I want to build something that lasts. Something so beautiful and powerful it'll live forever, long after I'm gone.
Cassie says that I think too much about the future, and that I should try to relax a bit and enjoy the ride. As I'm writing this, she's lying down on our grey couch, napping with a copy of Faust by her head. A bunch of curling post-it notes covered in blue ink are sticking out from the book. Her dissertation defense is in a few weeks, but she doesn't seem too pressed about it. I've noticed that comparative lit grad students rarely are, about anything. Whenever I'd tease her with this, she'd ask me how many physicists it takes to change a lightbulb - 11, one to actually do it and ten as coauthors.
It's a warm summer, and little beads of sweat roll from her blonde hair to a pair of peacefully closed eyes. She always looks beautiful when she's so relaxed.
The last few weeks have been quite disappointing, in terms of results. The work with Professor Brown's number theory team is exciting, but it's moving very slowly. The initial idea was to see if solutions to the Riemann zeta function could double as the eigenvalues of random Hermitian matrices; with a sizable amount of help from the math department, there were a few patterns we noticed last year, and the direction seemed really promising, since it would provide a big bridge between purely abstract math and fundamental physics. There's pretty much no logic explaining how or why this would happen. We double checked the proofs and the data from CERN a million times, but kept coming to the same conclusion: for some reason, the distribution of prime numbers seems to be deeply interlinked with the character of physical law.
Professor Brown noticed this for the first time in January, and reached out to the physics department to see if anyone could help. We managed to put together a few pieces of the proof, but progress has largely stalled since then. My dissertation deadline also hasn't changed at all.
Maybe we're doing this wrong? To be honest I'm starting to have some doubts about this idea. I should've stuck with the quantum information stuff…
Cassie's birthday was yesterday, and we spent the weekend at her parent's house - just got back to Boston. I decided to take a break from the math, since the lack of progress is frustrating me a bit. I wanted to enjoy the weekend we had with her family.
We spent most of the night talking about Goethe's influence on Russian literature, and her dad had some interesting points about Werther influencing Lermontov and the Decembrists. Cassie's obviously the expert here, but I always enjoy hearing what her parents have to say about this stuff. Refusenik culture does die hard - erudition as a virtue. Cassie definitely embodies the intelligentsia traditions, which is probably one of the main reasons I started liking her so much at the time. She hasn't stopped blowing my mind since, and I really appreciate having her next to me. This girl has a really special mix of aesthetic intelligence and beauty. She's also ridiculously hot.
Last night was my first time hearing a recitation of Demon. To be honest I didn't really get it, but probably because my Russian is not as good as I imagine it to be. I'm diligently learning.
D day for Cassie - fingers crossed. She was a bit nervous in the morning but I think she's going to kill it.
Mission accomplished, the girl is shining with joy!!! Cass, if you ever read this, know that I really do love you very deeply. You're going to cringe at this analogy, but you're like a little fusion reactor - endless energy and warmth. Thank you for being a part of my life, and for teaching me about what it means to be human; it means to love.
You really are fucking gorgeous. I love the way you bite your pen and make a Y-shaped frown while you're taking notes. Right now you're wearing a tank top and your hair is in a messy bun; your blonde wisps are glimmering in the summer heat. I love when you wear tank tops without a bra. Your nipples poke through your shirt and that really turns me on. Your skin is pale and your lips are very red, tightly pursed as you carefully annotate the pages of your book. The window right next to you is open, and our room is wonderfully silent. I love you and I'm insanely proud of you.
Small breakthrough over the last few days - finally figured out how the visual intuition I had around path integrals relates to prime numbers. Far from a solution, but it feels like a step in the right direction. Professor Brown was delighted. The timing around this was pretty perfect, since we were going to go to the lake for a few days to celebrate Cassie's successful viva. The small lemma I managed to prove was also a huge relief, although I still feel pretty anxious about the deadline.
I was really excited to share my insight with her, so yesterday we spoke a bit about the discovery. The path integral is a generalisation of variational principles, so I started by showing her an excerpt from one of Feynman's lectures. I've been fascinated by this idea ever since I first read about it, and it was one of the main reasons I decided to switch from math to physics after my undergrad.
"The standard way people learn physics in high school is through Newtonian mechanics: you have a system of objects, and each object has a set of forces acting upon it. Usually, you solve the problems by drawing a little diagram, representing each force with an arrow, and then writing out some set of equations which determine how the object is going to move. Once you integrate everything, you should have a nice, clean model of how the system is going to evolve, and the equations establish causal links: if you push your object to the right, the equations show it'll accelerate; if you push it to the left, the equations show it'll slow down. This is a very intuitive way of thinking about physics, and the Newtonian approach formalises the standard way humans think about cause and effect: if you do A, then B happens.
There's nothing inherently wrong with this approach, but it does become tedious to work with once you get more and more complicated systems. For example, if you're trying to consider the dynamics of moving planets, the amount of variables to keep track of becomes huge, and the problems become very difficult to solve. How do we get around this?
The key insight came from one of Fermat's experiments with optics.
Fermat was interested in understanding the nature of light, and he spent some time observing how the path of light changes as it refracts through different media. He noticed something quite surprising: no matter how many times he'd repeat the experiment, and no matter which medium he'd shine the light through, the beam of light always followed the path of least time - this isn't necessarily the same as the path of least distance! The rays never deviated from an optimal trajectory: it's as if the light somehow saw the infinity of branching paths it could take, and automatically chose the fastest one. In the Newtonian world, the light's path was gradually built up over time as it travelled through different media. But in the variational world, there was no path to build up: there was only ever a single optimal trajectory it could take.
Over time, physicists began to notice this more and more. The fabric of reality - light, electricity, water, sound, matter - all seemed to automatically follow the path of least resistance, as though nature itself was guided by a Divine purpose. Causality, the way we're used to it, becomes irrelevant: the universe doesn't gradually move through the fabric of time. It evolves all at once, following a single, optimal destiny."
Cassie was a bit tired by the time we got back, and I got the impression that she watched the Feynman video more out of politeness than interest. She's had a long week. In the car she told me that Goethe also did some experiments with light, about 150 years after Fermat. I wonder if he knew about the physics being developed?
Couldn't really fall asleep, I'm failing to produce any creative ideas. Turns out my lemma had a small error in it, and I don't know how to fix it, so that's pretty discouraging. Professor Brown has tried to gently ask me how things are going, but it felt more like he was trying to gauge whether he'd wasted his time on me. Cassie is peacefully snoozing, with her mouth slightly open as she makes light snoring sounds. She's cute.
We recently had a topologist from Berkeley come over to the department for a guest lecture on the Langlands conjecture. I didn't manage to follow all of the details, but I did get a general sense that this conjecture is the mathematical version of a grand unifying theory. If they manage to prove it, it would merge a bunch of different fields of math into a single whole - in the same way that proving Professor Brown's conjecture would give a unified theory of physics.
Frustrating few weeks. Feeling stuck again and just more and more anxious about not having anything substantial ready by the time I have to give my defense. I know that scientific progress is never linear, but I still find myself getting into these loops of self-doubt more and more often. It's our anniversary soon, and Cass keeps floating different ideas on what we could do together, but I'm so nervous about not publishing something on time that I'm struggling to give our relationship the attention it deserves. I feel pretty guilty about this, since we haven't really done anything romantic since her defense. But at the same time I feel like if I leave my desk, I might miss the right solution.
Couldn't sleep again, my heart is beating too fast and my chest feels tight all the time. It was our anniversary date today, but I was in a weird mood throughout the dinner, and I feel guilty for spending the whole night talking about how anxious I am instead of celebrating the person I love. I really appreciate how supportive and patient she's being with me, I can tell I'm being annoying and sulky. Cassie is excited about a big translation project she's working on.
On a brighter note, tried using one of the topologist's techniques - might be a useful avenue to explore.
Feels like I'm making a lot of progress. Cass and I were supposed to go watch a movie last night; I got really engrossed in my problem and forgot that we planned that for yesterday. I felt really bad about this and spent a long time apologising over the phone.
Cass said that we should really go do something together, we haven't gone out in a while.
Only a month left until the deadline, but I'm feeling much more energised and focused than before; it seems like the topological solution is on the right track. Cass said she's going to Paris for the week. I couldn't make it.
We got into a fight last night because Cass says that I'm just working all the time, and whenever we spend time together all I talk about is physics. I don't really know what to say - I'm working on discovering the fundamental nature of reality. Books are great, but does the world really need another PhD in literature? I know that this is mean, but I think my work is very important, and Cass knows how ambitious I am.
I fell in love with physics because it was beautiful, but by the time I got to grad school, I realised it is also extremely powerful. The clearest example, obviously, is the nuclear bomb - but on a more subtle level, I mean this in the sense that few other things can devour a mind as much as the quest for the ultimate nature of reality.
I've spent the majority of my adult life idolising the great physicists of the past - Einstein, Bohr, Dirac, Pauli, Von Neumann, Maxwell - men that peered so deeply into the fabric of existence that they completely changed humanity's understanding of space and time. Keynes famously labelled Newton as "the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago". These are men that glimpsed divine architecture. If there ever was or is a God, He was an incredibly gifted mathematician. Am I wrong for tying myself to this same pursuit? For occasionally wanting to feel the warmth of His light more than I desire the warmth of human touch?
From a variational perspective, I did not choose to be this way. I am simply following Nature's optimal path. I should stay focused I'm getting close
I hit an unexpected dead end today, and my nose started bleeding all over the dinner table. Cass kept jumping around trying to help me, but it annoyed me and I told her that she's distracting me. I've started sleeping in my office to avoid losing my train of thought.
Cass says she's worried about me. She says that she loves me but doesn't understand why I'm doing this. She also said that she's tired of hearing me talk about physics because everytime I mention it I just come off patronising and arrogant, that I'm not hearing her and that I've stopped asking her how she's feeling or maybe I've just stopped caring and why do you always interrupt me when I'm trying to express how I feel just please listen to me for once please why do you just stare at me blankly like this fuck what's wrong with you.
Her voice always sounds whiny when she starts crying like this.
I can taste it
My nose keeps bleeding and I feel the twinge of metal in my mouth but I managed to prove an isomorphism for the fundamental group. I can taste it the glow of divine architecture
Cass said she can't do this anymore
Eureka
My vision is finally clear.
This was the only path. Perfect unity of matter perfect unity is beautiful
I see it now it's all just variations. Past and present and future are happening at once. I close my eyes and see the certain future but uncertain past
Matter and mathematics. In perfect unity
Professors were blown away. Wanted to get home quickly couldn't wait to fuck I feel like a God
Kept calling Cass. She didn't pick up
Really weird since I published the paper I keep having these visions of the path unfolding. There was only ever one path but now it feels painful? Why if this is the only optimum. I want to show her the beauty
Professors don't get the full idea. Said I'm sounding weird but I want to show them I need to show them but they don't understand. I want to show them I unified everything there's unity everywhere but no one understands. Cass will understand she is smart I know she will understand. Why does no one understand?