Concepts

The phenomenon by which simple local rules, applied across many independent agents or elements, give rise to coordinated, complex, often startlingly purposeful-looking global behavior. The site’s primary subject. Three Rules, All Together Now, Traveling Waves, and The Social Reactor are each one form of it.

The site’s deep metaphor. The idea that nature reuses architectural patterns the way programmers reuse code patterns — that flocking and sync and selection and traveling waves are recognizable templates that show up in different substrates. Borrowed from the Gang of Four book on software design, with the same content (a reusable structural solution to a recurring problem) and a different scale (the universe rather than a codebase).

The material out of which a particular instance of a pattern is made. Starlings are a substrate; fireflies are a different substrate; the BZ reaction is a different substrate; oscillators in the cortex are a different substrate. The point of this site, recurring on most pages, is that the same patterns appear across different substrates because they reflect the math of the situation rather than the chemistry of any particular medium.

The site’s two stand-ins for the reader. Introduced in the prologue on the landing page; used across pages where naming a particular human makes a claim land more cleanly than “the reader” would. They are placeholders the reader steps into rather than characters with arcs — the way Adam and Eve serve as placeholders in some religious rites. They are also a couple, in the sense that the site’s former working title (When Entropy Met Sally) once owed a debt to. Harry is used where a male example fits naturally; Sally is the primary stand-in.

A measure of the number of microstates consistent with a given macrostate — effectively, a count of how many ways a system can be arranged that all look the same at human scale. Tends to increase in closed systems for purely combinatorial reasons. Entropy and Extropy walks through the technical content; How Sally Gets Away With It addresses the common misreading of the second law.

Max More’s term for the local upward eddies that survive against the entropy gradient. Not opposed to entropy — made of entropy at sufficient resolution, paid for by an energy gradient. Every persistent pattern on this site is an instance.

The asymmetry between past and future, given physics by the second law. The reason eggs do not unbreak. The reason memory is possible. Some philosophers argue it is the deepest thing about the universe; whether or not they are right, it shows up implicitly all over this site as the gradient that local order has to swim against.

Spatial coordination of many independent agents through local rules — in the canonical case, separation, alignment, and cohesion. Worked out as a simulation by Craig Reynolds in 1986. The reason starlings can murmurate without a coordinator. Three Rules is the page.

Temporal coordination of many independent oscillators, each with its own rhythm, weakly coupled to its neighbors. Above a critical coupling strength, the population locks into a common phase. The math was tidied up by Yoshiki Kuramoto in 1975. Fireflies in Thailand do this. So do pacemaker cells, audiences clapping, the Millennium Bridge. All Together Now is the page.

Indirect coordination of agents through traces left in the environment. Ants laying pheromone trails are the canonical case — an ant doesn’t coordinate with another ant directly; it coordinates with the chemical history other ants left behind. (No page yet.)

A state or pattern that a dynamical system tends toward and stays near, given a range of starting conditions. The fixed point of a damped pendulum is an attractor; the limit cycle of a heart is an attractor; the strange attractor of a chaotic system is an attractor of a stranger kind. Most of the patterns on this site exist because they are attractors of their underlying dynamics.

Sensitive dependence on initial conditions in a deterministic system. The system has no random elements, but the future is unpredictable beyond a short horizon because tiny differences in starting state explode exponentially. Lorenz’s 1961 weather model is the canonical example: the same equations, fed inputs differing by one part in a thousand, produce entirely different storms. Tomorrow’s Weather is the page.

The path some systems take from order into chaos: a stable cycle of period 1 splits into period 2, then 4, 8, 16, with the intervals shrinking geometrically by Feigenbaum’s constant (about 4.669) each time. Universal across many different systems with the right shape of dynamics.

About 4.669. The universal ratio between successive period-doubling intervals across a wide family of systems. Discovered by Mitchell Feigenbaum on a pocket calculator in the 1970s; not believed at first.

Stephen Wolfram’s term for a system whose future can only be known by running the system itself — no shortcut, no closed-form solution, no "skip ahead 100 steps." Many simple rules produce computationally irreducible behavior. Has consequences for free will and the limits of prediction. (Page coming.)

The original. Differential survival and reproduction of variants in a population produces, over generations, increased prevalence of variants that survive and reproduce better. Darwin, 1859. The mechanism behind biological evolution.

A subset of natural selection where the differential reproduction is driven by mate choice rather than survival. Can drive traits in opposition to survival selection — peacocks have spectacularly large tails because peahens prefer them, not because tails help peacocks live. Fisher’s runaway model and Zahavi’s handicap principle are the two main mechanisms. Sexual Selection is the page.

Anything that gets copied with occasional errors. Genes are the original; memes (cultural units) are the famous extension; replicator dynamics shows up wherever you have something that produces variants of itself that get differentially preserved. Dawkins’s contribution; The Selfish Universe is the page.

A unit of culture — tune, phrase, hairstyle, religion, recipe — that propagates through populations of human minds. Dawkins coined the word in 1976 specifically to extend the replicator framework beyond DNA. Memes vary, replicate, and undergo selection against the limited attention budget of brains.

A system whose elements have three modes — resting, excited, refractory — and where excited elements can trigger their neighbors. Produces traveling waves that move forward but cannot reverse. The heart, the cortex, the BZ chemical reaction, traffic flow under stress. Traveling Waves is the page.

The time after an element fires during which it cannot fire again no matter what its neighbors do. Crucial to the directionality of traveling waves — without it, waves would propagate in both directions and immediately self-cancel.

The pathological case where a wave in an excitable medium curls into a self-sustaining spiral rather than sweeping cleanly across. In the heart this is what defibrillators are designed to interrupt.

The relationship between the size of a system and some property of the system, expressed as a power: Y = Y₀ · N^β. The scaling exponent β tells you whether the property grows in proportion to size (β = 1), more slowly (sublinear), or faster (superlinear). The Social Reactor is the page.

β < 1. A property that grows slower than the system. Infrastructure in cities (sublinear at β ≈ 0.85). Metabolic rate in organisms (sublinear at β ≈ 0.75). Bigger systems are more efficient per unit.

β > 1. A property that grows faster than the system. Socioeconomic outputs in cities (superlinear at β ≈ 1.15) — bigger cities are more productive per person. Caused by combinatorial growth in pairwise interactions.

A distribution where the frequency of an event scales as a power of its size. Earthquakes, city populations, word frequencies, wealth distributions. Characteristic of self-organized criticality. (Page coming.)