Coral Forest

crochet_forest_7Given that you read here at this blog, you may well like to keep your boundaries between art and science nicely blurred, in which case you might like to learn more about the coral reef forests made of crochet spearheaded by Margaret and Christine Wertheim. The pieces mix crochet (a hand-craft I know and love well from my childhood – I got to explore my love for symmetry, patterns, and problem-solving by making doilies) with mathematics – hyperbolic geometry in particular – as well as biology (mimicking and celebrating the forms of corals – and drawing attention to their destruction in the wild). You can read much more about the projects here. I’ve mentioned the work here before on the blog, but the other day I went along to see a new set [...] Click to continue reading this post

Outstanding in Their Fields…

In case you missed it, Maryam Mirzakhani has been awarded the Fields Medal! This is regarded as the most prestigious prize in mathematics. Here’s a Guardian article covering it at a general level, and here is the page on all the award winners, with more detail on each, at the International Mathematical Union website. The reason this is a big deal (and why it is newsworthy) is because it is the first time the prize has been awarded to a woman. In a world where, despite the number of excellent women mathematicians out there, there is still a perception problem in the general populace about who (or more to the point, what gender) is associated with achievement in mathematics, it is important to note and celebrate such landmarks.

I also note that one of the other 2014 awardees, Artur Avila, is from Brazil! While not covered as much in the press as far as I can see, this is another big [...] Click to continue reading this post

Self-Similar Dinner

romanesco_fractal_20_04_2014_2
Eventually, although a bit over-priced in the Hollywood farmer’s market, I do fall for these at least once in the season. As someone whose job and pastimes involve seeing patterns everywhere, how can I not love the romanesco? It’s a fractal! There are structures that repeat themselves on different scales again and again, which is the root of the term “self-similar”. Fractals are wonderful structures in mathematics (that have self-similarity) that I urge you to find out more about if you don’t already know (just google and follow your nose). And [...] Click to continue reading this post

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