On chaos and the teaching of mathematics, in no particular order

The normal busyness continues apace but I fancy punctuating this chaos with a little update. I'm currently doing some proofreading of a book (not my own) which is both fascinating and densely packed with information (I'll reveal details when possible). At the same time I'm attempting to get two papers finished before Christmas and if at all possible next week.

Ah, yes, and I'm back in Santiago, if only briefly. My carbon footprint continues to increase month on month and December is no exception as I had to come back to Santiago for a week in between my Dublin trip and Christmas. After an 11 hour mammoth journey back to Spain on Thursday (starting from Oxford at 4am and culminating in a 4pm collapse back home) I have lots of things to finish before I head off again on Thursday including giving a short talk to the postdocs and grad students in the department. I'll be introducing in 15 minutes the depths of string theory, gauge theories, the problems with strong coupling dynamics, AdS/CFT and its applications to heavy ion physics, and more importantly why they should care about all this. This will be aimed at a diverse audience ranging from the groups which work on non-linear systems to those in nanotechnology and beyond. Anyway, it'll be a challenge but it should be a fun one.

Christmas farewells are filling the evenings, with a big party last night (in which I managed to make sushi for a group of 30+ whilst avoiding food poisoning, the latter being my principle triumph) and dinners until I leave but somehow I have to get these papers finished and as much of the book proofread as possible in the meantime (snide comments about my own bad spelling are not strictly necessary/neccessarry/necisary/nessacary).

On the night before coming back to Spain I had dinner with a friend of my parents, an ex maths teacher who has spent a great deal of time attempting to spread his ideas for teaching maths not only more effectively, but in a way which avoids the building up of the normal hierarchy of students in a class which leads to a range of bad feeling between those who can and those who can't. The method is simple and I'd like to talk more about this some time, but the basic idea is to get the students to read out a very short section from an appropriately chosen text book following which another student will explain what the section means. I think this is an extremely intelligent way to get pupils not only to be able to solve maths problems but to truly understand the workings of mathematics as they are introduced to it. Far too much emphasis is put on getting kids to learn through repetition of solving problems and not enough is put on building up the background of true understanding which is needed for getting onto ever more complex concepts without getting lost in the forest of terminology and notation. Clearly problem solving itself is necessary for polishing the edges but problem solving is infinitely easier if one has a thorough understand of the internal workings of mathematics rather than simply knowing how to turn the handle.  Unfortunately it seems that getting teachers to try this method is extremely difficult, especially in the current climate where schools are terrified of trying anything new for fear of dropping down the league tables - one of several curses of the current UK education system. Anyway, I'd love to devote some more time to discussing this so we'll see if the Christmas 'break' allows. Until then, it's back to reading and typing...

Ancient and modern

I hope to talk in more detail about this weekend soon, having had a fascinating Couchsurfer staying at my place for a couple of days.

Today we went for lunch with another of Santiago's 20 or so active Couchsurfers for a delicious, traditional Galician meal. I was thoroughly impressed when our host bought out his Gallego water cooler, a device which is traditionally taken into the fields while working a hard day in the hot sun. The jug is made of a slightly porous material which lets the water slowly through where it evaporates and cools the contents.

What is more, Fara has written the equation for the rate of cooling of the water onto the outside of his vessel. This formula takes into account the humidity in the air, the surface area of water in contact with the container, the outside temperature, and the specific heat capacity of water.

Flash Slideshow

At some point I'll also post up a photo of the crutch converted into a flute but that will have to wait until a more reasonable hour...

Inside out

Thanks to Bee at Backreaction comes this fantastic video illustrating how a sphere can be turned inside out. It's around 20 minutes long and you're not actually going to learn much solid mathematics, but the process is very very well explained and the animation is excellent.

Slowing down

Things have got marginally calmer though I still have work to do for Monday. I've been sitting in a cafe this afternoon doing some work and reading 'Godel, Escher, Bach: An Eternal Braid' by Douglas Hofstatder, a wonderful book on mathematics, logic, information, music and art. Well worth a read if you're interested in the deep workings of logical systems but a fascinating read even if this has never grabbed you before.

I mentioned Nav, my couchsurfer in my previous post. It turns out that Nav is a rather fine photographer and he spent a good length of time on Thursday evening showing me the basics of using Photoshop, which I had never truly appreciated the power of. My own photography, in its limited capacity owes a lot to a friend and designer explaining a few simple rules. Nav explained a more extensive list of factors which go into making a fine photo. I can see that almost all of my photos fail on at least one of the six factors he mentioned (often more), meaning that very few of my photos are quite as good as I'd like. This is surely a matter of practice and with these new guidelines I look forward to seeing what I come up with.

Looking back through some of my photos I noticed this one, which I don't think I've posted before. Unfortunately, the close and blurry foreground detracts from the photo but I am pleased with the look in the child's eyes and the gesture. Yesterday I went for a cruise around the hutongs getting a few more local shots which still need to be seen to.

Random computations

There's an amazing looking summer school going on here at the moment. Run by Chaotic Soliloquy's Dave Feldman, the Complex Systems Summer School is about as diverse as any I've ever seen. Though I'm not officially attending I'll try and pop along to some of the lectures. There are lectures on genetic algorithms, the origins of life, Chinese characters, anthropology, molecular biology and lots more. I'll report when I've been to some, hopefully beginning tomorrow.

For now I'll leave you with Nicholas Negroponte's 'One Laptop per Child' talk from TED 2006:

and a photo I took a couple of days back of perhaps the most blatantly dubbed concert I've ever come across. I was just passing and didn't stay for the bad Chinese pop which I could feel was about to descend: