Infinities, impossibilities, and the man in the white linen suit
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Re: Infinities, impossibilities, and the man in the white linen suit
#2I wrote this partly because nobody seems to know about Gödel who is arguably a more important figure than Turing.
The piece follows four threads where formal limits show up in AI practice today: learnable problems that mathematics cannot sort, neural networks that exist but cannot be trained, self-improving systems that dropped their safety proofs for benchmark scores, and the fact that “will this AI cause harm” is, mathematically, an unanswerable question.
The piece is long and the math is dense. I’m curious whether people see the connection as tight or as overextended—whether Gödel’s structural limits actually do constrain what we’re doing now, or whether I’m collapsing categories that should stay separate.
Re: Infinities, impossibilities, and the man in the white linen suit
#3I wrote this partly because nobody seems to know about Gödel who is arguably a more important figure than Turing. The piece follows four threads where formal limits show up in AI practice today: learnable problems that mathematics cannot sort, neural networks that exist but cannot be trained, self-improving systems that dropped their safety proofs for benchmark scores, and the fact that “will this AI cause harm” is,…
I’m curious how much you used AI to write it, as it’s just chock full of Claude-isms.
Re: Infinities, impossibilities, and the man in the white linen suit
#4I wrote this partly because nobody seems to know about Gödel who is arguably a more important figure than Turing. The piece follows four threads where formal limits show up in AI practice today: learnable problems that mathematics cannot sort, neural networks that exist but cannot be trained, self-improving systems that dropped their safety proofs for benchmark scores, and the fact that “will this AI cause harm” is,…
I’m curious how much you used AI to write it, as it’s just chock full of Claude-isms.
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Re: Infinities, impossibilities, and the man in the white linen suit
#5Aside from seemingly being 100% AI-generated, this article makes a really spurious use of Godel's argument, which I think is best exemplified by the following passage near the end:
"These four threads share a common ancestor in what Gödel proved in 1931, and Turing sharpened in 1936. Rule-based systems cannot fully account for themselves. A system cannot certify its own trustworthiness. A learning framework cannot determine its own boundaries. A safety strategy cannot verify its own completeness.
None of this is softened by the fact that a neural network feels organic rather than rule-like. A model’s weights are numbers, and its training is arithmetic, all of it running on von Neumann’s realisation of Turing’s imaginary device. AI is not adjacent to this mathematics. AI is made of it.
The AI industry, understandably, would rather not dwell on this. "
This is a complete non-sequitur. Godel's argument isn't even that profound: it just says that a system of axioms good enough to embed standard natural number arithmetic must be independent of a certain constructed sentence, i.e., it will run the same whether that sentence is true or false and you can't tell from its axioms which of these two options is in effect. While that sucks for philosophers, it doesn't make mathematics less useful, less dependable, or less correct in a practical sense. It has no practical implications to anything that the AI industry is promising today.
Re: Infinities, impossibilities, and the man in the white linen suit
#6I wrote this partly because nobody seems to know about Gödel who is arguably a more important figure than Turing. The piece follows four threads where formal limits show up in AI practice today: learnable problems that mathematics cannot sort, neural networks that exist but cannot be trained, self-improving systems that dropped their safety proofs for benchmark scores, and the fact that “will this AI cause harm” is,…
I’m curious how much you used AI to write it, as it’s just chock full of Claude-isms.
This does read a little like AI, but I can't see many vocabulary based Claude-isms. But it does start with an anecdote, and there are other aspects of the writing which seem AI.
Re: Infinities, impossibilities, and the man in the white linen suit
#7Yes, but does a computer system or tool or AI need to be provably correct or 100% guaranteed not to cause harm to be useful? Alternative methods (human, simple rules) aren’t either. Perfect can be the enemy of good enough. Just being pragmatic here.
Re: Infinities, impossibilities, and the man in the white linen suit
#8I wrote this partly because nobody seems to know about Gödel who is arguably a more important figure than Turing. The piece follows four threads where formal limits show up in AI practice today: learnable problems that mathematics cannot sort, neural networks that exist but cannot be trained, self-improving systems that dropped their safety proofs for benchmark scores, and the fact that “will this AI cause harm” is,…
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Re: Infinities, impossibilities, and the man in the white linen suit
#9The overall point feels strained to me.
Yes, formal mathematics has such limits. We can't expect machines to be perfect and provably perfect. But the industry isn't assuming that. Why would it? Natural intelligence is not perfect or provably perfect, either.
Rather than certainty, measurement is often enough. We can't prove a program will always halt, but we can check it halts in a specific execution.
Approximation is also often all we need. Even if we can't prove that we can train a network with more than 50% success, if we can get multiple shots at that (using different data, or initial random weights, or training techniques, or something else), then we can reduce that danger exponentially. (I don't know that we have a guarantee of succeeding there, but this would be the hope, and I am not aware of anything showing it is impossible, unlike perfect provability.)
Finally, it is possible that perfect provability does work on the problems we care about. Godel and Turing etc.'s proofs rely on finding rare situations where we can't prove things - cleverly-constructed pathological cases - but perhaps human behavior does not fall into that set. Human behavior may not be a pathological case for proofs or learnability.
Re: Infinities, impossibilities, and the man in the white linen suit
#10This wall of slop is just a long, boring ad.
> We help companies make sense of technology and build lasting improvements to their operations.
Could it possibly be any more meaningless? I could help make sense of words and build lasting improvements to drivel.