Straight

In class tomorrow I’ll introduce one of my favourite equations:

<br />
\frac{d^2x^\sigma}{d\tau^2}+\Gamma^\sigma_{\rho\nu}\frac{dx^\rho}{d\tau}\frac{dx^\nu}{d\tau}= 0\ .<br />

… Wait – Where did everyone go?!

Come back! I’m not expecting you to know what it means, I just wanted to talk a bit with it sort of … nearby. If you consider yourself a bit intimidated by mathematics, be assured that it won’t bite. (No more than a piece of sheet music lying nearby will harm someone who has not learned to read music.)

It turns out that it is pretty geometry! In the equation, we’ve the object
<br />
\Gamma^{\sigma}_{\rho\nu}\equiv\frac12 g^{\sigma\mu}\Biggl(\frac{\partial g_{\mu\nu}}{\partial x^\rho}+\frac{\partial g_{\mu\rho}}{\partial x^\nu}-\frac{\partial g_{\rho\nu}}{\partial x^\mu}\Biggr)\ ,<br />
called the “Christoffel symbols”. The set of objects g_{\mu\nu} (the “metric”) actually encode the properties of the space you wish to study (like the plane, or the sphere), and the equation at the top tells you what are the “straight lines” in that space. Well, in the plane (like your desktop) they are straight lines, while in other spaces they are the analogue of straight lines – if you want to go from one point to another point somewhere else in the space and desire to travel along the shortest path to do so, you want to follow such a line. It is called a “geodesic”. The equation is commonly called the geodesic equation.

231px-Longitude_(PSF)You know such lines, intuitively, in a non-trivial example. Next time you look at a globe (wait, does anyone but me look at maps and globes any more? I love them!), you’ll probably see examples of those lines drawn in. They are the “great circles”, the lines of longitude, and the equator. (Image used with permission.)

I just made a class worksheet that guides one through a bit of playing with this equation to get the class excited about [...] Click to continue reading this post

Abacus Cadabacus! – Flash Anzan

sorobanI was quite stunned by this. For the first part, it is great (and charmingly bizarre) that there is a craze based around the abacus that has such a following (abacus or “soroban” championships), and for the second part… it is nothing short of remarkable when they get to the stage where they go “beyond the abacus”, and are just doing it in the head, but using abacus moves. And so fast!!! The radio program “Land of the Rising Sums” by Alex Bellos that I learned this from is here. There’s also a Guardian article here. It is all mostly about how numbers and arithmetic are taught in Japan. I think it is great that (from the people they interviewed) there’s a sheer love of calculation and of numbers and that there’s none of the lamentable “I’m not good at this I’m a languages/sports/art person” attitude that is so common in our society and which is responsible for poisoning children’s education so early on. I also love that the abacus is so fundamentally old-fashioned – [...] Click to continue reading this post

Edible Fractals, and the Snowflake

In celebration and anticipation of the unveiling of the Mosely Snowflake Sponge fractal on the USC campus later today, I’m reposting an old post about an edible fractal that I did back in February 2008. They say they will be serving fractal-themed food in the reception, and so I wonder if this is one of the foods that might feature? Don’t forget to come to the event! Recall that I (jokingly) speculated that when this fractal is completed the universe will end, as its purpose will have been served? Well, it seems that this has not come to pass, so… whew.

For other fractal-related posts, click here. You might also enjoy the lovely fractal-related film, Yaddda Yadda Yada, that won a prize in the competition last year.

-cvj

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romanesque cauliflower

A small Romanesque Cauliflower. (Click for larger view.)

Imagine my delight when I spotted this lovely piece of edible mathematics in the Hollywood Farmer’s Market this morning. The stall has several of them of many sizes (this was a very little one) and of several colours. Wonderful. If you don’t know what I mean when I talk about the mathematics, or use the term fractal, look it up. There are several things of note, among which are the wonderful spiral structures that you can see (Fibonacci spirals) all over, and which in various ways, encode the infinite sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…. (you get the next one by adding the previous two) called the Fibonacci sequence. Ratios of successive members of the sequence, (e.g., 5/8, 8/13, 144/233, etc) approximate what I’ve already mentioned in an earlier post is definitely my favourite number (if I [...] Click to continue reading this post

In Defense of Teaching Algebra

Over at HuffPo, my colleague Nick Warner has posted a piece about why we teach algebra to people who supposedly “won’t need it”, and he makes some excellent points. (Recall the silly New York Times piece by Andrew Hacker entitled “Is Algebra Necessary?” that I mentioned a few posts ago.)

I recommend Nick’s piece.

-cvj Click to continue reading this post

New York Times Nonsense

I can’t decide whether to be annoyed or amused by the opinion piece by Andrew Hacker entitled “Is Algebra Necessary?” in the New York Times on Sunday*. Annoyed because it is such an obviously flawed piece of writing, essentially saying that since (in the US) the system is failing to teach lots of people basic mathematics in school, the solution is to stop teaching it rather than figure out what is going wrong with the teaching process, while at the same time very lamely trying to make the case that it has no use anyway. Amused because it’s obviously flawed, and hopefully anyone reading it will laugh – one’s first thought has to be that it is not a serious article, given that it it is published in a respectable newspaper with reasonably educated editors.

But one can’t – shouldn’t – laugh, since there are (sadly) many people (lots of whom [...] Click to continue reading this post

Working Group

It wasn’t all lecture halls, discussion rooms, and cafeterias for the workshop. The organizers arranged for a boat tour last week, and we all sat on one of those splendid long, wide and low tour boats that you often see on the canals in Amsterdam. It was nicely equipped with a bottle of wine at each table, and the crew members handed us each a glass of sparkling wine as we embarked. Very nice. There was a lot of fun chatter from each table for the whole trip around the canals (so much so that they stopped the attempts to inform us over the PA system about some of the sights we were seeing, since the sound was drowned out by the conversations), covering (from what I could hear) a wide range of topics from well beyond physics to matters concerning topics presented in the workshop.

Sometimes pads of paper and pens appeared. Above is a group (David Tong, [...] Click to continue reading this post

Fractal in Progress…

So last week we had a visit from Kelly Stelle (he’s part of the high energy theory group at Imperial College) who gave us an excellent talk about aspects of supergravity. His work connects to the fascinating ongoing story about finiteness, and the new techniques being used to do the multiloop computations (see a recent Scientific American cover story about some of that – it is misleadingly packaged by the magazine, as usual (preview here) , but the article itself, focusing on the computational issues, is nice).

After his talk, I gave him a tour of the campus, and as we passed through the Doheny Library to view the lovely interior, we stopped by the ongoing construction of the Mosely Snowflake Sponge fractal that I told you about here.

They’re making a lot of progress.

We spent a few minutes folding some business cards to contribute some component cubes to the construction, and I took a snap (see photo on left) of Kelly at work. We made two or three cubes each…

Here’s a shot of one of the completed modules [...] Click to continue reading this post

A Snowflake on Campus

Ever heard of the Mosely Snowflake Sponge? There is one being constructed on campus here at USC right now! (The image on the left is the poster for the event.) The fractal was discovered by engineer Jeannine Mosely, and she did a similar construction (of a different fractal, the Menger Sponge) some years ago out of folded business cards (see here for some great images!), and the same thing is being done here. You can learn more about the project here. Margaret Wertheim, of the Institute for Figuring, is running this project, with the help of Tyson Gaskill. Everyone is invited to join in. You can just show up and fold a few cubes as you pass by. I took a picture and made encouraging remarks on this visit. (My defense is that I’d just given an hour and a half presentation, it was getting late into the night, and I was tired.)

There’s Margaret and Tyson working on constructing it, alongside a colleague of theirs [...] Click to continue reading this post

Knots from a Master

witten_on_knotsAh. This is just perfect. I actually looked into my Institute For Advanced Study news magazine this time around and noticed a gem I’d like to share. Edward Witten gave a lovely talk entitled Knots and Quantum Theory for a (sort of) general audience, and there is video of it available. Ever wondered why mathematicians study knots? Why do physicists care? What do they bring to the table? Well, this could be a talk for you to take out a bit of time to watch.

Not long ago I wrote a post about Ed, his huge influence on the field of theoretical physics, and some of his role in my own development as a physicist during my time [...] Click to continue reading this post

Inspiration and Dedication

jaime_escalante_by_robert_gauthierYou might not have heard of him, so I thought I’d mark the passing, on Tuesday, of the mathematics teacher Jaime Escalante. (Photo on right by Robert Gauthier.) He was an extraordinary teacher who passionately believed in the abilities of the many East Los Angeles students from disadvantaged and traditionally ignored backgrounds he taught, enduring the ridicule of his colleagues to press on with the job of teaching them as well as he could, challenging them to reach impressive heights of mathematical ability, especially considering given the circumstances. Some people might know some [...] Click to continue reading this post

Picking Mushrooms

From Frances Bonahan s colloquiumAha. It’s one of those moments in mathematics press coverage that the journalists love, since all the stereotypes about how weird people working on abstract things can be are able to be brought out and highlighted, and words like genius, prodigy, recluse, eccentric, etc, get thrown about in equal measure.

Yes, Grigory Perelman has being turning down stuff again. You may recall him refusing the Fields Medal four years ago. Now he is refusing the Clay Mathematics Institute’s million dollar payout. Perelman proved the Poincaré conjecture a while back (see this older BBC article about that, along with a non-technical mention of the content of the conjecture – see also here, a related post the picture above right is from), which is on the Clay’s list of Big Problems whose collective heads have a bounty on them. He’s apparently a bit eccentric and the press love it, so most articles I’ve seen are mostly taken up with stuff like the following I saw in the Guardian:
[...] Click to continue reading this post

Mathematics in Your Business

Terry Gross interviewed Scott Patterson and Ed Thorp on NPR’s Fresh Air. I heard it yesterday. It was very interesting to listen to Thorp in particular, a mathematician, describing his curiosity about how to construct a system for beating various gambling games, and going from there to the stock market, in effect becoming one of the earliest of the “quants”,

Thorp and the people who use such systems have come to be known as “quants” — it’s a reference to the quantitative-analysis techniques they employ — and their stories are told in Scott Patterson’s new book The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It.

You can hear the interview here, and read an extract from the book. Very interesting are the questions about what they think really went wrong in the market crash of [...] Click to continue reading this post

Categorically Not! – Awesome

cat_not_optical_puzzleThe next Categorically Not! is this coming Sunday May 29th. The Categorically Not! series of events that are held at the Santa Monica Art Studios, (with occasional exceptions). It’s a series – started and run by science writer K. C. Cole – of fun and informative conversations deliberately ignoring the traditional boundaries between art, science, humanities, and other subjects. I strongly encourage you to come to them if you’re in the area. Here is the website that describes past ones, and upcoming ones. See also the links at the end of the post for some announcements and descriptions (and even video) of previous events. (Image above right is from the excellent Categorically Not! – Really? event back in April 2006, described in an earlier post here. It was all about illusion, with examples from the world of optical illusions, and from literature.)

The theme this month is Awesome. Here’s the description from K C Cole:
[...] Click to continue reading this post

Pi Day!

piIt is Pi Day today! (It is also Einstein’s birthday, and Talk Like A Physicist Day. See below.) To remind you about Pi Day, from Wikipedia we have:

Pi Minute is also sometimes celebrated on March 14 at 1:59 p.m. If ? is truncated to seven decimal places, it becomes 3.1415926, making March 14 at 1:59:26 p.m., Pi Second (or sometimes March 14, 1592 at 6:53:58 a.m.).

The first Pi Day celebration was held at the San Francisco Exploratorium in 1988, with staff and public marching around one of its circular spaces, and then consuming fruit pies; the museum has since added pizza pies to its Pi Day menu.[1] The founder of Pi Day was Larry Shaw,[2] a now retired physicist at the Exploratorium who still helps out with the celebrations.

This year it is officially National Pi day too, according to the U.S. Congress!

Be sure to do some pi-ous things, ok? (Making pies, walking in circles at 1:59 pm (at [...] Click to continue reading this post

Unambiguously Good

 Libby Lavella, performing at at Categorically Not! 8th June 2008

Libby Lavella, performing at Categorically Not! 8th June 2008

Tonight’s Categorically Not! event was rather good fun, and interesting too. There were three excellent presentations under the theme “Ambiguity”. (See here.) K. C. Cole did a great job in bringing these people together (and of course in acting as M. C. on the night).

Bart Kosko did a great job talking principally about “fuzzy” mathematics, contrasting it with more binary (if you like) systems of logic. I think that his overview was great, and he talked about all the grey areas in logic and questions of epistemology where a “fuzzy” system is needed. (The question of whether a door is [...] Click to continue reading this post

Categorically Not! – Ambiguity

The next Categorically Not! is on Sunday June 8th. The Categorically Not! series of events that are held at the Santa Monica Art Studios, (with occasional exceptions). It’s a series – started and run by science writer K. C. Cole – of fun and informative conversations deliberately ignoring the traditional boundaries between art, science, humanities, and other subjects. I strongly encourage you to come to them if you’re in the area. Here is the website that describes past ones, and upcoming ones. See also the links at the end of the post for some announcements and descriptions (and even video) of previous events.

The theme this month is Ambiguity. Here’s the description from K C Cole:

Nature loves ambiguity, even if human nature doesn’t. What exactly is a species? Where exactly is that subatomic particle? When did life begin? How do genes influence behavior? Why does music move us? What does that poem mean? What color is white? Is that guy flirting with me, or not? The answers are often far more indeterminate than we’d like to think. Heck, we still don’t know why the chicken crossed the road. Or what the meaning of is is.

Speakers at Categorically Not! - June 8th 2008

Bart Kosko, USC Professor of Engineering, attorney and author of best-selling books Fuzzy Thinking, Noise, and Heaven in a Chip will tell us how fuzzy math

[...] Click to continue reading this post

Categorically Not! – Puzzles!

The next Categorically Not! is on Sunday March 9th (upcoming). The Categorically Not! series of events that are held at the Santa Monica Art Studios, (with occasional exceptions). It’s a series – started and run by science writer K. C. Cole – of fun and informative conversations deliberately ignoring the traditional boundaries between art, science, humanities, and other subjects. I strongly encourage you to come to them if you’re in the area. Here is the website that describes past ones, and upcoming ones. See also the links at the end of the post for some announcements and descriptions (and even video) of previous events.

The theme this month is Puzzles! Here’s the description from K C Cole:

What isn’t a puzzle? The universe, life and everything are essentially puzzles that, to borrow from Einstein, “beckon like a liberation.” Designing buildings, choreographing dances, cooking meals and getting along with other people all involve solving puzzles (as, of course, does figuring out what’s right in front of your eyes—not to mention putting together a program such as Categorically Not!) A love of puzzles and the challenge of solving them is deeply embedded in human nature.

Categorically Not! - Puzzles! - Speakers

Gwen Roberts, Scott Kim, Gavin Scott.

Our March 9th Categorically Not! features puzzlemaster Scott Kim, who’s [...] Click to continue reading this post

Beyond Einstein: Fixing Singularities in Spacetime

Not long ago David Morrison (UCSB) came to the mathematics department here at USC to give a colloquium.

David Morrison Colloquium at USC

This was a treat for me for many reasons. Here are three:

  1. It’s always good to see Dave. He’s one of the people I’ve known in the field was since my very first postdoc when I was learning to survive in the big bad world on my own after graduate school. I mostly could not understand a word he or anyone there else said in those days (IAS Princeton, right in the belly of the

[...] Click to continue reading this post

A Delicious Fractal

romanesque cauliflower

A small Romanesque Cauliflower. (Click for larger view.)

Imagine my delight when I spotted this lovely piece of edible mathematics in the Hollywood Farmer’s Market this morning. The stall has several of them of many sizes (this was a very little one) and of several colours. Wonderful. If you don’t know what I mean when I talk about the mathematics, or use the term fractal, look it up. There are several things of note, among which are the wonderful spiral structures that you can [...] Click to continue reading this post

Möbius Transformations

This short video is simply lovely. It illustrates (with perfectly chosen music) an important set of mathematical transformations dear to many of us, the Möbius transformations. It is by Douglas Arnold and Jonathan Rogness of the University of Minnesota. It’s a pleasure to watch, whether you work in a mathematically related field or not. Try it:



Also worth looking at (for a host of other reasons) are the comments on the video from [...] Click to continue reading this post

Inside Out from the Inside

Last night’s Categorically Not! – Inside Out event was just great. The three topics contrasted really nicely, were very well presented as individual topics in their own right, and there were resonances between the different topics through the main umbrella theme – “Inside Out”.

Science writers Sandy Blakeslee and her son Matt Blakeslee did a sort of tag team presentation, taking turns to build up several aspects of the subject (covered in their new book “The Body Has a Mind of Its Own”) of one’s sense of self and that all-so-important division between inside (ourself) and outside (the rest of the universe) that we make with our minds. sandy blakesleeIt’s very dynamic, of course – you extend it a lot when you use tools, from a fork when eating to the car you’re driving in (everyone grunted in recognition when Sandy mentioned how you have the instinct to duck when driving under a low ceiling in a parking garage….). One of the things that I think resonated most with the audience is the description of the work on showing how many celebrated “out of body” experiences that people get have a foundation in [...] Click to continue reading this post

Inside Out

Part of K C Cole’s teaser for tomorrow’s Categorically Not! – Inside Out said:

Sometimes the results are surprising: circles in the plane can’t be turned inside out, but spheres in 3-dimensional space can be.

This is all the license I need to show you* this wonderful 21 minute video showing exactly that (and explaining some rather beautiful mathematics along the way):



Direct link to the Google Video (for larger viewing) here. [...] Click to continue reading this post

Categorically Not! – Inside Out

Paul Stein of Los Angeles PhilharmonicThe next Categorically Not! is a Blue* one! It’s on Sunday October 28th (tomorrow). The Categorically Not! series of events that are held at the Santa Monica Art Studios, (with occasional exceptions). It’s a series – started and run by science writer K. C. Cole – of fun and informative conversations deliberately ignoring the traditional boundaries between art, science, humanities, and other subjects. I strongly encourage you to come to them if you’re in the area.

Here is the website that describes past ones, and upcoming ones. See also the links at the end of the post for some announcements and descriptions (and even video) of previous events. (Above right: The Los Angeles Philharmonic’s Paul Stein demonstrating “small differences” on the violin, in the event with that theme.)

The theme this month is Inside Out Here’s the description from K C Cole: [...] Click to continue reading this post

Not Following the Script

Well, it was a weekend of an unexpected character. Fantastic outside, but I did not see as much of it as I’d have liked. I was working on a script, you see. It needed to be worked on immediately and at the last minute because the work of turning it into the final product that will get seen started this weekend, and so I wanted to make as many comments and suggestions as I could before it was too late. It’s science – don’t worry. Also it is rare to get to work on something that I know will get made (most things get shelved and never see the light of day), so that was sort of fun. I won’t tell you what it is (sorry) since I’m not actually a writer on the project, but I got the chance to look at the whole thing and make a lot of comments and suggestions, rephrasings, alternative lines, and so forth. All in a good cause. I think it will be out next year.

Yes, I know. “I was working on a script…” Sounds rather like I’ve finally caved in and succumbed to living in Los Angeles completely, working on a script like everyone else [...] Click to continue reading this post

Reading, Writing, and ’Rithmetic

Yesterday (depending upon who’s counting) was the 16th anniversary of that thing we call the World Wide Web becoming a public entity. The Web is not to be confused with the Internet, which is much older, of course1. I’m talking about Tim Berners-Lee’s idea and implementation thereof. (I should not neglect to mention that this was done at CERN, the particle physics laboratory in Europe.) His original posting (on the newsgroup alt.hypertext) proposing the structure can be viewed here, and here’s an extract:

The project started with the philosophy that much academic information should be freely available to anyone. It aims to allow information sharing within internationally dispersed teams, and the dissemination of information by support groups.

Reader view

The WWW world consists of documents, and links. Indexes are special documents which, rather than being read, may be searched. The result of such a search is another (“virtual”) document containing links to the documents found. A simple protocol (“HTTP”) is used to allow a browser program to request a keyword search by a remote information server.

The web contains documents in many formats. Those documents which are hypertext, (real or virtual) contain links to other documents, or places within documents. All documents, whether real, virtual or indexes, look similar to the reader and are contained within the same addressing scheme.

To follow a link, a reader clicks with a mouse (or types in a number if he or she has no mouse). To search and index, a reader gives keywords (or other search criteria). These are the only operations necessary to access the entire world of data.

What am I going to do to celebrate?

letter to anonSince everyday I celebrate the WWW by using it a lot, to commemorate the event I think I’m going to pay a visit to the (real, physical) library, then read a good old-fashioned book for a while, and then hand-write a letter. I used to write so many letters, long ago, and from time to time I try to stop everything and pick up a pen and write one. I got in the mood the other day while in Aspen, and went and found some letter-writing paper and envelopes, curled up on a sofa, and wrote for a [...] Click to continue reading this post

Showing a Different Way

danica mckellar from and AP articleDanica McKellar (the actress who played the girl “Winnie” in that show “The Wonder Years” that many of you might remember) has been working to try to encourage young girls to go more for “Cute and Smart”, as opposed to “Cute and Dumb”. Bottom line: Less Lindsay Lohan, and Paris Hilton, and more…. well, Danica. (I’m sure there are other Tinseltown examples here… can I have some help?).

Danica sets an excellent example of why the two (being considered attractive on the one hand, and smart on the other) are not mutually exclusive, while not suffering from the “geek” or “nerd” label that is attached by the entertainment industry to certain groups of people who enjoy using their brains a lot. She trained as a mathematician, in fact, doing her undergraduate work at UCLA so well that she did rather good published research work (NPR piece here – Update: It is actually more of a theoretical physics problem, it appears). This is from someone who struggled with the subject in sixth grade. Why is she in the news? She’s written a new book “Math Doesn’t Suck”, the aim being to encourage girls to avoid the (social) barriers to getting into mathematics. Excellent title. (I wonder if they’ll change it to “Maths Doesn’t Suck” if they publish it in Britain? “Suck” British kids have adopted from the USA cultural juggernaut, but “Math”? Not yet.)

danica mckellar math doesn't suckActually, looking at her site, I see that the full title appears to be “Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail”, which is more of a mouthful, a bit less zippy, but oh well. It’s all very Clueless, in a good way. Here’s a link to the book’s site, and it is due out tomorrow.

There’s an article1 on her recent Newsweek quote at CNN, from which I grabbed this:

“When girls see the antics of Paris Hilton and Lindsay Lohan, they think that being fun and glamorous also means being dumb and irresponsible,” the 32-year-old McKellar told Newsweek for editions to hit newsstands Monday.

“But I want to show them that being smart is cool,” she said. “Being good at math is cool. And not only that, it can help them get what they want out of life.”

but you should go and read the whole thing, by clicking here. [Update: Much better article here, by Corey Binns in Good Magazine. Extract:

"The book hones in on middle school’s trickiest points-––like fractions, ratios, and percentages—and presents them in a style that’s appropriate for the cool kids’ lunch table. Figure out your “type” in boys and you’ll understand greatest common factors. All of those iced lattes celebrities drink make multiplying fractions tasty. Plus, savvy shopping requires killer decimal skills."

]

Go Danica!

In other news, I learned2 that particle physicist Lisa Randall (author of the popular book with the curious title “Warped Passages”) appears in Vogue this month. Lisa [...] Click to continue reading this post

E8

E8 and the Gosset polytope 421

No, not another flower from my garden. This is a two dimensional projection (originally hand drawn in the 1960s by Peter McMullen, of a polytope that lives in eight dimensions, known as the Gossett polytope 421. Click here to be taken over to the American Institute for Mathematics (AIM) site for more information about it. (This image was computer generated by John Stembridge, and you can get higher resolution there for use on your T-shirts and so forth.)

What does this all pertain to? A new result from a team of mathematicians. They’ve done what some are calling the mathematician’s equivalent of mapping the genome of a Lie group, the one called E8. Groups pertain to symmetries. Symmetries are [...] Click to continue reading this post

Not Improbable

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

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