Self-Organized Criticality

"Who could ever calculate the path of a molecule?
How do we know that the creations of worlds are
not determined by falling grains of sand?"

- Victor Hugo (1802 - 1885), Les Miserables 

"How can the universe start with a few types of elementary particles at the big bang, and end up with life, history, economics, and literature? The question is screaming out to be answered bur it is seldom even asked. Why did the big bang not form a simple gas of particles, or condense into one big crystal? We see complex phenomena around us so often that we rake them for granted without looking for further explanation. In fact, until recently very little scientific effort was devoted to understanding why nature is complex.

I will argue that complex behavior in nature reflects the tendency of large systems with many components to evolve into a poised, "critical" state, way out of balance, where minor disturbances may lead to events, called avalanches, of all sizes. Most of the changes take place through catastrophic events rather than by following a smooth gradual path. The evolution to this very delicate state occurs without design from any outside agent. The state is established solely because of the dynamical interactions among individual elements of the system: the critical state is self-organized. Self-organized criticality is so far the only known general mechanism to generate complexity. 

To make this less abstract, consider the scenario of a child at the beach letting sand trickle down to form a pile. In the beginning, the pile is flat, and the individual grains remain close to where they land. Their motion can be understood in terms of their physical properties. As the process continues, the pile becomes steeper, and there will be little sand slides. As time goes on, the sand slides become bigger and bigger. Eventually, some of the sand slides may even span all or most of the pile. At that point, the system is far out of balance, and its behavior can no longer be understood in terms of the behavior of the individual grains. The avalanches form a dynamic of their own, which can be understood only from a holistic description of the properties of the entire pile rather than from a reductionist description of individual grains: the sandpile is a complex system.

The complex phenomena observed everywhere indicate that nature operates at the self-organized critical state. The behavior of the critical sandpile mimics several phenomena observed across many sciences, which are associated with complexity."

- Per Bak (1948 - 2002)
How Nature Works

Ethereal Being

"...this little hissing and buzzing
whirlwind, of wings of purple and
azure, in the midst of which floated
an elusive form veiled by the very

rapidity of its movement.

The ethereal being which took
shape confusedly through this
quivering of wings seemed to you
chimerical, imaginary, impossible
to touch, impossible to see.

But when at last the young lady
was resting at the tip of a reed
and you could examine,
holding your breath,
the long gauze wings,
the long enamel dress,
the two crystal globes,
what astonishment did
you not feel? "

- Victor Hugo (1802 - 1885)
The Hunchback of Notre-Dame

Interior of the Soul

"There is one spectacle grander than the sea,

that is the sky;

there is one spectacle

grander than the sky,

that is the interior of the soul"

- Victor Hugo (1802 - 1885)

Symmetries & Forms

"The beautiful has but one type, the ugly has a thousand. The fact is that the beautiful, humanly speaking, is merely form considered in its simplest aspect, in its most perfect symmetry, in its most entire harmony with our make-up. Thus the ensemble that it offers us is always complete, but restricted like ourselves. What we call the ugly, on the contrary, is a detail of a great whole which eludes us, and which is in harmony, not with man but with all creation. That is why it constantly presents itself to us in new but incomplete aspects."

- Victor Hugo

(1802 - 1885)