Computer scientists say they’ve solved the mystery of the orb in Leonardo da Vinci’s _Salvator Mundi_:

My colleague and co-author Mike Goodrich has been working with computer graphics specialists to model the refraction in the clear ball (representing the universe) held by Jesus in Leonardo's painting. Their work shows that the model that Leonardo painted from was likely a hollow glass ball, not a solid crystal. Original paper:

0xDE boosted

Robert MacKay's Chaos Machine. Its configuration space is a genus three surface. The dynamics of the machine are equivalent to geodesic flow on the surface, which is Anosov, hence chaotic.

Computational Geometry Media Exposition coming in Zurich in late June:

It's one of the events associated with the annual Symposium on Computational Geometry, formerly called the video review of computational geometry. This year it's expanding to a much wider range of media. Submission deadline February 21; see link for details.

A major breakthrough in quantum complexity and its applications in von Neumann algebra theory that I totally don't understand: MIP*=RE, or "two entangled provers could convince a polynomial-time verifier than an arbitrary Turing machine halts",

Bloggers closer to this area don't have much to say, but I'll point to their posts anyway:

Background from an author:

The algebra:

0xDE boosted

Interesting Quanta article explaining the "universal covering problem", aka finding the smallest convex region that can cover an entire set of shapes; even restricting to shapes of "diameter 1" still leaves a tough unsolved problem in

New blog post: Counting grid polygonalizations,

The golden ratio appears mysteriously in the asymptotics of the number of simple polygons that have all points of a \(3\times n\) grid as vertices.

The New York subway system thinks it has copyright on any stylized geometric map of its system and is sending takedown notices to the artist of the unofficial map used by Wikipedia:, via

(As the article clearly explains, none of the underlying data of the map, the approximate geographic locations of its stations, or the idea of geometric stylization are copyrightable.)

Russian Academy of Science cleans house:, via

Their investigation finds 2528 plagiarized papers in 541 Russian-language journals, gets roughly 1/3 of them retracted, and threatens uncooperative journals with de-listing from their indexes. They also recommended blackballing 56 candidates for academy membership over plagiarism and other misbehavior.

0xDE boosted

How few \(k\)-gons can make a polyhedron, for different choices of \(k\)?

The answers include an amazing high-genus polyhedron with 12 faces, each of which is an 11-gon, posted Nov 2018 by Ivan Neretin (sadly, with multiple adjacencies for some pairs of faces, dubious by some definitions of polyhedra, rather than having one edge per face pair).

Via and indirectly via

‘Rhapsody in Blue’ (1924) just reached the public domain, showing the insanity of U.S. copyright law:

0xDE boosted

John Wallis and the Roof of the Sheldonian Theatre:, via an @aperiodical description of a 3d print of the same structure,

It's an elegant way to build a wide roof out of short beams with no joinery. But the history is somewhat lacking: Similar structures were known much earlier to Leonardo Da Vinci, Villard de Honnecourt, and Sebastiano Serlio. See Sylvie Duvernoy, "An introduction to Leonardo's lattices",

I'm sad that Cambridge Zero ( is not a name for the convention that, in writing a decimal number between 0 and 1, the leading 1's digit is included (e.g. 0.618034, not .618034).

One of the books I've been reading this week: Robert Bosch's _Opt Art: From Mathematical Optimization to Visual Design_, reviewed in

Some others I'm also enjoying but are less mathematical: Susan Phillips _The City Beneath_ (the rare book about graffiti where the words are more interesting than the photos); Kelly & Zach Weinersmith's _Soonish_; _Spectrum 26: The Best in Contemporary Fantastic Art_.

New open-access journal Compositionality, on the mathematics of "how complex things can be assembled out of simpler parts":

It's not a good fit for my own research, and the word "fuzzy" in the title of one of the initial papers is kind of a red flag for me, but I think it's a good thing that the move towards diamond-model open access is continuing.

Are reputation management operatives scrubbing Wikipedia articles? (Answer: duh.) has details of one such case, involving Theranos.

Show more

A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes. Use \( and \) for inline LaTeX, and \[ and \] for display mode.