Category Theory
February is for love letters
Thanks for reading my newsletter! The breakdown: first a personal essay, a round up of my writing, then some thoughts on my recent work experiences, media I am consuming and finally some vegan food and recipe recommendations. All opinions expressed here are strictly my own.
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CATEGORY THEORY*
To have been enemies first, we would have had to find something to fight about.
Maybe we would have had to meet in a loud bar, loud because you were there with friends that yell too much or laugh too raucously. Maybe you would have had to come up to me and ask me something that was meant to be a joke but sounded kind of rude.
I’m not sure that would have been quite enough.
To have a start as enemies, maybe we would have had to endure a continuous and consistent feud for a while, maybe give each other side eye in the Espresso Royale across the street from the psychology building, the one where you could never find a table downstairs even though that was the nicer part of the shop. Would we have begrudgingly shared a table too small for both of our thin and disorganized laptops? Would we have kept spilling coffee in the general direction of the other?
I’m not sure people actually make enemies of this sort.
Perhaps, it would have been a party that we were both invited to by a friend of a friend, someone that managed to straddle our two departments in a town mostly defined by one’s academic allegiances. The kind of party where you talk to strangers and hope the conversation makes it past your research and which side of campus you live on. I’m not sure what exactly you could have told me to become my enemy, but we used to bond a lot over music in those early days so maybe it would have been an unnecessarily hot take about Iron Maiden or Metallica’s third record or whether Tom Araya can actually sing. A rehashing of a fight I may have had in high school with Croatian metalheads that I don’t call friends anymore.
I quite like this scenario - we feud about music for a while, we exchange a couple of playlists, maybe we end up seeing a show together and, of course, we eventually fall in love.
You know that Deafheaven show we both meant to go to, but both ended up staying at home instead? It would have been so cinematic to get trapped in a throng of bodies mesmerized by blast beats and cookie monster vocals then realize that it actually feels kinda good to be close to each other. But I’m not sure that anyone out there is writing romance novels set to the soundtrack of avantgarde black metal.
***
Every day at work I write news stories and you write a news story according to a formula.
Without an exception, the first two paragraphs have to give it all away. Even if the reader decides to stop scrolling, leave the page or close the print magazine shut, those first half dozen sentences or less should give them a big enough download of information to walk away with at least some knowledge. This is where you put in all the W questions.
Who? You and me.
When? Almost nine years ago.
Where? In Urbana-Champaign, Illinois then New Haven, Connecticut then Brooklyn, New York, and a few dozen places in-between.
What? Love, lots of it.
The next section of the story has to give the reader some sense of the context in which the news happened and the motivation of the characters driving those news. With science stories the context can be a long road towards a particular discovery or it can be an unexpected finding in a system that we thought we fully understand already or it can be that someone built something for the first time and they found something of note while doing so. When I write about scientists the context of their work is usually hard to disentangle from their motivation. Most scientists do what they do because they want to solve long-standing puzzles or they want to build something that does not already exist. This can be a difficult section to write in a short news article because you often have to compress years of work or many textbooks’ worth of complexity into a paragraph or two.
And for us? Was our context and our motivation that we were lonely? That would certainly make our story easy to write. Many readers could understand being motivated by loneliness and longing. The context of there not being enough love in a life is one that does not have to be embellished to make the paragraph pop.
The next section is where you reward the reader who did not give up after getting the short version of the story at its very top. If they kept reading then they must want to know more so you tell them more, more details about what the protagonists did and more details about the conclusions they drew and discoveries they made.
We went on three dates before you asked to kiss me at the bus stop. Once we got drinks, once we saw a concert, once we played pool with your friends and saw a strange movie. We had that conversation about whether we were dating a few months later around Valentine’s Day, in your kitchen, when you brought me home after dinner for a cup of coffee, but did not have any sugar to make it with. A few months after that I was shaking your mom’s hand in New York. I think I said “I love you” before that trip, maybe over a milkshake?
I’m doing this incorrectly. I’m giving the reader too much detail with not enough clarity. And I didn’t even get to the part where you move away and it takes more than five years and a global pandemic to bring us back to the same geographical location. And I forgot to tell you that what we found and what we concluded was, again, more love.
If you mess up your second to last section, like I just did, it’s hard to transition to the very last. If you do manage to get there, this is where you include comments from outside experts and speculations about the future. I think I can do this part for us.
In September of 2019, in a notarized affidavit, your mom wrote that we were “a loving, respectful and caring couple.” Your best friend at a time wrote one too, saying that we have “a fantastic, inordinately healthy, mutually supportive partnership.”
Honestly, at my day job we would never print comments that are this flattering. The stories I report are much more informative when the independent experts suggest a constructive way forward, like new parts of an experimental setup that researchers may consider building or new mathematical procedures they could try running on their data. Are there new procedures that you and I should adopt?
It may be better to close the story by speculating about our future instead. Editors hate lines like these because they are so cliche, but I do very much believe that the past nine years have only been a small taste of the love and togetherness that is still to come. As scientists often tell me, this is just the beginning.
***
I guess we could have been best friends first instead.
We would have definitely gotten along. Not just because we happened to be at the same school at the same time, but because we share so many seemingly random interests and influences. Like half-assed 80s aesthetics, like the side-swept-single-curl haircut we both sported for years, like late night screenings of bloody movies at that one local art theater, like piles of vinyls of post punk that sounds like industrial noise, like audiophile dads and being taken to divey bars too young, like always being the nerd in the group of kids who thought they were so hard and edgy, like having overcome a trial and a tribulation or two but still feeling like none of it is a real enough accomplishment.
Maybe we would have gotten along well enough to do many of the things we ended up doing in this timeline, like eating still warm homemade bread on your stoop and drinking Evan Williams and listening to Fuzz on your record player until it was somehow two days later and we both had to get back to classes and research. I’m pretty sure you would have let me take you on an ambitious X-Files re-watch even had we not been having sex in-between the episodes.
Would there have been a dramatic confession moment? That one summer when we went to New York for the first time there were nights when we would be going back to your parents home on the Q train just as the sun was coming up and I think that would have been a good time to throw a sweet twist into our story. Not that there weren’t plenty of long nights in Urbana-Champaign, where we met, when a 10pm text of “How’s your day been” turned into hours of free flowing conversation, many of which could have ended with an unintended “I love you.”
Look, I dislike it quite a bit when people say they are marrying or dating their best friend. It feels like a failure to cultivate more than one kind of love and care in their lives, and it makes me worry about how many other friends they have. But you would have been a great friend to me, and it took me years to make friends that I trust as much as I have always trusted you. So had you, one Saturday afternoon on that uncomfortable couch in my first graduate school apartment, leaned towards me and said “Can I ask you an awkward question?” and then “Can I kiss you?” like you actually did at a bus station after a date years ago, I can’t imagine that I would have leaned away.
***
Much of what doing physics is about, on the nitty-gritty level of coming into an office every morning and facing a blank notebook page and a stack of overly annotated papers written by other people, is finding a model that your problem can be made fit into. As a science that has been around since ancient times, physics as a whole has constantly moved from one model of how the world works to another.
Isaac Newton and Christiaan Huygens debated whether it was correct to model light as a particle or a wave and later quantum theory revealed that the most correct model yet has to include both. Newton’s model of gravity was replaced by the one Albert Einstein formulated under the name general relativity. There are numerous historical models of the insides of an atom, and they kept replacing each other over the years. We have the Standard Model of particle physics which explains how particles that make up our physical reality come together but this model is likely to eventually be discarded for something more accurate as well. More precisely, we are still looking for a model that can explain the mysterious dark matter that makes up most of our universe.
As a physicist in training you do not start with trying to overhaul or even fully comprehend any model that stands a chance of explaining everything. You start with a small and niche problem then spend lots of time looking for just the right equation to capture what you are trying to do. Preferably, you want one that has a name so you can look up the bigger theory, or the model, that justifies with experimental observations or some sort of calculation that goes back to well established fundamentals.
For me, for a long time, it was the Gross-Pitaevskii equation with which you could attack a certain type of nonlinear problem involving special quantum fluids. I was conversant in the Bose-Hubbard model which you would use to work out what some weird quantum magnet might do when exposed to another. Towards the end of my time in research, I studied quasiperiodicity, or systems that look like they have evenly repeating features except that the period between two repetitions is never quite the same.
Now, I sometimes come across papers that try to map the way people interact onto the way particles do. Two people disagreeing is like two tiny quantum magnets pointing their North poles in opposite directions, one model will suggest. Another may try to map relationships within a group onto a graph then employ geometrical arguments to extract some underlying patterns about why and how people within it form alliances. I’ve seen statistical mechanics models of Reddit and quantum operators meant to convey how parliamentarians vote on laws.
After you spend enough time thinking that every problem and every phenomenon can be sorted into a neat class of similar occurrences, all of which are captured by a few lines of math we then call a model, playing the game sort of becomes irresistible. In a conversation about the early days of the pandemic, a colleague recently asked me whether so many physicists suddenly threw their hats into the epidemiology ring because they have a “God complex”. The truth, I think, is less sinister. We just don’t stop to think about the limitations of our models, or the way we conceive of what a model is, all that often because we are taught to think they can solve everything..
I’m not going to argue that our story cannot be lumped together with many others, effectively forming a class or a category of story. Academics openly acknowledge the ‘two body problem’ that keeps them separated from their partners while they are in school or seeking a permanent research position. Most academics also couple up with other academics; finding two PhDs struggling to make their PhD-driven careers fit together is in no way novel or unique.
And certainly, I could force our story into a physics metaphor. In my classes we’d say that everything can be modeled as an oscillator and then you and I would fly really far apart just snap back into being remarkably close together then fly away again in quasiperiodic fashion. In research meetings we’d talk about how to model an effect that is nonlinear, an effect that grows disproportionately large or reinforces itself over time, then I’d lie in bed at night thinking about how some small joke you had made years ago still made me laugh.
I found it soothing to be able to compare what was happening with me, and with us, to what seemed to be the truths of the physical universe. Being in love can be stressful, but oscillating atoms and fluids that support self-reinforcing waves are not stressful, they just are. I wanted us to just be as well, to be as steady and as regular as something that neatly fits into a well-known, well-understood model.
***
It could have been one of the many other scenarios too.
A groundhog day type situation where we are stuck together for a long time? Now that I have had a few year’s worth of privilege of waking up next to you every morning, I know that I would enjoy the reliable stability of that one greatly.
An office romance? I have never worked in a palace that had cubicles, but I can imagine you leaning on the edge of one, with your perfect hair, in one of your perfectly anachronistic jackets, and it’s a very nice fantasy already.
I got a little stuck at whether I could really force our story into the mold of “opposites attract” or some dramatic “we come from different worlds” premise. In a very objective sense, these do come close to the truth. Me, a cold hard scientist from Eastern Europe, and a queer one at that, and you, a warm and funny straight boy who grew up in New York and invested years in studying people. Taking each other to our respective homes has always been a real learning experience with no small amount of culture shock. Spending time with friends too, whether they be your punk friends who played in rockabilly shows in basements of bowling alleys or cohorts of theoretical physicists with peculiar views of the world once it extends outside of the lab.
But I refuse to classify us as opposites because when it comes down to things that really matter, I know we can find a common language. Maybe this is what happens in romance novels too, through all the alternating fish-out-of-water experiences, the characters figure out that they’re not that different after all.
I’d like it better if they did what we did, leave quite a bit of room for difference, but find love regardless.
***
Narratives, models and archetypes exist outside of science and literature as well. More often than not they are encoded in laws, tax codes and a large set of unspoken rules for social engagements. We got married almost four years ago now because embodying that particular model of being together brought us material benefits. It still does. I am legally working in the United States as a foreign national. When my partner found himself without a job this past summer he could jump onto my health insurance. These are both occurrences that significantly influence the reality of our lives. Both also depend on our being seen as a unit in the eyes of the law. There are also benefits that are less easy to quantify, like the social capital one gets from being able to mention a spouse in certain types of company, or even just the lack of tension with parents who may be distraught by the thought of an unmarried child in their 30s.
The fact that we are married brought us lots of privileges and we could seek and reap them because we had some privilege already. I’ve written a lot about love in this letter, and I’ve written letters about the joy of our wedding day in the past, but our choice to play the kind of characters that get married and live under the narrative of marriage was motivated by anxiety and a need for economic and legal safety more than anything as rich as actual love. It frustrates me to hear pundits speak about the need to “bring back marriage” to address some or other overblown societal ill. If people like you and me are still choosing to get married, then how can the institution of marriage ever be in danger?
I’m grateful that we could marry, but much like every trope that sets out to capture romance and turn love into a formula, the idea of marriage is simply too small and too limited to do it justice. The same way we are not enemies that became lovers and we are not best friends that discovered they were soulmates and we are not opposite poles of two attracting magnets and we are certainly not a pair of particles caught in each other’s field, we are more to each other than a husband and a wife who signed a piece of paper in front of a few witnesses. At times I stumble over the word husband because I am ashamed of describing you in a way that flattens your love so much, that takes away from it the ability to be both soft and grounding, both pliable and supportive, and above all more abundant than something shared by people that file taxes as one exclusive unit.
***
Ultimately, if I chose a narrative or a model for our being together, I would be implying that I know what is going to happen with us next. After all, stories have endings and models are built to enable predictions. Both seems wrong to me because when I look at you, a bundle of blankets and hair in the early mornings when I am rushing out to work or feel the edge of your shoulder as I lose the battle with the TV and fall asleep on the couch late night, I feel something more euphoric than certainty. I feel a warmth and a brightness that does need streamlined edges and sharp boundaries, an overwhelming amount of hope that however we are going to happen to each other next will be just right.
Happy Valentine’s Day,
Karmela
*Category theory is a branch of mathematics that sorts mathematical objects, like numbers, into categories, like sets, and defines how they are related to each other, or what kind of functions can map one onto another, like the function ‘multiply by 2’ mapping 1 to 2. I heard Eugenia Cheng speak about category theory at New Scientist Live and would very much recommend her writing on the topic.
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ABOUT ME LATELY
WRITING
As tends to be the case in my line of work, I spent late January and early February jumping from topic to topic and wrote about a few findings that could not be more different from each other, like using lasers to make fiber optic cables out of air and a new materials for making soft robots that can not only change their shape, but also melt or solidify when necessary.
I was also invited onto the New Scientist Weekly podcast twice. Once to discuss my reporting on a brain scan study that set out to quantify how much entropy our brains produce when we are asleep and when we are awake and the second time to speak about an AI that designed proteins that were able to destroy bacteria once researchers synthesized them in the lab. At the time when I am writing this, I have a few more stories on deck, some about special clocks, some about quantum computers, some about water doing strange things.
There are days when this breadth and seeming lack of theme in my writing seems intimidating. When I have a chance to step back and take stock of it all, however, I am often just grateful for having a chance to constantly engage with so much science. This whole letter is a love letter and I have long loved science. I can only hope that turning some of it into digestible snippets of information that anyone can skim through on the Internet or in print conveys at least a bit of that sentiment.
READING
Since my last letter I have been pretty consumed by work and managed to read very little other than scientific papers, a few more chapters of Braiding Sweetgrass, which I am still very much enjoying, and a poem here and there. This poem by Joy Priest and this one by Brenda Hillman particularly stuck with me. They’re very different in choice of theme and language, but there is something about the rhythm of both that appealed to me.
LISTENING
My partner and I saw Oceanator and the Downtown Boys play a free show in our neighborhood and I was really blown away by both. We were there because I have long liked the unabashedly progressive and groovy punk that Downtown Boys play and they did not disappoint on either front. They played possibly the most punk show I’ve ever seen, not in the sense of punk like wearing the right pants and hair, in the sense of punk like speaking truth to power and getting in the mosh pit with your people. Oceanator’s music also really grabbed me and I’ve been listening to their record Nothing’s Ever Fine a lot since. This is heavy music that still manages to be melodic and pack a sort of upbeat nostalgia, not shying away from singing about the days that don’t feel right but also, despite the name of the record, keeping despair at bay.
I am just the right demographic to have been enthralled by the tree new songs boygenius dropped recently and I did quite like them. I feel a bit silly listening to someone describe what 27 was like because that age already feels so long ago. At the same time, I will never pass up the opportunity to listen to Lucy Dacus sing about a friend moving to Chicago nor will this music ever feel fully disconnected from who I may have been at that time or in that city.
Tom Verlaine of Television passed away recently so I revisited Marquee Moon and it’s still fantastic in its relentlessly cinematic quality and ever so slightly over-the-top-ness. I think about the classic Supercontext episode about this record fairly often, it put Television on my radar and gave me just enough knowledge to appreciate what they were trying to do in a way that leaves space for an occasional raising of the proverbial eyebrow.
Finally, Habibi’s self-titled record is all bops, like the Shangri-La’s reboot you didn’t know you needed.
WATCHING
Though I never played the game, the buzz surrounding the Last of Us has been enough to make me curious about this HBO show. Watching the first episode was also enough to make me want to keep watching. There is very little I could say here that someone else has not said already but much like Station Eleven, which I did not love but did spend a lot of time thinking about, this show brings out so many questions about what happens to humans when humanity as a whole is reduced to something ugly. And all those questions feel relevant right now. This too, of course, is a cliche thing to say, because it is not just the global pandemic we have been dealing for the last three years that plunged us into hateful policymaking, harmful divisions and a kind of scarcity mindset that both weaponizes the economy and depletes our ability to feel hopeful, but the Last of Us offers a new example of a place where that sort of thinking is all that is left. So far, the series has struck me as well thought out and filled with incredible acting performances. I do not expect any storyline within it to ever end well, but I am curious about crumbs of humanity and joy that might pop up on the way. I have also been listening to the “deep dive” episodes about this show on the Prestige TV Podcast from the Ringer and they keep being really insightful and helpful for processing this show.
We have been watching The English on Amazon Prime which is an oddly surreal and often quite gruesome Western starring Emily Blunt. Partly, I am in awe of how vividly this series portrays the unglamourousness and danger of the wild West. Partly, I feel like every actor is committing to their bit more than they have to, Blunt maybe more than anyone else. I’m not yet sure what one is supposed to make of a show where every villain seems so villainous as to be cartoonish. Yet the era of American history the show engages with does read like a villainy masterclass especially with regards to the history of Native American genocide which is something that has so far featured prominently in this series. You probably cannot watch this series without being at least a little uncomfortable, but that may just make it more worthwhile.
As another watching experience that was somewhat uncomfortable but for a very different reason we watched David Cronneberg’s Crimes of the Future. This is a body horror film that is actually about art, evolution and an overall trouble of dealing with change. I’m not sure that the whole thing fully worked for me, and this may not be Cronnenberg at his best, but the movie’s premise whether you read it to be about there being an art to how the human body changes, about how people in power will always want to stop and cover up the way the regular person transcends their regularity, or about how it is inevitable that the sepia-toned, overly polluted future will change us, did stay with me long after we stopped watching Viggo Mortensen writhe in an Giger-esque bed or Lea Seydoux take a laser to his abdomen.
EATING
We threw a Croatia-themed dinner party for some dear friends and it was a blast. The whole thing was supposed to both make up for and celebrate the time we had spent visiting my family at the end of last year so I cooked a giant meal inspired by my grandmas’ holiday foods. I took very few pictures, but my mlinci, the mushroom goulash with dried mushrooms my grandfather gave me, my veganized ‘chocolate salami’, ‘francuska salata’ and ‘kremšnita’ custard slices all turned out really well. I also made some braided Italian sesame bread, sauerkraut and a big bean salad which is all to say that we watched croatian music videos from the 80s and steadily ate for more than a few hours, all punctuated with laughter that I always feel I need rather desperately. It made me so happy to have a chance to cook so much and have it be received so lovingly.
On a less hyper-local note, I made a version of these lentils in peanut sauce from Vegan Richa recently, using peanut butter for my nut butter and cashew cream in place of coconut milk, but leaving out the tamarind in favor of some rice vinegar, and the dish turned out so well that my partner immediately suggested I add it to our “rotation”. This is a really flexible recipe that held up not only through the substitutions I already mentioned but also the fact that I only had yellow split pigeon peas and not even red lentils.