edge.” mean the same thing. That one uses a transitive and one uses an intransitive verb is unimportant. The differences lie in clarity and impact, just as they do when you choose to write a fraction as 2 1/2 or 5/2. Learning names for the differences before discussing how they read is counterintuitive.

High School Geometry: Instrument of the Devil

-Paul Lockhart, “A Mathematician’s Lament”

Why is our education system failing? Every subject in our curriculum reaches some point analogous to High School Geometry. Literature has Composition, Social Studies gives us Civics and Science teaches us Physics. Each of these classes take a core idea in its discipline and strip away everything save for rules without context that must be memorized and applied across the same sequence of homework problems, over and over again.

Composition is the damned art of putting words on paper, yet the class does little save forcing students to work through predefined style templates on a limited list of topics. Physics is the study of how the universe functions, but is taught the same way as Lockhart describes Geometry: lots of symbology, little crashing objects into one another. And as for Civics, a class which purports to cover the implications of the American Experiment, it can’t bother to do more than require its students memorize the names of our court systems. My civics class could be passed using nothing other than the Awesome Notebook passed down from classes past. Yours could as well, I’d wager.

I wish Lockhart was right. I wish that only mathematics was so corrupted as to teach its students effectively nothing. He’s not, and it’s not. Our system of education is built on principles so faulty that it should have collapsed years ago. We condemn buildings this unsafe and then we implode the things so that they won’t accidentally crush their occupants. Until we do the same to our schools, students will continue to emerge with their curiosity and creativity left as little more than splatters on the Chemistry Lab floor.

I have fairly specific sensibilities when it comes to fantasy and science fiction films.  It leaves me a crankier and far more picky critic of them than I would  be otherwise.  It’s not that I demand great storytelling out of every genre entry,  just that I expect a lot for the trade if you’re not going to bother.  Also I hate pretension, and the ghettoized genres of science fiction and fantasy ironically produce more self-important nonsense than those nauseating Oscar Films that come out on Christmas Day.

After hearing tons of praise about Night Watch, the blockbuster Russian urban fantasy film, I finally got it from Netflix and popped it into the DVD.  My friends love it.  A lot of critics I respect love it too.  Knowing that, please imagine my surprise at kind of hating the thing.

Look, there are a lot of good things about the movie.  I mean, it is a high budget urban fantasy film, and the simple fact that someone made a film in that genre and got money for it deserves respect.  I love urban fantasy.  It’s manna from heaven to me.  Yet every time someone tries their hand at the genre, they make something like Underworld and cause me to weep.  Night Watch, to start with, is not filmed entirely in blue monocrhome, so it’s already better than Underworld.  So bully for it there.

That’s not all, either.  There are a lot of strong aspects to the production, from set design to cinematography to the feel of the world.  This is not a piece of crap in the way many  movies are pieces of crap.  It is, though, exemplary of the kind of failures you find in most fantasy storytelling.

Night Watch manages to be both too big and too small at once.  It opens with one of those bombastic infodump prologues where we learn, basically, that there is good, there is evil, they are at war and that the war is at a stalemate until some bullshit prophecy comes true.  We’ve seen this plot hundreds of times; if you’re going to use it, at least trust us get it without your ten minute explanation. Anyway.

There’s this thing that happens in fantasy stories that’s hard to describe.  The plot revolves around the end of the world, which is a premise that carries with it some sort of scope.  This isn’t about stopping bank robbers.  It’s about saving the lives of billions of people and stopping the forces of pure evil.  That’s big.  Or, it should be big.  Night Watch is trying to tell a story with serious scope, but it fails miserably at it in a way that is not at all uncommon.

Scope consists of two parts.  One is the setup.  Your story needs to exist on a stage large enough to give the impression of Big Things Happening, even when they’re not happening on screen.  The other is the story itself.  This is where things get tricky, and it’s easier to understand what doesn’t work than what does.  When you get down to it, the story needs to travel.  It needs to move.

Night Watch is a classic example of what doesn’t work.  Sure, the story is about the battle between good and evil and the coming of a super-being who will unbalance the world, winning the war for the side he chooses.  That’s a big stage.  But from there, everything is both straightforward and small in scale.  The story takes place over what feels like 2 days and visits maybe a half dozen sets.  We open with our hero trying to save a boy from vampires, and we end with pretty much the same thing.  The first battle takes place in a run down apartment and the final one takes place on the roof of a different apartment with little in between.  That’s it.  That’s as far as we go.  That’s as far as we travel.

Night Watch plays like a two hour prequel to the second film.   We meet our hero, and we follow him as he does next to nothing other than fight the same vampire twice and protect a single boy in a single apartment.  The danger never escalates and the stakes never change.  What we know at the outset is almost exactly what we know ten minutes from the end.

It’s like being told, at the start of a movie, that China and Russia are in conspiracy to destroy the Western world.  We see armies gathering, helicopters firing up and nuclear missile silos opening.  Then we cut to a dock in downtown Manhattan and are told that if the hero can’t get a briefcase to the U.N. building uptown in an hour, war will break out.  We’re also shown a single Chinese villain with his Russian villain girlfriend who intend to stop the briefcase from arriving.  The rest of the film has two car chases and a fight in the garage underneath the U.N. before the hero brings the briefcase into the General Assembly and the world is saved.

Wait a second, what happened to the armies?   What happened to world destruction?  This was a battle for the lives of billions and it came down to a car chase and a fistfight?  No plot twists?  No moments of valiant heroism?  No helicopters with nuclear missiles flying into Taiwan?  What the hell happened?

That’s Night Watch.  It’s also Reign of Fire and Underworld and His Majesty’s Dragon and countless other films and novels.  Simple, straightforward stories are awesome, provided you don’t set them up by promising global carnage.   The Warriors is about nothing more than getting from point A to point B, but it doesn’t pretend to be about more than that.  And, frankly, it gets more out of its simple premise than things like Night Watch get out of the end of the world.

If you want to be a simple, vampire-hunting urban fantasy about saving a 13 year old boy, that’s fine!  Just be that thing, and be it well.  Dump the eternal battle between good and evil and let your characters do more than be vessels of exposition delivery.