On a recent plane trip, I was reading a very abridged version of (the ten thousand page long!) Church Dogmatics by Karl Barth, and I found something totally beautiful.

Read more »

Given a text in two languages, is it possible to uncover the meaning of individual words?

Read more »

Today, I was about to sit down and read a paper (in French--I may not speak in tongues, but apparently I can read in tongues, so to speak!), and I thought to myself about how nice it would be to have a cookie. I went to Uncle Joe's, I went to the Classics Cafe, I went to Cobb's coffee shop, and then I gave up, for there were no cookies in any of those places, places which so often appear to be the source of cookies.

Read more »

Someone contacted me with some questions about Bayesian document clustering; with that inspiration and a free afternoon a few weeks ago, I took a Hebrew bible and built a matrix $(A{ij})$ where $A{ij}$ equals the frequency of the $i$-th (Hebrew!) word in the $j$-th chapter of Genesis. I calculated its singular value decomposition (supposedly this is "latent semantic analysis"), and then took some dot products (calculating the "correlation" of chapters)...

Read more »

There are usually courses at Mathcamp about surfaces; there should be courses about orbifolds! For instance, knowing that the smallest hyperbolic orbifold is the (2,3,7)-orbifold, having orbifold Euler characteristic $-1/84$, immediately gives that a closed hyperbolic surface of genus $g$ has no more than $84(g-1)$ isometries (preserving orientation); this is "Hurwitz' $84(g-1)$ theorem."

Read more »

At a recent Pizza Seminar, Matt Day gave a lovely talk explaining why it isn't possible to classify 4-manifolds.

Read more »

This is a question I wandered into accidentally years ago now, which I think other people might be amused to think about (or more likely, put on an abstract algebra exam).

Read more »

I gave a Farb student seminar talk on a lovely paper,

Read more »

While on public transportation, my mind wanders... And one might assume the following about me and my buses,

Read more »

When I walk down the street, I create patterns in how I walk, often by controlling my stride length so I will step on cracks every third sidewalk square, or whatnot. If I were a true master, my stride length would be incommensurable with respect to the sidewalk length--surely this was the problem that forced irrationalities upon the Greeks...

Read more »