Linkage

How to tell someone how to get to your house without knowing where they’re starting (\(\mathbb{M}\)), how to translate a Penn & Teller trick into Spanish, and other applications of the Černý conjecture on synchronizing words. This video by Nóra Szakács is one of an enormous number of recent mathematics explanation videos in the “Some1” summer of math exposition video project.

One of our instructor’s strategies for dealing with sites like Chegg that cater to homework answer-copiers (\(\mathbb{M}\)): seek out and assign homework questions that already have particularly bad answers on Chegg. That way the copiers are more easily caught and the students who actually do the work have a better chance to shine over their copying peers. And if doing this ends up causing Chegg to get more of a reputation for inaccuracy, that’s not a bad thing either.

Facebook isn’t the only company changing its name in an unsuccessful attempt to separate itself from its poor reputation (\(\mathbb{M}\)). Around when the FTC fined OMICS for predatory practices, it began rebranding its journals and past papers with other publisher names (Hilaris, Longdom, iMedPub, and Research & Reviews), rewriting the editorship history of its journals, and even lifting other publishers’ papers to fabricate a legitimate-looking backlog for its journals.

Constructible number (\(\mathbb{M}\)), now a Good Article on Wikipedia. This concerns the correspondence between compass-and-straightedge constructions and formulas using square roots, and the use of that correspondence to prove the impossibility of classical geometric construction problems. Relatedly, see Joel Hamkins’ new blog post on how constructibility of one set of points from another produces an equivalence relation on pairs of points.

Quantum computers to run Sydney’s transport network (\(\mathbb{M}\), via). In other news, Sydney politicians are unable to distinguish hype from actual technology advancements, or maybe more cynically unwilling to do so when the hype would let them dole out lucrative contracts.

Terry Tao attempts to visualize vector spaces, linear maps, and exact sequences using arrows from arrows to arrows (\(\mathbb{M}\)). Ok, some of the arrows are really supposed to be half-open intervals, but drawn with a barred closed end and a pointy open end they look a lot like \(\mapsto\).

How Pinterest utterly ruined photo search on the internet (\(\mathbb{M}\), via). The title is a bit of an exaggeration given how easy it is to add -pinterest to every single image search you do (with quick feedback for why you need to do it when you forget). But they’re not wrong about it being a useless annoyance.

Farthest-first traversal / greedy permutation (\(\mathbb{M}\)): generate a sequence of points, choosing each one to be as far as possible from already chosen points. Its first \(k\) points form good cluster centers (approximating min-max-diameter or min-max-radius clustering) and are well separated (approximating max-min distance). Its applications include halftoning, color quantization, sensor network distribution, and underwater robot task planning. Now another Wikipedia Good Article.

Today in amusingly-named concepts: the Lorentz–Lorenz equation (\(\mathbb{M}\)) relating refractive index to polarizability. Even more amusingly, it was not a deliberate collaboration: Lorentz and Lorenz discovered the equation independently! Via a comment over on that other site, in a thread making fun of the new Meta logo for its resemblance to a strange attractor. Now if only we could somehow connect it to Paul Lorenzen…

How to search for number facts sites without searching for number facts sites and how to search for the mathematics of poker without getting a bunch of sketchy gambling sites: search for the numbers, not the words.

How memory-safe programming in Rust can complicate the design of data structures (\(\mathbb{M}\), via, via2). Rust data structures cannot have circular references, so if you need them you can either fall back to non-memory-safe techniques (reference counting or unsafe blocks) or make your top-level structure implement its own memory allocator and refer to everything by indexes into its vector of objects instead of by proper references.

Too few women at POPL 2022 (\(\mathbb{M}\)). The low 11% representation on the program committee is especially striking in contrast to the significant historical contributions of women to programming languages (Kathleen Booth, Cicely Popplewell, Grace Hopper, Jean Sammet, Mary Hawes, Gertrude Tierney, and Barbara Liskov among them). According to the same post, the major theoretical computer science conferences are only slightly better.

Handshaking lemma (\(\mathbb{M}\)), now another Good Article on Wikipedia. This is really about two different but closely-related results, both proved by Euler in his 1736 paper that kicked off the field of graph theory: in any finite undirected graph, the sum of vertex degrees equals twice the number of edges, and the number of odd-degree vertices is even.