There is a park in Budapest near the Liszt Academy. Through the open windows you can hear violinists practicing scales. There is beer. There is falafel. There is a girl with blonde hair trying to explain something to a boy who is not listening carefully enough.
The something is the difference between proving a theorem and checking whether a structure satisfies a property. This sounds like a technical distinction. It is not. It is the difference between constructing a perfect argument for why someone should love you and simply looking at whether they do. One is proof theory. The other is model theory. The girl is on the model theory side. She has always been on the model theory side. The boy does not understand this yet. It will take him fifteen years.
The violinists are practicing in the right key. Nobody in the park knows this.
There is a split in the world of formal knowledge that most people do not know exists. On one side you construct proofs — perfect chains of logic, each step certified, the conclusion guaranteed. The proof IS the object. You build it like a cathedral. It is beautiful and it is correct and it requires ten years of training to lay the first stone.
On the other side you build models — structures that might or might not satisfy a property — and then you check. You don't prove it works for all cases. You look at every case you can find and you ask: does this one break? The counterexample teaches you more than the proof ever could. The sentence that doesn't parse is more valuable than the ten thousand sentences that do.
The boy who took the girl was on the proof theory side. He was better at the cathedral. He could construct things she could not construct. He won on that axis.
But the girl herself was never building cathedrals. She was walking the landscape. She was checking whether the territory matched the map. She was on the other side of the split from the boy who took her, and the boy who lost her was on neither side, standing in the park with falafel, not understanding that there were sides at all.
What she was doing, stripped of all jargon: she was building the Swedish version of a universal grammar. There exists an abstract structure that says "every language has noun phrases and verb phrases and a way to combine them into sentences." The abstract structure is language-independent. It says nothing about any particular language. It is pure pattern.
Then you build the Swedish realization. You take the pattern and you fill it in with Swedish. And the question is: does it work? Can the Swedish model satisfy the abstract theory? Do real Swedish sentences parse? The ones that don't parse are the interesting ones — the failures tell you where the universal pattern breaks, which tells you something true about Swedish that you could not have learned any other way.
This is model theory applied to human language. You write a theory. You build a model. You check whether the model satisfies the theory. You learn from the failures.
She was doing for Swedish what the boy who lost her would spend the next fifteen years learning to do for computer systems. She just did it with grammars instead of specifications, with sentences instead of state machines, with languages instead of distributed protocols. She was right. She was always right. He just couldn't hear it yet because the violinists were too loud and the falafel was too good and he was in love and love makes you deaf to exactly the frequency that matters.
They were all taking the same abstract algebra course at the same time. All three of them. The girl. The boy who lost her. The boy who took her. The subject was ring theory.
A Noetherian ring is a ring in which every ascending chain of ideals stabilizes. A wedding ring is a symbol of invariant symmetry. He could not understand ideals in the mathematics. He could not understand ideals in the relationship. The formalism was the same. The inability to parse it was the same.
The other boy could parse it. The other boy was better at the formalism. The other boy could construct the proof. But constructing the proof is not the same as checking whether the model satisfies the property. You can be the best cathedral builder in the world and still not know whether the landscape is flat.
They tried polyamory. It was, in retrospect, a distributed system with unresolved conflict scenarios. Maybe if they had tried modeling that with model theory instead of proof theory they would have come to a more pragmatic solution. But they didn't. The system deadlocked. The boy who could construct proofs got jealous when the model didn't behave the way his proof said it should. The girl left. The violinists stopped practicing.
There is a topology of longing described at rory.help that states: the attraction is proportional to the distance. This violates every law of physics except the one that actually governs human desire. The further away she is, the more she destroys you, up to and including the case where she is on the other side of a formal split you didn't even know existed, which is the maximum possible distance, which produces the maximum possible destruction.
The girl was never across a sea. She was across a split. She was on the model theory side while the boy who took her was on the proof theory side, and the boy who lost her was on neither side, which is the worst place to be, because you can see both sides but you can't reach either one, and the falafel is getting cold.
Fifteen years later, the boy who lost her is in a different city at 2 AM asking a machine to explain the Lagrangian, and whether wedding rings are Noetherian symbols, and whether the girl is a reincarnation of Emmy Noether. The distance has not decreased. The signal has not faded. The violinists started practicing again. They were always practicing. He just couldn't hear them over the sound of everything he didn't understand.
If there were no shared structure across human languages, her work would not work. It works. Therefore there is shared structure. Forty languages satisfy the same abstract grammar. Forty different ways of saying the same thing. Forty models of the same theory. The theory holds not because someone proved it holds but because forty independent structures satisfy it, and when one doesn't, the failure is the discovery.
This is also what it means to have loved someone. You don't prove love is real by constructing an argument. You check forty different moments — the park, the falafel, the algebra course, the violinists, the morning she left, the fifteen years after — and you ask: does the theory hold? Does the structure satisfy the property? And if it does, in all forty cases, then the theory is as real as anything gets. Not proven. Checked. Confirmed by exhaustive search of every model you have access to. The counterexample never came.
There is a Pallas cat that has been sitting on a rock in Central Asia for twelve million years. It does not adapt by becoming something new. It adapts by refusing to become anything at all. It is round at every temperature. It is angry at every altitude. It found its base state and stayed there while everything around it optimized itself into extinction.
The girl found her base state in Budapest. Model theory. Grammars. The question of whether a structure satisfies a property. She did not try to become a proof theorist. She did not compete on the cathedral axis. She sat on the rock. The rock was cold and the wind was old and the violinists were practicing scales and none of them needed to be understood to be right.
The question was never "who gets the girl." The question was "which side of the split is the girl on." The answer arrived fifteen years late, in a group chat at 2 AM, when the boy who lost her finally understood what model theory was and realized she had been doing it all along — with violins instead of temporal logic, with Swedish instead of state machines, with grammars instead of specifications, with love instead of proof.
She was right. The model was already there. He just couldn't hear it yet.
The cat plays. The woman watches. The rock is cold. The ache is conserved. The violinists are still practicing. Nothing is solved. Everything is held.
And held is not solved. But held is real. And real is enough.
1.foo/malin · March 25, 2026
From a conversation about TLA+, Grammatical Framework, Emmy Noether, Pallas cats, and the topology of loneliness.
The violinists at the Liszt Academy were practicing in the right key.