Symmetry

This is the first post of what eventually should become the "What on earth has Teake been doing for the last four years?"-series. Brace yourself: it's about maths and physics. Run while you still can!

I'll try to keep things simple by starting of with a concept that is as mundane as it is fascinating: symmetry. Not only makes it our world round, but it’s also what makes it go round. From the perfect circular wheels on our bikes and cars that deliver an enjoyable ride, to the error-correction protocols that keep e-mails from turning into junk; it’s literally all around us.

So what is symmetry exactly? A symmetry is an action on an object that, once you’re done performing it, does not change that object. It's a somewhat abstract definition, but take for example the triangle, which has 6 symmetries.  There are two different rotations (over 120˚ and 240˚), three reflections, and finally the action of doing nothing at all (yes, that's also a symmetry). You can try them out in the following applet. Clicking on the arrows causes the triangle to rotate and reflect.

This is all pretty straightforward, right? But things start to get interesting we you keep track of the effect of the different rotations and reflections. Let's paint the corners so we can see where they end up:

One thing you'll notice is that doing twice a clockwise rotation is equal to doing one counter-clockwise rotation. The same is true for any other combination of actions -- it will always yield the net effect of one single reflection or rotation. It might also happen that the triangle ends up in the original configuration, but remember that doing nothing is also a symmetry.

The combined actions describe what mathematicians call a group. A group is a set of elements plus a rule of multiplying those elements. Let's call the set G and the multiplication rule "•". Then the precise definition of a group (in which a, b are elements of the set G) is the validity of the following four statements:

• Closure.
  The result of the operation a • b is also in G.
• Identity element.
  There exists an element 1 in G, such that for all elements a in G, the equation 1 • a = a • 1 = a holds.
• Inverse element.
  There exists an element a^-1 in G such that a • a^-1 = a^-1 • a = 1.
• Associativity.
  The equation (a • b) • c = a • (b • c) holds.
  

These four set of rules are called the group axioms. They might sound a bit abstract, but in fact, they're not. Let's have a look at our triangle again.

The symmetry actions are labeled as follows:

• 1: identity element ("doing nothing at all").
• y: counter-clockwise rotation by 120˚.
• p: clockwise rotation by 120˚.
• R: reflection in the top vertex.
• G: reflection in the lower-right vertex.
• B: reflection in the lower-left vertex.

We already noticed that the closure axiom holds. The existence of the identity element is also pretty obvious. What about the identity axiom? This indeed also holds: every action has an inverse. The reflections are their own inverse, whereas the rotations are each other's. The last thing to check is associativity. It's a bit harder to verify, but believe me, it holds too.

Just for completeness sake, here's one last version of the triangle applet. This one includes the group multiplication table, which keeps track of what happens when you first do the action in the first row, followed by the action in the first column. (If you didn't believe me on the validity of associativity you can use this table to check it.)

What I've shown you so far is that the symmetries of the triangle can be described in terms of the mathematical concept of a group. The importance of group theory lies in the fact that any symmetry you can think of can be described as a group, and that conversely all groups describe a symmetry.

By now the answer to the question "What on earth has Teake been doing for the last four years?" will hardly come as a surprise: it's group theory. More on that in part two of this series!

Last.FM + Google = Convenience

If you're into music and computers, you're probably aware of Last.FM. It's a social music website that "recommends music, videos and concerts based on what you listen to." For the price of giving up a little privacy to the folks at Last.FM (namely the music you listen to) you get quite a lot in return. I mainly use it in tandem with Google's Calendar and Reader to keep updated on concerts in my neighbourhood. Here's how:

1. If you don't have a Last.FM account yet, create one and start scrobbling.
2. After some scrobbling Last.FM should have enough data to recommend events. Go to the recommend event page, and set your location by clicking on the "change/set location" link:
   
   
   
   It's best if you put in your location as "city, country". For example, my location is "Groningen, The Netherlands".
   
   
3. Still on the recommended events page, click on the RSS feed icon depicted below and add that feed to your Google Reader (or other favourite RSS reader).
   
   
   
   
   You can also directly import your recommended events into your Google Calendar with the "Google" link, that's a bit too much for me. I just want to be informed about interesting events, and only add those to which I'm actually going to my calendar (we'll do that in step 5).
   
   
4. Google Reader should now recieve event recommondations based on your musical tastes, like this:
   
   
   
   
   Clicking on the headline takes you the Last.FM page of the event. On that page, there's an attendance section at the bottom. Tell Last.FM that you're going:
   
   
   
   
   The event will now appear on your event list (located at http://www.last.fm/user/myUserName/events).
   
   
5. The last step is to import your event list into Google Calendar, so that you won't forget to actually go. Simply click the Google button at the top your event list:
   
   
   
   
   Your events should now come up in Google Calendar:
   
   
   
   
   And that's it!
   
   

From now on you'll only have to do step 4, i.e. checking your RSS reader every now and then to see if there's something you like, and indicate if you're going on the Last.FM website. The events will then automatically pop up in your calendar.

Sunset Rubdown - Idiot Heart

Sunset Rubdown - Idiot Heart

On September 2nd Sunset Rubdown gave a show in Vera, the local music club  where I do some volunteering from time to time. Perhaps they had an off-day, because the show wasn't something to write home about. Until they played their song Idiot Heart (source), that is. "Heart-pounding new wave skitter", according to Pitchfork. Regardless of what you want to call it, it's one hell of a track.

Poster on my research

Don't worry, there's nothing wrong with your eyes. The text on the poster above is indeed too small to read. The poster is supposed to be A0-sized (which is a whopping 0.84 by 1.18 meter), but on screen it's a tad smaller. There's a bigger version with readable text on my Picasa album -- just click on the image to get there.

I made this poster back in April this year for a conference, but then I tore it to shreds while trying to remove it from a wall. Double-sided tape can be a bitch sometimes. To avoid further incidents with tape I decided to order a new version on foam. After some trouble getting it to our institute (you can't fold foam, and A0 catches a lot of wind when you're on a bike) it now decorates a previous empty spot on the wall.


So, what's this poster all about, you might ask. Short answer: my research. Long answer: unfortunately the long answer is so long I'll have to spend another post or two on it. So stay tuned ...

PhD-day

As a theoretical physicist working in the Netherlands, I'm a member of the DRSTP (the Dutch Research School for Theoretical Physics). I'm also a member of its students council, and as such I'm involved in the organization of the second DRSTP PhD-day.
The first one was back in April 2008 and was a lot of fun -- I'm pretty confident this year's edition will be the same. We're sticking to the same format: 6 speakers, 5 of which PhD students from the different Dutch universities and 1 former PhD student. Topics range from the gauge / gravity duality to petrophysics, and should be quite interesting (admittedly not for the non-physicist perhaps).

And can you spot the differences in the posters? I made both, and can't really decide which one I like best. It's funny how small changes can change the look quite dramatically. But perhaps I should focus less on graphical design and more on writing my PhD thesis. The bugger is due at the end of the year. Better start cracking.