Cats and Theories
a blog by coticheque
a blog by coticheque

Symmetry breaking

I’m something akin to muck on the wall, the lichen in the corner of a humid room. When God was creating creatures, he rushed and left me broken. He probably looked away when molding my face and body, and this is why all my proportions are distorted. My intestines are malfunctioning like a rotten onion, and my insides hurt. 

My nose stands out, looks like a misshapen piece of clay. My hair lies flat. It covers the contours of my irregular skull and all bumps are visible. My skin is porous, covered by scabs and ulcers that secrete mucus. No matter how much I swipe it away, it always comes back. My legs grow at a weird angle. Which makes me clumsy and awkward when walking, and I often fall. My nails flake off.

When others cast a glance on me, they quickly divert their eyes, for everything in me is bearing this imprint of divine inattention.

The other creatures around me were endowed with tools of communication with their kin. But when I utter words, it’s seems they emerge somewhere on the ocean floor, and when they ascend to the surface, there are just a few bubbles—a barely noticeable ripple on water. 

But I like flowers, roses of Sharon and lillies. I like the colors blue and red. The fragrances of petals and perfumes.

And most of all I like looking at the dark-haired girl. She appears near shepherds’ tents when the dusk falls upon the city. Among the flocks of grazing sheep and goats, among the blooming vineyards, she walks down the hills. She comes there every dusk searching for someone, looking around the cedar and fir trees. Her eyes are blue and grey, dazzling with green like a dove wing. Her necklace is full of jewels. She starts out near the hills, and at the daybreak she’s near the city walls.

My neck hurts from the ambush of thick shrubbery when I sit watching her.

Mirrors are supposed to reflect the symmetric state of the world, but when I look at myself in the water, there’s nothing in that image that resembles what I’m carrying inside of my body.

***

Evenings, I spend in the cave. Sometimes I have visitors. A friend of mine is an equally hideous being. He sometimes comes at night, wrapped in tattered rags, and one of his eyes has a milky spill on it, but his age and his occupation are otherwise unknown to me. All I know is that he comes from Nag Hammadi. 

Last time he came, he brought a group of followers with him. Mostly lepers on crutches, dressed in rags. I was resting in the far corner of the cave and didn’t hear everything he said, but I think he was preaching. He said: ‘And so we know and rely on the love God has for us. God is love. Whoever lives in love lives in God, and God in them.’

‘And love culminates in propagation. Propagation in beautiful medium. Love must have a result, a fruit. To produce this fruit you ought to find a suitable soil.’

‘Symmetry is God. God is beauty. And some say that symmetry is one of the greatest forms of beauty to be found only in the mathematical sciences’.

‘But don’t they say the world was created by the devil?’, said a man in rugs in the first row. 

‘Blasphemy!’, someone shouted.

That’s what was said that evening from what I remember, but I fell asleep too quickly to recall the rest.

On Sunday, I’m in the garden again. The girl with black hair isn’t there yet, so I sit and wait. The beautiful medium. Finally I notice her near the gates, this time she’s wearing a veil. As she walks past the watchmen, she looks down, then heads downhill past the vineyards. Her lips are tense. 

When she hears my approaching steps, she gets frightened and starts running away. Even in this simple act, I adore her graceful beauty. But the city gates are now closed and there are no guards around. 

God is in unity. The material world is something that splits us apart. But to be with God we need to be united.

There’s now fear in her eyes. Why is she running away? The one to cure me of being misunderstood. The beautiful substance to merge with. 

As she rushes through shrubs and weeds, further into the valley, thorns cut her bare ankles.

After half an hour, I stop exhausted. There’s a creek in the valley. I bend down and look at the water rippled by the wind. Then I freeze motionless. Curse the waters of all creeks and curse the rivers that fall into deltas of despicable seas. For the realization took shape in my mind:

I was not a beautiful medium to her.

***

Arthur Stresemann parked his old Fiat Multipla at the corner of Wilhelmstrasse. It was a Tuesday afternoon, and before exiting the car he sat inside for a minute. The smell. It smelled like decomposing plastics. These massive vortices of plastic rubbish in the Pacific Ocean, where there’s no hiding from the burning sun, only polypropylene smoldering on the hot water surface. It probably smells the same.

He exited the car reluctantly and walked into the glass doors of the EMB Consulting building. It was early spring and the prospect of spending the day in the dull office space was suffocating.  

Arthur worked as a software engineer in the biggest actuary company of East Berlin, an unbelievable upgrade from his hometown of Zebrzydowice, where dirt covered roads, walls, and settled on people’s skin, entering through its pores.

If there was one command that Arthur followed, it was that reason is a faculty unique to man, and man has a moral duty to live in accordance with reason. Life, death, politics, all of it ought to be governed by decisions made on the basis of rational calculation. His work responsibilities included calculation of people’s life expectancies depending on various parameters: gender, ethnicity, smoking status, family history. In the time not occupied by work, Arthur was working on finishing his PhD in physics at Technische Universität of Berlin, last few chapters left in the dissertation.

Quantitative methods. That was the name of his academic specialization.

***

‘I’ll give you a number, a winning number’, Tomas Huller told Arthur while leaning over his beer.

Tomas was in EMB’s department of statistics. They met for lunch. When they saw each other occasionally, they mostly talked about optimization of nutrition and physical activity. Although it was hard not to notice that Tomas’s hair was getting thin, and the belly under his tight shirt was getting more pronounced, and all the talks about optimal step count and amount of protein intake didn’t seem to stop it.

‘How do you make a choice when options don’t come altogether at once’ Tomas asked. ‘You cannot review the next option without rejecting the previous. So how do you know you are making the best decision?’

He leaned back on the cracked leather sofa.

‘Which kind of decisions are you talking about?’, Arthur lifted his head from studying the menu.

‘Hiring, for instance. The famous secretary problem. Imagine you need to hire a secretary and you want her to be the best, but you don’t know which candidates may come next.’

Arthur vaguely recalled this problem from his bachelor’s level statistics classes at TU.

‘You have to remind me of the details, he said, before turning around. A blonde waitress made a gesture she’d be right there.

‘Imagine you’re the boss and want to hire a secretary. So you open the vacancy. Wait until several people apply, invite a couple for interviews. There’s a blonde who seems fine, then there’s Mrs. Krüger with 20 years of experience. Both are competent. But you cannot just settle, you need the best secretary. So you wait and wait, keeping the vacancy open, hoping a perfect candidate will appear. You’re anxious because previous candidates eventually become unavailable, they accept other offers. And you’re nervous: a perfect secretary might come right after or she might not come at all. Maybe no one is more perfect than Mrs. Krüger with her 20 years of scheduling meetings.’

‘So how do you make the best choice?’ Arthur asked.

‘According to probability theory, to maximize the chance of making the best decision you ought to scan the first 30% of all available options. Then pick the next one that exceeds them all.’ Tomas sipped his beer. 

‘So take 15, or whatever number of applicants you expect, multiply by 30%, review the first 5. Then hire the next best one. It’s that simple’.

Of course. It had to be simple. How else could it be, Arthur thought in agreement. All that people had to do to live well was to be rational and ditch their faulty meaty processors governed by ephemeral emotions, impartial to statistics. Reason is the noblest faculty of man, and man ought to cultivate it.

‘So what I’m saying is that 30% seems to be the magical number’, Tomas continued. ‘Apply it to recruitment decisions or anything else’. He paused for a few seconds. ‘Take relationships, for instance.’

Arthur looked at him skeptically. The waitress passed by their table carrying something fishy on the tray.  

‘You first calculate the totals. Say, the average number of mates that a man in America can expect to have throughout his lifetime is 8,2. Round it down to 8.’

‘You can then adjust this number by a factor of attractiveness.’ He cast an evaluating glance over Arthur. His grey suit fit poorly in shoulder area.

‘Well, your gross enumeration is above average for this country but… Well, let’s just leave it at 8.’

In the far corner of the bar there was a TV silenced on the wall. An analyst on Bloomberg was saying something with a serious face, something about efficient markets hypothesis. Arthur remembered: efficient markets are those that reflect the full scope of publicly available information, which becomes priced in the current stock value.

‘How many girlfriends did you have so far?’ Tomas asked abruptly.

‘Well…’

Arthur briefly scanned 31 year of his life, which, when it came to human relationships, didn’t really comprise of much. There was Marianne, a girl he had met in high school through a chat room, with whom he spent a few dozen awkward afternoons in the food court of a shopping mall that promptly went bankrupt. Then, there was Christine, whom he dated for almost a year in college, who then moved across the country to study law. To his own surprise, he didn’t miss her as much as he thought he would. His last relationship faded naturally after a woman from an online app never reached out again when he slowly stopped initiating conversations.

‘I guess that makes it 3’, he finally responded.

‘OK’. Said Tomas. ‘So it’s been roughly 37% of all your lifetime options, according to statistics, of course. More than enough to make a choice. So all you have to do now is just pick the next option that would surpass the previous 3’.

Arthur remained silent.

‘Come on, you work with actuarial tables all the time, you know how it works’,  Tomas said impatiently. ‘If it’s easy enough to forecast when someone dies, it’s equally easy to forecast how he’s going to spend his years before death. Decades.’

‘Trust the numbers, mate. It’s all there is anyway.’  He sipped his beer.

That evening, when Arthur got back to his flat, he spent several hours polishing the last parts of his dissertation. It was a chapter about even functions. ‘Symmetry is a mapping of an object onto itself so it preserves the structure and remains unchanged under transformation’, the chapter started with this definition. ‘Functions are called even when the function of x is the same as the function of -x’. Then there were several paragraphs about symmetric tensors and polynomials. The final paragraphs were supposed to cover the topic of uniform distributions, but they were not finished yet.

Half an hour later, he fell asleep in front of the TV.

***

Next afternoon, Arthur was at the library of the Charlottenburg campus of TU. ‘This sequence is not going anywhere’, said Helen from across the desk. She was rubbing her temples, frowning.

Office hours had just ended, and now they met to revise distributions of polynomials. They sat at one of the many uniform chipboard desks lined along yellow-tinted windows where plastic shades covered the view.

‘This parameter is undefined’, Helen continued. She skimmed through the pages that Arthur printed that morning. Some of them were already marked by a few greasy stains of what smelled like tortilla.

She was sometimes too critical, Helen, but she was alright. He knew her for a while. She had brown hair and a fringe and wore checkered shirts and those rather old-school rectangular glasses in a red frame.

Since they met at the Master’s program, they both sustained interest in algebraic topologies, and now they occasionally met to review each other’s work and go through difficult parts of the PhD curriculum. She was alright, Arthur thought again while looking at Helen skimming through pages. She’s not very well kept, but she’s intellectually rigorous. She might even like him. 

While walking through narrow corridors with great carpets and brown linoleum that smelled like disinfection, Arthur contemplated whether it made sense to add Helen into his sample of lifetime mate options. But the thought seemed too ridiculous to ponder for more than a few seconds.

***

However, on the way home, Arthur laid out calculations in his head again. If Tomas was right, what options did Arthur have and what were the criteria to evaluate their fitness? Appearance is important, for sure. But there’s also compatibility in intelligence and interests too. The attitude, and of course reciprocity.

Reluctantly, he turned to Helen as an example. These glasses she had made her look slightly awkward. Looks-wise she was incomparable to Christine. Christine had this slender body, and black hair fell on her forehead like a beautiful curtain, while Helen’s face didn’t have much shape to it.

Although… He cross checked Helen across other parameters. She’s smarter than Christine and Marianne, that’s for sure. IQ is a market of life success, so she could give kids good genes. She seemed to come from a similar economic background, which is important, since historically it was mainly the arranged marriages that lasted longest. She’s passionate about her studies. She won’t spend her time at vain parties like Marianne did. She’s reliable and responds to his emails within several hours. She won’t ghost him like women on the apps.

And the way she looked at him… It didn’t happen often that women reciprocated his feelings. If what he experienced was ever serious feelings.

Was it five parameters out of six? Arthur went home in doubt.

In the evening, when he leaned over his equations, something didn’t feel right. Something was off in his model for symmetrical distributions, which he couldn’t quite figure out. He decided to go to bed instead.

***

On Sunday evening the statistics faculty of TU threw a party to celebrate the end of finals. Before entering the dorm, Arthur leaned down and briefly looked at the glass of the car to check his appearance. He was wearing dark jeans a blue shirt underneath a navy jumper. But the glass was so murky he could barely see his own reflection.

When he entered the large living room, a group of students sat on the floor playing some party game. Few people he knew well, others he came across a few times at the faculty. He didn’t join them, but it was that name game where you place stickers on each other’s foreheads and guess who you are. He thought it strangely resembled the human condition, where everyone around knows exactly who you are while you yourself have no clue. Isn’t it funny that you have no clue?

At the kitchen, someone laughed.

***

Last weeks of April were weeks and weeks of observation and calculation. Arthur took the task seriously. He’s a rational man, after all. Take 8, multiply by 30%, draw the line, pick the best option.

During the work days, he looked at women in the Sales department of EMB and evaluated them. It’s not like Sales was a big team in an actuary firm, but there was Claudia who had her hair dyed an unnatural shade of burgundy. She’s put on some noticeable weight in the past year after quitting smoking. And there was also that new trainee on the procurement team, whose name he didn’t know but who wore a sleek pony tail and had her lips always covered with a thick layer of pink substance. He often overheard their lunchtime chats about new Netflix series’ and elevator conversations about one million things trivial and particular, with zero attempt to conceptualize them. Their chats drove him mad. No, he couldn’t picture being with such a woman. He once even texted a random girl from the app after having too many beers one evening just to receive ‘idk’ in return. What makes women so passive and indifferent? 

And while at the faculty, Arthur also watched Helen attentively. At the seminars and under the low ceilings of the library, he observed her talking to others. She’s chatty, social, polite, and her email replies are always long and detailed. They have similar academic focus, so they will have things to talk about. The decision was clear.

***

So next Thursday, Arthur suggested to Helen that they meet at a coffee shop instead of the usual chipboard library. Obvious choice, for the dusty old rooms of Charlottenburg campus felt suffocating in this weather.

It was 5pm and the sun was low.

At the corner of Wilhemstarsse, Arthur entered a corner shop to buy water. An evening show was on the TV, where a hostess in tortoiseshell glasses was asking questions to a priest that looked stooped and skinny, as if he started lent 10 years ago and never touched anything more nutritious than a crumb of bread since then. 

‘Since the book of Job, the fundamental problem of God’s justice has been haunting the minds of people throughout the centuries… Why do the righteous get no reward and the evil prosper…’. The priest had a quiet voice.

‘Ought all our actions be rewarded as we deem it just… But who are we to know God’s own ways and will? And what do we actually deserve?’

Behind the counter with a Chinese lucky cat, the cashier raised his arm up to switch the channel but the remote didn’t seem to respond. With a frowning face, he looked at the screen again where the priest kept speaking.

‘… for centuries people argued whether rewards come here and now, or whether they only come in the afterlife… And are they a function of past deeds?’

‘In Hinduism you get rewarded for what you’ve done in your previous life, don’t you?’, commented the woman in turquoise shell glasses on the TV screen. ‘Not too far from the sins of our ancestors or the curse of the bloodline’.

While retrieving cash from his pocket, Arthur thought of efficient markets hypothesis again. Religion, finance, everyone’s dealing with the fundamental obscurity of the world, he thought.

‘…the feebleness and humility of us humans in the face of His judgement…’ The preacher spoke again. Then he quickly turned to a graphic description of the Day of Judgement. Something about the dead leaving their graves.

Arthur exited the store.

When he reached the cafe, Helen was already inside. A far table in an almost empty room. Next to it was a large window overlooking the street where flowers blossomed in wooden crates.

Her face was animated, rather tired, a bit weary. In the same checked shirt, still she was pretty, probably the prettiest in all the cafe, maybe in all of the cafes on the street. He wondered why he doubted his decision for so long. He was fairly confident by now.

So after putting his backpack on the chair, Arthur talked, and talked more, and he talked mostly of uniform distributions. But the words leaving his mouth dissipated in the air like the clouds of smoke, and her eyes were like nails holding the conversation together.

With his limited capacity for emotional intelligence, Arthur recognized an expression of puzzlement on her face that soon turned into expression of humility.

The last customers were leaving, making the cafe almost empty. Now they were almost alone in the large room.

Helen traced invisible circles on the table with her fingertip. Then she looked up and talked in a soft voice. ‘Arthur, if you’re intending to make a move, it’s just… I’m not sure it’s going to work.’

‘I don’t understand’, he responded after a brief pause.

‘I noticed how you looked at me recently. And I get you, and probably…’ she paused again and removed her glasses, then rubbed the bridge of her nose. ‘It’s kind of ridiculous, because it’s not like I have much choice given my situation, and I don’t completely correspond to beauty standards. But not telling you how I feel would be unfair.’

A cafe employee walked past the table and quickly disappeared behind the door. ‘Out of order’, said the sign on it.

‘But…’ Arthur quickly interrupted her. ‘If it’s about finances, I have it all figured: I already got a full time position in an actuary firm. It pays very well.’

‘That’s not the thing’, Helen said. ‘My father held a principal position over pediatrics ordination at Montlake hospital. We’ve always had money in the family. I know I’ve never showed it off, but I have a trust fund.’

Arthur pressed his lips. ‘I’m finishing the dissertation soon, too’, he continued. ‘I can show you the last pages already. We have a big overlap in research areas, so we can always talk about…’ 

‘That’s not what I’m looking for.’ Helen responded. ‘You know that I ended a long relationship with a professor of mathematics last year. And I’ve had enough quantitative stuff in my life. Constant tutors and courses since the childhood…’

‘No, Arthur’, she added. ‘It’s just with you… I don’t think I want a life of solving equations in the evenings.’

The silence fell upon the dark room.

‘But we can talk about other things too, Helen!’, he started to object, but quickly realized he had no clue what else she’s into apart from mathematical distributions. It was a new idea to him that people had hobbies outside their work.

The quiet music was no longer playing. The cafe was now completely silent.

Suddenly Helen lifted her face again, with empathy returning to it. ‘You know what? It’s actually not the last relationship I had. Last autumn… it only lasted for a few weeks, but I was with someone from the theater group of TU. He was even singing in the student’s choir, which I always found ridiculous for a technical university, but he had this light in the eyes that I couldn’t properly describe. I think I was happy back then. And fun, all the fun we had… For those few weeks, I felt like I can feel life itself.’

She got quiet and tapped her fingernails on the stack of papers.

Theater, singing, how was any of that related to the degree they were both pursuing, Arthur pondered.

‘Helen, I don’t think you’re behaving rationally here’, he finally said.

‘Ah, rationally?’, she looked up. ‘Well, yes, we broke it off and I’m not in a position to choose. But it’s just… I just don’t think I could convince myself we’re a good match, Arthur. Let’s get it straight. Dating you would be dating down.’

She stood up and started to shove papers into her tote bag.

‘Ah, and except that – I also like men above 6.2’, she added looking straight in his eyes.

‘But how do I…’ Arthur started to say, but she was already on the way to the exit.

Defeated, he turned his eyes away. There was no point in talking further.

He was not a 30% most optimal option to her.

***

When Arthur exited the cafe 10 minutes later, it was already dark, and occasional groups of teenagers congregated next to bodega stores. It was lively around Rosa-Luxembourg-Platz, but where exactly people were heading through the evening streets was completely beyond understanding. 

Arthur opted to walk home by foot. On the way, he turned back to his models. 

It was not a mere miscalculation of parameters. Some fundamental assumptions were wrong. Theater? Light in the eyes? All these words sounded like empty babbling. Perhaps he fitted his parameters to the wrong models. So for a moment he thought that maybe souls could only be comprehended as vectors. It’s not about where you start but where you’re heading. Maybe he should switch his specialization from distributions to vector behavior, he pondered.

No, it couldn’t be just a mistake. Some axes were clearly off. 

For a few minutes, he entertained the thought that perhaps his models were missing karma from past lives, or the sins of his parents, or whatever else determined his height. Of course, that must be the case. The models, it’s clear now, should be extended to the past and future. And not just some path dependency, but a few generations at least, he assured himself. The genes of his ancestors that determine everything about his faulty human configuration.

No, it would be ridiculous.

As he walked along Friedrichstrasse, the sky was getting darker and his mood was getting gloomier. And when he glanced around, the faces of people looked strange and weirdly distorted, and he saw lepers deformed. And he saw a blind man smiling. And the bus he took home got rerouted to a depot. He only realized it a few stops before the terminus. At the large town square, where some wooden stalls still reminded of what was a Sunday farmers market, he spotted some leftover fruits scattered on the asphalt, mostly the ugly misshapen ones. The ones that broke their central symmetry. 

‘And how we are judged and what do we actually deserve…’

Later, out of the window of S-Bahn train he took home, everything seemed to him mismatched, out of order, poorly fitted and in disarray. ‘This world is a product of divine inattention’, he recalled a phrase from the preacher on the TV show.

He googled the phrase. There wasn’t much trace of it from the Internet, and the only match he got after putting the phrase into brackets was a review of some academic book about Gnosticism. Something about heresies spreading in Roman-controlled territories of Levant around the second century CE.

‘The world is something created in a haste, born out of neglect. A fleeting thought in the grandeur of the divine consciousness, no more than faint ripple on the water’, he kept reading.

The S-Bahn train was shaking. Arthur scrolled down the page until there was an embedded video that launched on auto-play. It was a dialogue between two men in some tiny grey studio. One had a bold top of the head, another wore a cracked leather jacket. It all looked like a second-rate podcast about books. Or about theology. Or whatever obscure topic anyone fancied to discuss in front of the Internet audience of 8 people.

‘Is the theory of intelligent design true?’, the first man asked.

‘Well, it is true, but there’s a catch. What makes you think you’re so important for God that he had time to plan this world out? The hubris, human self-importance’, the second one replied.

‘You know what I bet on?’ the bold man continued. ‘I bet he didn’t spend more than 5 minutes crafting it. You see it everywhere. It’s just all so lousy, it’s barely holding together, almost falling apart.’

The grey walls had good sound isolation to them, and the grey studio looked liminal.

‘And as long as it’s true, this universe is shaped by randomness or indifference rather than intentional, purposeful design.’

Arthur put the phone back at the exit of Alexanderplatz.

The station beamed with electric lights. Fifteen minutes along the concrete grey houses of Bundesstrasse, walking past the graffiti covered walls, past the poplar trees, past the heap of rental bicycles, lights blinking, all fallen. Until he reached building 9. Fourth floor.

At the desk at home Arthur opened up the laptop, retrieved his papers, and started to type. Since the evening was cut short, maybe he would at least have time to finish the last chapter of his dissertation. One last topic to cover. Parity violation, that’s what he needed to focus on. If he assumes its truth he’d virtually disprove his previous hypotheses. But he’ll just do what ought to be done. To accept it is to become more intellectually rigorous.

He didn’t intend to finish the paper this way.

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