Under the west grandstand of Stagg Field at the University of Chicago, on December 2, 1942, Enrico Fermi and his team made the first sustained nuclear chain reaction. Chicago Pile-1, 45,000 graphite blocks interspersed with uranium-oxide pellets, was a deliberate exercise in controlled positive feedback. Each fission of a uranium-235 nucleus released about 2.5 neutrons; if one triggered a new fission the reaction sustained itself, more than one and it grew exponentially. They measured the multiplication factor k by withdrawing cadmium control rods. At 3:25 PM, with k = 1.0006, the pile went critical and the neutron count doubled every two minutes. Positive feedback — the structural opposite of Watt's-governor stability — had been demonstrated as an engineering principle.
A positive-feedback loop is one in which the output reinforces the input: a deviation produces a force that amplifies the deviation. Where negative feedback is governed by dX/dt ∝ −X (exponential decay to setpoint), positive feedback is governed by dX/dt ∝ +X, with solution X(t) = X₀ · e^(kt) and doubling time ln(2)/k. The phenomenon shows up across every domain. Action potentials in neurons (Hodgkin-Huxley, 1963 Nobel) are positive feedback constructively used: depolarisation opens voltage-gated sodium channels, which depolarises the membrane further, until potassium channels and sodium inactivation provide the negative-feedback termination. Blood-clotting cascades amplify a small wound signal into a coagulation event. Runaway sexual selection (R. A. Fisher 1930) explains peacock tails by positive feedback between female preference and the genetic correlation between trait and preference. Asset bubbles: rising prices attract more buyers, lifting prices further (Hyman Minsky's 1986 Stabilizing an Unstable Economy; Robert Shiller's 2000 Irrational Exuberance turned it into a dot-com forecast). Bank runs: each withdrawal weakens the bank, encouraging more withdrawals (Diamond-Dybvig 1983); Silicon Valley Bank's March 2023 collapse — $42 billion withdrawn in hours by smartphone — was the first fully digital instance. Viral spread: when R > 1 the epidemic grows exponentially. Every positive feedback loop saturates somewhere — at a carrying capacity, exhausted substrate, or delayed negative-feedback regulator. Verhulst's 1838 logistic equation corrected Malthus by adding a saturating capacity K. Negative feedback produces stability; positive feedback produces qualitative transitions between regimes, often with hysteresis.
Climate change is structurally dominated by positive feedbacks. Ice-albedo feedback: less sea ice means lower planetary reflectivity, more absorbed solar radiation, more warming — Arctic warming has run at ~4× the global mean rate over the past 40 years partly for this reason. Water-vapour feedback: warmer air holds more vapour, itself a greenhouse gas, with a feedback factor of ~1.6×. Methane release from thawing permafrost and carbon release from drying tropical forests are slower positive feedbacks. Social-media outrage cascades are positive-feedback by algorithmic design. AI training-data feedbacks have become serious: model-generated content increasingly populates the web, then is scraped into training corpora; Shumailov et al. 2023 showed recursive training can cause model collapse. The 2023 banking events were textbook digital-era bank runs, positive feedback compressed from days to hours by smartphone apps.