Linkage

Ultralightweight pavilion made from woven bamboo strips, aided by modern computer modeling (\(\mathbb{M}\)). Not very good for keeping sun or rain off in the form shown, but I imagine one could stretch a membrane over it if that were the goal.

Corruption in old images stored in Google Photos (\(\mathbb{M}\), via). Let this be a reminder that if you care about the permanence and stability of your data, keep a safe copy on media you own and control, not on someone else’s machine on the cloud somewhere.

“The University of Idaho administration has abandoned its duty to uphold the mission of the institution and signaled to all the world that the university is no longer committed to academic freedom” (\(\mathbb{M}\)), according to The American Association of University Professors. The context is a memo sent out by the university’s lawyers requesting faculty to “remain neutral on the topic of abortion”; for more on that, see Inside Higher Ed’s story and editorial.

Gasarch asks for advice on whether it’s acceptable for an academic publication to cite Wikipedia (\(\mathbb{M}\)). Comments concern stability of Wikipedia articles, but that’s easy: every article has “cite this page” in the toolbar with sample citations that permalink stable versions. The bigger issue is the purpose of the citation. As background reading: fine. As credit for a figure: necessary. For a technical result: you should probably follow the references to a more-primary source.

Computer search for faster matrix multiplication algorithms (\(\mathbb{M}\), see also).

In place of the prime numbers, consider the numbers \(p^{2^k}\) for \(p\) prime and integer \(i\ge 0\) (\(\mathbb{M}\)). Each positive integer has a unique factorization into a product of these without repetition. For example,

They are called the Fermi–Dirac primes because of an analogy to fermions and bosons from physics: like bosons, primes can appear repeatedly in an energy level (prime factorization), but these numbers appear only once.

I linked to Milman and Neeman’s preprint on the triple bubble conjecture last June (\(\mathbb{M}\)), but now Quanta has a popularized explainer of it.

An aperiodic set of 11 Wang tiles (\(\mathbb{M}\)). Wang tiles are edge-colored squares that tile the plane as a grid, without rotation and with matching edges. B. Durand and A. Shen explain a result of E. Jeandel and M. Rao from a 2015 preprint and 2021 journal publication using a computer search to prove that sets of 11 Wang tiles with 4 colors (but no fewer of either) can force the tiling to be aperiodic.

The first link is on the site of an organization led by people who have publicly opposed mandatory statements of support for diversity or inclusiveness, and the organization itself conspicuously lacks any statement of support for those values. This led to some discussion on Mathstodon over whether we should link to even purely-mathematical content by these people. My position is that it would be a mistake to shun them. I think their position that mathematics can and should be above such concerns is naive and overly idealistic, but we cannot find solutions to societal problems such as institutionalized discrimination if we shut down free and open discussions of alternatives by banning anyone at the slightest misstep from the political orthodoxy of the minute. Also, doing so would strengthen their position by playing into their storyline of good mathematics getting pushed aside for political reasons. As I wrote in the linked comment, “Let’s not be the monsters they think we are.”

How to make yourself a copy of Wikipedia on a flash drive, usable offline (\(\mathbb{M}\), via).

The shape of a Go stone (\(\mathbb{M}\)): A project from 2013 to create “a physically accurate computer simulation of a Go board and stones” starts by trying to understand the shape of the stones, settling on an intersection between two balls, modified by using a torus to bevel the sharp edge where they meet. Which sort of looks right, but a 2020 discussion suggests that a more accurate model needs to take into account how real Go stones are made.

Percolation: a Mathematical Phase Transition (\(\mathbb{M}\)). One of many recent mathematics exposition videos from the “Summer of Math Exposition 2”; this one is mostly about the bond percolation on an infinite square grid, the study of the connectivity of random subgraphs of the grid. There’s a more complete listing of the other videos on Metafilter.

Intentionally-bad and anti-accessible user interface design by Apple, in order to undercut the competition (\(\mathbb{M}\), via, via2).

MathJax 4.0.0-alpha.1 now available (\(\mathbb{M}\), via, via2). Because it’s still an alpha-test version, it’s probably not the right time to switch unless you really need the new features (more fonts, better line breaking, html within math expressions).

An appreciation of triangular grids (\(\mathbb{M}\)).

The interesting number paradox (\(\mathbb{M}\)) is the argument that there cannot be a smallest uninteresting natural number, because that property would make it interesting. I had thought that it dated from a 1958 “Mathematical Games” column by Martin Gardner in Scientific American, but now another Wikipedia editor has found an earlier reference, a 1945 letter to the American Mathematical Monthly by Edwin F. Bechenbach (see bottom of last page of link).