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.” ...He could make a similar comment about fractals. Textbooks give examples using self-reference, and then say that the weather is also an example. But self-reference is not used to model the weather.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. ...
But the idea that you’d need explicit self-referentiality before you could get convincing and world-changing conversational intelligence? Let it be buried in a Westminster Abbey or Arlington National Cemetery for the most important wrong ideas in human history — geocentrism, Aristotle’s teleological physics, aether, phlogiston, Freud’s psychology, Marx’s prediction of a workers’ uprising followed by a classless utopia, etc. But buried it needs to be.
There is a distinction between the mathematical tool used for proof/pedagogy and the actual mechanisms that generate the phenomena in the real world.
Diagonalization can be used to construct irrational or transcendental numbers, but most transcendental numbers are not obtained or studied this way.
(I tried to post this comment on his blog.)
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