Path Integral
Hi and thanks for subscribing to my newsletter! The breakdown is as follows: a personal essay on top of the message and some more concrete life updates, current media favorites and a recipe at its bottom so feel free to skip to whatever interests you.
The essay portion is rather long this week so if you do read it, I appreciate you bearing with me. The spring is almost over but it seems that I am still feeling quite introspective. Instead of a recipe this week, I am sharing my meal plan for the next week, so if you do just want to scroll to the bottom, I hope that will prove helpful for your own cooking and grocery endeavors.
PATH INTEGRAL
Some days I am very tired. The tiredness can be kept at bay with well-spaced meals, a slightly worrisome coffee regimen and a to-do list overflowing with prompts that require the kind of thinking that is intriguing and gratifying but also frustrating and torturous enough to keep one awake and focused. I go to the gym to shut down some of this thought overflow. I try to suppress it by focusing on my body as a machine rather than a carrier for my thoughts. But then the tiredness hits and, already crashing after that endorphin high triggered by a hard workout, I find myself sitting on the locker-room bench with one shoe in hand, one on foot, and feeling my focus slip and my muscles be terribly heavy. It starts to feel like I am trying to complete some Herculean task rather than, extremely mundanely, change from one pair of sneakers (Nike, black) to another (Converse, black). The music in the locker room is more often than not absolutely terrible and it grates on me when my mind hits one of these troughs and I am suddenly unable to tune it out. A few nights ago, in this post-workout-pre-dinner liminal space, campus recreation radio played UFO’s 1974 classic Doctor, Doctor.
Before I wrote this letter, I looked at the UFO page on Spotify and I could recognize only one other of their songs listed as ‘popular’ – I am not a UFO fan. However, hearing Doctor Doctor in that locker room, walls lined with green and grey metal lockers and the floor perpetually wet from old lady swimming classes, flung me right into a face-to-face confrontation with my sixteen-year-old self. She has a whole mess of curly brown hair and a slanted fringe that gets into her eyes, really skinny jeans, really heavy boots and glasses framed by thick plastic lines of orange and fuchsia. She wears oversized band shirts without tucking them in or rolling the sleeves to combat the bulk. She’s read some books, ran some races, done some calculations, but really, she knows little. However, she does know that every Iron Maiden show in recent years starts with Doctor Doctor, before the curtain even goes up and the band, so old that they were revolutionizing heavy metal before she was even born, reveals their own fuzzy hairs and tight pants.
Recently, a friend asked me what kind of music I liked. They had just finished telling me about a local a country musician they liked, and I had thought to myself that I would have never guessed my friend was a country-lover had it not been for this exchange. At the same time, for years I have operated under the assumption that just by looking at me everyone could immediately guess what kind of music I liked. At sixteen this belief was rattled by my move to the United States where being a metalhead somehow was not an easily recognizable category. Still, the overwhelming amounts of black in my closet, the studded faux leather bracelets (which I still wear every day), the strict reliance on only two pairs of equally stereotypical shoes, the heavily lined eyes, it all registered as familiar enough to put me in the right category of music appreciation. This has always been an integral part of the identity I have built for myself. At a dorm gathering my junior year of high school we were prompted to bring something indicative of our culture; I played an Iron Maiden song. Ten years later, casually explaining I liked metal, slightly rushing out of that part of the conversation and realizing that I do not read that way anymore felt like a breaking point of some sort.
People are bad at thinking about themselves as objects that move through time and space and as beings that evolve along both of those coordinate axes. Routinely, they report thinking they changed tremendously compared to their past selves but that they will change little in the future. Psychologists call this the “end of history illusion”. In a way, this is congruent with the stories we like to tell ourselves about how people change. In a rag-to-riches story, or any story of an underdog, there is a fixed life point the person flows towards and then the goal is simply to stay there, in that good place. Big dreams of who we might want to be in the future come with a critical point in time. Before that time there is a struggle and a rising towards who you want to be (who you were meant to be?) but after this very special time value the plan is to just sort of stay there as if the life-goodness level has been saturated. Maybe that is why comics about super heroes growing older always do well, because we don’t expect to see a decline, or really any stark change, after a certain level of personal achievement has been checked off of our aspirations list.
I am interested in un-learning as a driving force of my own upwards character trajectory. There are many modes of learning and the same way teaching can happen without triggering any learning, often learning happens even though we are not being explicitly taught. I want to know what I have learned without knowing I was learning, then examine it, then discard the parts that stuck like ticks or whatever other gruesome creature can feed on you and then make you sick and tired. I have been trained to approach complex systems in an organized and analytic way, to consider all of their limits and special parameter regimes, to try to both reduce them to something more simple and generalize them to something more complicated yet universal. Thinking about how I think, the mechanisms that conspire to give rise to my ‘intuition’ and my ‘gut instinct’, is thinking about an incredibly complex system. People learn the best when they think about learning as they are doing it. Maybe I can think better by thinking about thinking. Maybe I can be better by un-learning things I have not thought about enough as I learned them.
Sometimes this means confronting the person that I used to be and the bad, insensitive, offensive, selfish things she has said and done. There’s this word – reckoning – that I keep hearing on NPR and I keep wanting to use it to frame this process. I am undergoing a reckoning with my past self. Much more uncomfortably, she is doing the same with me. I am haunted by this notion of a younger me, the halo of hair, the thick glasses and all, stepping out from behind the row of ugly lockers and staring me down, questioning whether bobbing our heads to this one cheesy 80s song in a locker room is all we have in common.
I saw my first Iron Maiden live show the year before I moved to the US and when they played a song I did not expect to see on the setlist, and I had meticulously studied so many old shows, I teared up. It is not that the lyrics were all that meaningful, in fact they were just cartoonishly devilish enough for a boy in high school to accuse me of all sorts of unsavoriness for liking it, but that the experience of the music meant so much to me. I could feel an echo of that feeling two years ago, somewhat dulled by my being older and more acutely aware of how cheesy the whole thing must be to an outsider, when I saw my fourth Iron Maiden live show. Standing not too far from the stage, I watched them play while sandwiched between my dad and my boyfriend (the first thing he ever told me was that I seemed like someone with a good taste in music) in a foreign city I was visiting to present at a physics conference. Feeling the overwhelming need to throw some horns up in the air at that first minute of what is essentially a retelling of a Tennyson poem with a bit more drum and guitars, a quintessential Iron Maiden song experience, is maybe really the only thing that provides some sense of continuity for the past ten years of my rise towards being someone who does not think she has to change, who can maybe believe in this false end of history.
In so many ways, I feel that my past selves and I would not get along. That the sixteen-year-old would hate the Friday nights I spend at home or at the gym, the twenty-year-old would hate my short hair cut at a men’s barbershop and how rarely I am in a skirt and knee socks these days, the twenty-two-year old would hate how much I talk about having changed my diet and how long it has been since I have made two dozen cupcakes just because I wanted to. They would all be disappointed that I never ended up at MIT, like I planned from the moment I first heard I’d be leaving Croatia. They’d all think less of me for giving two years of my life to a college boyfriend that demanded respect at every step but berated me for everything from my politics to the way I folded towels after showering. I’m not sure I could even begin to tell the younger copies of myself about my parents’ divorce, about growing distant from my brother and every single friend I had left overseas. And then there are a thousand other small things, small missteps and embarrassments and ways in which I have surprised myself and become someone that needs to be reckoned with.
In 1948, Richard Feynman introduced the notion of a path integral into studies of quantum phenomena. The path integral is a strange object, built up from P. A. M. Dirac’s work on the quantum action principle and (still) somewhat shaky when it comes to mathematical rigor. It has since become a staple of quantum field theory and as an undergraduate first learning quantum mechanics one is routinely promised that they will understand the famed path integral, and the related Feynman diagrams, at some later point in their career. The words are not said out loud but there is a hint of a rite of passage or an initiation ritual when it comes to dealing with this object. The idea behind the path integral is as odd as it is complicated. Namely, it puts forward the fact that to understand the behavior, or motion, of a quantum object one has to take into account all of the possible paths it can take between two points in space and time. Paths forbidden in classical mechanics, paths so elaborate that they could never be energetically favorable, and simple, reasonable, observed paths all end up on the same footing and factor into the same unruly calculation. In a sense, introducing such an object is very much in line with Feynman’s quirky legacy, yet the method was revolutionary and has been used in order to predict true physical facts about our world. The treatment of similar problems we encounter in classical mechanics is very different. There, we are always utilizing a different sort of mathematical machinery in order to identify one true path a system is bound to take and we discard all the rest. The path integral, on the other hand, assigns them all the same weight.
People are not quantum objects (we are too large and too warm) but we do sometimes take strange paths between different spacetime points and the strangeness of those paths rarely means that the simpler, more straight-forward, trajectories would have been more correct. As in a classical system, those paths might cost more energy, but they are still not forbidden, and we do undertake them instead of obeying any proverbial mandate of ‘least action’. Maybe this is why we falsely assume that where we are right now is a stable point – after so many twists, turns and curlicues and so much energy spent to execute them, how could there be a need for more of that in the years to come? There is fear hiding behind certainty when it comes to assessing our trajectories. There is fear in me when I recognize that I have become someone unexpected, someone my past selves would have to corner and reckon with. Being able to believe that this is it, that I will be who I am now in a decade, would almost be a relief. Academic research, as well as my gut, says otherwise.
On Sunday mornings I wake up early and run along a road that connects my current apartment with the apartment complex I lived in at the very beginning of my time in graduate school. I have been too stingy to invest in an armband, so I hold my phone in my hand and listen to an app equipped with a robot voice that announces every mile I traverse and an extensive selection of classic metal with good bass-lines that help my feet keep moving. There’s a fair amount of Iron Maiden on that list: Back in the Village, Aces High, Only the Good Die Young, Die with your Boots On …, songs that offered me comfort and sense of belonging when I was younger; songs that were not the most technically profound metal performance nor the most lyrically deep-cutting pieces of art just like they are not now, but that somehow got under my skin and felt good being a part of that outer, shielding, layer of who I am. An ideal run is one when I am not thinking and the motion feels seamless, when my mind operates on a level of awareness rather than active processing. The music is a part of that seamlessness. It is a part of me so it helps me move. Some of those moments feel timeless. It feels like something I could carry with me and reproduce in any direction along my timeline.
There are many ways in which I could have moved from sixteen/twenty/twenty-two to where I am now. They all matter. Some as missed opportunities and mistakes, some as informative hypotheticals, some as a reality I’ve digested and some as fine-tuned course corrections I am still contemplating. The twenty-six-and-a-half version of me reflects that totality. In a reckoning with my past selves all of the paths and possibilities are presented as bullet points that make up the larger argument. They fuel the confrontation between who I was, who I could have been, who I thought I would be and who I find myself being. But in calling it a reckoning and an argument and a confrontation I insinuate violence to my past and present self and suggest that one of us has to be correct and that one of us has to win. Winning is overrated.
As most people, at sixteen I needed encouragement, confidence and kindness. At twenty I probably needed it even more. At some point I also learned that these are things that I can always give to others and that this giving is important and meaningful. I would want to be kind to my past selves if I ran into them, to assure them that what they have built of themselves is more than enough. And I would want them to tell me the same. The haunting stops when I look at myself through my old eyes and see the twists and turns in my many possible paths as symbols of perseverance and the ability to adapt instead of giving up, when I see that there is really no end of history in sight for me and that I will not stop moving forward. And maybe we would disagree on a thing or two, maybe in some ways I would be a surprise, but I am doing my past selves a disfavor by painting them as so rigid and judgmental. I am doing myself a disfavor by thinking that there is so much about me that invites criticism and could cause a fight. We are all better than that, we could all help each other find a better path instead of fighting. If all else fails, though, at least Iron Maiden is still on tour.
Best,
Karmela
***
ABOUT THIS WEEK
LEARNING: One of my collaborators and office-mates has returned from his travels abroad so this week has been marked by meetings meant to catch everyone in my group up on the various projects we are juggling in various pairing. Coming to a meeting with a list of three or four concrete things to talk about has been a good reminder of how much actual work we are all constantly trying to undertake. And then we only talked about two things and still went over the planned meeting time. Another good reminder – physicist can and will talk about their work for hours, that’s just what caring for our jobs looks like. By the end of the week, however, some of these half-baked conversations had proven fruitful and trying to remember exactly where my days went does make me want to say that I made some small amount of progress on at least one front. On Monday, I will try and shift gears and work on a different project but hopefully keep that momentum. There has definitely been a lot of energy in various organizing meetings I have attended in between pushing matrices around and fighting with Mathematica and this also I really approve off.
LISTENING: Somewhat on-topic, Stuff to Blow Your Mind recently ran an episode on “quantum immortality” which makes some very scientifically dubious claims but also offers scenarios so absurd that they cannot be uninteresting. Slightly more down to earth, this episode of Hidden Brain starts out asking whether as adults we recognize that ads we had seen as children have misinformed us. Shockingly, adults think cereals are more nutritious than they really are based on ads they had heard as pre-schoolers. On the topic or reckoning with past selves, on a national rather than an individual level, this episode of On the Media struck me as really important as it follows Brooke Gladstone’s visit to a museum in Alabama documenting some of the worst racial violence American history has to offer and the ways in which most people unaffected by it has simply not dealt with it in any way. It is an hour of radio that seems like essential listening for anyone who cares about justice or equity overall.
The rest of the story is quite interesting as well, but I was struck by that small echo of who we used to be in how we make mistakes now. Finally, largely off-topic to the rest of this letter, I wanted to shout-out How Stuff Works’ Dressed for consistently exceeding my expectations. It is a show about fashion history hosted by two young female fashion historians that are scholarly and well informed but also in no way shy about having opinions. In this episode about Gaby Deslys and this one about Kashmiri scarves they confidently grapple with sexism and cultural appropriation while at the same time presenting a whole lot of history.
On the music side of things, the warm weather always leads me to seek out the more psychedelic, borderline-chill, corners of the metal spectrum so I listened to a lot of Dead Meadow this week. Their first album is probably my favorite but the latest is quite good too. They make me feel like there is a lazy afternoon, on a porch with a drink in hand and my head in the clouds, somewhere in my future and I enjoy that.
EATING: I had two really good meals last week: a French lentil salad with a shockingly good garam masala spiced dressing (from Gena Hamshaw’s Power Plates i.e. that cookbook I impulse bought a while back) and a mix of red lentil and zucchini noodles smothered in homemade tomato sauce with butter beans mixed in. Both will need to make it back into my rotation soon. I also made possibly my best loaf of sourdough yet over the weekend and improving my bread-making has really been very satisfying. I am leaving town in ten days, but I am already plotting how to take this new-found hobby with me.
Instead of sharing a recipe this week, I am simply sharing a break-down of everything I plan to eat in the next week. I write out my plan for the week on Friday, get groceries on Saturdays, do most of my cooking on Sundays and then spend very little time on re-heating and assembling my meals during the week. Friends often ask about this, partly because I am annoying always posting pictures of food on social media, so it seemed appropriate to describe the process here.
DINNER
S dinner with friends (bring tomato galette)
S coconut curried red lentils + brown rice + roasted broccoli crowns + squeeze of lime
M Greek potato zucchini casserole + marinated tofu ‘feta’ + cucumber parsley salad
T tomato galette + romaine lettuce + navy beans
W mentoring program dinner meeting
R coconut curried red lentils + brown rice + roasted broccoli crowns + kale + squeeze of lime
F Greek potato zucchini casserole + marinated tofu ‘feta’ + cucumber parsley salad
LUNCH
S miso soup + udon noodles + steamed pak choi + edamame
S sourdough toast + cilantro hummus + avocado + coconut yogurt + strawberries + peanut butter
M tomato galette + romaine + navy beans
T coconut curried red lentils + brown rice + roasted broccoli crowns + kale + squeeze of lime
W Greek potato zucchini casserole + marinated tofu ‘feta’ + cucumber parsley salad
R tomato galette + romaine lettuce + navy beans
F coconut curried red lentils + brown rice + roasted broccoli crowns + kale + squeeze of lime
BREAKFAST
S farmer’s market snacks
S tomato galette + romaine lettuce + tofu scramble with spinach
M baked sweet potato wedges + chickpeas + tahini + hemp hearts + spirulina green smoothie
T sourdough toast + cilantro hummus + avocado + coconut yogurt + peach + peanut butter
W baked sweet potato wedges + chickpeas + tahini + hemp hearts + spirulina green smoothie
R sourdough toast + cilantro hummus + avocado + coconut yogurt + banana + peanut butter
F baked sweet potato wedges + chickpeas + tahini + hemp hearts + spirulina green smoothie
Tips: Since I am vegan and eat in a fairly restrictive way I try to be very conscious of what sort of plants I am eating once I sit down to plan my meals. This means that I try and have protein in every meal and also have something green on every plate. Breakfast is the one meal where including protein and veggies is somewhat difficult, so I have come around to eating breakfasts that are both sweet and savory and more filling than simply granola or a bowl of fruit with a cup of coffee (which is often the temptation).
I also try and pay attention to serving sizes so will typically eat 1/2 a cup of rice or beans at one time, no more than a tablespoon of peanut butter and barely ever a whole avocado or a whole (sweet) potato in one sitting. I try to aim for variety rather than large quantities of anything and I read labels quite religiously to make sure I am not over-doing any one component to my meals (or eating something that is not obvious like copious amounts of sugar added to, for instance, pasta sauce and salad dressings).
I eat a piece of fruit after every dinner, usually an apple or an orange, and if I snack I try to make those choices at least somewhat balanced as well. Small cucumber salads with either lemon juice or just a drop of soy sauce or just carrots with a few teaspoons of peanut butter have been some of my favorites lately. When it is less warm, I will often make myself popcorn without any butter or oil as well. As most people eating plant based diets, I am also quite partial to nuts and dried fruits although many are quite calorically dense.
This approach to meals requires committing a fair amount of time to having everything ready by Monday. Most Sundays I spend a couple of hours cooking and that block of time is always factored into my schedule the same way my work and academic obligations are. This can be avoided by either only prepping for a few days at the time or buying more pre-made items. Instead of cooking rice and beans from scratch and making my own bread and hummus I could have easily bought all of those already made.
Please reply to this message if you want recipes or details on anything currently on this list – a lot of it is improvised or cobbled together from various food blogs but I can always offer some pointers.