Karthik Srinivasan<p>Wow!! What a breathe of fresh air this paper is in the midst of suffocating levels of "AI solves everything" hype cycle. </p><p><a href="https://arxiv.org/abs/2303.10798" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/2303.10798</span><span class="invisible"></span></a></p><p>They have found at long last, a single tile, an "einstein", which they call a "hat"/polykite that tiles the entire plane aperiodically. </p><p>Previously the best known aperiodic tiling of the plane required at the least two different tiles, the most famous ones being the Penrose tiles, and those that adorn Alhambra. </p><p>It is all the more wonderful that the first two authors don't have any academic/research affiliations. They write somewhere in the paper, how it all started, so wonderful: </p><p>"One of the authors (Smith) began investigating the hat polykite as part of his open-ended visual exploration of shapes and their tiling properties. Working largely by hand, with the assistance of Scherphuis’s PolyForm Puzzle Solver software (<a href="http://www.jaapsch.net/puzzles/polysolver.htm" rel="nofollow noopener noreferrer" target="_blank">www.jaapsch.net/puzzles/polysolver.htm</a>), he could find no obvious barriers to the construction of large patches, and yet no clear cluster of tiles that filled the plane periodically." </p><p>Why is the study of tilings such a big deal? Well, it hints at and tries to formalize various physics concepts that are of immense interest to many of us (and dare I say, even neuroscientists): quasi crystals!, possible new states of matter, emergent structures from simple units, how symmetries and asymmetries arise, stability of heterogenous media, soft matter physics, order without periodicity, criticality etc., etc., </p><p>On quasi-crystals and their search, applications, uses etc., I recommend the wonderful Paul Steinhardt's book: "The Second Kind of Impossible: The Extraordinary Quest for a New Form of Matter" </p><p><a href="https://neuromatch.social/tags/Physics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Physics</span></a> <a href="https://neuromatch.social/tags/Maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Maths</span></a> <a href="https://neuromatch.social/tags/Combinatorics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Combinatorics</span></a> <a href="https://neuromatch.social/tags/AperiodicTiling" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AperiodicTiling</span></a> <a href="https://neuromatch.social/tags/PenroseTiles" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>PenroseTiles</span></a> <a href="https://neuromatch.social/tags/Einstein" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Einstein</span></a> <a href="https://neuromatch.social/tags/Emergence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Emergence</span></a> <a href="https://neuromatch.social/tags/condensedmatter" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>condensedmatter</span></a></p>