Was trying to precisely understand the phrase, "self-organized criticality" for a class assignment—I learned of this phrase in high school when i was programming a sand-pile simulator game, it's the coolest concept: The angle at which the sand pile suddenly settles when you add another grain of sand is called the angle of repose; this is why poured sand avalanches in rivulets. Self-organized criticality refers to the emergence of this behavior from the individual movements of the sand grains.
But what is self-organized criticality exactly? Wikipedia says:
In physics, self-organized criticality (SOC) is a property of (classes of) dynamical systems which have a critical point as an attractor. Their macroscopic behaviour thus displays the spatial and/or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to precise values.
What is the critical point? For the class, my interest is in the analogy between critical in physics and critical in the humanities.
Hmm, looks like the critical point is when a liquid is put under more pressure than liquids can exist at—so it takes on the properties of both a liquid and a gas at the same time!
What would that even look like?
Wow, that's exactly what I expected, except the ending. It reminds of collapsing a mental dichotomy by generating its opposite and deconstructing the difference in meaning between the two polar terms. So now I want to understand the math intuitively:
Cool, so it's like a liquid on a an alien planet being crushed by an extremely dense atmosphere. I always thought that increasing pressure but maintaining temperature would turn a liquid into a solid, like squeezing coal into a diamond, but as far as can tell this graph says that a liquid will not condense into a solid under higher pressure—instead it will go supercritical. The point on the graph at which this happens is the critical point.
So the video above must be a liquid that underwent a rapid increase in pressure, because it flipped suddenly from liquid to supercritical.
So what does this mean for self-organized criticality? The angle of repose of a pile of sand is the strange attractor that the measured angle of the pile of sand fluctuates around. The tumbling motion of an avalanche is analogous to a phase transition. The sand pile is attracted to avalanches, and that's what makes him so sensitive to new sand.
This sounds like how I intuitively understand the behavior of quantum foam, and explains how the universe might arise from it—in a statistical field (e.g., 3D vector field of quantum spacetime) during a phase transition, fluctuations in the vectors become scale-invariant. So you will get little fluctuations and big fluctuations and they will appear in the same patterns at any scale. Quantum foam is constantly churning with virtual particles. Maybe the universe is so unimaginably unstable that even virtual particles can give rise to stable macro-phenomena. (Maybe the attractor of the universe is strange attractors? Maybe its self-organized criticality is organized around self-organized criticality? Could the lack of any absolute reference for scale be explained by the universe being scale-invariant?)
(As I was writing this post, I accidentally left personal pronouns out of the middle of a sentence not once, but TWICE. What kind of typo is that. am now ashamed to be kind of proud of that. SUPERCRITICAL)
And now let's compare this with the first video:
SUPERCRITICALITY ARCHETYPE (there's a nested contradiction in that term; it infects everything. The roots "super-critical arche-type" mean "above-decision first-model".)
