Science and physics
Critical mass and tipping points
Below a threshold a chain reaction fizzles; above it the same process feeds itself, and the change between the two is sudden.
Nuclear physics of the 1940s; carried into social science by Thomas Schelling's segregation model (1971) and Mark Granovetter's threshold model (1978).
The US Nuclear Regulatory Commission defines critical mass as the smallest mass of fissionable material that will support a self-sustaining chain reaction. Each fission releases neutrons; in a small lump most of them escape through the surface before they hit another nucleus, so the reaction dies out. Make the lump bigger, or denser, or wrap it in a reflector, and the fraction of neutrons that find a nucleus rises until on average each fission causes exactly one more. That is criticality. Below it, a reaction started by a stray neutron fades in microseconds; above it the same reaction grows every generation. Nothing about the physics changes at the threshold. What changes is whether the multiplication factor is below or above one.
Schelling's 1971 paper showed the same structure in a social setting with pencil and paper. He lined up 70 people, 35 of one type and 35 of the other, drawn from a table of random digits, and gave each a mild preference: at least half of your eight nearest neighbours should be your own type. Anyone unhappy moves to the nearest spot that satisfies them. After two rounds the line had sorted into six single-type clusters of 8, 15, 10, 15, 16 and 6 people, and 440 of the 540 neighbour relations (81.5 percent) were same-type. A wish not to be in a minority produced near-total segregation that nobody had asked for. The mechanism matches the neutron's: each move changes the neighbourhood of others and pushes some of them over their own threshold.
The caution is about the phrase. 'Tipping point' gets claimed for any fast growth, usually after the fact and usually without anyone naming the threshold or the feedback that crosses it. Fission has a measurable multiplication factor. Schelling's model has a stated preference and a stated neighbourhood. If the story you are told has neither, it is a curve drawn on a growth chart, not a mechanism. Thresholds in people are also not uniform: Granovetter's point was that the distribution of individual thresholds decides whether a crowd tips, and moving one person's threshold can change the outcome for everyone, which makes real tipping points hard to predict in advance and easy to explain afterwards.
Example
On 2 December 1942, in an abandoned rackets court under Stagg Field at the University of Chicago, Enrico Fermi's team brought the first nuclear reactor to criticality. Chicago Pile-1 was a stack of 57 layers built from 771,000 pounds of graphite, 80,590 pounds of uranium oxide and 12,400 pounds of uranium metal, with cadmium rods to absorb neutrons. Fermi had George Weil pull the cadmium rods out, then announced that the pile had gone critical: the chain reaction was sustaining itself. It was allowed to reach a thermal output of 0.5 watts and was shut down after less than five minutes, with 49 scientists and workers watching.
Where it applies
A marketplace, a messaging app or an internal platform is dead below its threshold and self-sustaining above it, so the question is what the multiplication factor is (how many new users each user brings in), not how fast you grew this month. In a retry storm, each failed request that spawns more than one retry is a system above criticality; cap the factor below one.
Think about it
For the thing you are trying to make catch on, can you name the threshold and the mechanism that carries it over, or are you hoping?
Applied it to something real? Log it.
Test yourselfWhat actually changes when a lump of uranium crosses its critical mass?
Only the multiplication factor: enough neutrons now hit another nucleus before escaping that each fission causes at least one more, so the reaction sustains itself instead of dying out.
Related models
- NonlinearityCause and effect are not proportional: a push can do nothing or everything depending on where the system sits relative to a threshold.
- Network effectsA product becomes more valuable to each user as more people use it, which makes leaders grow faster and makes leaving hard.
- Feedback loopsA system's output feeds back into its input: balancing loops hold a level steady, reinforcing loops make change grow on itself.
- EquilibriumA state where opposing processes balance so nothing changes on net; push it and it pushes back, but balanced is not the same as good.
- The adjacent possibleAt any moment only the ideas one step from what already exists can be built; the rest wait until their parts arrive.