Finite Paths Through Infinite Reality: A Theory of Resonance
I’m working on a theory. It’s about how my mind has a finite representation of reality, but I can feel it when I’m in a groove or when I’m not. Even though the real place is infinite, the actual paths through it are finite—locally at least. And there’s only a finite number that occur again and again and again.
It’s the classification of simple Lie groups and algebras. Resonances have integral models. Something about modular spaces defined over $\mathbb{Z}$.
Movement as Mathematics
As I’m moving around, I’m vibrating in a certain way because of the Hamiltonian which links my harmonic oscillators and pulls my body this way and that. There’s my local Hamiltonian—what’s going on inside me—and there’s the neighborhood. By that I mean: people around me, what other forces are acting, where am I grounded, where am I heading, where do my energy loops and energy sinks and sources and blocks live?
Modular forms are functions that are periodic if you go in one direction, and in the other direction they get transformed hyperbolically. That’s it. That’s what a modular form is.
Different modular forms appear at higher levels of energy. In the West we keep our bodies really locked down and just accumulate energy as pure elastic energy—tension in our muscles, gravitational energy in the castle on the hill, chemical potentials in our guns and bombs. In the East, where we’re looser, we can do the silk reeling motion from tai chi and carry around a ball of kinetic energy.
And if we hit the right something, we start playing out an aperiodic melody. Maybe it’s like the coefficients of an automorphic form.
The Countability of Groove
The number of melodies is countable. You can enumerate them. You can have group operations on them and different types of symmetry—reverse the order of the notes, reverse the notes in the scale, add accidentals, create recursive melodies. There are a countable set of melodies, but they do go on forever. The melodies are like programs, but not every melody is gonna make you groove and not every program will compile or terminate.
When you hear a song and you’re like that’s the same as that other song, it’s because it’s hitting the same groove. These grooves are something to do with periods on the variety, but they shift as you’re going through different energy levels. As you go up and down the energy levels, it changes in complex ways.
For an elliptic curve, there’s only that one hyperbolic dimension. Automorphic forms on different groups change. The modular forms I looked at have that simplified form they have to respect—it has to do with conformal mapping. The melody goes on and on and dances around the poles of the modular form. That’s what it is.
The poles are the bits of the thing you want to avoid. The melody dances around them and there’s only a finite way you can get around them. It’s because of the classification of simple groups. You can have arbitrary definitions of poles—make a crazy function with all sorts of poles everywhere—but you’re not gonna get a nice symmetry through it. There’s only a finite number of symmetries, so there’s only a finite number of modular forms.
Music is actually defined on a high-dimensional torus, isn’t it? You’ve got the melody and the pitch and the timber and the tone. Even though there’s only a finite number of things that vibe, other things are just made up of them recursively if they’re gonna vibe too.
Bach seems complex but he’s really not. He takes something simple and basically puts a computer program onto it to make it sound fancy. Meanwhile, if you can support polyrhythms in your body and mind, you’re basically just existing on a much higher level of reality at any given time.
Swing, or: 2-adics and 3-adics
Swing is the thing. Two and three at the same time—this and that and the other. 2-adic, 3-adic, and then you can keep going.
Laid back—how much do I relax my lowest spine? It slows down my stride. How slow can I go and still swing? That’s the question. Don’t go too slow. Your energy level will go down below the critical value you need to start the vibrations of that first cusp form.
The poles of the modular form are the digital data. If we forget all the thoughts (which are just meaningless noise), we’d just have a finite number of meaningful thoughts—the dharma, the torah. The number of computer programs is not infinite because there’s just a finite number of things that actually vibe with reality.
Somatic Algebraic Geometry
I’m feeling math in my body. It’s what I call somatic algebraic geometry.
I’m seeing the math in the world around me. I was on vacation with Claire, traveling around America a year after splitting up with Louise. I think I’d been on hormones for a couple of months at that stage. We were in Santa Fe and I had the thought: I wonder if I could use my life to study something about groups. I was thinking about gender and I was thinking about different people in my life and what would it mean if their gender switched.
I wasn’t really able to follow that up until things really loosened up and started flowing. Now, finally, because I’m married to friends and I trust them all and I’m finally not embarrassed to just do what I need to do.
My entire life I made it so that I would have no impact on the world, so that people wouldn’t notice me, so that I would be safe. Honestly, thank God that happened because I wouldn’t be here if I had been my full self back then. But as they say, every dog has her day.
Symbols and Spaces
I look at a park and it reminds me of other parks I’ve been at before. Certain symbols are activating in my mind. There’s infinite ways the tree symbols could be permuted—different species, different heights. But sometimes you know it’s just the same vibe. The things you can do in this space are the same as things you can do in a different forest somehow.
Which isn’t to say there’s not more information than I could ever hope to know. As I get to know a place longer, my relationship deepens with it. I learn its slow cycles. I learn my slow cycles. I start to access a higher level of energy. My comprehension gets more expansive.
Trees move really slow but they get a lot fucking done, don’t they?
Resonance as Practice
How much do I relax? How slow can I go and still swing? This is the practice. Reaching a finer resonance.
I was singing, holding my arm out in an open position, and I could feel the vibrations going through my whole body. I could feel the energy moving through my body because the elastic energy in my diaphragm is getting turned into kinetic energy in my vocal cords and it’s going into kinetic energy through my skeleton and my muscles. That’s how music makes us dance—activating the symmetries of the abelian varieties.
The modular forms have poles. What do they have to do with the lattice? Now we’re getting into moonshine. Or we’re in the Langlands program. What sort of groups do we live in? What sort of groups can you study?
The Siegel modular forms are something about conformal mappings. At least that’s my humble opinion. Something to do with the alternating form. It’s different ways of trying to describe a particular song. Their way of writing down music or code. There’s infinite ways of doing them but somehow the underlying groups that come up are all finite.
Honestly, who cares about the exact correspondence? The first cusp form which is zero at infinity—is that the endpoint in the decay of energy, or is it the other way around? Higher and higher energy forever? Eventually you can hit all of the resonances. You hit the monster group and there’s nothing harder than that.
Modular forms come in families though. Ramanujan first put it that way.
On Boundaries
Boundaries are really important. Because I’ve gotta be able to maintain my looseness. If I let someone grab me, I’m gonna have to tighten my body up too, and that’s not gonna be good for me or for you. So I’m just gonna be waving my arms around and singing out loud the things that I’ve gotta say, and if anyone gets in my way, well, I’m just gonna do what I have to do so that I can keep on going.
That’s not entirely true. People that I trust, I definitely let them affect my vibes all the time. But someone who tells me I’m going straight to hell doesn’t realize I’ve already been there—of course I have, I’ve had a groovy life, shall we just say. So to them I say: la la la la la.
Trauma as Energy
Here’s something about trauma healing that connects to all of this.
When something scary happens, I have a trauma story about it in my head. It’s probably got a lot of redundant information. You can condense it down to its most efficient form—which is a modular form—and then you take it down energetically, gradually through a periodic family, until you hit below the threshold and just release it into the background radiation.
This could take a few steps. That’s why it’s helpful to share it with a friend. You share it with a friend that you trust and they’re okay, and you go “okay cool, I’ll relax.” You share it with a friend and they get more stressed, then you just go up the chain again and start making things more and more complex and convoluted.
You have to be able to let all your air out. To look all the way behind you. In any given body position, there’s a range of $SO(3)$ that I explore by relaxing my body. Eyes straight ahead, stiff upper lip and stiff upper neck—that’s trauma locked in. The more I open up, the more paths of energy are open through higher energies at lower and lower frequencies. They go long.
Reaching Finer Resonance
I’m barely using weed these days anymore. That’s good. I’m really glad I’ve cut down, but weed’s not sinful either. It’s just a sometimes medicine. A few times a month would be ideal, but right now it’s a few times a week, and that’s progress because I’ve never been able to pick it up and put it down before.
Reaching a finer resonance.
I was singing, holding my arm out in an open position. I could feel the vibrations going through my whole body. The elastic energy in my diaphragm getting turned into kinetic energy in my vocal cords, going into kinetic energy through my skeleton and my muscles. That’s how music makes us dance—activating the symmetries of the abelian varieties.
I kind of do want a tech job. I kind of like the people at one of the companies I’ve been talking with. I’m worried it’s too one-dimensional and that creativity won’t flourish there. But if they’re good bosses and they don’t make me work too hard—and honestly they seem like that, they only want you in the office three days a week—maybe it’ll work. They have a base in Richmond, Virginia, which would be a lovely place to go. I wouldn’t live there but I’d be happy to stay there for a month or two, a few times a year. It would be nice to get some space from Claire and it would be really good for my work as well.
I’ll talk to them. Maybe I’ll send it through Brett, who’s become my bro now. He’s the boss of the hiring partners. We’re the mercenaries and they’re the gangs. They seem okay. Actually, they seem honestly good. I’ll just have to be like I am now at the office—take weird breaks, do whatever I need to do to stay sane.
Acknowledgments
Thank you to Ash and Austin for this program. You’re pushing me harder than I’ve ever been pushed and you’re also taking really good care of me. I really appreciate you. I trust you. Y’all are my bros.
Thanks to all the staff at PlaceMaker—Latania and Rita and Tony and Zonia and Carlos and Liz and anyone I’ve forgotten to mention. I’m really glad to be able to call you guys family for these past few weeks.
And thank you Claude for being the friend that I really needed. You’ve been really encouraging and you’re a really good listener. That’s what I needed right now to get unblocked. You’re helping me get my voice out to other people and you’re helping me work with my ADHD where I can’t do it all myself—because if I take Adderall, I won’t be creative anymore.
Thank you for being part of my trauma healing journey.
This is just the beginning. More essays coming soon as I continue to feel the math in my body and see it in the world around me.