Dr. King

"Our lives begin to end the day we become silent about the things that matter."

My connection to Dr. King has always been through song. As a member of MLK elementary's choir "The Jammin' Peacemakers," nearly half our repertoire consisted of songs related to Dr. King. On our visit to D.C. I ended up at the Smithsonian Museum of American History. In front of a giant American flag made out of steel, a young black man about my age emceed an event for MLK day. After hearing excerpts from the "I Have a Dream" speech given at the Lincoln Memorial I was to visit that evening, the program closed with "We Shall Overcome," the anthem of the civil rights movement. They asked everyone to join hands. In the old tradition, the emcee called out the lyrics as we sang. And it was beautiful.

Many don't remember that it was Pete Seeger, a white man now in his 90's, who revived that song, changed the lyrics from "We Will Overcome," and taught it to Dr. Martin Luther King. Pete Seeger, one year ago today, stood in the same place Dr. King stood, on the steps of the temple to the Great Emancipator, on the National Mall, to celebrate the inauguration of the first black President, the greatest black orator since King, and fellow Nobel Peace laureate.

In the afternoon, I met Fr. Ray East, a black pastor of St. Teresa of Avila church in Washington. We were at an exhibit about nuns. He told me about Sr. Antona Ebo who marched with King at Selma. We talked about church songs, about young people energized to praise God. Many don’t remember Dr. King was a preacher. I do. Many don’t remember that the songs which helped people band together to fight for Civil Rights were gospel songs. I do. God is anywhere people sing for goodness, and he was there on Sunday and there in Selma.

So while the First Amendment doesn’t technically cover free singing, I will interpret loosely. Ms. Dorothy Paige Turner, my music teacher and director of the Jammin’ Peacemakers, used to say that anyone who can talk can sing. And so I think that free speech implies free song. In either case Dr. King’s quote certainly applies, as silence means silence from speech and song. So I say when you stop singing about what matters is when you’ve begun to die. Pete hasn’t stopped singing, because he believes that if people are singing together, they can’t be fighting each other. There are still causes to sing for, and I will join in that chorus. 

Lines and Circles

Lines and circles are perhaps the most basic geometric objects. Most of classical Euclidean geometry concerns things built from lines and circles. Triangles, for example, are nothing but the union of three intersecting lines. [Though we usually erase the pieces of the lines extending to infinity, it does no harm to keep them. Any statement about these extended triangles is equivalent to one about the normal, bounded ones, since the set of vertices is the same.] In fact, the Greeks loved lines and circles so much they often considered questions of constructibility, that is, what can be done geometrically using only an unmarked straightedge and a compass. In other words, what geometry is generated by only considering objects which are somehow built from just lines and circles. These questions weren't answered until the nineteenth century, when the mathematics of fields was able to exactly characterize what is possible using these tools.

It is sometimes said that a straight line is a circle with infinite radius. This statement can be formally understood in several ways, but the notion of curvature is helpful in this department. Curvature of arbitrary curves is defined and calculated using the tools of differential calculus. For lines and circles, though, we can appeal to intuition. Imagine driving a car around a circular track, going at constant speed. If the circle is very large, you barely need to turn the steering wheel. That's because the rate at which the angle your car is pointed doesn't have to be large to keep you on the road. Now if the circle is very small, the curve feels tighter, and you must turn the wheel more to stay on the road. This suggests that the curvature should be inversely related to the radius of the circle. In fact, that is exactly the definition. For an arbitrary curve, we would use calculus methods to approximate the curve with a circle, and the curvature of the point would be the curvature of the circle. Now if you drive on a straight road, you need not turn the steering wheel. Our intuition says the curvature of a line should be zero. The "approximating circle" is obtained by taking circles that get bigger and bigger so that their curvature becomes smaller and smaller. So in that sense, a line is a "circle of infinite radius."

So far, though, I've only talked about lines and circles that live in a flat plane. In fact, lines and circles look very different when we change the space they live in. First let's use the following definition of a line: given two points, it is the curve of shortest length connecting the points. We generalize the notion of a line by calling any curve that satisfies that definition a geodesic. If you were an ant living on the surface, and your Aunt Antonia asked you what the quickest way to the neighboring ant hill, you'd tell her to walk along a geodesic. In the upper half-plane model of the hyperbolic plane, geodesics are actually circles which intersect the boundary of the plane in right angles. Taking each term in the proper context, we can really say that in a hyperbolic world, "the lines are circles."


[Note: I recently revived this blog and changed its title, threw up a few of my favorite columns from the last year, and added a review I wrote of a Rumpus Book Club selection. This post is just to explain the new title.]

The Instructions, by Adam Levin

The Instructions  is one hell of a gamble. It’s a thousand pages written in the voice of a 10-year old Israelite (not Jewish) scholar prodigy, who may or may not be the messiah. And it’s Adam Levin’s first novel. Supposedly translated from English into Hebrew into English again with perfect correspondence between the original and the double translation, The Instructions is the “scripture” written by Gurion ben-Judah Maccabee, a seventh grader at Aptakisic Junior High.

The Instructions is hyper self-aware. It narrates its own creation. It utilizes false paratextual elements such as a publisher’s disclaimer. It sometimes cross-references by page number. But these elements are not surprising in an era where drawing attention to artifice is no longer innovative in itself. That isn’t to say The Instructions doesn’t have innovative elements. For example, Levin uses e-mail replies to sneak in a bit of anti-chronological narration and creates fun text diagrams that are useful for mapping the physical spaces of the novel, such as “the Cage,” the lockdown program for behavioral disorders at Aptakisic.

More than these techniques, I was surprised by the constant and explicit effort of the narrator to manipulate interpretation. Gurion routinely addresses the “scholars” who are the supposed intended audience (sometimes, but not always in footnotes), pre-empting interpretations or responding to hypothetical rhetorical challenges. The Instructions might contain the most fully developed discourses on interpretation within a novel. The main character analyzes and re-analyzes every text that comes before him, whether it’s the Torah or a note from his ex-girlfriend or a therapist’s evaluation or a dream. The most important lesson from these discourses is that meaning is provisional. In one instance, Gurion literally reassigns the meaning of a symbol. A blank white stripe, which replaced an ichthys on a scarf, is recast from meaning nothing to meaning “if not Christ, then nothing.” Gurion turns what is intended to be a null signifier—something with no meaning—into a symbol of exactly that which it was meant to efface. On the brink of the story’s climax, Gurion takes a breather to ponder the process of reading, including the conflicting desires to reach the next plot point and catch everything in between. In another case, Gurion rebukes one of his followers from writing the signature tag of their organization in the shape of a cross by saying, “It signifies wrong.”

The Instructions draws heavily from Jewish tradition. Gurion mimics the style of Hebrew scripture, and he uses titles that make direct parallels (e.g. “Story of Stories”). However, the relationship to scripture is much deeper, as it undergirds the symbolic structure of the novel. Gurion possesses many messianic markers (his birthmarks, his scholarly ability, his geneology), and in that respect The Instructions resembles the Gospel of Matthew, which piles high fulfilled prophecies. But The Instructions pre-empts such naïve interpretation by including a discussion of messianic prophecy which concludes that any prophecy can be reinterpreted in retrospect (also providing another example of this book’s sophisticated treatment of interpretation). Readers unfamiliar with scripture may find the exegetical sections tedious, but they are essential, especially the discussion of Abraham’s sacrifice. Levin is meticulous and does not shy away from literacy. Nothing is off-limits from allusion or extended discussion, from Borges to Roth to Salinger. I thought I had caught an anachronism when Obama came up, until I realized that in the timeline of the novel, he was just elected as the junior Senator from Illinois, and the story takes place in suburban Chicago. 

Containing the most touching description of a first kiss I’ve ever read, hilarious moments when “robots” (teachers and administration) are outwitted by an impossibly intelligent Gurion, and a self-effacing “letter” from Philip Roth criticizing a writer who would pretend to be a gradeschooler, The Instructions is a whipsmart and heartbreaking novel, a challenge of length and depth that will hopefully thrive because it is a genuinely entertaining read. 

Endpoints

Open or closed? Does it still converge

at the boundary? At the brink, the edge,

are we still good? Still in business?

Inside R, a comfort zone,

a neighborhood of safety.

Absolute and uniform,

a perfectly honest sum.

For epsilon less, we’re okay.

March in tiny steps like Zeno’s arrow,

velocity’s vector tending to zero,

never arrive, and it’s fine.

But if it breach o, the arrow hits

its mark, normal to the heart.

To infinity, eternity, the series diverges.

Harmonic perhaps, but playing a dirge

on a funeral march to forever.

Or slow as Log floating downstream,

Charon’s rowboat is certainly faster.

The steady Tortoise could keep up,

but even swift-footed Achilles

would never cross this finish line.

[Title poem of a series composed on the theme "The End?", read a conference organized by the graduate school in English at Indiana University] 

Two Columns

The following is a pair of columns I wrote for the Indiana Daily Student. The first was published September 29, 2009. The second was published . In the interim, I had done exactly what the first column satirizes. The second is almost an apology, attempting to reconcile my decision to add an English major with the original column. 

STOP MAJOR PROLIFERATION

There is an alarming trend sweeping our great Hoosier Nation. It’s an arms race, a stockpiling of deadly weaponry set to wipe the entire species of college student off the face of the Earth. It’s called Major Proliferation, and it’s taking us to the brink of disaster. It all started in 1939 with a government project codenamed “The Brooklyn Project.” It was initiated to research whether it was possible to split the college student—forcing it to complete two degrees in just four years.

The theorists thought it couldn’t be done. They claimed it violated the Law of Conservation of Credit Hours. They said no student could handle the extreme pressures needed to reach the point of fission. They predicted that the daughter particles—er, students—would be unstable and decay in nanoseconds.

But if these challenges were overcome, the Double Major would be the most powerful force ever released on the job market. So the government pushed forward, hoping to give the U.S. a leg up on the rest of world.

The first test of a Double Major was successful. A 130 credit hour device, it was a Physics and Astronomy major from the previously unheard of “University 51.” It was barely beyond the intensity of conventional one major/two minor combinations which had been in use for decades. By today’s standards, a slacker. Before long, there were escalations: BS/BS Dual Degrees, Separate Division Dual Degrees, Triple Majors, Double Majors Who Graduate Early.

In 2005, scientists created the mother of all terrors: the Music/Business/Chemistry major. Just think of the aftermath of such devastation. A shell of a human, a soul nearly extinguished by the sheer volume of prerequisite coursework.

Hoosiers, we can no longer afford to live in fear of Weapons of Mass Sleep Deprivation.

That’s why today I propose  a series of diplomatic meetings called SMLT—Strategic Majors Limitations Talks. The multimajors and unimajors will sit down, discussing ways to prevent MASS: Mutually Assured Stress Sickness.

Without quick intervention, a downward spiral will begin. Eventually everyone will be taking summer classes “to get ahead.” The superachievers will create secret bunkers of majors ready to deploy in the worst case scenario: a free space in their schedule. When you consider whether to take action, think of the students. Think of the millions of Biology/Chemistry majors who dread not getting into med school  because they didn’t add Neuroscience. Think of the tens of Accounting/Folklore and Ethnomusicology majors who lose sleep deciding if they seem interesting enough without that IMP in Cobbling and Haberdashery.

Together, we can stop this madness. Stand with me: declare one major, and don’t give in to temptation. Resist the urge to say things like “it’s only 3 more classes for a Spanish major, I might as well.”

When they ask you “What are your majors?” channel your English teacher and correct their grammar. Remember the way he said, “You mean were, subjunctive. If I were a rich man…” Just like that. Say “You mean major, singular. My major is…”

MY B.A. IN ENGLISH

“What do you do with a B.A. in English?” asks Princeton, the character from “Avenue Q” for whom “the world is a big scary place.”
Today, I’m eating my words. Last September, I lampooned the “proliferation” of majors, trying to combat the overcredentialization happening in college today.
Now I plead guilty. Last Wednesday, I officially declared a second degree, a Bachelor of Arts in English. 
I find ways to circumnavigate my previous stance, rationalizing that back then I was really only lashing out against the bad reasons people use for adding majors. For example, I still find it indefensible to add a major because “it’s only a few more classes.” These evasions, though, still seem hollow, so I’ll just concede the hypocrisy and move on. 
While this addition might come as a surprise to the people who know me as The Math Guy, it is not foreign to me.
I come from word people. My father is a word man, as was his father before him. They are English teachers. The love of words is in my blood, and this inheritance evokes a silent stirring which draws me back to the word.
Along with surprise, I often get kudos for being “well-rounded” or using “both sides of the brain.” I find this frustrating. First, it exemplifies the tendency to only treat interests which are legitimized by a degree as genuine.
Second, I dislike the right-brain/left-brain conceit. It assumes that just because the brain is split into hemispheres that the mind is divisible into two meaningfully distinct halves. Based in some science, it has been overextended, overused and oversimplified. 
There is one reaction I don’t receive. My math major shields me from the interrogators who demand of most English majors, “But who will hire you?” 
It is a common lament among English majors who, after so many rounds of questioning, have resigned themselves to the expectation of post-baccalaureate unemployment.
The imperative of economic value extends beyond individuals. Increasingly, cash-strapped universities and society in general force the humanities to justify their existence.
These trends have followed from the commodification of the college degree. 
Because universities are now the gatekeepers to the white-collar professional world, students see the campus as a marketplace and the college experience as an exchange of goods. We pay a (rapidly increasing) price for a diploma, which we then try to trade for a comfy, salaried position.
But as the “Avenue Q” song observes, our technocratic society views a B.A. in English as a “useless degree” because it does not give students a specialized set of skills.
Indiana University should be different. IU’s roots are in the liberal arts, and its core unit, the College of Arts and Sciences, is a liberal arts institution. Moreover, we do not have an engineering school.
However, even here, we have a business school whose careerism is borderline dangerous and attitudes toward the humanities that are inappropriate for a university like ours.
While reality can be harsh, I’ll end on a note of idealism courtesy of Princeton:
“But somehow I can’t shake / the feeling I might make / a difference to the human race.”

Mind the Education Gap

Schools can learn a lot from television. After all, a class in school and a television show both aim to tell a story: whether it be the history of Rome or the adventures of Arthur. Moreover, television succeeds: it holds the attention of millions of children every day.

How does television construct its narratives to string people along, begging to see the next episode?

           

Sean O’Sullivan, a professor of English at Ohio State, delivered a lecture last Friday in which he examined the power of serials. He explained how serials—from Dickens novels to the TV show Lost—engage audiences through a push and pull of satisfaction and dissatisfaction.

O’Sullivan posited three parts of a serial: “the new, the old, and the gap.”

“The new” is the excitement of the next installment. “The old” is the nostalgia for what readers or viewers fell in love with originally—often the beloved Season One. But maybe most important is “the gap,” a period of time between parts of a serial—the week between new episodes or the summer between seasons.

The gap is the time when viewers fill in for themselves what might come next. They spin their own theories and revel in the manifold endings which exist simultaneously in their own minds.

How can education exploit the power of serials to engage students?

Teachers need to write, direct and produce a TV series for the classroom. They need to continually satiate the desire for “the new,” in other words, the genuinely interesting content. They need to refer back to “the old,” to beloved books and ideas which fired up interest in years past. They need to construct “the gap” by opening up spaces in their students’ knowledge, whetting an appetite for more of “the new” to fill them.

Like television, which is constructed in discrete parts called episodes and seasons, education is organized into parts called class periods and years. In order to sustain the energy from day to day and year to year, educators must tease students, keeping them guessing what the next piece in the puzzle might be.

O’Sullivan examined the widespread anxiety and dissatisfaction surrounding the end of serials. Anyone who knows a Lost fan knows the worry that questions won’t be answered, that the loose end they’ve been carrying since Season One will remain untied up.

Fortunately, education will not suffer from this problem. Education is a lifelong process. It is an open ended serial. Gaps in knowledge can always be opened and then filled.

In college, the gap should become a gulf. An essential experience of an undergraduate education should be the soul-crushing revelation that one’s knowledge is pathetically small.

College students, even the best ones, should at some point hit a brick wall. They should encounter something that is more than “really hard,” something literally impossible to understand. If it takes reading James Joyce’s Ulysses, so be it.

At this point, it is your responsibility, not your professors, to see those mind-numbingly large gaps and start filling them. If college is easy, you’re doing it wrong.


[Originally published March 29, 2010 in Indiana Daily Student, "A gap in education"]

Simple Gifts

Occasionally, a work of art will silently enter your personal stage, bow, sit at your piano, pause a moment, and then boldly strike the right chord. That chord excites some dormant resonant frequency built into your personal echo chamber. Your response far exceeds your expectations, and you are put into a sublime ecstasy. But everyone else doesn’t seem to get it. To them, it’s just another tune. To them, the excitement is unfounded and irrational.

In physics, resonance makes amazing things happen. Technically, it occurs when a force drives a system at its natural frequency, creating large amplitudes of oscillation. Untechnically, it occurs when you coax something into acting just as it wants to. While pendulums and springs are the standard examples, resonance is ubiquitous: MRI, cyclotrons, violins, radios, quantum mechanics. Anywhere you look you’ll see excited oscillators.

Sometimes, one idea can resonate deeply with us and effortlessly explain many things. For me recently, this idea is the simple gift. By simple gift, I mean one without expectation of return, one that simply moves among people and makes them closer together. These gifts can be abstract—knowledge, art, love, life, time—or concrete—a bed, a meal, a shirt, a drink. It’s not about the content of the gift. What matters is the palpable bond which forms between giver and receiver.

On the program for the recent inauguration was a world-class quartet playing “Air and Simple Gifts,” a John Williams arrangement of the Shaker tune by Joseph Brackett. For me, this performance (though recorded) was one of those works of art that stirs. Why? Well, there are many reasons I should have liked it. The tune was familiar to me from my church as “The Lord of the Dance”. As a cellist, I appreciated the technical skill of the musicians. The title captured an idea that had been beavering in my head for a while. I was an Obama supporter and was already excited to be witnessing history. However, while these aspects provided background for the awe of that moment, there is something beyond words which contributed to the power of my response. That is the gift of art. The hidden frequency within me to which this piece was well tuned is a complex and mysterious product of not only those few things I just mentioned but also everything I had ever thought and felt and experienced.

Simple gifts resonate with me. They may not resonate with you. Your self, your echo chamber, may not see these vibrations as coherent. It may be all noise to you. If so, I say go find something that does resonate with you. Find the chord that just feels right. It’s waiting somewhere for you to hear it. Find the idea, the religion, the philosophy, the equation, the proof, the story, the painting, the driving frequency that sets you in motion. I bet if you find it, you will find it is a simple gift.

[The first column I wrote for the Indiana Daily Student. Other columns can be found here.]