Science, Maths & Technology

Do crowds behave like fluids?

Updated Tuesday 1st August 2006

It used to be believed that crowds behaved like fluids - until Keith Still proved otherwise.

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

"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."

 

For further information, take a look at our frequently asked questions which may give you the support you need.

Have a question?

Other content you may like

Health, Sports & Psychology 

Audio
10 mins

Science, Maths & Technology 

An introduction to complex numbers

In this free course, An introduction to complex numbers, you will learn how complex numbers are defined, examine their geometric representation and then move on to looking at the methods for finding the nth roots of complex numbers and the solutions to simple polynominal equations.

Free course
16 hrs

Science, Maths & Technology 

Mathematical striptease

Does maths get your knickers in a twist? Watch this video to see how maths can hold the solution to some everyday problems

Video
5 mins

Science, Maths & Technology 

Beating the odds: The maths of a World Cup 2014 win

Dr Katie Chicot provides us with a statistical insight into this year’s World Cup event.

Article

Science, Maths & Technology 

Babylonian mathematics

This free course looks at Babylonian mathematics. You will learn how a series of discoveries has enabled historians to decipher stone tablets and study the various techniques the Babylonians used for problem-solving and teaching. The Babylonian problem-solving skills have been described as remarkable and scribes of the time received a training far in advance of anything available in medieval Christian Europe 3000 years later.

Free course
8 hrs

Science, Maths & Technology 

Understanding numbers: Taking it further

Want to know what it's like to study at the OU? Explore how you can use numbers to describe the natural world and make sense of everything from atoms to oceans in this free course. 

Article

Science, Maths & Technology 

Surfaces

Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this free course, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the classification theorem of compact surfaces.

Free course
20 hrs

Science, Maths & Technology 

Beating the bookies: The maths of a World Cup 2010 win

The World Cup is a statistician's dream - but can you use maths to break a bookie's bank and heart?

Article

Science, Maths & Technology 

Talking primes

What is so magical about prime numbers - and what makes them musical? The Material World wanted to find out...

Article