Linkage for midMarch

Robin Houston wonders about cuboid terminology. The specific question is whether it should mean a shape with six rectangular sides (as commonly taught in school) or a shape with six quadrilateral sides (as used in some research communities). Let’s not even speak about Branko Grünbaum’s use of it to mean a shape formed by gluing together a poweroftwo number of sixquadside shapes.

Tiny period15 glider gun and period16 glider gun in Conway’s Game of Life (\(\mathbb{M}\)).

Surprisingly good art exhibit on AIgenerated and AImanipulated photography (\(\mathbb{M}\)), at the California Museum of Photography in downtown Riverside, unfortunately recently ended (I caught it on the last day). I think part of what made it good is that, in the selections from each artist, the artist’s intent was clearly visible: they were humanmade artworks, but made using AI generation as a medium.

Communications of the ACM goes openaccess (\(\mathbb{M}\)).

ChatGPT and history of mathematics misconceptions (\(\mathbb{M}\)). Unsurprisingly, the answers to your questions are often current folk views rather than uptodate scholarship.

Elliptic curve murmurations (\(\mathbb{M}\)), Quanta roundup of recent discoveries sparked by an attempt to predict elliptic curve parameters using machine learning.

In honor of women’s day, an incomplete list of iconic women Wikipedia editors. See also The Guardian: “Wikipedia’s female volunteers, a hive heroism that changes history”.

Gasarch on how to write an informative and not merely overinflated recommendation letter (\(\mathbb{M}\)), and on the interpretation of letters in light of the old boys’ networks of their times.

Sarah Hart’s book Once Upon A Prime, on mathematical connections in literature, looks intriguing (\(\mathbb{M}\)). Chalkdust reviews it as part of their Book of the Year shortlist. A few more reviews: World Literature Today, Math Horizons, The New York Times, The Washington Post, The Guardian, The Wall Street Journal, NewScientist, and The Economist.

Computation from onedimensional particle collision systems (\(\mathbb{M}\), via). At first glance these look a lot like 1d cellular automata, and can be proven universal through simulation of 1d CA, but they have some other phenomena as well, involving infinitely many collision events happening within a finite time and space.

The following appears to be an open problem (\(\mathbb{M}\)): what is the expected number of vertices of the convex hull of \(n\) random points in a regular octahedron? The context for this is a 1988 paper by Rex Dwyer, “On the convex hull of random points in a polytope” (J. Applied Probability, 1988, doi:10.2307/3214289, [jstor:3214289(https://www.jstor.org/stable/3214289)). Dwyer shows that, for uniformly random points in a fixed \(d\)dimensional convex polytope, the expected number of convex hull vertices is \(O(\log^{d1} n)\). He proves a matching lower bound for simple polytopes (including hypercubes) and more strongly for polytopes that have at least one simple vertex. A colleague asked me today about the case for cubes; Dwyer’s paper provides the answer. Dwyer poses as an open problem whether the lower bound can be extended to all convex polytopes. The octahedron is the least complicated polytope not covered by Dwyer’s results. My searches didn’t find any followup papers improving on Dwyer, but maybe someone else knows of more.

A nod to \(\pi\) day in the letters section of my newspaper (\(\mathbb{M}\)), comparing the infamous Indiana \(pi=3\) bill to modern rightwing legislatures’ attempts to define gender\({}=2\).