How Do People from Different Cultures Draw Circles?

Here is a really interesting article about how people from different cultures draw circles.

I was once — well, at least once — told in elementary school that I was drawing circles the wrong way (because I was using the wrong sense around the clock). I think I responded with the definition of a circle and that the definition doesn't depend on the sense in which one draws it, and I think my teacher did not appreciate that.

On a similar note, in high school, I once lost 50% of the point total on an answer for misspelling ellipse (by using one 'l' instead of two), which was the correct answer. I called bullshit (on the grounds that it was my mathematics knowledge that was being tested), but unfortunately I lost.

More closely related to the article, one thing I noticed in the UK is that the most common way to write an 'x' there is with two arcs, so that they won't always cross if one writes quickly. In contrast, I write two attempts at lines that explicitly cross. (I haven't checked if this is US versus UK convention.)

And, indeed, most Americans drew their circles counterclockwise in this data set, and I draw mine clockwise.

(Tip of the cap to Improbable Research for their Facebook post.)

Update: Here is a lovely quote from the article: In a 1977 paper Theodore Blau, then-president of the American Psychological Association and creator of the torque test, argued that drawing clockwise circles was a sign of learning and behavioral aberrance.

"Gifted, Passionate Student Really Stretching Limits Of School’s Resources"

And The Onion wins yet again.

High School Chalkboard Writing from 1917 Unearthed

Some chalkboards with writing from 1917 were recently unearthed (figuratively) during a high school's renovation. They're pretty cool.

RIP James Q. Wilson (1931-2012)

James Q. Wilson, well-known political scientist and author of the textbook I used for AP Political Science when I was in high school, died today.

I love his quote about moving back to the Boston area a few years ago: [his descendants] "feel a legal obligation to live within 30 minutes of Fenway Park."

(Tip of the cap to Andrew Waugh.)

What We Should Have Been Taught in High School

Here is The Oatmeal's version of what we should have been taught during senior year in high school. There is a lot of truth here.

And after reading several vivas with tons of elementary English mistakes, I am even more tempted than I might usually be to buy the poster version of 10 Words You Need to Stop Misspelling.

(Tip of the cap to Maria Satterwhite.)

Teaching Networks to High School Students

Yesterday Somerville had its "Study Day", in which high school students from several schools came to Somerville to visit Somerville, meet some students (who gave them tours of both Somerville and, briefly, other parts of Oxford), learn some general things about Somerville with 'global' presentations, and have a 1.5 hour session with one of a few Somerville Tutors who volunteered to help out. I helped out, as did one of our first-year mathematics students, which is essential because the perspectives and insights of our current students are absolutely crucial to any endeavor like this

I was one of the faculty volunteers, and I gave a presentation about the mathematics of networks and then I talked about studying mathematics at Somerville and Oxford (and gave a preview of some of the curriculum changes in applied mathematics that are currently under discussion; these are currently slated to start in Fall 2012, though first we need to decide exactly what they are). I had 17 students in my room, and apparently my mathematics presentation was among the more popular choices of the students who wanted to visit us. (We obviously didn't have room to accommodate everybody who wanted to come.) The abstract that I wrote to be circulated to the selected high schools---and I don't know how they were selected---was the following:

MATHEMATICS: What do Financial Markets and Facebook have in Common?

This session will introduce you to the sheer joy of applied mathematics, and it will also tell you about the mathematics course at Oxford. Changes are brewing in our mathematics course, and here is your early chance to find out what some of them are. If you are considering studying mathematics at university, then this is the session for you! We'll discuss some modern ideas from an area of mathematics called "network science" that can be used to help understand everything from how Facebook works to how financial markets (don't) work. And then we'll talk about possibly mundane but certainly important stuff like the mathematics degrees at Oxford and how you can get involved in research at an early stage. The only requirement for this session is excitement about mathematics and its applications.


This abstract was what was used to advertise mathematics, and I like to think that my experience communicating with the media helped me to write a good abstract.

After the students were chosen, I asked them to read The Physics of Networks by Mark Newman. (I later stressed that the 'physics' of networks and 'mathematics' of networks are, in my view, interchangeable.)

I checked with the students who attended, and they confirmed that Newman's article was at the right level for them, and I think their having read that article as background made the whole presentation easier.

I needed to show lots of fancy, pretty pictures, so I prepared a powerpoint presentation, but I want to stress that this was guidance for our discussion. I asked the students to speak up early and often, because I don't think that my droning on would be the best way to do this. One can't tell this always tell this purely from the posted slides, so I am happy to comment further about that aspect of things. But it is crucial to make sure that one is actually having a discussion with the students, even if one is using slides to facilitate this discussion. One conscious decision I made was not to bother with the references and acknowledgements for results, figures, etc. I am normally a stickler about such things, but I felt in this case that it would be intimidating and actively detract from what I was trying to do---which was to be as accessible as possible and just open the students up to the excitement of the subject and the fact that they could get into it really quickly. (And I hereby apologize to my colleagues for this, but doing the usual thing would in my opinion have massively hindered the students' experience in this case.)

I also wanted to mention that purposely gave an illustration of how networks can be represented in terms of matrices because the students had had some exposure to matrices before. I wanted to relate this active fascinating field to mathematics they have seen in their high school classes. I also wanted to relate it to their personal experiences with social networks such as Facebook. It is this last aspect that makes it easier to explain networks to high school students (and more general lay audiences, for that matter!) than is the case for most active research areas in mathematics.

One thing that I made a point to stress was that undergraduate researchers have been intimately important to my work in this area, that they are really only a couple of years to be able to contribute to such research efforts, and that such opportunities awaited them in Oxford and Somerville. I made a point to show them what one of my current Somerville students is doing and also made a point to show them a really exciting (though admittedly preliminary) result that she showed me just last week. The point of showing the result from last week was to illustrate that mathematics isn't static---knowledge changes, and it can do so very quickly---and also what we want to do to really get somewhere with the preliminary result. I think that this message isn't given even close to often enough. We're not merely teaching or doing research on a body of knowledge that was handed down to us by the luminaries from yesteryear, but we're constantly discovering new things, obtaining more refined understanding and insights on even very old ideas, etc. Sure, there are a lot of mundane subjects to learn that are well-established, but there are lots of new ideas and applications to be found even in traditional subjects like linear algebra.

I spent roughly half the time discussing networks with the students and roughly half the time discussing Oxford and Somerville mathematics with the students. (We occasionally forayed into the differences between the mathematics and physics or engineering degrees, as some students are also deciding not just where they want to apply but also what specific major they would like to have.)

In deciding on one Oxford College versus another, the thing I stressed was that the students should judge the people with whom they would be working (namely, people like me). More than anything else, what Somerville or any other College has to offer is its people. I refuse to toe the company line and say that Somerville is automatically better. That would be stupid and would contradict my true beliefs (as some of you know, there are some things here that are causing me significant displeasure, to put it mildly). Students should decide for themselves whether or not they want to work with me---I hope so, because I think that I'm a damn fine educator and that I have things to offer on both the teaching and research sides that very few others can offer---but the point is that I think that this is the main decision. Prospective Somerville mathematicians should decide for themselves whether they want to work closely with my colleagues and me. The official literature seems to stress the importance of things like our library, and I think that is seriously misguided. The other Colleges have libraries too, and I'm sure that they're all fine libraries. A College's greatest strength is its people---the ones who will frame your College experience more than anything else ever will---and any College that advertises itself differently is doing it wrong. I know that I'm biased, but in mathematics and allied subjects, I think that Somerville has excellent people (including both faculty and students).

Incidentally, the student response seems to have been extremely positive. The students were engaged and they thanked me warmly at the end of the presentation. One student has already e-mailed me for more information about networks. (I gave the students my e-mail address because I figured they'd have more questions later, and I wanted to be able to answer them.) I can't say if Somerville or Oxford will get any additional applications from prospective mathematics students as a result of the presentation and related efforts, but there are 17 high school students who I feel are more excited about mathematics and its applications than they were before I talked to them. And that counts for a lot.

(By the way, this isn't my first time speaking to high school students about my research. When I do this, I always make it a point to show them some of the stuff my undergrads have done and are currently doing. It's really important to show them the research efforts of somebody who was in their position not that long ago.)

What Education is Supposed to Be

I could rant on and on about this, but let me instead just to a recent high school valedictorian speech, which I won't debase by calling a rant. This student described what education is supposed to be far better than I ever could.

As for my reaction to this speech, all I have to say is: Amen!

I am sure I am sometimes guilty of some of this stuff with my own teaching, though I try not to be. Also, some of the points in this essay chime rather well with what I always appreciated at Caltech. I worked really hard and it could be a royal pain in the ass, but that is part of the price of encouraging independent thinking. There is typically a ton of hard work that needs to go with it in order to help such efforts work.

(Tip of the cap to Greg Fricke, who once had to put up with my attempts at teaching. I still wish that I brought that pillow to class one day in order to assist with your sleeping!)

Wikified Classmates

I now know of two of my fellow Beverly High classmates [in this case, people who I actually know] from the class of 1994 who have been wikified. (Maybe there are more, but I just found out about the second one today.)

I went to both Beverly High and Hawthorne elementary school (since 1st grade, if I remember correctly) with Dina Rae (though I know her as "Dina Franks"). I went to Beverly High with Saba Soomekh, whose sister Bahar has also been wikified. I took classes with Saba, but I don't remember whether I met Bahar (maybe I did), who has appeared in MI: III (among other films).

Then, of course, there is also Angelina (who I mever met, though my collaborator JP Onnela can tell you at least one story about her; she was one year ahead of me in school and apparently left after sophomore year) and this person (whose family lived a block away from mine and whose brother is the one who first taught me how to throw a frisbee).

So much for my sordid past. At least I can have second-order fame through the people I know.