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Linkage with new kittens

May 15, 2023

  • Numberphile on book embeddings of graphs (\(\mathbb{M}\)), and on the long-awaited proof of the claim that some planar graphs require 4 pages. For more reading on this, see the Wikipedia article on book embeddings.

  • Deltahedra with mostly-concave edges. Joined excavated icosidodecahedra can get 68% of the edges to have concave angles, but it appears that digging a joined-icosahedron tunnel out of a larger surrounding shell can get up to 91%. The image below shows the best gluing pattern I found, in which four icosahedra are each cut along two edges and then glued to each other.

    Four icosahedra glued to each other after cutting two edges in each icosahedron, as constructed with Geoshapes and blue painter's tape

  • How to flip a lampshade upside down (\(\mathbb{M}\)), where the lampshade has the shape of a truncated cone and you have to deform it without self-intersection and without ever getting a horizontal tangent line. Marty Théo, via Ian Agol.

  • Two newly listed Wikipedia Good Articles in one day (\(\mathbb{M}\)):

    • Midsphere, a sphere tangent to every edge of a polyhedron. Among other properties, all Hamiltonian cycles on a polyhedron with a midsphere have equal lengths.

    • Rook’s graph, the graph of rook moves on a chessboard, the Cartesian product of two complete graphs, and the line graph of a complete bipartite graph.

  • Why I should stick to Mastodon and not even dip my toes into Bluesky (\(\mathbb{M}\)): apparently the choice is between serious and technical discussions that exclude the Nazi trolls, on the Mastodon side, versus “Lots of butt-pictures. Then it was sexualized images of Alf” on the Bluesky side. I know what I prefer, and it’s not butt-pictures and Alf. Later developments make clear that BlueSky also fully intends to encourage content that includes violence and gore, political hate, spam, and impersonation, and then charge readers for the moderation tools to keep it at bay.

  • Rick Salafia’s wildly shaped aluminum rulers measure impractical proportions (\(\mathbb{M}\)).

  • Republican-led US states are banning topics from university courses and watering down or eliminating the entire tenure system for university faculty (\(\mathbb{M}\)). Los Angeles Times columnist Michael Hiltzik argues that this is already causing a brain drain from those states and that “This trend is almost certain to get worse before it gets better as America devolves into two countries: one that nurtures brainpower, and one that watches proudly as it drains away.”

  • Research under a cloud (\(\mathbb{M}\)). Wikipedia editor XOR’easter rebuts an academic publication, “‘Too Soon’ to count? How gender and race cloud notability considerations on Wikipedia”, by Lemieux, Zhang, and Tripodi, purporting to show biases against women and non-white academics in Wikipedia’s deletion processes. Those biases may well exist but “Too Soon” makes a bad case for that. As the link describes, its arguments rely on severe misrepresentations of Wikipedia’s notability criteria and on selective quotations that in many cases reverse the intended meaning of the quoted text. A condensed version of this recently appeared in the Wikipedia Signpost. I’m quoted, both without attribution in “Too Soon” and by name in the rebuttal.

  • John MacCormick unintentially created a racially biased face-recognition system 25 years ago (\(\mathbb{M}\)), by using unrepresentative training data. He points out the difficulty of spotting the bias in the resulting system (which mostly consists of big matrices of numbers representing training weights) and wonders if current AI system creators too might have made a similar mistake.

  • A construction in a proof is producing square matrices of the following form (\(\mathbb{M}\)): the main diagonal is nonzero (red in the image below), each diagonal coefficient has zeros either directly above it in the same column or directly to the left of it in the same row (pale yellow), and the rest of the coefficients can be anything (blue). Fairly obviously, such matrices have full rank, which is what my proof needs. Does anyone know whether there is a name for this class of matrices?

    A 16x16 grid of squares, with red squares down the main diagonal. Each red square has an associated line of pale yellow squares either directly above it or directly to its left. The remaining squares are dark blue.

  • AI is tearing Wikipedia apart (\(\mathbb{M}\)). Vice story on the ongoing disagreement among Wikipedia editors on whether to ban or how to handle AI-generated content. In the linked post, Erin Kissane points out that AI-generated talk page sophistry may be an even bigger concern.

  • Every Author as First Author (\(\mathbb{M}\)): “Finally, a solution to the unfairness of authorship ordering in scientific papers!” By Erik Demaine & Martin Demaine.

  • Chegg stock sinks because too many students have switched to ChatGPT instead of Chegg to get bespoke cheats for their homework that are harder to detect than copied-and-pasted cheats (\(\mathbb{M}\)). Oh no. What will we do without them.

  • These two six-week-old kittens arrived at our house yesterday (\(\mathbb{M}\)). Names still not definite but we think maybe we’re going to name the more adventurous one on the upper left Mist, and his shyer brother on the lower right Smoke.

    Two six-week-old gray kittens looking out from an open cupboard behind some chair legs. The one on the upper left has a white striped nose and white abdomen; the one ont e lower right has a white ruff.

  • David Eppstein

Geometry, graphs, algorithms, and more