Linkage

Claas Voelcker on academic work-life balance (\(\mathbb{M}\), via). I think we all know that many academics (myself included!) struggle to keep our weekend and evening time free of work-related distractions. Voelcker investigates where this pressure to work comes from (often internally) and suggests that overwork may block creativity; taking time off can make you more productive.

From a face-up deck of cards, repeatedly deal off the number of cards showing on the top card (counting Jacks as 11, etc.). What’s the probability that you empty the deck by dealing out exactly the right number of cards in the last step? Christian Lawson-Perfect’s post inspired a group discussion leading to the result that, for decks with large numbers of suits, the answer should tend to 1/7, and that for a standard 52-card deck it is approximately 0.1420342593977892.

Another Wikipedia illustration (\(\mathbb{M}\)): empty regions for the Euclidean minimum spanning tree. If the red vertical segment is to be an MST edge, the outer white lens needs to be empty of other points; this emptiness implies that the edge is part of the relative neighborhood graph. The emptiness of the light blue diameter circle inside the lens defines the Gabriel graph in the same way. The inner rhombus must not only be empty, but disjoint from the rhombi of other edges.

Shunting yard animation (\(\mathbb{M}\)). Cutesy train animation of the shunting yard algorithm for parsing infix expressions.

Pseudo-cylindrical concave polyhedral packaging (\(\mathbb{M}\)). This post describes multiple examples of the Yoshimura buckling pattern or Schwarz lantern in food/drink packaging, not in the obvious way (it happens when you crumple a can end-on) but deliberately by the manufacturer. It doesn’t say why they did, though. Maybe because it looks cool.

Threelds (\(\mathbb{M}\)). I have no idea whether it’s useful for anything, but a threeld is a pair of fields where the multiplication operation on the inner one forms the addition on the outer one. The finite ones have inner order 3 and outer order 2, or inner order a Mersenne prime and outer order the adjacent power of two, but there also exist infinite ones with inner field of characteristic 0 and outer of characteristic 2.

Roundup of recent Quanta popularizations and the research they come from (\(\mathbb{M}\)):

• Near-optimal expansion for 2d surfaces, based on “Near optimal spectral gaps for hyperbolic surfaces”, by Will Hide and Michael Magee.

• Inequality between cohomology rank and number of Hamiltonian flow orbits, based on “Arnold conjecture and Morava K-theory”, by Mohammed Abouzaid and Andrew J. Blumberg.

• Among pairwise-coprime sequences, primes maximize \(\sum 1/n_i\log n_i\), based on “A proof of the Erdős primitive set conjecture”, by Jared Duker Lichtman.

• Fast maximum flow algorithms, based on “Maximum flow and minimum-cost flow in almost-linear time”, by Li Chen, Rasmus Kyng, Yang P. Liu, Richard Peng, Maximilian Probst Gutenberg, and Sushant Sachdeva.

Kirk Smith asks Mastodon: “Do people on here edit/write Wikipedia articles related to your field? and what’s your experience/motivation?” There’s a conflict here between desiring academic credit for your work, and maintaining the protection of pseudonymity. But the real-world harassment that pseudonymity prevents is real, whereas I think the possibility of getting much academic credit for this sort of work is largely illusory.

New Wikipedia article: Staircase paradox (\(\mathbb{M}\)), on the familiar example of staircase curves in a unit square that uniformly converge to the diagonal of the square, while their lengths converge to the wrong number (\(2\), rather than \(\sqrt2\)). Somehow we don’t seem to have already had an article on this example. I’m sure there must be many more published sources on this example than the ones I used; if you think I missed something important, please let me know.

Physicists discover never-before seen particle sitting on a tabletop (\(\mathbb{M}\)). Peter Woit’s headline for this Not Even Wrong post repeats the breathless hype from the churnalism on a new condensed-matter-physics preprint, which promises applications to dark matter and quantum computing and turns out to be much much less. From the comments, it seems that the condensed matter physicists have been guilty of misapplying the tag “Higgs field” for a long time.

Yoshimura crushing patterns on the Inside MathSciNet blog (\(\mathbb{M}\)). I don’t think it’s accurate to say that a crush pattern and a crease pattern are synonyms, though. One is a description of the output of a crushing process; the other is an input to a folding process that guides you to put the folds into their intended places. The similarity of the crushing pattern and the Yoshimura fold is not coincidental but the purpose is different.

Study of all open-access papers on BioMed Central from a month-long window (\(\mathbb{M}\), via) finds that although 42% claim their data to be available on reasonable request, only 7% actually responded and provided their data.

Formalization in Lean of Thomas Bloom’s proof of the density version of the Erdős–Graham problem (\(\mathbb{M}\), via), according to which every set of integers with positive upper density includes the denominators of an Egyptian fraction representation of one. The blueprint appears to show Theorem 2 of Bloom’s preprint as verified, but Theorem 3 (log density) still to go.