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Comment by svat | Hacker News Reader

The very next lines say:

> At first I did not understand Fable’s explanations. But I asked questions, and then asked more questions, and drilled down towards the core of the problem. Gradually I started to understand parts of the argument. I have seen enough now to arrive at the tentative belief that the main result is possibly correct […] In the sections below I will try to explain what I have learned so far, and why I lean towards thinking it might be correct.

So the whole paper is about things the author does understand. (BTW the author David Harvey was behind the big advances in integer multiplication, in 2014 and 2019/2021.)

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This is just textbook Gell-Mann amnesia. If the author doesn't read the paper how can he possibly know that? Even in this case when it's someone who has related knowledge, how can you know that you're being told something that's actually in the paper? LLMs confidently state nonsense all the time because there's no difference between how they produce a correct or incorrect answer. LLMs seem incredibly good at convincing people that they're now experts in everything. "Drilling down" is just giving more and more opportunities for that to happen.

Gell-Mann amnesia doesn't really apply to the world expert on a topic discussing a paper that builds on his own work. It might apply to a world expert on a topic discussing a topic on which he is not an expert.

- The author is already the world's best expert on this topic.

- You're right that it's possible Fable came up with a different o(n log n) algorithm that is not in OpenAI's paper, but (apart from being unlikely) it doesn't matter, as he talks of the belief that “the main result is possibly correct”, not necessarily that OpenAI's paper is: whether the argument comes from the paper or from Fable, the question of interest is whether multiplication is really possible in o(n log n) time. The point is that there's a genuine idea here, somewhere between OpenAI's paper and Fable's explanation of it and the author's understanding of it.

- This is in fact how mathematicians have evaluated papers for decades: is there any way this result could be true? Is there an actual idea here that could help? Do I understand enough of the argument to be convinced it's likely true, modulo some details that need to be filled in? The last step (actually filling in the details) happens when teaching it to someone else or writing it again in one's own words.

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