(A more technical post follows.) By the way, in both sets of talks that I mentioned in the previous post, early on I started talking about orthogonal polynomials , and how they generically satisfy a three-term recurrence relation (or recursion relation): Someone raised their hand and ask why it truncates … Click to continue reading this post
It’s pi day today! Don’t forget to celebrate! Options include walking around in circles at 1:59pm, baking a pie, eating pie, etc! Or maybe explain what pi is to somebody… I won’t list irrational behaviour as there’s a bit too much of that already… –cvj (Above image snapped from a … Click to continue reading this post
My big task this afternoon was not baking but making a hexahexaflexagon! I can’t tell you why right now, but as far as I know it has nothing to do with my recent paper on JT gravity in case you were trying to see a connection.
So Tuesday night, I decided that it was imperative that I paid a visit to one really good restaurant (at least) before leaving Santiago. My duties at ICMP2015 were over, and I was tired, so did not want to go too far, but I’d heard there were good ones in the area, so I asked the main organizer and he made a recommendation.
It was an excellent choice. One odd thing: the hotel is in two separate towers, and I’d noticed this upon arrival and started calling it The Two Towers in my mind for the time was there. Obviously, right? Well, anyway, the restaurant is right around the corner from it plus a two minute walk, and…. Wait for it…it is called Le Due Tonni, which translates into The Two Towers, but apparently it has nothing to do with my observation about the hotel, since it got that name from a sister restaurant in a different part of town, I am told. So… An odd coincidence.
I will spare you the details of what I had for dinner save to say that if you get the fettuccini con salmon you’re on to a sure thing, and to warn that you don’t end up accidentally ordering a whole bottle of wine instead of a glass of it because you’re perhaps used to over-inflated wine prices in LA restaurants (caught it before it was opened and so saved myself having to polish off a whole bottle on my own)… Another amusing note is that one of my problems with getting my rusty Spanish out for use only occasionally is that I get logjams in my head because vocabulary from Spanish, French, and Italian all come to me mid sentence and I freeze sometimes. I’d just been getting past doing that by Tuesday, but then got very confused in the restaurant at one point until I realized my waiter was, oddly, speaking to me in Italian at times. I still am not sure why.
It was a good conference to come to, I think, because I connected […] Click to continue reading this post
Yesterday I sneaked on to campus for a few hours. I’m on family leave (as I mentioned earlier) and so I’ve not been going to campus unless I more or less have to. Yesterday was one of those days that I decided was a visit day and so visit I did. I went to say hi to a visitor to the Mathematics Department, Sylvester James Gates Jr., an old friend who I’ve known for many years. He was giving the CAMS (Center for Applied Mathematical Sciences) distinguished lecture with the title “How Attempting To Answer A Physics Question Led Me to Graph Theory, Error-Correcting Codes, Coxeter Algebras, and Algebraic Geometry”. You can see him in action in the picture above.
I was able to visit with Jim for a while (lunch with him and CAMS director Susan Friedlander), and then hear the talk, which was very interesting. I wish he’d had time to say more on all the connections he mentioned in the title, but what he did explain sounded rather interesting. It is all about the long unsolved problem of finding certain kinds of (unconstrained, off-shell) representations of extended supersymmetry. (Supersymmetry is, you may know, a symmetry that […] Click to continue reading this post
(Photograph: Allstar/Black Bear Pictures/Sportsphoto Ltd.)[/caption]
Since this time I don’t think I’ll be getting the call from the folks at Screen Junkies to talk about this one, I’ll do a quick post on my thoughts while they are still fresh. (There are no real spoilers in what follows, but if like me you like to know as little as possible about a film before going to see it, forming your own opinion before having to see the film filtered through those of others, do wait until you’ve seen it before reading beyond the second paragraph.)
I enjoyed the film very much. As a piece of human drama, it was a great story to tell, and frankly it does fill me with dismay that few people seem to know the story, so I am glad it is getting mainstream attention. It was done extremely well, in terms of standard things like all the acting performances (more or less), photography, and the overall tone of the direction. Given the subject matter – its social and historical importance – this was a beyond the ordinary human drama well told. I enjoyed it.
But. BUT…
But it missed an opportunity to not just be “beyond the ordinary” but truly exceptional and ground breaking. All we needed was about 5 or so minutes of extra screen time to achieve this. I’m talking about the ironic fact that Interstellar, which is I remind you a science fiction film (which many scientists […] Click to continue reading this post
So while at a hotel somewhere down South for a few days (pen and watercolour pencil sketch on the right), I finally found time to sit and read Graham Farmelo’s book “The Strangest Man”, a biography of Dirac. (It has a longer subtitle as well, but the book is way over in the next room far from my cosy spot…) You may know from reading here (or maybe even have guessed) that if I were to list a few of my favourite 20th century physicists, in terms of the work they did and their approach and temperament, Dirac would be a strong contender for being at the top of the list. I am not a fan of the loudmouth and limelight-seeking school of doing physics that seems all so popular, and I much prefer the approach of quietly chipping away at interesting (not always fashionable) problems to see what might turn up, guided by a mixture of physical intuition, aesthetics, and a bit of pattern-spotting. It works, as Dirac showed time and again.
I’ve read a lot about Dirac over the years, and was, especially in view of the title of the book, a little wary of reading the book when I got it four years ago, as I am not a fan of going for the “weren’t they weird?” approach to biographies of scientists since they serve too […] Click to continue reading this post
Given 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
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
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
In class tomorrow I’ll introduce one of my favourite equations:
[tex]
\frac{d^2x^\sigma}{d\tau^2}+\Gamma^\sigma_{\rho\nu}\frac{dx^\rho}{d\tau}\frac{dx^\nu}{d\tau}= 0\ .
[/tex]
… 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
[tex]
\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)\ ,
[/tex]
called the “Christoffel symbols”. The set of objects [tex]g_{\mu\nu}[/tex] (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.
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
I 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
Given that I am frequently mystified by the obsession with making lists at the turn of the year, I was pleased to see* the New Yorker’s parody of the same with its list of “100 best lists of all time”.See […] Click to continue reading this post
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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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
Yeah, Bill is still awesome.
Loved the Arithmetic line in his Democratic National Convention speech. Go give it a listen.
Yes, Arithmetic rocks.
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