Linkage

I was interested to see a familiarlooking graph drawing as one of the answers to the prompt “multiplicity” for the first entry in Mathober 2021 (\(\mathbb{M}\)). It’s a multigraph formed by a triangle with tripled edges, and looks a lot like the drawing I made for the Wikipedia Shannon multigraph article, prettied up by making an infinitely recessing sequence of these drawings rather than just one. Good choice for multiplicity.

Nonconcentration of the chromatic number of random graphs (\(\mathbb{M}\)). Uniformly random graphs, \(G(n,1/2)\) in the Erdős–Rényi–Gilbert model, turn out to have chromatic numbers that, for infinitely many \(n\), are spread over roughly \(\sqrt{n}\) values. But there are weird fluctuations so that, conjecturally, for some \(n\) the concentration is much tighter, more like \(n^{1/4}\).

University System of Georgia moves to gut tenure (\(\mathbb{M}\)). The proposed new policy includes procedures for removal of tenure under certain enumerated grounds, including failure to perform their jobs (this is pretty normal) but then adds a massive escape clause in which the board of regents can remove tenured faculty at any time as long as their reason for doing so is not one of the enumerated ones.

The first physical models of the hyperbolic plane, made in 1868 by Beltrami (\(\mathbb{M}\), via), blog post by Daina Taimiņa from 2010. Maybe you could make something like this by wrapping and stretching a disk of wet paper in a roll around a pseudosphere (https://en.wikipedia.org/wiki/Pseudosphere)? The rolledup photo of Beltrami’s model suggests that he did that. The via link shows this as a tangent to a story about triangulated polygons, frieze patterns, and the Farey tessellation.

Why do bees make rhombic dodecahedrons (\(\mathbb{M}\))? Nice video from Matt Parker (Standup Maths) on why bees usually end the cells of their honeycombs with rhombic dodecahedron faces, why this isn’t the optimal solution to fitting two layers of cells together (in terms of minimum wax usage), and why it isn’t reasonable to expect bees to find exact optima for this problem. If I have to quibble with something, though, it’s his plural. It’s not wrong, but see Google ngrams.

Mathematicians prove melting ice stays smooth (\(\mathbb{M}\), see also). The headline is a little overstated: you’re probably familiar with thin necks of ice melting to sharp points at the instant they separate. But these singularities are instantaneous: mathematical models of ice stay smooth for all but a measurezero set of times. Original paper: “The singular set in the Stefan problem”, Alessio Figalli, Xavier RosOton, and Joaquim Serra.

Discussion of the recent meme telling programmers and mathematicians that summation notation and for loops are the same thing. They’re not quite the same, though: summations don’t have an order of evaluation. But which is easier for people who don’t already know what they are to search and find out about? And why do programmers get angry at nonprogramming notational conventions?

Mathematics, morally (\(\mathbb{M}\), via), Eugenia Cheng, 2004. Somehow I hadn’t run across this before. It argues that much philosophy of mathematics is irrelevant to practice (“You can’t tell from somebody’s mathematics if they are a fictionalist, a rationalist, a platonist, a realist, an operationalist, a logicist, a formalist, structuralist, nominalist, intuitionist.”) and instead considerations of the right way of handling certain topics are more central.

The SIGACT Committee for the Advancement of Theoretical Computer Science is collecting information on women in theoretical computer science (\(\mathbb{M}\)). If this is you, please see their announcement for details of how to be counted.

Cynthia Rudin wins major award with silly name (\(\mathbb{M}\)), for her work on machine learning systems that learn to predict behavior using simple, interpretable, and transparent formulas.

According to the SODA web site, SIAM has decided that their conferences will be hybrid through July (\(\mathbb{M}\)). So if (like me) you wanted to participate in SODA/SOSA/ALENEX/APOCS, but were worried about planning a trip to Virginia with another predicted winter wave of Covid, now you can stay home and conference safely. Or, if you feel hybrid conferences are problematic and organizers should do one or the other but not both, now you have another reason to be annoyed.

Rarely is the question asked: Are math papers getting longer? (\(\mathbb{M}\)). Following earlier work by Nick Trefethen, Edward Dunne provides some data suggesting that (for certain journals, at least, and not the ones with page limits) the answer is yes. I’m not convinced by the suggested explanation that it’s because they are taking more effort to explain “connections with other work”, though: is that really a big enough fraction of most papers?

I haven’t been using my office desktop Mac much because I haven’t been into my office much, so it took me a while to pay attention to the fact that much of its networking had recently broken. Here’s why (\(\mathbb{M}\)). It was still running OS X El Capitan (10.11.6) and a crucial toplevel certificate expired. The machine is too old (late 2009) for the latest OS X but it looks like I can and should upgrade to High Sierra, 10.13. So much for getting anything else accomplished today…