Where does critical mass collide?

The smallest amount of fissile material, in a given shape, density, and surround, for which the neutrons released by each fission produce on average exactly one further fission, so that the reaction sustains itself without growing or dying out. The criterion is the effective multiplication factor reaching one; below it the chain decays geometrically, above it the chain grows. The number is a property of the material and its geometry, computable from cross-sections before any assembly is built, and measurable by approaching it. Nothing in the material decides anything.[1]

Unit

A mass of fissile material in a specified configuration

Recovery means

Not applicable, subcriticality is restored by removing material or adding absorbers

Measured by

Kilograms; the multiplication factor k, from neutron counts as material is added

A population size below which per-capita growth turns negative and the population collapses toward extinction rather than recovering. Courchamp, Clutton-Brock, and Grenfell's 1999 review set out the mechanism known as the Allee effect: at low density, animals cannot find mates, defend against predators, or forage cooperatively, so growth is inversely density-dependent and there is an unstable threshold between recovery and extinction. The threshold is a biological fact about a species in a habitat, and it is usually estimated after the fact from populations that did and did not persist.[2]

Unit

A population in a habitat

Recovery means

Population growth resuming once the Allee threshold is exceeded

Measured by

Per-capita growth rate against density; the Allee threshold fitted from time series

The smallest set of subscribers to a service whose value rises with the number of other subscribers, such that everyone in the set finds it worth staying and the service can grow from there rather than unravel. Rohlfs derived it in 1974 for telephone-like services: demand is interdependent, so there is an unstable low equilibrium below which nobody subscribes because nobody else does. Katz and Shapiro generalised the externality in 1985 and showed it can lock a market into an inferior standard. The threshold is an equilibrium of a demand system, and it moves whenever prices or expectations do.[3][4]

Unit

A market for a good whose value depends on how many others hold it

Recovery means

Not applicable, the low equilibrium is a trap, not a state to return to

Measured by

The unstable equilibrium in a demand model; installed base at which growth becomes self-sustaining

The number and mix of early users of an interactive medium (electronic mail, a shared calendar, a video system) at which enough of the people one needs to reach are on it that further adoption feeds itself, and below which the early users defect and the medium is abandoned. Markus argued in 1987 that interactive media are unlike other innovations because the value to each user is zero until others adopt, so diffusion is all-or-nothing: universal access or none. Who adopts early matters as much as how many, which the economists' count of subscribers does not capture.[5]

Unit

A community of potential users of one medium

Recovery means

Not applicable, a medium that falls below critical mass is discontinued

Measured by

Proportion of a community using the medium; presence of high-resource early adopters

The point in the diffusion of an innovation at which enough individuals have adopted that the rate of adoption becomes self-sustaining, Rogers's definition, which places it around the inflection of the S-curve and treats it as a stage of the diffusion process rather than a number. Valente reworked the idea in 1996 as a personal network threshold: each adopter has a proportion of their own ties who must adopt before they will, and the system's critical mass is what those local thresholds add up to. This is Granovetter's threshold model measured on an actual sociogram. The threshold is a property of a person's contacts, not of the population.[6][7]

Unit

An adopter and the adopters among their network ties

Recovery means

Not applicable, a curve that never reaches critical mass simply stalls

Measured by

Network exposure at time of adoption; the proportion adopted when growth accelerates

A small set of highly interested and resourceful people whose early contributions to a public good make it worthwhile for everyone else to contribute, Oliver, Marwell, and Teixeira's 1985 formulation, which took the term from physics deliberately and put group heterogeneity at the centre of it. Granovetter had supplied the mechanism in 1978: each person has a threshold, the number of others who must act before they will, and whether a riot or a strike happens depends on the whole distribution of thresholds, not on the average. Schelling's tipping models showed that a population of mild preferences can produce an abrupt aggregate outcome. There is no fixed mass; a single missing threshold can stop the cascade.[8][9][10]

Unit

A distribution of individual thresholds in a population

Recovery means

Not applicable, a cascade that fails leaves a subcritical equilibrium

Measured by

Threshold distributions, usually inferred from outcomes; contribution functions in experiments

In gender and politics, critical mass refers to the idea that women's influence in a legislature changes once their share passes a threshold. This meaning comes from Dahlerup (1988) in Scandinavian Political Studies.[11]

Unit

Recovery means

Measured by