Linkage

A stained glass window of a Latin square (\(\mathbb{M}\)) will be removed from Cambridge University because it honors prominent eugenicist R. A. Fisher. The window visualizes a nice piece of mathematics, with a long history that surprisingly originates in Korea (predating Euler) but in context among windows celebrating Cambridge luminaries it could not be separated from Fisher’s racist history, so it’s sad but I think it’s the right decision.

What is it about Quanta’s oversimplifications (\(\mathbb{M}\))? A recent article is on a variation of the problem of squares in Jordan curves, known to exist in smooth curves but unknown for some nastier ones. The new result described by Quanta concerns rectangles of given aspect ratio in smooth Jordan curves. Wikipedia editors have had to fend off repeated edits by Quanta readers who came away thinking the new paper solved the original problem. It doesn’t.

Hex puzzles by Matthew Seymour (\(\mathbb{M}\)). 500 of them, designed to guide you to greater Hex mastery, in an online applet. In the Mastodon post, Jacob Siehler explains that he can justify playing with these as work, because it relates to an upcoming course he’s teaching.

David Mumford on the long history of ridiculous word problems in mathematics (\(\mathbb{M}\), via).

A tiny improvement sometimes makes for a big result (\(\mathbb{M}\)): In a new preprint “A (Slightly) Improved Approximation Algorithm for Metric TSP”, Anna Karlin, Nathan Klein, and Shayan Oveis Gharan claim a reduction in the approximation ratio for traveling salesperson in arbitrary metric spaces from \(\tfrac{3}{2}\) to \(\tfrac{3}{2}10^{36}\). But it’s the first such improvement since Christofides and Serdyukov in 1976, on a central problem in approximation algorithms.

US Department of Homeland Security tried to require foreign students in the US to either attend inperson classes or leave the country (\(\mathbb{M}\), via, see also). After facing pushback in the courts, they gave up. But while it was happening, it had the appearance of pressuring US universities into opening up inperson classes despite the ongoing pandemic, using the threat of taking away all of their foreign students.

Sad news from the AMS: Ron Graham has died (\(\mathbb{M}\)). See also the blog posts about him by Lipton and Regan, Gasarch, Dominus, Haran, and (mostly from earlier) Wright.

Experiments on reverse perspective (\(\mathbb{M}\)), recent post by Paul Bourke with a link to a recent video, “Hypercentric optics” by Ben Krasnow, showing how to achieve reverse perspective physically using a giant Fresnel lens.

On the asymptotic complexity of sorting (\(\mathbb{M}\)), Igor Sergeev. We still study the number of comparisons for sorting in introductory CS, although other factors like locality of reference may be more important in practice. Common topics are the \(\log_2 n!\) comparisontree lower bound and the nearlymatching \(\log_2 n!+O(n)\) merge sort upper bound. Better sorts were known but still with an \(O(n)\) error term. Now Sergeev has reduced the error term to \(o(n)\).

A messy story of unethical doings at ISCA, a major computer architecture conference (\(\mathbb{M}\), via):

Junk research accepted to ISCA causes its student coauthor to kill himself.

The ensuing investigation brings to light apparent serious breaches of ISCA’s doubleblind reviewing process, but ACM and IEEE find no wrongdoing.


“Spied on. Fired. Publicly shamed. China’s crackdown on professors reminds many of Mao era.” (\(\mathbb{M}\)). (If the paywalled LA Times link is a problem, trimread might help.)

A cute dissection proof of an area calculation of a tilted square within a square (\(\mathbb{M}\)). But to generalize from there to: tick marks that split the sides in the ratio \(x:y\) (in this example, 1:2) give a ratio of areas of the inner tilted square to the outer square that is \(y^2:(x+y)^2+x^2\) (in this case 4:10, simplifying to 2:5) it seems easier to apply similar triangles and then use Pythagoras in the tilted grid.

Quinoa packing 2 + 1 = 4 (\(\mathbb{M}\), via). This blog post theorizes that the combination of 2 cups of water and 1 cup of quinoa to form 4 cups of cooked quinoa might happen because the water fills the spaces between the grains before cooking, but merges into the grains causing them to pack like spheres with air pockets between them afterwards. On the other hand, maybe they just expand into a lessdense combination of materials that takes more room.