E-mail, but for infinity

This site has a new home at e-infinity.space — the third address it has had, and with luck the last for a while. It started on WordPress as The Bright Obvious, moved to a Jekyll site on github.io in 2021, and has now been rebuilt from the ground up.

About the name: it’s like e-mail, but for infinity. Also a space with a multiplication that is associative and commutative up to coherent higher homotopy.

The pun turned out to be load-bearing in a way I hadn’t planned. The animation on the front page is a loop in ${\mathrm{Conf}}_{11}({\mathbb{R}}^2)$ — eleven points stirring a rectangle, never colliding, spelling out a braid word as they go. But the little 2-disks operad satisfies $E_2(k)\simeq {\mathrm{Conf}}_k({\mathbb{R}}^2)$, so that picture is really a loop in $E_2(11)$, and its fundamental group is the pure braid group $P_{11}$. Which is exactly why $E_2$-algebras are braided rather than symmetric. Let $n\to \infty$: the spaces become contractible, the braiding collapses into symmetry, and what survives is $E_{\infty }$. The braid on the front page is precisely the structure that dies in the limit the site is named after.

What’s here

Visualizations. Twenty of them, all running in your browser and phoning home to nobody: closed geodesics on the space of unimodular 3-lattices, a free group of rank two sitting inside $SO(3)$, nets of four-dimensional polytopes, the Schwartz pentagram map, and — newest — train-track taffy, which drags a loop through a braid word until its intersection numbers grow like Fibonacci.

Teaching. Every course I’ve taught, forty-three of them going back to Michigan in 2006. The recent ones have full schedules; the older ones link out to wherever they still live.

Writing. Everything since 2013, including the whole Bright Obvious archive, which had been stranded on WordPress. Old permalinks still resolve — if you have a link to something of mine from 2021, it will land in the right place.

That archive is not embalmed, either. While moving it I got a lovely email from Nathan Smith, a senior at Brown, explaining that my answer to the follow-up puzzle in Aha! A percolating pandemic and a perfect proof was wrong — I had answered a question adjacent to the one I asked. He was right, and the post now says so.

There is a light/dark switch in the corner, the whole thing is fast and static, and nothing here tracks you.