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.