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tesselation with 5-fold symmetry

My head still throbbed lightly and the smell of the new scrubby grey floor tiles did not help to improve it. I concentrated on the unusual pattern of the otherwise ordinary floor covering. The tiles were light and dark grey and laid out in an unexpectedly complex arrangement. Areas can be filled completely and symmetrically with tiles of 3, 4 and 6 sides, but it was long believed that it was impossible to fill an area with 5-fold symmetry though Kepler played with the idea. I knew this because my mother loved the work of M.C. Escher who was intrigued by mathematic patterns and used them in his illustrations. It did perplex me that the library floor tiles were cut out of so called kite and dart shapes which actually allow a surface to be completely tiled in an asymmetrical, non-repeating manner in five-fold symmetry with just two shapes based on phi. As a result the tessellation of the dense felt tiles in the lobby made it impossible to arrange my thoughts according to the floor pattern – a technique I had used since childhood to soothe anxiety. Instead I began to draw shifting lines through the pentagrid in my mind, preferably coming up with glowing triangle shapes. The forms danced in front of my eyes. I felt faint.

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genius

Bild

tarnished brass bracelets jingle on your wrists,

over your shoulder you carry

the same scratched leather satchel

full of papers and books.

worn sandals on naked feet.

even now,

i recognize you in an instant.

 

it’s winter.

you keep well in the background.

between shelves M-Z in biographies

you are not at risk.

 

you have had your share of abuse

and are weary of it,

though not afraid.

 

the red letters of a franchise bar

reflect in the deep black tar

of a recently paved parking lot.

another new strip mall.

the evening is patiently enduring

the loneliness of a friday night.

 

people climb out of sport utility vehicles

half the size of their houses, i assume,

and file into the barnes & noble

for a grande non fat latte

and some magazines or bestseller titles

to while away the hours.

 

and you, in the background,

leafing through

a mussorgski biography.

how in the world this got there

you can’t imagine,

then Frank Zappa,

but that’s not why you came.

 

finally, your head clears.

you carefully deposit yourself

in an armchair.

still, no one pays attention.

the anxiety subsides.

the numbers start dancing.

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Plinius, the cat logarithm

Finding Plinius could be impossible at times. For days on end the only sign of his existence could be that his cat bowl was empty in the morning. At some point, mostly drawn by Phoebe’s calls in the evening, he would walk out of the shadows in the garden and return home to sleep in the margins for a couple of days or on his favorite chair in the kitchen. I was never certain of his return. In that way he was like my father, too. It was very likely he would come to pick us up for a weekend but never entirely. When I shared this observation with my mother once, she quoted from “The Hobbit”: It’s a dangerous step, the first step out of your own front door.” Implying, I guess, that no one really knows whether they are going to return at night. But the remark wasn’t all that helpful. Some people do make more of an effort than others to come back. My father had a challenging work schedule in a big law office in the city. I guess, I was somewhat harsh towards him. Still.

Walking into the kitchen that night I found Plinius right away. He was sitting in his favorite chair, looking up and squinting his eyes as if he had actually been waiting for me. A small reading light had been kept burning as every night in case we girls were to walk into the kitchen in search of something to drink. I walked over to Plinius and kneeled down in front of his chair. He yawned and turned his head to the side. “Plinius,” I whispered, putting my fingers in his fur. He felt real, shaggy softness, powdery cat fur smell with a hint of cat litter. I put my nose into his fur and inhaled. A real cat. When I looked up, Plinius had closed his eyes again. He wasn’t purring, mind you. But he let me be. Unusual. As I looked at him, my face close to his face, noticing a bit of mucus leaking from his dirty pink cat nose, the long whiskers, the white grandpa beard on his chin, there seemed to be, in his very presence, a message. It was like working on a math problem, knowing you just had to think right about and even more importantly look right, look in the right way, whatever that meant, at the equation and you would understand it. That was how math usually was for me, the answer to a problem was right there, in front of my eyes, on the paper, I just had to bring it into focus.

And that was what Plinius seemed to be to me that night in the kitchen, a living and breathing logarithm to express a specific, meaningful relationship between an unknown value and me, cat2me is the output from the function cat2 when the input is me. I looked at him really hard. Did Phoebe speak cat as well? Did she know what kind of a cat logarithm Plinius was? Plinius himself couldn’t be bothered to help me. cat2phoebe is the output from the function cat2 when the input is phoebe. Plinius sighed as if bored by my slow mind, moved a bit under my hands, and farted.