GoKawiilI woke up yesterday with the following thoughts, which are probably either obvious or dumb.
A central thesis that many readers, including me, took from Douglas Hofstadter’s Gödel Escher Bach when young was that the secret of intelligence (and therefore, of AI) was going to have a lot to do with self-referentiality and “strange loops.”
Even Roger Penrose’s The Emperor’s New Mind, which in some ways was the anti-GEB, ironically agreed with GEB about the fundamental importance of self-reference to the success or failure of the whole AI project. It claimed (incorrectly, in my view and in most experts’) that AI could never work because there was something about Gödel’s Theorem and self-reference that no computer program could ever capture, but that could be captured by exotic physics accessible to the human brain.
Now, in 2026, we’ve succeeded at building AIs that outperform most humans at most intellectual tasks that are well-defined enough to judge. And at no point in the tech stack of those AIs — neither in the transformer neural nets, nor in the GPU clusters they run on, nor in the training process, nor anywhere else — did anyone need to build in anything about self-reference. (Excepting, eg, the system instructions that tell the model about its role and identity, which aren’t needed for intelligent behavior. Also, I’m not going to count the autoregressive nature of LLMs as “self-referential”; that’s just dynamical feedback.)
Of course, GPT 5.6 Pro and Fable can talk about themselves, about Gödel’s Theorem, about self-reference, about what we’re talking about right now, all of it, better than most humans. But at no point did anyone need to build self-referential abilities in. They popped out as a byproduct of the same pretraining that let the models talk about Pokémon and long-chain polymers and cognitive behavioral therapy and plate tectonics and everything else.
No wonder Hofstadter says he’s been stunned by the success of LLMs, and has seemed depressed about current AI capabilities in essays like this one. He’s way too smart to deny what’s happened or invent reasons why it doesn’t really count (the approach many have taken). But he realizes that we now have true conversational intelligence from a path that the GEB worldview would’ve regarded as far too cheap and simple, and that certainly has no “strange loops” built in anywhere.
Of course, a Hofstadterian could argue that a strange loop emerges in LLMs — indeed, nothing in GEB ever said that strange loops would need to be explicitly engineered at the outset. But would anyone who hadn’t been brought up on GEB arrive at this as a useful way of thinking about LLMs?
What can we say about this with hindsight? While the ideas of diagonalization and self-reference of course played a central role in the birth of modern mathematical logic and computer science, the most famous uses were negative: there is not a bijectjon between the natural numbers and the reals. There is not a complete sound proof system for arithmetic. There is not an algorithm to solve the halting problem.
If your goal was only to build the axioms of ZFC and the rules of first-order inference, or build an electronic computer, you wouldn’t explicitly need self-reference for that. You would just … start building, taking care that your instruction set didn’t fall short of universality.
Yes, ZFC can formalize and prove theorems about itself. Yes, electronic computers can run programs that take their own code as input. But no one ever needed to build those abilities in, any more than self-reference needed to be built in to the alphabet or the rules of grammar. It popped out as a free byproduct of universality.
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