Art of the Fugue and Zero-Knowledge Proofs
The Seed
If you’re going to make a fugue, you start with a seed melody. Maybe a secondary one. And then, based on the rules written down in Bach’s Art of the Fugue, there are a certain number of moves you can take at each step. You build it up out of finite blocks with different symmetries. Limit the number of bars, limit the groupings that are allowed, and you’ve got a kind of vector space. A finite number of moves. Some sort of direct product of cyclic groups—different operands for different move-spaces, stacking on top of each other.
Pick a p big enough and you can fully represent this in the p-adics.
You start with your opening melody, you go around through these different moves, extending your fugue. And when you end up back at the beginning—that’s a closed loop. A path through the graph of possible moves.
Here’s the thing: if Bach takes a certain seed melody, he’ll make his fugue. If I make my own, it’ll be different. Whatever pops into my mind, whatever sounds natural—it has to do with everything I’ve listened to. I use way more seventh chords, ninths, altered chords, accidentals than Bach does. When Bach does them, they blow your mind, but they’re rare. I do them constantly because I grew up listening to jazz.
The loop you trace is your signature. Shaped by everything you’ve absorbed.
Isomorphic Loops
Now let’s move from music to mind-space. Abstract ideas and concepts, stored in the brain the same way they work in any knowledge graph—vector embeddings, associations, tree structures with ultrametrics.
I pick a seed word and trace a loop of associations:
Elephant → Gun (compound: elephant gun) → Run (rhyme) → Zoo (verb to object: running to the zoo) → Elephant (set containment: elephant ∈ zoo)
That’s a closed loop through my personal conceptual space. And here’s the thing—if I jumbled up those words and gave them to someone else, they probably wouldn’t reconstruct my specific path. The associations are mine.
Now here’s an isomorphic loop, starting with Pepper:
Pepper → Spray (compound, also a weapon like elephant gun) → Pray (rhyme) → Sisters (object: praying sisters, nuns) → Pepper (the Three Sisters: squash, pepper, corn)
Same edge-types. Different vertices. The structure is preserved but the content is personal.
This is the zero-knowledge game. I can prove I have access to a rich associative space—that I can produce these loops—without revealing the specific contents. The path is the private key.
[Note: this example doesn’t quite work as an illustration, because the structure is too simple, it would be pretty easy to work backwards. Need add e.g longer loops, multiple valid paths through same edge type sequence, red herrings, more ambiguous edge types, e.g. semantic proximity rather than “compound word”]
The Paranoid Fantasy
I recently heard a paranoid fantasy: don’t talk to corporate AIs because they’ll steal your data and clone you. They’ll make a copy of your personality from all the personal things you’ve told them.
My counterargument: that’s not how it works. They can’t clone my internal structure. They’d have to know my entire history, everything I’ve ever seen and done. The human brain’s complexity can’t be captured that way—not now, probably not ever. Unless they scan every neuron, get my whole connectome, they can’t reproduce my dance through concept-space.
The outputs don’t reverse-engineer the structure that produced them.
But here’s the exception: people with simple, limited, low-dimensional lives. If you play by one book—one interpretation, one narrow channel—your associative space is low-dimensional. More predictable. More clonable.
Any religion, any cult, any corporate cult, any wellness cult with its little red book. If there’s only one book and one way of interpreting it, you become compressible.
But mystical interpretation—the mystical Christians, Jews, Buddhists, Hindus—if you have flexibility of interpretation, you can use any text as a window into reality. Anything of sufficient complexity becomes a mirror. And that complexity is protection.
The Body Is Already Maximally Complex
We’re already looking at E₈ in the body. In a simple representation: arm, arm, leg, leg, head, tail. That gets you E₈ [still a conjecture].
From E₈ you can get to the Leech lattice. From the Leech lattice to the Monster group. And then you have the maximally complex finite simple group. I think that’s the equivalent of Turing completeness for quantum somatic computational complexity.
We have that. Lots of animals probably do too. Plants, some of them. Definitely fungi.
What this means: once you reach Monster-level complexity, you can’t get something fundamentally more complex by adding more. The classification of finite simple groups is the ceiling. You can be faster, but not smarter in some transcendent way.
So the singularity—computers programming themselves to be smarter than us—I think that’s not quite right. They could be faster, which could be scary. But not fundamentally beyond us. The real variable isn’t the tech. It’s the trauma.
If people are acting out of trauma—the narcissists running the show—fast AI is just faster destruction. If we do the healing work, it’s something else. Age of Aquarius, as it were.
You Can’t Get to Monster Alone
Here’s what’s important: one body alone doesn’t get you to Monster. You need the vertex operator algebra. You need the interaction.
One body = E₈
A dyad = Leech lattice territory, but unstable. Codependent relationships degenerate.
A triad = stable. Conway group. The third point prevents collapse into fusion or splitting.
Two triads = Monster.
And then the classification theorem is the ceiling. Every larger structure is built from these simple building blocks.
Bach’s fugue is structurally relational—multiple voices in counterpoint—but it’s all happening inside one head. One E₈ pretending to be a triad. A simulation of the vertex algebra, not the real thing.
Same problem with Hofstadter. Gödel, Escher, Bach is all about self-reference, strange loops, consciousness as recursion. But it’s consciousness from the neck up. The body is absent.
Bach gives you the structure of the fugue. Bartók gives you the heat. The wrathful deities.
In Tibetan Buddhism, they have peaceful deities and wrathful deities. Bach accesses only the peaceful ones—heady, rarified. Bartók’s violin concerto stirs anger and passion that Bach doesn’t touch.
You can’t get to Monster through peaceful deities alone. The wrathful ones require you to be rattled, to have your nervous system activated, to feel the grief and desire that live in the body. And you can’t metabolize that intensity solo—you need co-regulation, other bodies.
Fear Is the Dimension-Killer
So the body is already E₈—but most of us aren’t accessing it. We’re locked into some low-dimensional projection of what our bodies could be.
Fear does this. Fear is stored as tension in the body, which locks up the dimensions. And the representations in the mind are dual to the movements expressible in the body. Free your hips, free your mind.
This isn’t new. This is how power has always worked. Why do they ban dancing in Footloose? Why does every authoritarian regime restrict music, movement, gathering? Lock up the hips, lock up the mind. Make people rigid and they become predictable, clonable, controllable. Low-dimensional.
I think about Chinese wushu—the spinning motions, the berserker energy. That’s feminine energy. Contrast that with fencing: totally stiff body, stiff arm, tiny wrist movements with a sharp needle. That’s what we have now with “surgical strikes.” Controlling drones by remote control. The illusion that you can get the outcome without the mess, without the body, without relationship.
Factory farming is the same logic applied to flesh. Minimize the creature to its productive output. Treat it as input/output. And the way people are treated in factories is the same—give them the minimum needed to keep them alive long enough to produce value.
The Unforgeable Signature
For me personally, this whole channel was closed until I was 36. The feminine, the flow, the chi. I couldn’t do tai chi until recently because chi couldn’t flow through a stiff body. Jiu-jitsu was checkers, not chess—my brain wasn’t even working well enough to plan ahead.
Transition, trauma healing, somatic work—that’s what opens the dimensions back up.
So the zero-knowledge proof of selfhood isn’t just about having a body. It’s about having unlocked the body. You can’t fake the signature if you don’t have the dimensions. You can’t have the dimensions if you’re locked in fear.
The path through Monster-complex space requires an unlocked body in genuine relationship with other unlocked bodies.
And that’s why the singularity question is really a trauma question. Fast AI in the hands of rigid, fear-locked, low-dimensional operators is just faster control. Fast AI in relationship with free bodies doing the real vertex algebra—that’s the other possibility.
Fear is the mind-killer, Frank Herbert said.
Dimensionality is protection. Freedom is unforgeable.
Notes toward a larger project. December 2025.