From the 1999 lecture programme:
Even in our everyday lives on Earth, there are many phenomena which seem to show self-organised behaviour which emerges in time, despite a seemingly chaotic environment.
In fact it has been suggested that such critical states, delicately balanced as they are between complete order and utter chaos, occur throughout Nature: possible examples include earthquakes, forest fires, avalanches and biological evolution. Human activity can also be included: for example it has been shown that traffic on a motorway will evolve in time to a state where there are traffic jams of all sizes, and that this situation is actually the most efficient that can occur. The traffic system hence evolves in time so as to optimise some global pay-off, even though the individual drivers are each acting selfishly!
This idea of self-organisation to a critical, yet somehow efficient, state where there are fluctuations of all sizes may offer a new principle for describing how our world evolves in time.
Another fascinating example of such critical behaviour is offered by the world's financial markets. We all know, sometimes to our cost, that market crashes can suddenly occur. But is there any hope of predicting when these large movements will arise, and do they follow some universal law?
Remarkably, the model of market movements being used by banks world-wide is based on plant pollen! It was the botanist Robert Brown who, in 1827, discovered the seemingly random motion of pollen particles under his microscope. This finding led to a mathematical model, called Brownian motion, upon which all modem financial theory is now based.
However, this theory cannot account for the large market movements which seem to arise every few years, and which have such costly consequences for many of us.