A rather pretty video of an L-system made by my friend Steve.

LACMA, which I finally saw with a friend in February, has decided to offer high-resolution downloads of many of the items in its collection. This Ganesha has a pretty impressive belly. Via MeFi.

This may answer David Bowie’s question.

This slideshow makes me want to go to Slurping Turtle again.

Sometimes I wish we could just name p-values something else that is more descriptive. There’s been a fair bit of misunderstanding about them going on lately.

I was in New York on Sunday afternoon and on the suggestion of Steve Severinghaus we took a trip to the brand-new Museum of Mathematics, which is a short walk from the Flatiron building.

The Museum of Mathematics

It’s a great little place to take kids — there are quite a few exhibits which illustrate all sorts of mathematics from recreational math and Martin Gardner-esque pastimes like tessellations to an interactive video-floor which draws minimum distance spanning trees between the people standing on it. It apparently does Voronoi tessellations too but it wasn’t in that mode when I was there. There’s also a video wall which makes your body into a tree fractal, games, and a car-racing game based on the brachistochrone problem. The kids were all over that so I just got to watch.

One of the nice things was that there was a touch-screen explanation of each exhibit from which you could get three different “levels” of explanation depending on how much detail you wanted, and also additional information and references in case you wanted to learn more. That’s good because I think it will let parents learn enough to help explain the exhibit to their kids at a level that the parents feel comfortable. That makes it a museum for everyone and not just a museum for math-y parents who want to indoctrinate their children. On the downside, a lot of the exhibits were broken or under repair or under construction, so we really only got to see about 2/3 of the things.

Apparently it’s also a good place to go on a first date, as evidenced by some surreptitious people-watching. So if you’re in New York and want a romantic or educational time (aren’t they the same thing?), go check it out!

Via Allie Fletcher, here is an awesome video on the SVD from Los Alamos National Lab in 1976:

From the caption by Cleve Moler (who also blogs):

This film about the matrix singular value decomposition was made in 1976 at the Los Alamos National Laboratory. Today the SVD is widely used in scientific and engineering computation, but in 1976 the SVD was relatively unknown. A practical algorithm for its computation had been developed only a few years earlier and the LINPACK project was in the early stages of its implementation. The 3-D computer graphics involved hidden line computations. The computer output was 16mm celluloid film.

The graphics are awesome. Moler blogged about some of the history of the film. Those who are particularly “attentive” may note that the SVD movie seems familiar:

The first Star Trek movie came out in 1979. The producers had asked Los Alamos for computer graphics to run on the displays on the bridge of the Enterprise. They chose our SVD movie to run on the science officer’s display. So, if you look over Spock’s shoulder as the Enterprise enters the nebula in search of Viger, you can glimpse a matrix being diagonalized by Givens transformations and the QR iteration.

An animation of integer factorizations. Goes well with music. (h/t BK).

Graphics from the Chicago L (via Chicagoist)

Tony Kushner is kind of a tool. I find this unfortunate. But I still want to see Lincoln.

Aaron Roth reports that the DIMACS tutorial videos have been posted. A perfect time to brush up on your differential privacy!

An analysis of the Thai government’s menu served to President Obama.

A Choose Your Own Adventure version of Hamlet, from the creator of Dinosaur Comics.

I don’t tweet, but all of this debate seems ridiculous to me. I think the real issue is who follows twitter? I know Sergio is on Twitter, but is anyone else?

Food : An Atlas is a book project on kickstarter by people who do “guerrilla cartography.” It is about food, broadly construed. \$25 gets you a copy of the book, and it looks awesome, especially if you like maps. And who doesn’t like maps?

I remember reading about the demise of the American Chestnut tree, but apparently it may make a comeback!

William Thurston passed away a little over a month ago, and while I have never had the occasion to read any of his work, this article of his, entitled “On Proof and Progress in Mathematics” has been reposted, and I think it’s worth a read for those who think about how mathematical knowledge progresses. For those who do theoretical engineering, I think Thurston offers an interesting outside perspective that is a refreshing antidote to the style of research that we do now. His first point is that we should ask the question:

How do mathematicians advance human understanding of mathematics?

I think we could also ask the question in our own fields, and we can do a similar breakdown to what he does in the article : how do we understand information theory, and how is that communicated to others? Lav Varshney had a nice paper (though I can’t seem to find it) about the role of block diagrams as a mode of communicating our models and results to each other — this is a visual way of understanding. By contrast, I find that machine learning papers rarely have block diagrams or schematics to illustrate the geometric intuition behind a proof. Instead, the visual illustrations are plots of experimental results.

Thurston goes through a number of questions that interrogate the motives, methods, and outcomes of mathematical research, but I think it’s relevant for everyone, even non-mathematical researchers. In the end, research is about communication, and understanding the what, how, and why of that is always a valuable exercise.

Research often takes twisty little paths, and as the result of a recent attempt to gain understanding about a problem I was trying to understand the difference between the following two systems with $k$ balls and $n$ (ordered) bins:

1. Synchronous: take all of the top balls in each bin and reassign them randomly and uniformly to the bottoms of the bins.
2. Asynchronous: pick a random bin, take the top ball in that bin, and reassign it randomly and uniformly to the bottom of a bin.

These processes sound a bit similar, right? The first one is a batch version of the second one. Sort of. We can think of this as modeling customers (balls) in queues (bins) or balls being juggled by $n$ hands (bins).

Each of these processes can be modeled as a Markov chain on the vector of bin occupation numbers. For example, for 3 balls and 3 bins we have configurations that look like (3,0,0) and its permutations, (2,1,0) and its permutations, and (1,1,1) for a total of 10 states. If you look at the two Markov chains, they are different, and it turns out they have different stationary distributions, even. Why is that? The asynchronous chain is reversible and all transitions are symmetric. The synchronous one is not reversible.

One question is if there is a limiting sense in which these are similar — can the synchronous batch-recirculating scheme be approximated by the asynchronous version if we let $n$ or $k$ get very large?

Watch this now : Diana Davis‘s entry into the Dance Your PhD contest, entitled Cutting Sequences on the Double Pentagon. (via Dan Katz).

Via Amber, a collection of grassroots feminist political posters from India.

Via John, some fun investigations on how 355/113 is an amazingly good approximation to $\pi$. Also related are the Stern-Brocot trees, which can give continued fraction expansions.

I had missed this speech by a 10 year old on gay marriage when it happened (I was in India), but it’s pretty heartwarming. For more background on how the principal originally deemed the story “inappropriate.”

What is a Bayesian?

Unrelatedly, ML Hipster — tight bounds and tight jeans.

I’m being lazy about more ISIT blogging because my brain is full. So here are some links as a distraction.

Via John, George Boolos’s talk entitled Gödel’s Second Incompleteness Theorem Explained in Words of One Syllable.

D’Angelo is back!

This short video about a subway stair in New York is great, especially the music.

Luca’s thoughts on the Turing Centennial are touching.