Linkage

The state space of a \(2\times 2\times 2\) Rubik’s cube under halfturns turns out to be yet another way of describing the Nauru graph.

French painters inspire new insights into the physics of soap bubbles (\(\mathbb{M}\)): Jennifer Ouelette in Ars Technica on how blowing bubbles through a long narrow air tube affects their size, based on a preprint “Unstable growth of bubbles from a constriction” by Marc Grosjean and Elise Lorenceau.

Good news for teaching faculty in my department (\(\mathbb{M}\)): my friend and colleague Michael Shindler just got tenure, as an associate professor of teaching. Michael is local: he was an undergraduate here before getting a Ph.D. in theoretical computer science with Adam Meyerson at UCLA, and then taught at the University of Southern California before returning to us as an assistant professor of teaching. Whenever I see an exceptionally bright undergraduate asking to take my graduate data structures class, it’s almost always because they were encouraged along the way by Michael.
The “professor of teaching” series is relatively new for us, added about five years ago alongside our “Unit 18” lecturers (named for their union) and replacing our previous “lecturer with security of employment” series. Compared to other regularrank faculty they have a higher teaching load and lower but nonzero research expectations, typically focusing on computer science education. They can also advise doctoral students (and Michael is doing so). Although we have hired some into the more senior ranks, Michael is the first to go through the tenure process. He says that when he recently went to SIGCSE, the question everyone wanted to ask him was: is it true that computer science education specialists can be senate faculty in your department? It is true, and they can get tenure for doing it.

The mysterious dodecahedrons of the Roman empire (\(\mathbb{M}\), via, see also). One plausible theory: they are spool knitting devices for making gloves.

Architecturallystyled photographs of the interior of musical instruments (\(\mathbb{M}\)).

The New York Times has a profile by Siobhan Roberts on the Online Encyclopedia of Integer Sequences, celebrating its 50th anniversary (\(\mathbb{M}\), archived).

In 3d, every polyhedron has a combinatorially equivalent form with rational (or integer) coordinates, but in higher dimensions that isn’t true (\(\mathbb{M}\)). Daniel Bernstein in The Matroid Union examines connections between irrational polytope constructions and matroid theory.

A pseudodeterministic algorithm for finding primes (\(\mathbb{M}\), via), by Lijie Chen, Zhenjian Lu, Igor Carboni Oliveira, Hanlin Ren and Rahul Santhanam. More precisely, this is a randomized algorithm for finding an \(n\)bit prime number that runs in time polynomial in \(n\) and, with high probability, for infinitely many \(n\), outputs the same prime whenever you run it.

The silent (r)evolution of SAT (\(\mathbb{M}\)), new survey in CACM on SATsolvers and their applications, by Johannes K. Fichte, Daniel Le Berre, Markus Hecher, and Stefan Szeider.

Music industry requests Google to censor Wikipedia (\(\mathbb{M}\), via). The Wikipedia article in question: Comparison of YouTube downloaders. It’s not a great example of a highquality Wikipedia article but the precedent of asking for censorship of any mention or discussion of content piracy (beyond going after the pirates themselves) is extremely troubling.

Ethics professor asks “Am I the unethical one?” (\(\mathbb{M}\), via) after setting an online trap for cheating students and catching nearly half his class.

A chiral aperiodic monotile (\(\mathbb{M}\), see also), like the hat (actually, exactly like an equilateral hat) but with no flipping required. It’s called the spectre. New preprint by Smith, Myers, Kaplan, and GoodmanStrauss.

Supposedly practical application and deployment of cuckoo hashing in the TikTok recommendation system (\(\mathbb{M}\), via). For more, see “Monolith: Real time recommendation system with collisionless embedding table”, Liu et al. The cuckoo hashing is what makes this “collisionless”, and is used to map sparse feature data to something more dense.

Interesting “nearmiss” of two integer sequences (\(\mathbb{M}\)): OEIS A000240, counting permutations with one fixed point, and OEIS A182390, generated by a recurrence involving XOR. The rencontres numbers (the first sequence) also have a similar recurrence, but with \(\pm\) in place of \(\oplus\), and some binaryrepresentation coincidence causes them to be equal for surprisingly many terms.