“Working through a small tiling result” by James Payor

Audio note: this article contains 154 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.

tl;dr it seems that you can get basic tiling to work by proving that there will be safety proofs in the future, rather than trying to prove safety directly.

This is not a new idea, e.g. here is Giles saying it 13 years ago. But this seems to me like it's relevant to a general answer for tiling, and I'd appreciate engagement, literature references, and discussion.

I'll keep this post self-contained, but here are some links to relevant discussion from the past.

Setup

I like the simplicity of the problem presented by cousin_it, and I'll adapt it for this post. It starts like this:

A computer program X is asked one of two questions:

• Would you [...]

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Outline:

(00:50) Setup

(01:48) Accepting provably-safe successors

(02:37) Failing to prove ourself safe

(03:22) Regaining self-trust with a tweak

(04:53) But does it blend

(05:48) Musing on what remains

The original text contained 4 footnotes which were omitted from this narration.

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First published:

May 13th, 2025

Source:

https://www.lesswrong.com/posts/akuMwu8SkmQSdospi/working-through-a-small-tiling-result

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Narrated by TYPE III AUDIO.