Post #2920358

2026-05-17 16:26 UTC

@tao@mathstodon.xyz I want to emphasize first that I do think this is a wonderful and informative talk. In particular, I am extremely happy to see the point about optimization being sometimes detrimental to progress being discussed openly. That said, while I agree with the problems you have articulated, I continue to disagree with the proposed solutions. I will attempt to be a bit more productive than my previous comments on your posts, and try and articulate the solution to the problem that I see as best as I can, but I am not sure how to articulate it concisely, so please forgive the length. There is a tl;dr at the end extracting the main points. What I have to say is based on an assumption: that the part of the human mind that is relevant to the 'utilitarian' aspects of mathematics is either completely reproducible by a computer, or it isn't. If the former is true, then any attempt at trying to change our workflow in terms of 'infrastructure' will at best be a temporary fix. The bottom line is that there will be no incentive for anyone to enforce this infrastructure without a drastic cultural change. Over a long enough time scale any workflow change along the lines of creating 'walkable' cities will get stamped out. This may seem pessimistic, except if the utilitarian aspects of the human mind are not reproducible by a computer. I am not sure which is true, but without any serious investigation of whether this is true or not, we cannot make meaningful progress on the 'crisis' mathematics faces in the future, because without this investigation, our proposals may be based entirely on faulty assumptions. (1/n)

Replies (1)

@wikiemol@mathstodon.xyz 2026-05-17 16:27

To at least attempt to convince you that the problem is worthy of investigation and is not 'trivial', we can consider the 'inquisitive' version of the Liar's paradox. Essentially "Are you going to answer no to this question?" No one is able to answer this question truthfully. However, through our own inner experience, we can observe our own volition, and find e.g. "I am going to answer no in the future" without saying it aloud. Then, we can reason based on this observation that the true answer is therefore yes, even though we cannot say it. Current AI will correctly answer that the question is paradoxical, but will begin to hallucinate when you ask follow up questions about what the actual answer was. One can apply a similar thought experiment to an inquisitive Knower paradox. "Are you going to know the answer to this question is no?" When we attempt the same observation of our volition, we can see directly (not through memory) that our minds go back and forth on the answer. Then, we can reason in a semi formal way that the answer must be no. And so the question is in some sense the opposite of the previous one: we can say the true answer aloud, but we cannot know the answer. (2/n)

Open ##2920359