## December 28, 2021

### Spaces of Extremal Magnitude

#### Posted by Tom Leinster

Mark Meckes and I have a new paper on magnitude!

Tom Leinster and Mark Meckes, Spaces of extremal magnitude. arXiv:2112.12889, 2021.

It’s a short one: 7 pages. But it answers two questions that have been lingering since the story of magnitude began.

## December 25, 2021

### The Binary Octahedral Group

#### Posted by John Baez

It’s been pretty quiet around the $n$-Café lately! I’ve been plenty busy myself: Lisa and I just drove back from DC to Riverside with stops at Roanoke, Nashville, Hot Springs, Okahoma City, Santa Rosa (a small town in New Mexico), Gallup, and Flagstaff. A lot of great places! Hot Springs claims to have the world’s shortest street, but I’m curious what the contenders are. Tomorrow I’m supposed to talk with James Dolan about hyperelliptic curves. And I’m finally writing a paper about the number 24.

But for now, here’s a little Christmas fun with Platonic solids and their symmetries. For more details, see:

- Greg Egan, Symmetries and the 24-cell.

All the exciting animations in my post here were created by Greg. And if you click on any of the images in my post here, you’ll learn more.

## December 4, 2021

### Surveillance Publishing

#### Posted by John Baez

Björn Brembs recently explained how

“massive over-payment of academic publishers has enabled them to buy surveillance technology covering the entire workflow that can be used not only to be combined with our private data and sold, but also to make algorithmic (aka ‘evidenceled’) employment decisions.”

Reading about this led me to this article:

- Jefferson D. Pooley, Surveillance publishing.

It’s all about what publishers are doing to make money by collecting data on the habits of their readers. Let me quote a bunch!

## December 1, 2021

### Mysterious Triality

#### Posted by David Corfield

When we started this blog back in 2006 my co-founders were both interested in higher gauge theory. Their paths diverged as Urs looked to adapt these constructions to formulate the elusive M-theory.

Over the years I’ve been following this work, which has taken up a proposal by Hisham Sati in Framed M-branes, corners, and topological invariants, Sec 2.5 that M-theory be understood in terms of 4-cohomotopy, culminating in what they call Hypothesis H. I even chipped in sufficiently to one article to be included with them as an author:

- David Corfield, Hisham Sati, Urs Schreiber, Fundamental weight systems are quantum states.

Philosophically speaking, I’ve been intrigued by the idea that the novel mathematical framework of twisted equivariant differential cohomology theory, required for Hypothesis H, may be formulated via modal homotopy type theory. This is the line of thought I mentioned a few weeks ago in Dynamics of Reason Revisited.

But I’ve also been thinking that you can’t add something important to fundamental physics without it causing ripples through mathematics. So I was interested to see appear yesterday:

- Hisham Sati, Alexander Voronov,
*Mysterious triality*(arXiv:2111.14810).