So, a whirlwind of a day finishes in the pub with an in-depth analysis and team review of the Convocation. Performance targets have been met, or exceeded in the sense that our exhibit actually all worked under the strain, and we survived the interrogation of phalanx after phalanx of FRSs.
Actually, we had a ball. Lots of interaction - five of us talking pretty much non-stop for 4 hours. So we're pretty talked-out, but we've honed the sales pitch to a sharp edge! Good to catch up with some people in particular - supportive comments from some of the mathematicians in the Fellowship and interested conversations with a wide range of people, from geologists to biochemists.
So, I was going to continue the tour around our exhibit, each day focussing on a new area. Yesterday's topic was going to be flocking, swarming and crowding, but it got pushed to one side to squeeze in the link to the bicycle article in Metro, and its seemed really natural to continue with the double pendulum stuff since its all classical mechanics.
So today's topic is: flocks, swarms and crowds. In fact our exhibit does flocks and swarms - the crowds are just too tricky to say much about yet! Our exhibit has two screens for flocking and swarming: one is running a loop of videotape from the BBC Natural History Unit showing some dramatic footage of starlings intercut with shoaling fish. The behaviour is remarkably similar between the two! The second screen is running an Agent-based modelling simulation called NetLogo. To be precise we're running NetLogo 3D Preview 5. This is freely available software for a PC, available from
The NetLogo software is running a a simulation of flocking based on very simple rules: the individuals prefer to move towards each other (but not get too close!), to be aligned with each other, and to move towards the centre of the computational box they're confined to inside the program. The original version of this demo had an extra feature: when birds hit the top of the box they died, and fell straight to the ground! Although that adds some variety, it's hard to weave the mounting body count into our (lively!) complexity story, so we took that feature out. And then changed the symbols to multicoloured fish. It looks very nice, except that sometimes the fish start swimming backwards. That's actually not a big disadvantage overall, but now I've mentioned it, hopefully punters will look more closely to check that it happens!!
Here's a picture of some real fish:
So, now we turn the mathematics, as I know you've been waiting for. The essence of the story is that for a bunch of physical systems, including plain vanilla gases, liquids and solids, mathematics has helped physical scientists establish excellent 'averaged' equations for the behaviour of lots of molecules all at once. I've covered this before in a previous post: 'It all begins with Newton'. So I'll cut to the chase: in these physical cases there are many orders of magnitude in scale to average over, so fluctuations are 'small' compared to the average value. In a flock of far fewer birds, the fluctuations are much larger so the averaging process isn't so reliable. In the case of crowds, we're trying to 'average' over only a few tens of people, so the fluctuations are maybe just as large as the average itself! It's hard to know what averaging means in this case.
I've observed quite a lot of crowd dynamics myself this week, having come up from Bath to the Festival Hall on several days. The crowds 'flowing' through Paddington Station itself are rather good to muse on. It's a pity I can't put video up here, so you'll have to make do with a link to a videoclip on my home page:
This was taken last Monday evening, around 7.45pm, as a scheduled train to the West Country is finally given a platform number. It's platform 8, so a few hundred patient weary travellers pick up their bags, pin their ears back and stride purposefully to platform 8. Other brave travellers try to dodge them. Some combination of order and stochasticity ensues.
You'll notice that the video quality is poor - I've downgraded the quality on purpose to obscure faces. After all, the NetLogo fish don't look a lot like fish either (and they swim backwards too). But there are some nice bits, for example after the fade-out-and-in in the middle, where groups of people cross at right-angles, threading their way through between each other. How can be describe that with an 'averaged' equation? Looks pretty tough to me! It's good to be able to show that there are not just a few challenges left in science, but a whole host of problems to look at. The current and next generations of applied mathematicians will certainly not be working themselves out of a job!