Paul Boccaccio

The very notion of a ‘mathematics of chaos’ seems to suggest a grotesque domestication, such as the enfeeblement of chaos into a statistically intelligible randomness. For this reason my immediate reaction to the mathematics of chaos was one of visceral suspicion, even though a thread of eighteenth and nineteenth century German philosophy had prepared me for its topic. Nevertheless, it is not easy to imagine a mathematician ceasing to be a Platonist. Nor easy to remain immune to the virological seduction of ‘a geometry of the pitted, pocked, and broken-up, the twisted, tangled, and intertwined’ as Gleick summarizes it in his popularizing book [Ch 94], or to sustain an indifference to topological explorations characterized by mathematical orthodoxy as ‘monstrous, disrespectful to all reasonable intuition about shapes and… pathologically unlike anything to be found in nature’ [Ch 100].

A glance at the purportedly chaomorphic ‘Sierpensky-’ or ‘Menger sponge’ both confirms and undermines such suspicions; it is a shape that is homogenized, saturated with equalities, inanely geometric, yet also irresolvable, paradoxical, unhealthy. A Menger sponge results from the endless recursion of a simple operation. A cube is divided into twenty-seven identical smaller cubes, with the central block and each of the six orthogonally adjacent ones being removed. The resulting frame consists of twenty blocks, which are then all treated in the same way as the initial cube, and so on, recursively. Each transformation increases surface area with a tendency to infinity, and decreases volume with a tendency to zero. However far this process is taken the sponge remains cohesive, and it is possible to trace a line in three dimensions from any point on the surface to any other. In its ideal conception a Menger sponge is thus a model of infinitely complex immanence; a universe of endlessly intricate distances, without inaccessible depths or absolute ruptures. Exceeding a surface, but evading volume, the Menger sponge is a shape of between two and three dimensions, or of a fractional dimension; a fractal to use Mandelbrot’s term. Like the Möbean band of the early Lyotard, or the ‘smooth space’ of Deleuze and Guattatri, it is a libidinal geometry without inaccessible recesses, a topography without transcendent repression.

—Nick Land, The Thirst for Annihilation: Georges Bataille and Virulent Nihilism

Listen!
You can hear her pale voice
from within the conflagration.
It always speaks truth.
It always lies.
She crackles like marrow-bone
when she walks.
Her eyes and mouth open
and burn like magnesium.
She is a contrary Gorgon;
everything she looks at
is forced into frenzied life.
If you are very lucky
and can run after her
until she catches you,
you can put her in a canning jar
to hold in the air:

a blaze of fireflies
to light the darkness.

—Sandra Kasturi, “The Burning Woman” from The Animal Bridegroom via Megan Kurashige

“And then the queer thing happened. I had seen his back from the street, as he sat in the balcony. Then I entered the hotel, and coming round the other side of him, saw his face in the sunlight. His face frightened me, as it did everyone; but not because it was brutal, not because it was evil. On the contrary, it frightened me because it was so beautiful, because it was so good.”
“Syme,” exclaimed the Secretary, “are you ill?”
“It was like the face of some ancient archangel, judging justly after heroic wars. There was laughter in the eyes, and in the mouth honour and sorrow. There was the same white hair, the same great, grey-clad shoulders that I had seen from behind. But when I saw him from behind I was certain he was an animal, and when I saw him in front I knew he was a god.”
“Pan,” said the Professor dreamily, “was a god and an animal.”
“Then, and again and always,” went on Syme like a man talking to himself, “that has been for me the mystery of Sunday, and it is also the mystery of the world. When I see the horrible back, I am sure the noble face is but a mask. When I see the face but for an instant, I know the back is only a jest. Bad is so bad, that we cannot but think good an accident; good is so good, that we feel certain that evil could be explained. But the whole came to a kind of crest yesterday when I raced Sunday for the cab, and was just behind him all the way.”
“Had you time for thinking then?” asked Ratcliffe.
“Time,” replied Syme, “for one outrageous thought. I was suddenly possessed with the idea that the blind, blank back of his head really was his face—an awful, eyeless face staring at me! And I fancied that the figure running in front of me was really a figure running backwards, and dancing as he ran.”
“Horrible!” said Dr. Bull, and shuddered.
“Horrible is not the word,” said Syme. “It was exactly the worst instant of my life. And yet ten minutes afterwards, when he put his head out of the cab and made a grimace like a gargoyle, I knew that he was only like a father playing hide-and-seek with his children.”
“It is a long game,” said the Secretary, and frowned at his broken boots.
“Listen to me,” cried Syme with extraordinary emphasis. “Shall I tell you the secret of the whole world? It is that we have only known the back of the world. We see everything from behind, and it looks brutal. That is not a tree, but the back of a tree. That is not a cloud, but the back of a cloud. Cannot you see that everything is stooping and hiding a face? If we could only get round in front—”
“Look!” cried out Bull clamorously, “the balloon is coming down!”

—G.K. Chesterton, The Man Who Was Thursday