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Infinities, impossibilities, and the man in the white linen suit

iain.so

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Re: Infinities, impossibilities, and the man in the white linen suit

#11

Post by c2c2c »

skippyfish wrote: post #5

Aside 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 de…

I think this is selling Gödel a little bit short. He proved for the first time that in any system of mathematics with enough complexity to be interesting, there are statements that cannot be proven true or false. The Gödel sentence might seem like a trivial example, but other examples of such things have been discovered since, such as the continuum hypothesis which the article mentions.

Re: Infinities, impossibilities, and the man in the white linen suit

#12

Post by lubujackson »

This is a fantastic article with lots of interesting questions raised between the halting problem and applications of AI.

The MRI example is very interesting - add a bit of noise and the crisp results fall apart. But we know we can carve out some determinism by orchestrating around LLM (validation loops) but they are only as good as the coverage of validation and the fidelity of expectations.

Which raises a fundamental question: where is the line between an effective harness and a broken one?

To put it in halting problem terms, if we have an outside program that checks the internal program for halting, we know we will capture some number of previously incatchable halting problems. How can we quantify this? We know there is a class of halts we can catch and prevent, but there will always be more complex ones that escape us.

In the real world, knowing the task is impossible doesn't impact the value of reducing the problem. More importantly, knowing which types of halting problems can be fully captured and which ones are intractable. Agent orchestration could directly benefit from layering a framework over this fuzzy space of knowableness.

Re: Infinities, impossibilities, and the man in the white linen suit

#13

Post by skippyfish »

c2c2c wrote: post #11
skippyfish wrote: post #5

Aside 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 de…

I think this is selling Gödel a little bit short. He proved for the first time that in any system of mathematics with enough complexity to be interesting, there are statements that cannot be proven true or false. The Gödel sentence might seem like a trivial example, but other examples of such things have been discovered since, such as the continuum hypothesis which the article mentions.

The article is massively overstating the implications of Godel to the AI industry, so to be clear - are you defending the article, or are we bikeshedding about my phrasing? Because my "not that profound" should be interpreted as relative to the article.

Re: Infinities, impossibilities, and the man in the white linen suit

#14

Post by bglusman »

iainharper wrote: post #2

I 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,…

This is a wild statement to me that “nobody seems to know about Gödel”… I think I learned about him when I was like 12? And while I’ve certainly met plenty of people who haven’t heard of him, until 10-15 years ago the same was true about Turing, mostly changed by a some Hollywood and/or literary references… and Gödel had a tiny bit of that in Oppenheimer if i recall, though not to the same degree? I bet if you asked 100 comp sci students if they’ve heard of Gödel at least 50 would say yes? On what basis do you think no one has heard of him? Not many have read the original math, sure, but… the idea that he was a mathematician who wrote an incompleteness theorem? VERY widely known.

Re: Infinities, impossibilities, and the man in the white linen suit

#15

Post by Swizec »

azakai wrote: post #9

The 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 i…

> We can't prove a program will always halt, but we can check it halts in a specific execution.

The computer scientist says “The halting problem cannot be solved, I have proven it” and the software engineer goes “30 second timeout, if the answer’s not ready by then we don’t need it”

Re: Infinities, impossibilities, and the man in the white linen suit

#16

Post by srean »

skippyfish wrote: post #13
c2c2c wrote: post #11

Earlier quoted context omitted.

I think this is selling Gödel a little bit short. He proved for the first time that in any system of mathematics with enough complexity to be interesting, there are statements that cannot be proven true or false. The Gödel sentence might seem like a trivial example, but other examples of such things have been discovered since, such as the continuum hypothesis which the article mentions.

The article is massively overstating the implications of Godel to the AI industry, so to be clear - are you defending the article, or are we bikeshedding about my phrasing? Because my "not that profound" should be interpreted as relative to the article.

Ah that "with me or against me" dichotomy again.

Re: Infinities, impossibilities, and the man in the white linen suit

#19

Post by sorokod »

iainharper wrote: post #2

I 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,…

Gödel, Escher, Bach (1980, Pulitzer prize) was how I first got exposed to Gödel.

https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach

Re: Infinities, impossibilities, and the man in the white linen suit

#20

Post by hardbass »

azakai wrote: post #9

The 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 i…

I don't understand the point at all. Mathematical theorems like godel's incompleteness theorem or the halting problem are applicable to everything including the human brain. If they were a limitation to developing general intelligence then human beings wouldn't have existed.
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