In 1999, the Danish physicist Per Bak proclaimed to a group of neuroscientists that it had taken him only 10 minutes to determine where the field had gone wrong. Perhaps the brain was less complicated than they thought, he said. Perhaps, he said, the brain worked on the same fundamental principles as a simple sand pile, in which avalanches of various sizes help keep the entire system stable overall — a process he dubbed “self-organized criticality.”

As much as scientists in other fields adore outspoken, know-it-all physicists, Bak’s audacious idea — that the brain’s ordered complexity and thinking ability arise spontaneously from the disordered electrical activity of neurons — did not meet with immediate acceptance.

But over time, in fits and starts, Bak’s radical argument has grown into a legitimate scientific discipline. Now, about 150 scientists worldwide investigate so-called “critical” phenomena in the brain, the topic of at least three focused workshops in 2013 alone. Add the ongoing efforts to found a journal devoted to such studies, and you have all the hallmarks of a field moving from the fringes of disciplinary boundaries to the mainstream.

In the 1980s, Bak first wondered how the exquisite order seen in nature arises out of the disordered mix of particles that constitute the building blocks of matter. He found an answer in phase transition, the process by which a material transforms from one phase of matter to another. The change can be sudden, like water evaporating into steam, or gradual, like a material becoming superconductive. The precise moment of transition — when the system is halfway between one phase and the other — is called the critical point, or, more colloquially, the “tipping point.”

Classical phase transitions require what is known as precise tuning: in the case of water evaporating into vapor, the critical point can only be reached if the temperature and pressure are just right. But Bak proposed a means by which simple, local interactions between the elements of a system could spontaneously reach that critical point — hence the term self-organized criticality.

Think of sand running from the top of an hourglass to the bottom. Grain by grain, the sand accumulates. Eventually, the growing pile reaches a point where it is so unstable that the next grain to fall may cause it to collapse in an avalanche. When a collapse occurs, the base widens, and the sand starts to pile up again — until the mound once again hits the critical point and founders. It is through this series of avalanches of various sizes that the sand pile — a complex system of millions of tiny elements — maintains overall stability.

While these small instabilities paradoxically keep the sand pile stable, once the pile reaches the critical point, there is no way to tell whether the next grain to drop will cause an avalanche — or just how big any given avalanche will be. All one can say for sure is that smaller avalanches will occur more frequently than larger ones, following what is known as a power law.

Bak introduced self-organized criticality in a landmark 1987 paper — one of the most highly cited physics papers of the last 30 years. Bak began to see the stabilizing role of frequent smaller collapses wherever he looked. His 1996 book, “How Nature Works,” extended the concept beyond simple sand piles to other complex systems: earthquakes, financial markets, traffic jams, biological evolution, the distribution of galaxies in the universe — and the brain. Bak’s hypothesis implies that most of the time, the brain teeters on the edge of a phase transition, hovering between order and disorder.

The brain is an incredibly complex machine. Each of its tens of billions of neurons is connected to thousands of others, and their interactions give rise to the emergent process we call “thinking.” According to Bak, the electrical activity of brain cells shift back and forth between calm periods and avalanches — just like the grains of sand in his sand pile — so that the brain is always balanced precariously right at that the critical point.


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