Infinity Booklet [Revised]

7/27/2019 Infinity Booklet [Revised]

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∞



MAPPING THE

LABYRINTH

An Exploration of Innity

Kina M. Viola

(In fulllment of an

Emerson Foundation Grant.)



We have dreamt the world. We have dreamt it

resistant, mysterious, visible, ubiquitous in space

and rm in time; but we have left in its architec-

ture tenuous and eternal interstices of unreason,

so we know that it is false.

—Borges

© 2013

Made possible by the Emerson Foundation.



7

MAPPING THE LABYRINTH: AN ARTIST’S

STATEMENT ON WHY I WROTE ABOUT ∞

I’ve learned that poetry isn’t poetry, but a map of the world. It isn’t what you’d expect and those

that pronounce it dead just haven’t been looking in the right places. Poetry’s happening every-

where—in your books, your computer, your e-mail spam folder, in the crumpled note you wrote

to remind yourself to do the laundry, in the sentiments you can’t quite put into words when you’re

sitting next to a friend and there’s rain pouring down outside and nobody’s talking. I like to think

more things are connected than we let ourselves believe.

I got an Emerson Grant to write about math, creatively. More specically, about the history of

innity, where it’s going, where it’s been, and what it actually means for something to be innite.

Everywhere? Everything? The project is as daunting as the subject matter.

Why study innity, a concept that humans may not even have the cognitive ability to grasp, accord-

ing to some scholars? And on that note, why write poetry, when hardly anyone reads the stuff, when

it’s changed so much even the boundaries of genre can’t dene what a poem might be?

But the combination felt surprisingly natural—felt right. It felt, in many ways, like the only way to

talk about the sprawling lyrical narrative that is innity’s story.

—

Think of a dark room, the blackness of the room which has walls that aren’t walls but shadows

expanding, like the universe expanding as if a breathing mass. Scared yet? Good, me too. Innity

is what we tell our children will happen to them if they misbehave. The Pastor in Joyce’s Portrait of

the Artist as a Young Man promises him that Hell is a

neverending storm of darkness, dark ames and dark smoke of burning brimstone, amid which thebodies are heaped one upon another without even a glimpse of air. Of all the plagues with which

the land of the Pharaohs was smitten one plague alone, that of darkness, was called horrible.

When I was a teenager, we’d drive down a narrow street lined with rocks looking for things we

couldn’t explain. The place was called Buckout Road and it was where we went to collect our ghost

stories. The windy road connects the Eastern parts of my hometown, White Plains with the next

town over, West Harrison.

Driving in, there’d be a ranch house on the r ight with a yard lled of hunting equipment—deer

made of plastic sporting holes in their hollow shells, targets, camo tarps and cardboard cutouts of

vicious hunting dogs bearing their teeth, sitting on their haunches as they waited for orders. This

freaked us out. And then we’d keep driving.

There’d be a very small family cemetery on the l eft side right of the road where you can nd what

we used to think was Old Man Buckout’s grave. It was here we’d stop and dare each other to open

the door, step out of the car, and touch the gravestones one by one in the darkness.



9

and parallel themes. We can look back to romantic poets and nd notions of innity in Blake’s

Auguries of Innocence, where the world, to a child, is a realm of innity possibility.

There is no formal answer that describes to how to navigate the maze of innity. The process of

drawing the map is all we can do, akin to our lives—crazy, messy, human. Our formal systems have

answers in some ways, of course. We build bridges, can y, can measure a person’s white blood cell

count. But the process doesn’t stop there. The answer isn’t the answer.

Our answers, or lack there of, grant us the space to step outside formal systems we do have and look

at them differently. Growth. I keep going back to Kurt Gödel’s Incompleteness Theorem, which,

long story short, states that in any formal system, there will aways be statements that are true, but

impossible to prove.

In the Principa Mathematica, Whitehead and Russell create a system—rules and axioms—through

which they argue one can prove any mathematical truth. Gödel comes over and says, hey, what

about this: “This statement of number theory does not have any proof in the system of Principa

Mathematica.” We know that the statement is true because there is no real way to prove this newtranslation of the age old-Liar Paradox [footnote], but we only know this by stepping outside the

system itself, removing ourselves from its boundaries, changing our perspective.

Kick down the hedge maze, dig a hole underneath, build a new labyrinth with new rules, then

change them. Innity causes issues in mathematics like the Incompleteness Theorem, paradoxes—

does the set of all sets contain itself?—and it makes us remember that this imperfect world resists

formulas and answers. The character Chloe in Arcadia reconciles the predictability of the “laws of

physics” with the unpredictability of human life. Sex becomes the ultimate argument against deter-

minism, the randomness of love and attraction. Look at quantum mechanics, that proved classical

mathematics closer to an approximation than coding of the world. When we see the exibility of

what was once “concrete,” we look at a tree’s leaf in awe and nothing is ordinary.

—

Years later when jogging in the larger cemetery in my neighborhood, I saw Old Man Buckhout’s

real grave. Apparently he wasn’t buried on the infamous Buckhout road, but miles from it, only

paces away from my house. This whole time. It was a large but plain headstone with just his name,

nothing else. The last time I passed that street, I saw that the road had been paved. Rickety and

weathered no more, and they had built huge condos on either side of the street. It may seem like a

relief, or perhaps a disappointment. But I see neither. There are more stories to collect, and othermysteries very much alive and well.

I began writing about innity and somehow found myself writing about growing up. The poems

you’ll read here are less about mathematics and more about living. But perhaps you’ll begin to see

that they are pretty much the same. I found myself relating the theories and equations of things like

self-reference and randomness to fears of abstraction in my own life, the darkness of not-knowing,

the vagueness of transition, but also nding within these concepts sources of personal growth and

triumph.

Poetry has been the only way to think about innity, for me. It’s been my Incompleteness Theorem,

my way to step outside the system and see things differently. That is my “why.” Innity theory is

an abstract world, and so is writing. In both, we grapple at ways to talk about what there is. This is

both difcult and terrifying, a courageous act. This is being alive. I’m trying to humanize a formal

mathematical concept, and I’m not sure if I’ll convince you. But these poems try. Innity is part

of our world in some very fascinating ways, real as the breathless wonder we feel as we look at the

stars, real as missing someone.

8

It was the not-knowing that was uncanny, not knowing who or what was out there in the woods,

along with a spacial uncanny of standing in a road and not knowing the road’s width or length, or

your own location. Ghosts are anything if you make them that way. And I always hated the argu-

ment of whether or not they exist. Do you believe in ghosts? Answer: I believe in people.

—

Do you believe in math? In English, or poetry? All share similarities if you consider them as formal

systems. As David Foster Wallace writes in Everything and More, “A language is both a map of the

world and its own world.” There are layers to meaning, and to existence.

What, when we talk about innite sets, numbers, or mathematical paradoxes, is real? In my

research, I’ve learned that a study of the history of innity is simultaneously a study about ab-

straction. About, you might be tempted to add, “ghosts.” The word “exist” begins to feel very, very

curious.

Most people have a concrete answer if you ask whether numbers “exist.” They’ll say “yes theydo” and talk about the way physics translates the natural world into equations, how mathematical

objects are independent on our minds and that we nd them, name them, put them to work. Or,

they’ll say “no they don’t” and argue that mathematics is something we’ve made up, like a story. My

views have come to oat in between these notions.

Are thought processes so different from “actual” processes? What makes us think that a story isn’t

“real” when it can mean something to us? Make us feel things? Does “beauty” exist as an abstract

concept? “Love?” Or only in particular examples? Quine argues that what “is” or “exists” means

nothing more than to be the value of some bound variable. It’s a logical term. Can the “red uni-

corn” exist as a bound variable even though there are no traces of unicorns on our physical earth?

And what are we to make of the thought that to posit what “is” is entirely under our control?

These questions alone are enough to make your head whirl. At times, I wonder if I’m even asking

the right questions. Change your perspective, and instead ask: “in what way do abstractions exist?”

Here we escape the realm of y/n questions and enter a realm of possibility.

—

In history, innity is seen either as evil or good. It’s chaos, or it’s perfection. From Zeno to Cantor to

Gödel and beyond it’s a paradox. It’s Joyce’s Hell, or a hallway changing shape at night, something alien and terrifying that could eat you. You use it in calculus and let it be, hidden in equations to

which you have no attachment. Or, it’s a god-like ideal that we can reach towards, according to

Aristotle, but never actually grasp. Whether you’re talking about a heaven or a hell, they’re both ce-

lestial, other-worlds. Where, I began wondering, is the middle ground? I’d argue that innity resides

with us in the world of the living. As Keats writes in “On the Grasshopper and the Cricket,” it’s the

“poetry of the world” which is “ceasing never.” It’s who we are.

Douglas Hofstadter wrote Gödel, Escher, Bach as a “metaphorical fugue” dissecting the mysteries

of human consciousness, but the parts I found most fascinating detailed the connections we can nd

in the most unlikely places. There are “strange loops”—where, when we move through a system we

somehow, almost magically, nd ourselves back where we started—in music, in art, in our DNA, our

language, zen buddhism. In poetry. And vice-versa.

The characters of Stoppard’s Arcadia are trapped in a strange loop—innity makes its way into

their lives through the concept of time, where the modern-day characters are looking to the past,

and the historical characters are looking towards the future, their lives showing striking similarities



11

ERGODIC

Spell-check: erotic, ergotis, argotic, periodic, erode. But isn’t it erotic

that the word itself contains god,

or another word for innity.

Paths aren’t as easy to follow

after a while

. The word is Greek, ergon (work), odos (path). So draw one.

See the bowl become the oatmeal1, the syrup

a part of the air. I’m eight again

studying the behavior of my calico cat

ridden with cancer and two weeks later, wedding

an oval stone to the earth. My father said,

you bury her & a body

disappears into soil.

Or becomes it.

That’s what I’m asking:

The collection of all states of the system

form a space, X. For any transformation T :

X becomes X where Tx is the state of the system at a time,

t=1, when the system was initially (at t=0) in state x.

What state are we in? What happens on the other side of the arrow?

Who says the syrup won’t just sink and sink until the whole hot mass of grains just swallows it ?

Flash-forward:Ian Malcolm dons his leather jacket, business shorts, tells us

“Physics does bad with turbulence.”

He points to the clouds gathering: “Weather.”

He pulls out his heart: “The movement of blood

like a spigot of water.”

I was twelve when I watched Jurassic Park the rst time

but my father lectured me about randomness since the day I arrived swaddled and bald, repeating

like a proverb

1 “if the set is a quantity of hot oatmeal in a bowl, and if a spoon of syrup is dropped into

the bowl, then iterations of the inverse of an ergodic transformation of the oatmeal will not allow

the syrup to remain in a local subregion of the oatmeal, but will distribute the syrup evenly through-

out. At the same time, these iterations will not compress or dilate any portion of the oatmeal: they

preserve the measure that is density.”

10

LEFT AT EVERY CROSSROADS 1

1 Te common procedure for determinine the central point, and thus, the way out, of a labyrinth.

A map is not a plan, but

a webbing. Its ngers ache.

I think of childhood:

my brother in overalls

hand on the hedge of a corn maze.

I didn’t want to let him in

there, where the stalks

reached above his head

and the hair used to be

blonder, but Mom said

to let him go, that any small

boy could nd his way, left

hand on left wall. We watched him. Go,

she said. Turn

left at every fork—the walls

will run out. The light

will run in.



13

RULES FOR BRANCH ING

1.

Plants are the mirrors to mathematics;

an arching pine is all directions

weeping its pins into the soil. The fern

repeats itself like a Greek chorus;

every point eventually becomesone as if

molded.

We o ver loo k t he lea f

c uto uts

and f oc us on t he bod y —

per f ect b ut not,

senseless but not—

W e ’ d r a t h e r

s p e a k

a dif f er ent lang uag e.

and decide we’d rather be

a forking path

of leaves in the shade

of oak trees.

12

a buttery aps her wings,

causes an avalanche in Nepal

Imagine what you might’ve caused, or uncaused.

drag your feet in water

it gets colder

I thought this meant my father

could predict the future. I realize now

he was just trying to explain that he won’t live forever.



15

lik e v elv et bef or e it dies.

3.

The complexity of an object can be measured by the length of the shortest algorithm that

generates it.

And so t he dist anc e f r o m y o u t o me i s t h a t o f a f o r e a r m

, a p i n

k y , a

f n g e r n a i l .

I l i e m y s e l f o u t i n t h

e d i r t ,

l e a v e

m y b o d

y a

n d t

r a c e i t

t o

m a

p a

w a

y d o w n c o a s t l i n

e s

.

I m

a k e m

e a s u r e m e n t s , t u r n

m y t o r s o i n t o t he ho l low of a bo a t, m

y f e e t i n

t o r u

d d e r s, hand s

into oars.

I realize thewaters are smoother here.

14

2.

A l l o f botan y las hes out, re f uses

to be categorized. It’s a time bomb. Carr y a fern a wa y f rom its roots —don’t say carry,

say cut . Ow n u p t o r i p ping half a leaf f r om it s st em and dig it alizing

its d y ing ce l ls. I’m sorr y I’m sorr y I’m sorr y I’m sorr y;

but this is how we see ourselves. Through repeating architectures,

t he s lo w l y crum p l ing green in m y hand.

It loses its s pr ing, its gusto, f ee ls



17

CHESS PLAYERS DO

“This was our paradox: no course of action could be determined by a rule, because every course of

action can be made out to accord with the rule. The answer was: if everything can be made out to

accord with the rule, then it can also be made out to conict with it.”

—Wittgenstein, P.I. §201

§1

My uncle plays chess and loses, something like an elegy. His ngers

are tiny sausage links tied together and I don’t know how he moves that fast, makes the timer

sweat like he does, losing. It doesn’t matter. What matters is the touch.

§2

A dried leaf is either an imprint or an outline. Hold it up

to the light, trace the shadowy veins. Measure its area

with a function—There is no code for nothingness, spaces, holes.

§3

Nobody’s whole. I wish I could remember your face at middle-age

but it didn’t happen. Does a Ying/Yang exist? And/or, y/n. I wish I had better balance. I’m a child

on a curb; I’m middle-aged, crying with a butter knife.

§4

The system involves more than the rules of the game.

It also involves the players, moments, mothers burying their sons. I wonder

if pawns remember their deaths as separate bleeding monologues.

§5

My uncle reaches as if there’s something left there. The game is over, the pieces

dropped in handfuls, lling two tupperwares. He reaches like a child, thick

hands unfurling for once like a rose.

16

A COMPUTER CHIP IS A CITY

When I looked down, he had removed the shell of my sighing computer. Inside was a city. I had

never seen something as like the glittering constricted blocks of NYC when my plane began landing

into LaGuardia, when it was midnight and the lights were alive, and I was starving, ravenous. Hun-

ger, and a city like reecting glass closing in around a toy plane.

I remember I stopped in a Pizza Hut on the way out that night when I landed, sitting on a food

court barstool and wondering if the world was big or small, and which was more lled with wonder.

“Miss,” said the repair guy, rousing me from my own head dreaming of the folds in a cotton shirt

ecked with marinara sauce. “There’s nothing we can do.”



19

THE HEART RATE INCREASES IN THE

SPACES BETWEEN

Every body is always

where it is

where you are is

two steps beyond me

standing in the kitchen and

at the same time you live inside

the small tiny innite space behind

my left ear. Breathing. No such thing as

a “next moment” we live and then we are l iving

next to the potted plant in the doorway, then underneath:

there you are.

18

ON LEAVING A PLACE

“But Plato has two innities, the Great and the Small.”

—Aristotle, Physics Book III Chapter IV

A man walks into a post ofce to buy stamps. He’s wearing a herringbone vest / white button-up

combo that smells like the morning’s oatmeal, but it’s two in the afternoon, and his glasses are bifo-

cals. What does sadness smell like? Is it reminiscent of the glue on the lip of the envelope?

His name is Indiana, resident of Little Falls which is the kind of small town you pass on your way to

somewhere else. Indiana taps his toe in the line at the post ofce, because there are still three more

people to go before he gets to buy his stamps and mail the letter tucked into his vest, held there with

his right hand as if hiding it. He doesn’t really think he has anything to hide, but still feels the desire

to keep it there, like a small burrowing animal in the soil curled into itself.

Rabbits had been nesting in the hole outside his house. Indiana had watched the mother gather

sticks and bits of grass, uff, feathers, pieces of newspaper from the garbage can into the hollow to

form a nest-like thing. Why are rabbits also birds? Or any non-human animal g raced with speed or

ight, the world opening out for them in a secret way hidden from us.

Indiana thinks of his dead grandfather’s puzzle box. You shifted the wood blocks certain ways,

and the second you forgot what you were trying to do in the r st place, the lid would open. Inside,

empty.

But empty also means a place to ll. The rabbits have their babies, which then leave, hollow in the

yard forgotten. There are other places, too. Indiana wishes to be a bird. He has convinced himself

the world is innite. A bird is innite. The letter next to his breast is a tiny bird skeleton unfurling

its wings.



21

REFRIGERATOR NOTES RE: HEXAGONS

Your rst apartment will be chalky at the sides, imsy, like if you pressed the plaster hard enough,

a thin trail of dust would cling to your hand’s soft underbelly. It will crumble, like the seam on the

windows

that don’t shut that let in bees, and

you’ll wonder why they left their honeycombed womb-like cradles, left their children with nectar on

lips—the heat?

Inside the garbage disposal, you’ll smell a foul odor. You’ll think it’s your mother, you’ll think

you haven’t called your mother in a month. You’ll be surprised at how much dirt you unearth from

that drain.

It could go on and on. You’ll wrestle with a plunger, buy DrainO, dig out the stuff in clumps and

masses. All your dreams will be of honeycombs:

honeycombs, perfect hexagonal homes that tessellate like bathroom tiles, tiling without cracks, dips,

valleys in between. Hexagons, most efcient structures to take up space.

You’ll pick up books strewn across tables and oors.

Bees, orderly, organized, coming in where the rooms won’t tessellate, but will t together like clumsy

cake layers.

The rooms will be lled with human curves and angles, dimpled, freckled, veined—hard and soft,elbows and knees. They will be rooms of movement

as your lover breathes in bed. You’ll think of symmetry, or lack there of, and you’ll remember pu-

berty, middle school, left breast growing faster than right, one foot in front of the other.

You’ll reconsider messiness with your ngers tracing lips you’ve kissed, wondrous and chapped.

You’ll kiss them again and again, goodnight, each time different.

You’ll open all the windows so the bees can breathe. And they’ll y out.

From the garbage disposal, you’ll pull a universe. You’ll scrub, clean, watch new mold grow back,

wish for things to be simple, then take it back. You’ll nd ash stinking up the kitchen black like the

sky and out there,

on the balcony, you’ll be looking for stars.

20

MEDITATIONS ON BORDERS

In Mississippi, the whole state sweats:

cars, the blue-black pavement. The trees

allow themselves to be overtaken, wrapped.

Monday we passed through Tennessee, you

at the wheel looking stooped

and little—this is g rowing. Bodies expand in heat,

hearts in alcohol. The border is wider

than a thin g rey line.

Our rst Southern sunset ared like a gas stove,

your arm sticking to mine. I could watch

the great yellow disk for hours, wondering when

I could consider it set. When does a state become another?

The kudzu swallowed another gold day.

Everything we knew cut in half

and half again, like a sun disappearing.



23

I TELL MY DAUGHTER AN ANECDOTE

ABOUT LIGHT

I keep thirteen angels in a jar next to me when I sleep. I keep them on the bedside table so that they

can watch me—I’m not sure why. I found them like that, trapped. Someone had poked small holes

in the metal top so the angels could breathe. Really, you’d be surprised at how small they are.

Angels are smaller than we are so they can t between one moment and the next, in Time I mean.

Because the laws of time work differently for different creatures, or at least that’s how it seems to

me. They seem to vibrate, like little orbs of yellow light, not white, a more muted glow. Sometimes,

I think they’re human. I think they can hear me.

I might have found them, or I might have caught them, too. “Now” is an object I don’t have

anymore, or couldn’t hold. Like you couldn’t hold those little angels without them being in a sealed

container. I have dreams about wanting to live forever.

I have dreams about living forever, where I watch my lover’s skin age and hang, then nally fall to

pieces like old plaster. I have dreams where I’m holding onto a steadily shrinking human, smaller

and smaller until he ts in the palm of my hand, then disappears.

I have dreams that I never have children, that they die in my arms before I know them. They live

their whole lives in my arms, that dream, dripping into the carpet like sludge.

The dreams make me sick, like I’ve done something wrong but I can’t remember. I keep the thirteen

angels, but and night they’ve started to whisper, plead with me to let them go. The difference be-

tween eternity and time is an accidental one—I don’t think they’re related.

I know they’re not human. On a Thursday, I decide to let the angels go. They have been my secret,

my constant falling star. I hold the jar like an infant in the crook of my elbow and realize all along that they’ve been warm. I gasp—the feeling is in my bloodstream, it’s all along the hair s of my arm.

The jar shakes.

I unscrew the lid. With an opening like a ower, the sun rises.

22

PARABLE

The half-blind man stumbles

through bedsheets and the tangled

web of dreams, turns the lamp

on all the room cast in half-

light. He cups his face in his hands, sees

the wrinkles through ngertips

like tiny metal-detectors searching

in sand, searching for years

instead of gold. Same thing .

He rubs his eyes, hears a blackbird

shufe in the night. He looks

to face a mirror as though it is a void.

And he walks through.



25

LEMINSCATE

I would give anything to leave this place

and come back to it again

fold the leaets into threes, then nines

scatter them in a sealed drawer. I carve the night

from a piece of soap and make it

something new. Tell me: when you trace

the hills and bends of the human back

do you see a setting sun or

a rising moon? Don’t tell me they’re the same.

Palms t together. Bodies

t together. I fall asleep in the crevice

under your collarbone. Love is a knot

and it dips and falls

burrows under and emerges

as changed. We measure each other’s

breaths with our hands. The lines

and roads bend back to meet us.

24

PORTRAITS OF REPEATING DECIMALS

Picture a movie played on loop, or this guy

on the Amtrak who had been riding back and forth

in between Albany and Poughkeepsie all day, smelled

of beer and slurred his good morning, & again,

good morning, like the words were awake

when he rested his forehead on the tray-table. Later:

looks out the window, says, how beautiful. The Hudson

rising, patterns underneath mountains that dictate

their growth. I’d like to think they don’t stay the same.

Even sitting on a train, I’d like to think I’m moving

towards you. You hold my hand at the station

when we nally arrive, walk me to the old arcade

to play Pacman after hours where the woman

up front at the ice cream counter tells us, come in

& play, see some need to plod through a maze

of dots and two-dimensional pixels. Like a reminder

that we’re human. You eat your way through cherries

frustrated that each time you have to start again

& again from the beginning. & I wonder

what kind of maze we’re in, how different it must look

from Pacman. & is it possible to peer down into it

like an arcade game, see where the ghosts appear, where

we start over, take trains, remain in transit, arrive somewhere

new? I can’t feel what it’s like to get older, only the tiny hairs

on the back of your neck. But even echoes on loop come back

softer, and changed: that’s not my voice that’s not my forehead that’s not my hand that’s



Documents

Infinity Booklet [Revised]