Linkage

Dollarbill origami octahedron (\(\mathbb{M}\)), From @valentinabalance on Instagram.

This week’s newlypromoted Good Article on Wikipedia: Gale–Shapley algorithm (\(\mathbb{M}\)), a method for finding stable matchings. Many textbook sources describe this as “stable marriage” rather than “stable matching” and then cover the algorithm in terms of a sequence of marriage proposals, but this can be unnecessarily triggering for some students. For the Wikipedia article, I put some effort into avoiding this, going so far as to find published sources calling the marriage metaphor both sexist and inaccurate (that’s not how actual people proposing marriage behave). But the same oldfashioned gendered view of the problem still persists in other parts of Wikipedia’s coverage of stable matching.

Cauchy’s theorem for the prime 6 (\(\mathbb{M}\)). Peter Cameron asks if anyone has seen the following already: a finite group of order divisible by six contains a subgroup of order six or twelve.

The many face(t)s of zero forcing (\(\mathbb{M}\)), Hicks and Brimkov, Notices of the AMS. This concerns a graph problem in which an initial subset of vertices of a graph are marked, and then at any step a marked vertex with a single unmarked neighbor can mark that neighbor. The goal is to find small initial marked sets that cause the whole graph to become marked. Applications include minimumrank partialmatrix completion in recommender systems, designing monitoring systems for power grids, and controlling large quantum ensembles.
Hicks and Brimkov state that (once the initial set is chosen, the hard part of this area) the steps in which marks spread from vertex to vertex (the easy part) can be performed in any order, but they gloss over the explanation for why the order is unimportant. The explanation is simple: it’s an antimatroid! Each neighbor that could become marked remains available to be marked until it actually is marked; this continued availability is the defining property of antimatroids. And in any antimatroid all completed orderings of the elements use the same set of elements.

Every finite phoenix has period 2 (\(\mathbb{M}\)). A phoenix is a Game of Life oscillator in which every live cell dies in every step. Infinite phoenixes can have other periods.

Zoll surfaces (\(\mathbb{M}\)): deformed spheres on which every geodesic is a simple closed curve.

Mechanics of knitting (\(\mathbb{M}\)). On research by Randall Kamien and Geneviève Dion on the design of selffolding but stretchy materials.

When “AI’s error rate is like a feature, not a bug” (\(\mathbb{M}\)): UnitedHealth uses AI model with 90% error rate to deny care, lawsuit alleges.

The rot of trading a careful selection of papers in a circumscribed topic for “drastically shorter turnaround times”, special issues, and unsustainable growth in the name of being “eclectic”, “unified”, and “broad” (but also in search of those openaccess publicationfee profits) appears to have spread to Springer Nature’s journals, causing the editorial board of sociology journal Theory and Society to resign in protest (\(\mathbb{M}\)). There also appear to be some disciplinespecific political currents in play, the details of which I am unfamiliar with, but which Springer took advantage of to quickly repopulate the journal.

While searching for where Kepler described antiprisms and whether he called them antiprisms (Harmonices Mundi Lib.II Def.X, and no; \(\mathbb{M}\)) I found an interesting paper, “New light on the rediscovery of the Archimedean solids during the Renaissance” (Schreiber, Fischer, and Sternath, Arch. Hist. Exact Sci. 2008) through which I learn that he may not have been the first: a printing block attributed to Hieronymus Andreae (a collaborator of Albrecht Dürer who died 1556) shows the net for a hexagonal antiprism.
The same paper also claims that Dürer was not the first to represent polyhedra by their unfolded nets: It says that there are some nets by Leonardo da Vinci in Paciole’s Divina proportione, including the net of the regular dodecahedron. I cannot find this in the copies of the first printed edition of this book from 1509 available on archive.org but maybe they are in a different edition?

Tools for thinking about censorship (\(\mathbb{M}\)) by Ada Palmer, a historian at the University of Chicago. This mostly stems from a recent kerfuffle involving inadequately explained disqualifications and blatantlyfudged voting numbers from the 2023 Hugo awards in science fiction and fantasy. (Let me explain! No, there is too much. See metafilter, or recent posts at file770.com, such as the one where I found this link.) But I think the lessons it provides are far more broad. First among them: “The majority of censorship is selfcensorship, but the majority of selfcensorship is intentionally cultivated by an outside power.” So if you are asking, did a government censor, or was it just individual bad actors, you are asking the wrong question.

Glider synthesis of the smallest c/6 diagonal spaceship in the Game of Life (\(\mathbb{M}\)).

“Clarivate has excluded the entire field of math from the most recent edition of its influential list of authors of highly cited papers” (\(\mathbb{M}\), via, see also) because of logrolling among “citation cartels” of “lesser known mathematicians” from “institutions with little mathematical tradition, many based in China, Saudi Arabia, and Egypt”.