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on equilibria [feature]

and other balancing acts

  1. In game theory, players are assumed to be rational actors, meaning they make the “move” that best benefits them given the choices of other players. That’s why, in economics classes, you draw tree diagrams, starting at the very end and working backward, allowing players to evaluate every future possibility before determining their decision-making in the beginning. These repeated games sometimes result in a Nash equilibrium, defined by John Nash as a stable outcome in which no player can improve their position or increase their payoff by changing their strategy. In other cases, though, players continuously adjust their moves based on the previous actions of others, creating a repeating loop of “tit-for-tat” where they never settle on an optimal agreement. 

  2. My friends and I climb the stairs of a Boston bar called Arya. On the walls are photos of the restaurant owner with various celebrities. I stumble slightly around the turn—my ballet flats and two glasses of wine make me clumsy—spotting a younger Dwayne Johnson hanging in the corner. Then, a Paloma and me at the end of our mahogany table, I make myself concentrate on the candle (there’s fresh snow on the tops of my bare feet, and I don’t think I’ll ever get used to how frozen things scald in their own red-hot way). A tells us about T. 

“I think, before my relationship happened, I became so tired of men that didn’t care about me,” A says, his chin tucked into the heels of his palms. “It got to the point where all I wanted was someone to care about me.” I watch the little flame jump. “Attraction wasn’t as important. And now I am back to only caring if they’re hot and not as much about how they treat me. It’s like some pendulum, going back and forth,” he says. 

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“Really hot and don’t treat you well versus treat you well and not as hot,” I summarize, imagining those county fair pirate ship rides that swing up and back down an imaginary half pipe.  

I think about Y and how I needed him and those feelings at 19. How, today, I don’t want anything like it. Perhaps I will again soon. I see A’s pendulum and wonder if it will all slow down at one point, if I will swing in smaller and smaller “U’s” until one extreme doesn’t incite the pursuit of the other, until there’s no energy left, and I come to rest. 

  3. The vestibular system, comprising the balancing organs, is located in your inner ear. Three fluid-filled loops respond to head movements: the superior canal for up-and-down motions, the horizontal for left-to-right shaking, and the posterior for tilts side-to-side. Two sac-like otolith organs are located just below—the saccule, which detects acceleration in the vertical plane, and the utricle in the horizontal plane. When balancing, your brain takes in information from these five organs, as well as the eyes and the joints, and sends it to other organs, allowing us to adjust to where our body is in space. 

  4. I used to say that Y taught me how to relax—that he balanced me. Sitting opposite each other on a seesaw, he straightened me out, as if he carried just the right amount of rocks in his pockets.

One night in a London club called Cuckoo, Y’s best friend Z leaned over and told me, “Y really loves you.”

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I was drunk at the time so I believed it. But I’m not saying that Z was wrong.  

  5. I used to think about wanting my younger self to know Y. She would be astounded to know she could be this loved, I wrote last February in a journal I bought from a stationery store. I think I did feel this, albeit in a weird and Jungian-esque inner-child way. 

  6. One time, I popped my ears really hard, plugging my nose with a thumb and a pointer finger and blowing. I must have been sick at the time. My room started to turn, just a bit, and then suddenly it was upside down, warped. I stumbled into my mother’s office, sat on the carpet, and vomited into a beach towel. 

  7. This spinning sensation is called vertigo. Benign paroxysmal positional vertigo (BPPV), the most common cause of vertigo in adults, occurs when the tiny calcium crystals come loose from their normal location within the utricle, allowing them to flow freely into fluid-filled spaces of the inner ear.

  8. In March, I wrote: What will I do when Y dies? 

(Y always said it was weird that I thought about death.) 

I feel like he is my lifeline. 

What do I do if I’m not his?

  9. Although equilibrium is a state of balance, it does not necessarily imply “equality” in the sense of identical quantity or value. In chemistry, equilibrium is reached when the forward and reverse reaction rates are balanced, meaning the system will remain stable over time without further net change. But this doesn’t mean that the actual amounts of things in the system are the same—in fact, only a very small percentage of chemical equilibria will involve equal quantities of reactants and products on each side of the equation. Only some isomerization reactions are perfectly balanced in this way. 

Similarly, when a Nash equilibrium is achieved, players’ gains are not necessarily balanced or equal—only settled in a way that leaves no one with a better alternative, even if fundamentally uneven. But this was not always the case. Before John Nash came John von Neumann and Oskar Morgenstern, who first developed the concept of a game theory equilibrium. Their definition of equilibrium was solely for the special case of “two-person zero-sum games,” in which one person’s gain is always another’s loss; the payoffs always sum to zero. Nash proposed an expanded notion of equilibrium that applied to a much wider class of games, including those with different payoff structures. 

  10. When I broke up with Y, I told my therapist I wasn’t mourning him. I said, “I’m mourning who I was when I loved him”—a woman-child certain of her own incompleteness.

  11. My fifth-grade teacher said that 11 was the best age to be. On my 11th birthday, she drew two number ones with the thick edge of a green whiteboard marker. “At 11, you have one foot in your childhood,” she said, pointing to the first. “And then the other half of you has entered the older numbers—your adulthood. You have the best of both.” 

This teacher and I had the same birthday, January 11, which made me feel special. But I always wished I was born in 2001 so that I would be even, 01/11/01—you could draw a line down the middle of the date and have the same thing on both sides.  

I have always cried on my birthday, maybe because it reminds me of my asymmetrical origins. Or maybe because it always feels like I’m standing in two places at once.   

  12. From Central London, I take the Jubilee Line to North Greenwich, the nearest tube station to Greenwich Park. At the park’s highest point is the Royal Observatory, through which the “prime” meridian passes, splitting the Earth into the Eastern and Western Hemispheres at 0° longitude. I try walking into the observatory, just right through the gates. “Adult tickets are 24 pounds, miss,” a staff member stops me. I apologize and begin to turn around. 

“Did you want to see the prime meridian?” 

I look back at him. 

“Because if that’s all, I can show you.” 

He walks me down a steep path running along the edge of the observatory gates, all the way to a thick bronze strip in the ground. Carved faintly above it on the rock wall is: 

GREENWICH MERIDIAN

East Longitude | West Longitude 

I look up and see people’s shoes on the gated balcony, realizing (quite dumbly) that the actual meridian isn’t confined to the observatory’s display. I thank the man and put my back to the wall, placing one foot on each side of the line, straddling east and west for free.

  13. It turns out that, unlike latitude, which is measured from the equator, the designation of the prime meridian (0º longitude) in Greenwich was completely arbitrary. As international travel increased in the 19th century, the need for a standardized global map system became clear. An 1884 conference of 25 nations chose the Greenwich Meridian as the “prime” meridian, mainly because of Britain’s dominance in maritime navigation at the time. France disagreed and continued using its own meridian through Paris for another 30 years. 

In the 1980s, the International Reference Meridian (IRM) established the precise location of 0° longitude. With satellite technology, scientists realized that this point is not a fixed location, and will continue to move as the Earth’s surface shifts. Currently, it is about 334 feet east of the prime meridian paid exhibit in Greenwich Park.

  14. “The child motif represents not only something that existed in the distant past but also something that exists nowa system functioning in the present whose purpose is to compensate or correct, in a meaningful manner, the inevitable one-sidedness and extravagances of the conscious mind.” (Carl Jung, Archetypes and the Collective Unconscious, 1969)

  15. They say relationships shouldn’t complete you. But doesn’t it feel really good when they do?

  16. Asymmetrical balance in art refers to the “comfortable” feeling you get from a piece that is not necessarily symmetrical, but still feels balanced. For instance, bright colors are visually heavier than dull colors. If something is large and dull, something small and neon could match its perceived “weight” despite being objectively smaller. 

  17. In balancing yoga poses like Vrksasana or “Tree,” I am told to find a Drishti—some steady point like the tip of my nose or a groove in the baseboard. When you stand on one leg, new information from the vestibular system is always being processed by the brain, spurring slight but continuous adjustments in muscle activation—really, we are never still. The Drishtis must laugh at our will to be.

  18. All velocities are relative, meaning they are measured with respect to some reference frame. Because of this, no object in our universe is truly still; it rests only relative to a given frame of reference. 

  19. In his Principia, Newton writes, “It is possible, that in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest.”

  20. Maybe balance is just a feeling. Something we tell ourselves. 

  21. Something in the stars. Or in us. 

  22. It is midnight on my twenty-second birthday, and I weep. 



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