Non-Linear

Regarding some equations.

On first introduction to the idea of convergence, it is natural to take an optimistic view. However, in certain cases it is clear with moral certainty that whatever else happens, convergence does not.

Consider subharmonics. Proving their bare existence, we begin with a theorem of our own before beginning any proofs.

Suppose a positive constant, some fixed function bounded by a given. From there, find a local maximum. Suppose the velocity of a given around a stationary point, spinning.

Consider any variable whatsoever, and let it be x. It follows immediately that the notation parallel to that for symbol y is denoted by an alternate symbol.

We are always supposing. 

We suppose always,

assume the truth.

***

Today is the anniversary of the death of celebrated British mathematician, Dame Mary Cartwright (1900-1998), who is considered one of the pioneers of what came to be known as chaos theory. This exercise is a collage of phrases found in this paper she published in 1945.

Valley

Between us.

Between being and becoming, a valley holds the wasted lives of a time when we thought we could not know what we were except by testing hot fire against some idea of what it felt to be a god, before the end of the world, and we are in this valley now, still with this longing, and what can it be but nostalgia for the days when it was possible to imagine anything but this relentless fragility with its incessant reminders, that there is no becoming beyond this? Instead of a world, see this baby, head bandaged from the last strike, another attempt by a would-be god of our own making, to make some urgent point, but there is no scorecard without a world to rule, only this child looking up, eyes glazed and the dead all around.

Crossings

Keeping watch in the dark.

Hundreds gather beneath the remains of a bridge they meant to cross. They wait, watching the river, for the next chance to move. One, looking back, says the children are scaredthey are killing them over there. When a cloud of dust settles, some are still unmoving in the road, a dog beside them barking, and even David is shrouded in black now, to mark the deaths.

At the border, a woman waits for her cousin, traveling for days with children. The men are back home fighting, but where is home now? 

We are trying to get them out, she says, to save their lives, at least. Do you see me, cousin? She jumps and waves. A child runs to her, hooded in a pink parka. There is weeping all around and weary smiles of relief. It is calmer now, she says, and they move from the wire fence of the thin border between the known world and the next.

***

Details culled from New York Times coverage of events on the eleventh day of the Russian invasion of Ukraine. With love and prayers for all who flee war and persecution.

Hope in the Dark

Against other constants, and at random.

“Everything I ever thought to be a nightmare is nothing compared to what I am witnessing.”

Voice of Diana Berg, Mariupol Resident, in “No Water, No Electricity: Life Under Siege in Mariupol”

I wanted to tell you, when we spoke last week, about the child returned to the swing before the bombed-out building where he once lived, lifting his foot to the sky anyway, before he can know the word for resistance; and also about the the women gathered close in a kitchen, by the thin window before it broke, passing cake around on patterned plates with good silverware, saying to one another Here, here. Eat––

but the conversation followed another line, and then time was up, and now the shelling is constant and at random and I don’t think the child is swinging anymore, and I don’t know what happened to the women with the cake, if they got on a train the next day, or went underground, and I don’t want to end with this––

constant

––did you hear about the babies born in the basement of the Metro station? Yes, there were several and you could hear the mothers’ screams below against the shelling above, but it is said they are okay now, these babies not because they are at home––and where will that be–– the shelling constant

and at random

––when this is done, 

when is this done? It is constant

but they are at their mother’s breasts and there is still milk even as the mothers are weeping, especially as the mothers are weeping, there is weeping constantly now and at random, and there are also the tiny fingers wrapped tight around a mother’s pointer finger, as if to hold her pointing in place

this

finger like a compass needle dotted with this row of little nails. Strong grip, people say, for some excuse to laugh, and everyone agrees, because this is here now, the grip of the newborn whose first days begin and end here, whose home is mother.

***

Inspired by the documentary mentioned above, featured in the New York Times, March 5, 2022 (Created by Masha Froliak, Ainara Tiefenthäler, Dmitri Khavin, and Sarah Kerr), in which Diana Berg also observes, “The shelling is constant and at random.” Also by stories like this, of births in the metro station. The title of this piece nods to Rebecca Solnit’s brilliant work, especially her Hope in The Dark: Untold Histories, Wild Possibilities.  

Holding

Our pieces.

The babies are at the window 

of the train, watching the smoke 

rise, and here’s another reminder 

that words are only shards of 

of our shattering selves, collected 

in each aftermath, in pockets, and

in the corners of silence, to be

glued into the mosaics we are 

always making with the bits, and

to give some shape to the next

cry when it comes, whenever

it comes, faces pressing this 

window of whatever that is at

the border of a full breath. 

Exodus

It’s an old story.

There’s a chronicle, now familiar, which begins with the names of the dead, to announce how the land was filled with them before their children ripened and became more and mightier than those that had meant to harvest them year after year for profit.

The king got wise, orchestrated erasure of the boys first. But the midwives saved them and among these was one from the tarred basket in the river who once saw his brother badly beaten by a guard and was moved to kill and bury the body. Back into hiding, he was found again by a woman at the water, and because he helped her, she bore him a son, and when the king died it was time to cash a check in the name of the children.

So went the keeper of Jethro’s flock, to the mountain to witness a burning light. Take off your shoes, said a voice. Here is holy ground.

The voice continued: I’ve heard them, know their sorrows. Now you go, release them. The man asked for a name, saying they will want to know who sent me, but all that came was this reminder, I am.

He got the elders, and they took a lamb to the desert, and nothing was known at all but this command to go forth, and begin the work of ––don’t say freedom, because if salt loses its flavor what is the point? Say instead, not having to hide the babies in the river. Say instead, not having to hide the bread, or trade bodies for bread for hidden babies in the river.

Again, the voice: Take the serpent by the tail. Show them a sign with your hands. If they won’t see it, offer another. Teach your mouth, too, and leave me to the ears. 

***

With prayers for the safety and protection of all who flee persecution and war.

Chorus

Against the dread.

Where terror shattered our speech, there came some who showed us how to make a song with the silences between our words. We listened, and the poets taught us how to meet what was coming. Look, they said. When the enemy explodes the bridge between the beginning and the end of a thought, only the form changes. What was concrete is now a fibrous web, and all of us in it. What was solid is now porous, and like other porous substances, we now absorb what may come. While the enemy creeps its silent convoy, we are here, and as we listen, one among us begins to sing. Soon, our bodies are saturated with song. The fullness is almost too much, but here we are, holding.

***

Inspired by stories like this of people singing while sheltering from attack. And by poets across time and nations, united against war. With love and prayers for the persecuted people of Ukraine in this hour. May you continue to hear one another, and hold.

On the Bridge

Portraits in courage.

Waiting, somebody asks, what will happen when the silence breaks? When the sirens come, so does this announcement: turn off the lights, gas, water. Take what you can. At the window of the train, a hundred Pietàs. Close up on camera, the most hunted among them is refusing his chance to escape. We are here, he says, both reminder and call. Here, Our weapon is truth. This is our land, our children, our country, he says, and we will defend. Civilians run to the wrecked tanks in twos and threes to pick up armor. The defenders are on the bridge. The attackers are coming soon. The living pass the dead, over the river. The bodies need collecting. The holes need repair. Certainty? A grandmother laughs. That’s only for the dead, she says. And then, as if remembering, she crosses herself, and says an inaudible prayer.

***

With love for all who are persecuted by greed, tyranny, and war, especially the people of Ukraine in this historic moment. A prayer for your safety, peace and continued courage. May every witness to your example take heart, and offer it to others in your name.

Go Down

Waiting in the dark.

When it came time to hide in the cellars again, in that dark damp we all feared, some would not go. One of the grandmothers said, I’d rather die in my perfectly decorated flat. Whatever moves in the dirty basement she will not enter, it does not scamper like the mice in the attic. What moves here is slow like the drips from the faucet. There are candles, flashlights. Faces glow against the screens before them. Some close their eyes, try to sleep. 

Do they dream? Fitfully. The cellar dreamer knows that the walls of the cellar are buried walls, with the entire earth behind them. Tell me, where is the fear that does not become exaggerated? The cellar becomes buried madness, walled-in tragedy. When they say take shelter, we wait.

***

The grandmother’s protest is a reference to Nika Melkozerova’s recent guest essay in the New York Times. Other italicized lines are from Gaston Bachelard’s The Poetics of Space.