Home > Positioning > Persons > Lorenz

Edward Lorenz (1917–2008)

Lorenz discovered that simple deterministic systems can produce behaviour indistinguishable from randomness — the phenomenon that became known as chaos. His 1963 paper on a stripped-down model of atmospheric convection showed that tiny differences in initial conditions produce wildly divergent trajectories, making long-range prediction impossible even when the governing equations are known exactly. The discovery upended the assumption that deterministic meant predictable, and it opened a field.

Life

Born 23 May 1917 in West Hartford, Connecticut. AB in mathematics from Dartmouth (1938); AM in mathematics from Harvard (1940). Served as a weather forecaster for the US Army Air Corps during World War II — the experience that drew him to meteorology. ScD in meteorology from MIT (1948). Faculty at MIT from 1948, rising to Professor of Meteorology and head of the department. Died 16 April 2008 in Cambridge, Massachusetts.

The 1963 paper

“Deterministic Nonperiodic Flow” (Journal of the Atmospheric Sciences, 1963) is the founding document of chaos theory. Lorenz was running a simplified model of atmospheric convection — three coupled ordinary differential equations with twelve terms. The model was deterministic: given exact initial conditions, the equations produce a unique trajectory. But Lorenz noticed that when he restarted a simulation from a printout that had rounded the state variables from six decimal places to three, the new trajectory rapidly diverged from the original.

The implication was radical. The divergence was not a numerical error or a modelling deficiency — it was a property of the system itself. Nearby initial conditions produce trajectories that separate exponentially fast. For a system with this property, long-range prediction requires infinite precision in the initial conditions — which is physically impossible. Determinism does not guarantee predictability.

The paper introduced what is now called sensitive dependence on initial conditions. The popular name — the butterfly effect — came later, from the title of a 1972 talk: “Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?” Lorenz did not claim that butterflies cause tornadoes; he used the image to convey that in a chaotic system, perturbations too small to measure can have consequences too large to ignore.

The Lorenz attractor

The three-equation system from the 1963 paper produces a trajectory that never repeats but never escapes a bounded region of state space. The trajectory traces out a double-lobed structure — the Lorenz attractor — a strange attractor with fractal geometry. The system orbits one lobe for an unpredictable number of cycles, then switches to the other, with the timing of each switch sensitive to initial conditions.

The attractor demonstrated that deterministic chaos has its own geometry. The trajectory is confined to a low-dimensional structure even though its behaviour is aperiodic and unpredictable in detail. The strange attractor became the visual icon of chaos theory and a foundational object in the mathematical study of dynamical systems.

Chaos and weather prediction

Lorenz’s discovery had immediate implications for his own field. Weather forecasting depends on numerical models initialised with observed atmospheric data. If the atmosphere is chaotic — and the evidence strongly suggests it is — then forecasts must eventually diverge from reality regardless of model quality or computational power. The question shifts from “can we predict the weather?” to “how far ahead can we predict it, and with what confidence?”

The practical answer: useful weather forecasts extend to roughly 10–14 days, beyond which chaotic divergence overwhelms the signal. This limit is not a failure of models or observations; it is a property of the atmospheric system. Lorenz’s work provided the theoretical foundation for ensemble forecasting — running many simulations with slightly different initial conditions and treating the spread of outcomes as a measure of forecast uncertainty.

Reception and influence

The 1963 paper was published in a meteorology journal and went largely unnoticed by the mathematics and physics communities for over a decade. The rediscovery came through David Ruelle and Floris Takens’ work on strange attractors (1971), Robert May’s work on chaotic dynamics in population ecology (1976), and Mitchell Feigenbaum’s discovery of universality in period-doubling cascades (1978). By the 1980s, chaos was a major research programme across mathematics, physics, biology, and engineering.

James Gleick’s Chaos: Making a New Science (1987) brought the subject to a wide audience and made Lorenz a public figure. The popularisation was effective but contributed to the confusion between chaos theory and complex adaptive systems — a conflation that persists in popular treatments. The technical distinction is clear: chaos describes deterministic systems with sensitive dependence; CAS describes adaptive populations whose agents change their strategies. The overlap is in non-linearity; the difference is in adaptation.

Where Lorenz stops

Lorenz’s discovery is about deterministic systems — systems whose rules are fixed and whose behaviour, though unpredictable, is fully determined by initial conditions. The agents in the system do not learn, adjust, or change their rules. Chaos shows that simple rules can produce complex behaviour; it does not show how complex behaviour can produce new rules. The step from chaos to adaptation — from sensitivity to learning — is the step that CAS takes and that Lorenz’s framework does not.

Key works

See also: Complex Adaptive Systems