Category Archives: mathematics

Not Improbable

By | | , , , ,
13 Comments

elaine chewOn Wednesday night, accompanied by Tameem, a student of mine, I wandered across campus to attend the “Mathematics in Music” event. I blogged about it earlier. I don’t really want to talk about the event itself in this post. It was a nice enough recital of three pieces. I don’t know why, but the promised “mathematics” was disappointingly virtually non-existent. I’m not exaggerating, I’m afraid.

Keep in mind that it may simply just be my misunderstanding of the intent of the event, but there’s simply next to nothing to report in the way of what was said about mathematical aspects of music. There were plenty of opportunities, but (almost) none were taken. I got out my notebook and pen, all excited at what the presenters might say at various points… and the mathematics never showed up. There were a few extremely elementary remarks about tonal ratios in chords, about scales, keys, and time, and that was it, more or less. This was a bit of a shame, since I suspect that Elaine Chew could have talked at length and with some authority on the matter (given the projects she’s involved in see e.g. here), but mathematics was almost completely missing in the event – despite the title. I imagine there were what seemed like good reasons for this. I was not party to decisions made behind the scenes, so cannot comment further.

More interestingly on that front was what took place in the minutes leading up to the delayed start of the event. First, although it was a free event, they pointed us to the box office where an attendant printed us two tickets from the computer so that we can show them to someone at the door who wasn’t really looking anyway. Fine. We got into the recital hall, but rather than sitting at the obvious available seats, I suggested that we move to the other side of the room where one can get a better view of the piano keyboard. I’m less than happy when I can’t see what a musician is doing, you see, so I always try to sit with the pianist’s view of the piano. So we did that, and found two seats. While we chatted and looked around us at the growing assembly, I spotted a friend and colleague of mine, the composer Veronika Krausas. She was in the company of someone who she introduced as Brian Head, who is a composer, performer (guitar) and music theorist (a “triple threat”, Veronika joked), also in USC’s Thornton school of music. They were looking for seats and there was one on either side of the two we were sitting in, and so they joined us and we chatted some more.

When the event start was about ten or fifteen minutes late -they were trying to get the reassuringly large crown all seated, they announced- Veronika idly looked at her ticket, pointed out that they were numbered, and wondered if we should have been […] Click to continue reading this post →

Hooking Up Manifolds

By | | , , , ,
11 Comments

lorenz manifold

I love crochet. I spent a huge number of hours doing it when I was young, and only in later years did I realize that the same things that attracted it to me then are the same things that drive and motivate a lot of my research interests. (I many have mentioned this before, but it’s worth saying again).

It’s the love of patterns, plain and simple. If your child -of whetever gender- gets […] Click to continue reading this post →

BBC Publishes Onion Article?

By | | , ,
25 Comments

Well, what else can it be? It is not April 1st, so my only explanation is that it is an Onion article that somehow was picked up by the BBC. What do you think? It reads exactly like one, right down to the picture of the pleasant bearded academic at the board, the well-scrubbed English schoolchildren, and the quotes from the children. The only thing missing is the […] Click to continue reading this post →

Poincaré In Our Time

By | | , ,
6 Comments

I don’t know whether you caught this already, but if not, do consider listening to the 2nd November edition of BBC Radio 4’s “In Our Time”. It is about Poincaré, his work, and the famous conjecture. From their website’s page on the programme:

The great French mathematician Henri Poincaré declared: “The scientist does not study mathematics because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing and life would not be worth living. And it is because simplicity, because grandeur, is beautiful that we preferably seek simple facts, sublime facts, and that we delight now to follow the majestic course of the stars.”
Poincaré’s ground-breaking work in the 19th and early 20th century has indeed led us to the stars and the consideration of the shape of the universe itself. He is known as the father of topology – the study of the properties of shapes and how they can be deformed. His famous Conjecture in this field has been causing mathematicians sleepless nights ever since. He is also credited as the Father of Chaos Theory.

So how did this great polymath change the way we understand the world and indeed the universe? Why did his conjecture remain unproved for almost a century? And has it finally been cracked?

It is a particulalry good programme this time. This is a programme that focuses mostly on philosophy, and is often accused of being only rather superficial when it comes to covering the more hardcore and up-to-date science, but not this time. The guests are […] Click to continue reading this post →

A Man Out Standing In His Field

By | | , , , ,
10 Comments

Two of our colloquia this semester were concerned with work very much in the public eye this year. The first was from Francis Bonahan of the Mathematics Department here at USC.

F bonahan colloquium

He talked about the work that won the Fields medal – the proof, by Grigori Perelman, of the Poincaré conjecture. Or better, I should say the work toward the proof, since the citation does not explicitly mention the conjecture, but his larger body of work. (MathWorld link, Wikipedia link.) In fact, Francis spoke about a lot more than just the Poincaré conjecture. He talked about the larger setting in which that work fits, something mathematicians call the “geometrization conjecture”, which Mathematicians care a lot more about. Perelman’s work does more than just prove the Poincaré, it addresses the whole (3-)ball of wax, so to speak. He told us quite a bit about that in the talk, spending most time talking about what they were and how they fit into the scheme of things, rather than […] Click to continue reading this post →

A Positive Sign

By | | , , , ,
8 Comments

I’m always pleased to see this sign. It is at Heathrow, on the walk down the perpetually dingily lit underground corridors connecting the terminals, the tube, the extortion Heathrow express, and the parking lots.

For a start, I generally like the idea that the ground floor of a building (the one you walk onto off the street) is the “zeroth” floor. (I mean no disrespect to this splendid country I live in, that has largely chosen otherwise, although every now and again in older buildings you see it.) So it is just great to see […] Click to continue reading this post →

Those Self-Fulfilling Prophecies

By | | , , , , ,
13 Comments

You may recall that we were recently discussing stereotypes as a result of an earlier post. Particularly, I was talking about the effects those sterotypes can produce as a result of modifying the expectations of others, making it hard for some people to be taken seriously, and resulting in them having to go that extra mile (or several) as a result.

Well, I’d like to point your attention to a recent study about the direct effects of those stereotypes on the stereotyped. Quoting from an article by AP science writer Randolph E. Schmid:

[Steven J.] Heine and doctoral student Ilan Dar-Nimrod wanted to see how people are affected by stereotypes about themselves. They divided more than 220 women into four groups and administered math and reading comprehension tests between 2003 and 2006. Their results are reported in Friday’s issue of the journal Science.

What they actually did was to provide the different groups with different images and reading materials before they did the tests. They seem to have found significant differences in the results that suggest that having a negative stereotype of yourself in mind actually makes things worse. In other words:

It’s a process psychologists call a stereotype threat, Heine explained. “If a member of a group for which there is a negative stereotype is in a position to test the stereotype, they are likely to choke under the pressure.”

So reminding them of the stereotype affects them.

Here’s what they found: […] Click to continue reading this post →

Manifold Yau

By | | , ,
30 Comments

Well, here’s yet another discussion of Yau to gobble up. It is a New York Times article by Dennis Overbye on Yau, his life and work*. I’ve no idea why this was written, or what the timing was. I’d like to believe that it was just because it is a good subject -because it is- and that it is worthwhile to do an article about a Mathematician of considerable stature in the field, and about the ins and outs of the world of Mathematics -because it is. But I can’t help but wonder if this would have seen the light of day if there was not the big argument going on about the New Yorker article and Yau’s displeasure with its contents. […] Click to continue reading this post →

Update on the Giant-Killers

By | | ,
16 Comments

Good News Everyone! I learned just now from Good Math, Bad Math there may well be a successful proof of yet another of the great Millennium problems. This one pertains to solutions of the Navier-Stokes equations which are of central importance in fluid dynamics, for example. (The figure to the left -click for larger- is from a computer simulation, by Greg Ashford, of the airflow around an aircraft wing (in cross section) and the foil that it uses to change the overall shape of the wing for maneouvering. I got it from a site linked here.)

Penelope Smith, at Lehigh University has presented a preprint with her proof, which […] Click to continue reading this post →

Irrational Memories

By | | , , , , , ,
16 Comments

Back when I was young enough to care to try to list such things, I had a favourite number. Really, really faourite. I lived and breathed that number for a while. Today’s session in the freshman seminar “The Art and Science of Seeing and the Seeing and Science of Art”, about which I have blogged here and here, was all about it. Rather than do chapter and verse about it (don’t get me started!), I will instead leave you with the image that I ended with…

… and let you tell me and other readers – if you like – what you think the number is, what it means to you, and perhaps share whatever you like (or hate) about it.

-cvj
Click to continue reading this post →