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."

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