I found this research via @Ionicasmeets and the Huftington Post. What if there would exist a mathematical equation that might be able to help predict complex calamities, such as financial crashes. Well, a study led by the University of Sussex has developed such a thing. A mathematical crystal ball?

From the press release:

In a collaboration between the University’s Sackler Centre for Consciousness Science and the Centre for Research in Complex Systems at Charles Sturt University in Australia, researchers used mathematics and detailed computer simulations to show that a measure of ‘information flow‘ reaches a peak just before a system moves from a healthy state to an unhealthy state.

Such ‘phase transitions‘ are common in many real systems, and are often highly significant: epileptic seizures and financial market crashes are just two examples of transitions. Until now, though, ways to predict these transitions in advance have been lacking. Previous measures, which peak at the transition itself, have been of no use for purposes of prediction.

Lead researcher Dr Lionel Barnett says: “The key insight in the paper is that the dynamics of complex systems – like the brain and the economy – depend on how their elements causally influence each other; in other words, how information flows between them. And that this information flow needs to be measured for the system as a whole, and not just locally between its various parts.”

Essentially this means finding a way to characterize, mathematically, the extent to which the parts of a complex system are simultaneously segregated (they all behave differently) and integrated (they all depend on each other). In the present study the research team managed to do just this, and to show for the first time that their measure reliably predicts phase transitions in standard systems studied by physicists now for many decades (the so-called ‘Ising’ model).

Professor Anil Seth, Co-Director of the Sackler Centre, says: “The implications of the work are far-reaching. If the results generalise to other real-world systems, we might have ways of predicting calamitous events before they happen, which would open the possibility for intervention to prevent the transition from occurring.