Broken Symmetry: How Structure Arises
Perfect symmetry is featureless. It is when symmetry breaks that structure, direction, and distinction appear. Much of the richness of...
Month: July 2026
Symmetry: The Deep Economy of Physics
That the laws of nature look the same from different viewpoints is no mere elegance. Symmetry constrains what can happen...
Renormalization: Seeing Across Scales
To understand a system one need not track every detail. By systematically blurring the fine structure and asking what survives,...
Phase Transitions: Matter Changing Kind
Cool water and at a precise point it becomes ice, its character transformed. Such abrupt changes of kind, driven by...
Percolation: The Sudden Onset of Connection
Add links to a scattered set of nodes and for a long while little changes. Then, at a precise threshold,...
Scale-Free Networks
In many real networks, most nodes have few connections while a handful have enormous numbers. This lopsided structure, lacking any...
Power Laws: The Signature of Scale
Most things cluster around an average, but some do not. Earthquakes, cities, and word frequencies follow a different pattern, where...
Criticality: Poised Between Order and Chaos
At the knife's edge between rigid order and formless chaos lies a special state where systems become exquisitely responsive. Poised...
Self-Organization: Order Without a Designer
Order can arise from within, unbidden and unplanned. From the interactions of many simple parts, global patterns emerge that no...
Attractors: Where Dynamics Settle
Left to run, a system tends toward certain states and shuns others. These preferred regions, toward which many starting points...
