Guest Blog: “Infinity Breathes” by Jesse Han

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Joan Didion writes that writers—archivists, keepers of private notebooks, of memory’s palace—are of a different breed altogether, anxious malcontents, lonely and resistant rearrangers of things who have learned, from an early age, a preternatural preoccupation with loss. Writing is a sort of nervous tic, a stab at survival for those who continually run from that elemental private reflection: This must end.

The summer I was thirteen, back when I still felt like I could remember everything, could still draw for you, if asked, a clean narrative arc from my first conscious memory (December sunlight streaming through the half-open window of my parents’ bedroom) to the there and then—I spent an idyllic August weekend alone in my room scrawling on college-ruled filler paper a twenty-page autobiographical manuscript.

At the end, before signing my name, I wrote “I’ll be gone soon, just a fading memory. But I’m here now, and I exist, and I’m alive. Remember me. Everything I’ve told you. Remember who I was, who you were. Who we are. All this; the music of our dreams. Now: go.”

Or something like that; I’ve half-forgotten.

* * *

I write: I am a writer. I cast ideas into the blue and words soar up to surround them.

Of course those words above don’t really mean anything, will return a type error if you try too hard to parse them. But they read like how it feels—to write.

When learning—exploring—some new part of mathematics, I feel often as if I’m lost in some vast forest of crystalline ideas, miles underground. Here, everything has a different timbre than I’m used to, resonates at alien frequencies. Here, I write to think. Listen: I tap one with my pen, and it, then a hundred (and then a hundred hundred) others glow and ring out in phosphorescent echo; a shifting kaleidoscope in the dark. I could spend lifetimes here, transfixed. That’s what it feels like.

Of course I’m just at my desk, writing and writing. Burning through paper. Flipping, rotating, palimpsesting in different-colored inks whole sheaves of paper. Working towards understanding why.

(A remark made by my professor, halfway into a discussion of Kan extensions in homological algebra: contemporary mathematics, he says, is far removed from the mathematics of the late nineteenth or even the mid-twentieth centuries. There’s now incredible amounts of language involved. It’s no longer enough to just be clever, good at solving problems—you now also have to care to sift through and systematize whole systems of systems of language to find the undescribable thing at the center of it all.)

I approximate truth with language: I am a mathematician.

* * *

There are those mathematicians who would deny the existence of infinity, who would claim that quantification over infinite domains is meaningless. Finitists fallen from Cantor’s paradise. But does infinity exist? We may as well ask if ideas, or ideals, exist: if we live our lives faithful to some ideal—like points spiraling in thrall around some transcendental (hence strictly finitistically undescribable, hence, through language, untouchable) asymptote, spiraling ever-closer to it but unable to attain it—do we make that ideal real, do we realize it, by dint of our devotion, our love? Through us, through our love, does it live and breathe?

What about God?—whom, for Cantor, was the Absolute Infinite atop his aleph-hierarchy of uncountable infinities, that hierarchy whose structure Cantor made into his life’s work to unearth, reveal, illuminate, a prophet preaching his revelation, so as to bring us closer to Him, towards understanding Him and his perfection, towards touching infinity…—the same God for whom Cantor died his prophet’s death, penniless, mad, forgotten in a sanitorium in the Alps: did he make Him real? Our devotion, our love…

On the morning of her fiftieth birthday, my mother reminisced to me, at length, about the endless summer in Spain, half a lifetime ago, that she and my father spent together. I exist: their love breathes.

* * *

 A year after that magical summer, I’d lost the manuscript—thrown away. I can’t remember, now, what it’d even been titled.

But I was happy that summer, happier than I’d been in months (or maybe years; I can’t remember now.) I felt like I was finally breathing free, after a long time lost in a subterranean dark, and I just wanted to capture everything—because what if I forgot? Forgot what all this felt like, that I could feel like this—what if I lost my way again? I wanted it all to be for something. To freeze time, to collect all those shining moments mid-fall before they shattered forever, and to array them perfectly on a page in geometric stasis. For myself (whom I’d begun, that summer, to learn to love): Here. Look.

I remember finishing, putting down the pen. The magical hours afterwards, when nothing else mattered. My happiness now glowed from the pages on my desk. Time couldn’t touch me. I had written.

 * * *

 Some things I still remember only because I have written. Memories: Here. Look. In one, I stand at the cliff along Ocean Avenue, overlooking the beach, at the end of one of my nighttime walks. The sun had broken over the tops of the buildings and there was a band of clouds low over the horizon that caught the light just at that moment and was lit up a brilliant reddish-pink. But the clouds were at a low-enough angle to the water so that the whole ocean turned into a mirror, captured and threw back all that light—and so for a short time the world was this pastel layering of color—the brown-yellow of the sand; the entire ocean and the clouds above dawn-red, with a band of perfect blue sky in between.

In another, I prove for the first time that the subobject classifier for the the category of presheaves over the rational numbers viewed as a poset category must be isomorphic in a natural way to the reals viewed as a dense linear ordering with endpoints. Two days it took me. Hours alone at my desk. I lost myself, along the way, down a dozen dead ends. So many abortive attempts. And yet, when I slid the last keystone into place, set down my pen, felt in my mind the proof humming to life—I can still remember it now, because I gave so much to write it—I could’ve sworn, marveling at the ultimate symmetry of the structure I’d unearthed, had revealed on the pages around me, that I was watching the very same sunrise.

In another, someone I love touches me the way light falls through leaves.

Am I an aesthete (so I ask myself in a journal entry of a year ago) or an ascetic? Do I live more intensely, or less? Do I, as a writer and mathematician, experience and remember all these moments the way I do because they explode (as colors flaring into some new spectrum) or because they reverberate (as whispers echoing through some vast space, empty as a cavern; as waves rippling away from a disturbance in a pool of water that had been, until then, stilled to glass?)

I submit this: that if the purpose of literature is to make heads throb heartlike, then the purpose of writing, of mathematics (two manifestations of the same abstract activity), is to make language throb lifelike. We write, not to survive, but to live. We sound truth with language; we press ourselves into pages; we step back, and—looking at what is now before us, at what until then we could only have dreamed of, at what now on the page lives and breathes—we know that we are alive.

 * * *

It’s exactly those moments, of realization, of having written, of having passed myself into pages, of: I-have-dreamed-of-you-and-now-you-are-real—that I have learned to live for.

Consider this: I glance at a problem and the outlines of a solution flash through me—a shiver down my spine, lightning through sand—and I spend the rest of the night lost in that crystal forest, hunting for glints of lightning-glass. Because I know what comes after: I set down by pen, and at a flick of my mind the forest lights up and glassens, turns perfectly transparent, a shimmering lattice—and then, after a few seconds, the light vanishes, and the forest shatters, comes down in total blackout, without one glint, only great invisible crashing. And all that’s left is all I need; it’s there, the solution, my hard-won understanding, all of it, all the Antikytherean complexity of it, glowing from the pages on my desk. I have dreamed of you. I have made you real: infinity breathes.

 * * *

One last memory: I wake up dreaming, at dusk, of a synaesthesia sunrise. Colors you wouldn’t believe. I’d been sprinting across a vast fog-shrouded suspension bridge (chasing after Batman, no less, who’d taken off mid-conversation, cape aflutter, as soon as I’d raised the touchy issue of his secret—remember, dream logic—Amish heritage.) I remember tearing through a velvet dark, my body screaming for air, ready to collapse—when suddenly the fog vanished, and a great wind was blowing around me, through me: I breathed and breathed. And the sky had been shot straight through with color. Crimson-to-gold-to-indigo. Gasps and hues. Jazz. I might’ve been standing on Ganymede, watching Jupiter rise into half the sky. And as my eyes traced the sky’s outlines (near its edges, where streaks of fire faded into the night) I heard—I felt—voices, angels, first a baritone, his voice a breathy glow, and then others in close harmony chiming in, cathedral echoes, branching into adjacent melodies, then every melody, and as I saw more of it, came closer and closer to grasping the whole, seeing it all—as the sky exploded, as I heard whole other choirs, all the voices building on each other, rising as one, soaring with the sunlight breaking over the horizon:  finally, I could see, I could see—this universe and this world and my own life and everything in it, totally illuminated, pierced by light—and it was so beautiful, beautiful; so vast, vast—

And exactly a week later, as I watch the sun break over the Bay from the center of the Golden Gate, as I laugh and feel the wind tear my laughter away, as I stand and look at all that light and smile and breathe and breathe, I know that I’ve made myself—my vision—real, that I’m here now, that I exist, that I’m alive.

11124740_10152760594023091_1426710998_nJesse Han is a fourth-year pure math major, interested in mathematical logic and algebra (specifically, model theory and algebraic geometry.) He is twenty-one years old.


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