A crowd consists of many individuals each exploiting their best opportunity. Although each of these individuals are doing what’s best for them, they are not aware of what is best for the crowd.

Keith Still was stuck in a queue with 10,000 other people trying to get into a concert and the queue was moving in a very strange way.

Inflatable people in a blow-up crowd [Image: 7-how-7 under CC-BY-NC-ND licence] Creative commons image Credit: 7-how-7 via Flickr

"If you imagine an eggtimer where the grains of sand are flowing in the centre, then that’s one type of fluid flow, granular flow where you can really understand this in terms of frictional forces and particles.

Then here I was in the centre of the crowd and I was moving much slower than the edges. So this seemed to be back to front to the standard thought."

Clearly a crowd isn’t fluid. At this point, he really got excited:

"You begin to understand that you’ve found something that is very different from what everybody else has been seeing."

The mathematics needed to be inverted in some way. Keith's research in the last few years has really been to understand the nature of crowd flow as opposed to the nature of granular or fluid flow.

A different type of mathematics needs to be used to solve these sorts of problems. The only way you can really build models of these types of phenomena is to go out in a crowd and walk around. He explains:

"You time yourself, you use metronomes to see if your pace is keeping consistent, you use security cameras, video cameras, use as much material as possible in order to record the event and then you can sit down in the lab afterwards and analyse what it is you’re seeing.

I must have taken thousands and thousands of photographs, many hundreds of hours of video footage. I have a double garage and I can’t get the car into it – that’s the amount of material I have collected!"

After an operation on his back, Keith had to rest for a while for a long time.

"When you lie down and you only have your mind really to experiment with mathematics, you start to look around you and assess things around you in a different way. In the corner of the room was a cobweb just swinging in the wind.

Within the cobweb was a very complex set of movements but I could see in the shadow on the wall a much simpler object which was reduced to just two dimensions.

Suddenly it gave me the idea that if I deconstruct three dimensional objects into series of one or two dimensional properties, I can calculate the maths much easier. I have reduced the problem from many dimensions down into a simple problem of one step only.

If we understand the principles of what we need to do to solve that one step, we can reconstruct that object now by thousands of entities each doing one step at a time and you solve the whole problem. If you get the maths right at the bottom level, everything else works out about it."

His hopes for the future are very simple. By applying simulations, crowds can be made safer and the guidelines can be changed. He says that this has given him fantastic insights into other types of problems.

For example, how the foreign exchange market works, how the phenomenon of business opportunities and how marketing works because that’s crowd behaviour.

"The interesting thing is that you don’t just solve the one problem of how a crowd moves but you open up a new area of mathematics, of large scale interactive systems. This is where science comes into play.

If the information that everybody else is using is inconsistent with the observations you have made, either your observations are wrong, or the rest of the world is wrong."