Read more: 鈥�Mind maths: Five laws that rule the brain鈥�
The familiar chords of our favourite song reach the ear, and moments later a neuron fires. Because that neuron is linked into a highly connected small-world network, the signal can quickly spread far and wide, triggering a cascade of other cells to fire. Theoretically it could even snowball chaotically, potentially taking the brain offline in a seizure.
Thankfully, the chances of this happening are slight. 鈥淧erhaps 1 per cent of the population will experience a seizure at one time in their lives,鈥� says at Indiana University Bloomington. This suggests there is a healthy balance in the brain 鈥� it must inhibit neural signals enough to prevent a chaotic flood without stopping the traffic altogether.
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The sweet spot
An understanding of how the brain hits that sweet spot emerged in the 1970s, when , now at the University of Chicago, realised that this balance represents a state known as the critical point or 鈥渢he edge of chaos鈥� that is well known to theoretical physicists. Cascades of firing neurons 鈥� or 鈥渘eural avalanches鈥� 鈥� are the moments when brain cells temporarily pass this critical point, before returning to the safe side, he said.
Avalanches, forest fires and earthquakes also result from systems lying at the critical point, and they all share certain mathematical characteristics. Chief among them is the so-called 鈥減ower law鈥� distribution, which means that bigger earthquakes or forest fires happen less often than smaller ones according to a strict mathematical ratio; an earthquake that is 10 times as strong as another quake is also just one-tenth as likely to happen, for instance.
鈥淎valanches, forest fires and cascades of firing neurons all share certain mathematical characteristics鈥�
How does the brain compare? In 2003 Beggs and Dietmar Plenz, both then at the National Institute of Mental Health in Bethesda, Maryland, checked whether neural activity matches Cowan鈥檚 theory by using a grid-like array of electrodes hooked to a chunk of rat cortex. Sure enough, they found that an excited neuron passed its signal to just one neighbour on average, which is exactly what you would expect of a system on the edge of chaos: any more and the system would lie in permanent, full-blown disorder. Importantly, larger neural avalanches do occur, but they are much rarer. Like earthquakes and forest fires, their frequency drops with size according to the precise ratio predicted by a power law.
Since Beggs鈥檚 initial work, further functional MRI scans suggest that the same kind of edge-of-chaos activity can be found at much larger scales, across the whole human brain; indeed, computer models suggest it might be a result of the small-world structure of the brain (快猫短视频, 27 June 2009, p 34).
Balancing on the edge of chaos may seem risky, but the critical state is thought to give the brain maximum flexibility 鈥� speeding up the transmission of signals and allowing it to quickly coordinate its activity in the face of a changing situation. Some of the researchers are beginning to wonder whether certain disorders might arise when the brain veers away from this delicate balance. 鈥淭here鈥檚 now some evidence that are not at this critical point,鈥� says Beggs. 鈥淛ust as there鈥檚 a healthy heart rate and a healthy blood pressure, this may be what you need for a healthy brain.鈥�
This article appeared in print under the headline 鈥淭eetering on the edge of chaos鈥�
