Linkage

The exciting new world of AI prompt injection (\(\mathbb{M}\), via). Promote your business by running a bot that uses other people’s social media post text to prompt a text-writing AI that generates customized responses to those posts. What could go wrong?

Ed Pegg constructs and visualizes Engel’s 38-sided space-filling polyhedron (\(\mathbb{M}\)), the most possible for a Voronoi cell of an isohedral Voronoi tessellation, surrounded by 38 copies of itself.

Cyclography, an old form of data visualization in which 3d points are visualized as 2d circles, with the third coordinate used as their radius. Sort of an inverse to the lifting transformation in computational geometry, which turns 2d circles into 3d points in order to use point-based algorithms on them.

Terry Tao on his new preprint with Rachel Greenfeld, “A counterexample to the periodic tiling conjecture” (\(\mathbb{M}\)). The Schmitt-Conway-Danzer biprism and Socolar–Taylor tile tile \(\mathbb{R}^3\) and \(\mathbb{R}^2\times{}\)finite only aperiodically. The einstein problem asks if \(\mathbb{R}^2\) has an aperiodic tile. This work looks at analogous questions for tiling by translation of \(\mathbb{Z}^2\).

Descriptive combinatorics and distributed algorithms (\(\mathbb{M}\)). Nice survey article by Anton Bernshteyn in Notices of the AMS about implications and in some cases equivalences between topological statements about whether certain infinite sets are Borel or measurable, and whether certain corresponding finite computational problems have distributed algorithms with sub-logarithmic round complexity.

Irish librarians protest (\(\mathbb{M}\), via) as Wiley suddenly removes over 1300 ebooks from the existing subscription packages of academic libraries, in order to convert them to a fee-per-student individual-textbook subscription model. Now also affecting US universities.

Do you need another demonstration that the physics of liquids is strange and counterintuitive (\(\mathbb{M}\))? I learned from this “What’s eating Dan?” video that, if you have the kind of peanut butter that needs mixing, but is too liquid (swimming in extra peanut oil), you can make it thicker by mixing in a little bit of water. The water droplets in the oil make an emulsion that is thicker than either the water or oil would be by themselves. I had occasion to try it recently and it worked! Science strikes again.

Two swirly rhombus tilings of 4-subdivided 20-gons.

The new math of wrinkling (\(\mathbb{M}\)). Quanta on the research of Ian Tobasco on the way that crumpling thin surfaces (like paper) can sometimes lead to disordered folds and sometimes lead to regular patterns, like Yoshimura buckling, depending in part on local curvature. Based on two papers by Tobasco, “Curvature-driven wrinkling of thin elastic shells” (2021, arXiv:1906.02153) and “Exact solutions for the wrinkle patterns of confined elastic shells” (2022, arXiv:2004.02839).

Girls Who Code appears on this year’s list of books banned by US schools (\(\mathbb{M}\)). Apparently this happened not directly because the kind of people who ban books want women to be ignorant, but rather because these books appeared on a diversity resource list and the kind of people who ban books oppose diversity (meaning anything that would challenge the white cis male evangelical-Christian point of view) in all forms. Fortunately local protests got the ban rescinded. More on BoingBoing and in The Guardian. The statement in The Guardian from a book-banning spokesperson “This book series has not been banned, and they remain available in our libraries” appears to actually mean that the ban blocked students from reading the books but failed to remove them permanently from the libraries, and that they became available because the ban was rescinded.

Mutilated chessboard problem (\(\mathbb{M}\)): remove opposite corners from a chessboard and try to cover the rest with dominos. It’s just planar bipartite perfect matching, easy for algorithms. There’s a cute trick for human problem solving that I won’t spoil. And yet, a logical formulation has been a test case for automated reasoning for nearly 60 years, and is provably hard for some systems (especially resolution). How can it be so easy and so hard? New Wikipedia Good Article.

Publication laundering (\(\mathbb{M}\), via): James Heathers on how “proceedings journals” that accept whole special-issues without any internal oversight over relevance or quality ease the collaboration among academics desperate for publications, middlemen who sell authorship slots on mass-produced junk, and big publishers hungry for that publication-fee and subscription-fee cash as long as they can point the blame elsewhere.

Foxagon: A hexagon with exactly one line of reflective symmetry and one reflex angle. Or maybe more specifically it’s what you get when you glue equilateral triangles onto two adjacent sides of a square. The more specific version tiles the plane; the tiling below hides a snub square tiling but other tilings are possible.

The strange Wiki-history of Sethahedra and Chestahedra (\(\mathbb{M}\), via, via2). The Chestahedron is a polyhedron whose faces are four equilateral triangles and three kites of the same area as the triangles. Frank Chester makes bronze sculptures of it. The Sethahedron is a nonexistent variation with golden-ratio dimensions. If made of paper it will fold along kite diagonals to form ten faces. The promoter of the Sethahedron has been edit-warring to keep their erroneous version in Wikipedia.