https://hackerpaper.kaipfister.de/p/1006.4131/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMThttps://news.ycombinator.com/item?id=41070150urn:hackerpapers:mention:1006.4131:41070150Thu, 25 Jul 2024 15:57:36 GMT<p>A different but to my taste more mathematically conventional way to make this argument would be instead to say that a symbol is a function from the square to [0, 1], that is, a grayscale image. A symbol, because of limitations of either its writer/printer or its reader/viewer, should have some &quot;regularity&quot;: as you move around the image, there should be some quantitative restrictions on how rapidly the darkness of the gray color should change. In this kind of setup, the space of symbols is compact by a version of the Arzela-Ascoli theorem, which I think was fairly well-known by the time Turing…</p><p><a href="https://hackerpaper.kaipfister.de/p/1006.4131/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.HO