Do you like my new header?

OK, so I'm no Banksy, but I do like green. I'll probably be playing around with themes a bit over the next few weeks.

Hopefully the header captures how "kinetically constrained" can apply to complex statistical systems and that sort of stuck feeling that I can never quite shake off. Look at me full of bollocks, maybe I can get on Newsnight review or something.

How should we teach Maths

I came across this new feature in the NYT via Science Blogs by Steven Strogatz. You may remember him from his paper with Duncan Watts on small-worlds that arguably kick started modern network theory. It looks like it's going to be a regular series so I highly recommend adding the feed to your rss reader.

The article that first caught my eye was called Rock Groups. It starts by differentiating between the serious side of arithmetic and the playful side. This is something I've long gone on about but never quite had the nice way of putting it like these guys do. Maths teaching for kids is like torture. I was having a discussion a while ago where I questioned whether we really needed to recite endless times tables aged 10 years old. A suggestion that drew scorn from my opposite number. But really, why?

The book that is heavily quoted in the article, "A Mathematician's Lament" by Paul Lockhart. It starts with a musician having a nightmare that children are not allowed to touch an instrument until they have mastered the theory of music and how to read a score. Only after many painful years are they allowed to lay their hands on an instrument.

This is a powerful analogy. You don't have to learn all the nuts and bolts of mathematics before you can start playing with numbers. Back in the Strogatz article he shows how much you can discover without being able to do any addition at all, just by grouping rocks. I wish I could quickly multiply two large numbers in my head but it wouldn't make me a better mathematician. It's like arguing that the best playwright should be able to spell every word in the dictionary.

The beautiful thing about the rocks is that it shows how much you can learn about number by pushing things around with your hands and being creative. Perhaps all those people who complain to me that "oo I could never do maths me" would have enjoyed it more if it was based on this rather than being expected to master "a complex set of algorithms for manipulating Hindi symbols".

Make sure you keep up with the Strogatz series. I found a pdf of the essay that inspired the Lockhart book. If I ever get through my Christmas backlog I might get around the getting the book.

Laser Cooling

Last semester I was helping out teaching a bit of quantum and atomic physics. It was quite fun going back to stuff I was a little hazy on the first time. I finally understand the periodic table for one thing. Another thing that I knew about but never really got the detail is laser cooling. This is really nice, I'll blast through it here. Watch out for the stat-mech bit, blink and you miss it.

In an atom electrons are not free to sit anywhere they want (more or less), they inhabit precisely defined quantum states that have well defined energies, angular momenta etc. Therefore if you give an atom a kick then it will release the energy you give it in precisely defined packets of energy. So if you take the light emitted by the atoms and put it through a spectrometer (could just be a prism) you'd see something like this, from here, for sodium.

You'll recognise the orange line from the street lamps that are slowly on their way out. I did a version of this experiment when I was an undergrad where we did the opposite, we shone white light through sodium gas and while most of it goes through the frequencies that match the right transition frequencies get absorbed and are missing from the final spectrum. Might look like this, ish

Notice that the lines aren't all that sharp whereas I said they should be precise lines. This is for a number of reasons. One is that the uncertainty principle doesn't like precise energies. There's an uncertainty attached to the lifetime of atomic transitions or collisions. Another, more important effect is Doppler shifting due to the temperature of the gas. We can assume that the atoms in the gas have a distribution of velocities that comes from the famous Boltzmann distribution

Light emitted from a moving atom will be Doppler shifted which will take our precise emission line and spread it out around the average. This property turns out to be very useful and what we'll use. First a mention about the laser.

Lasers are brilliant. With a laser you can send in a beam of photons with a highly tuned narrow band frequency. When a photon hits with a frequency that matches the absorption frequency of the atom, they collide and scatter. When it's too much or too little it will most likely just go straight through.

So finally we get to how you cool the gas. If you send in a laser pulse into a warm gas of atoms then different atoms will see different things. Thanks to the Doppler shift, an atom moving with speed, v, will see the laser frequency, f_0, Doppler shifted to (c = speed of light)

Atoms moving away from the laser see it red shifted (lower frequency), atoms moving toward the laser see it blue shifted (higher frequency). If we tune the laser to just below the absorption frequency of the atom then the only atoms that collide with the beam are those moving towards it (the ones that see the blue shift).

Were it not for the precision of the transition level the laser would equally kick atoms moving towards it and atoms moving away - adding no net energy into the system. However, if we only collide with atoms moving towards the beam then we can actually remove energy. What's even more staggering is that this actually works!

Laser cooling can make things seriously cold. You may have seen the headlines that the LHC is colder than space. Impressive given the size of the thing, but space is about 2 Kelvin. This is peanuts compared to laser cooling. This can get a gas down around 1 mK - that's a factor of a thousand. You can get even colder with new techniques but somehow laser cooling pleases me the most.

So that's laser cooling. It's beautifully simple, uses basic ideas from quantum mechanics, relativity, statistical mechanics and then makes something brilliant thanks to a laser.

LA's big lake of colloids

The New York Times is running a piece about tap water and the regulation thereof called "That Tap Water Is Legal but May Be Unhealthy". One particular contaminant becomes dangerous on exposure to sunlight so, at a lake in Los Angeles, they've tipped 400,000 plastic balls into the lake to block out the sunlight.

Perhaps this shows I've been in stat-mech too long. All I could think about upon seeing this picture was - "cool, a massive 2D elastic disc simulation!".

It's quite interesting where the crystal structure is interrupted - each one of those interfaces costs a lot of free energy. You can also see it's not truly 2D as along certain stress lines the particles have gone up and over to reduce the energy.

I wonder if it's in equilibrium or whether it'll age with time...

This is what science can do to you :-s

Don't know what fair use would be for stealing this photo but hopefully if I link to the NYT enough they won't mind - go and click on one of their ads of something...

Backup news

Anyone that's been here from the start will know I have a slightly unhealthy obsession with backups.  A couple of things have changed since I last blogged about this.

Time Machine
Firstly, I now have a mac at home and I've started using Time Machine. I don't want to pat Apple on the back too much because that really gets of my nerves, but Time Machine is absolutely fantastic.

It's exactly how personal backup software should work. You buy an external hard disk, tell Time Machine to backup there, and then you're done. You never need to worry about it again. Most of the time when I need my backup it's because I've accidentally deleted something I shouldn't. Time Machine allows you to, as the name suggests, just go back in time and find it before you made the mistake. Works like a dream.

After a botched attempt to upgrade to Snow Leopard I recently had my first call to do a complete system restore. All I can say is that it seemed to work perfectly for me - it didn't even take that long.


Rsync + windows
At work we backup to an external file server. Until recently that was Linux based and so I had no trouble using Rsync. Now we've been moved to a Windows server which creates all kinds of problems. Rsync just doesn't get on with Windows. Anyway, after a bit of poking around I finally have a script that does the job. This is my basic rsync call now:

rsync -rptgoDhpP --modify-window=1 --delete --log-file=RSYNCLOG --exclude-from=./exclude /home/username/ username

I'm pretty sure most of those options could be replaced with the -a but honestly, now it's working I don't want to touch it! The key command is the modify-window. This accounts for the different way that Windows and Unix file systems time stamp modified files.

SVN - Subversion
For programming and writing papers (in LaTeX) I've started using subversion to take care of version control. I'm also using a shared repository to co-write a paper at the moment - it handles simultaneous editing quite well. There is a start up cost in getting your head around how it works, I found this page very helpful, but once you're there it works very nicely.

I mention it here because the version control works a bit like a backup. You can step back through committed versions very easily. If you use OS X then it's installed along with XCode so you probably have it. With Linux it'll be in the standard repositories.

Well that's enough backup geekery for this year. Anyone using anything that they're particularly happy with? I've kind of given up on backing up over the internet for now but would be interested if there's been any developments.

An unintuitive probability problem

Probability can do strange things to your mind. This week I had a probability problem where every time I tried to use intuition to solve it I ended up going completely wrong. I thought I'd share it as I think it's interesting.

Consider a one dimensional random walk. At each time step my walker will go left with probability , and right with probability . It stays where it is with probability . Furthermore these probabilities are dependent on the walker's position in space, so it's really and . I'm imagining I'm on a finite line of length, L, although it doesn't matter too much.

Now if , then we just have a normal random walker. In my problem I have the following setup: but . What does this mean? At any given point, x, my walker is more likely to go left than right. If it does go left it will come back with the same rate (although it's more likely to go left again).




So here's the question: If I leave this for a really long time, what is the equilibrium probability distribution for the walkers position, ?

Great LHC animation

The purpose of this blog was to showcase other types of physics other than the LHC. But I can't resist, this is a really nice animated video showing the stages of getting stationary protons up to 7TeV

http://cdsweb.cern.ch/record/1125472

(via @CERN)