Credit: MIT

Edward Norton Lorenz, whose pioneering studies of atmospheric dynamics led to his accidental discovery of chaos theory, died of cancer at his home in Cambridge, Massachusetts, on 16 April. A modest, unassuming and kind man, his personal qualities and intellectual insights had been a constant feature in the field of meteorology for more than 60 years; he co-authored his last paper just weeks before his death.

Born on 23 May 1917 in West Hartford, Connecticut, Lorenz took bachelor's and master's degrees in mathematics at Dartmouth College, New Hampshire, and Harvard University, respectively. Service as a weather forecaster for the US Army Air Corps during the Second World War led him into meteorology, and he received a doctorate in the subject at the Massachusetts Institute of Technology (MIT) in 1948. He remained in MIT's Department of Meteorology for the rest of his academic career, becoming emeritus professor there in 1987.

Lorenz made crucial contributions to atmospheric science, many of which are still routinely taught to students and widely used in weather forecasting. Perhaps foremost among these is his formulation in the mid-1950s of the concept of 'available potential energy', which he used to explain how potential energy and kinetic energy are interchanged in the atmosphere. His application of these ideas culminated in his influential book of 1967, The Nature and Theory of the General Circulation of the Atmosphere. He was also instrumental in the development of numerical techniques for weather prediction. One example — again, still widely used — is his scheme for the numerical treatment of changes in atmospheric variables with height, now known as the Lorenz vertical grid.

But the work for which Lorenz is undoubtedly most widely known is a now-classic paper published in the Journal of Atmospheric Science in 1963. Entitled 'Deterministic nonperiodic flow', it presented surprising results from a simplified computational model that simulated thermal convection in a fluid layer heated from below and cooled from the top. The calculated flow of the fluid was extremely irregular, with almost random qualities. But more importantly, it exhibited extremely sensitive dependence on initial conditions: two fluid states that were at first just slightly different diverged from each other exponentially, with their differences doubling repeatedly at a consistent rate. When Lorenz plotted variables representing temperature and flow against one another, the system eventually adopted trajectories that traced out something akin to a pair of butterfly wings — a pattern since called the Lorenz attractor. He further observed that the system trajectory moved from one wing of the butterfly to another in a seemingly erratic manner.

In his book The Essence of Chaos, Lorenz recounts how he came to discover the extreme sensitivity of his model to small changes. Wishing to repeat his simulation, he restarted it with numbers that had been printed out for the start conditions, and left it to go down the hall to fetch a cup of coffee. On his return, he found that the result was nothing like the previous one. He soon identified the reason: the numbers from the print-out were rounded off. In the course of a coffee break, that small error had propagated with exponential speed to change the result completely.

This discovery was epoch-making for two reasons. The first lay in Lorenz's integration of analytical methods with computational simulations, with which he — albeit with a pre-1960 computer that was bulkier, noisier and vastly slower than the PCs of today — set an early precedent for a mode of research that has since become a norm. But much more profound ramifications stemmed from Lorenz's realization of just how general the types of motion he had uncovered were in nonlinear systems such as the atmosphere. Most immediately for Lorenz's field, this meant that long-term weather predictions were impossible, because the atmosphere's initial state can never be specified precisely enough. That was a situation that increased computing power could not change.

Lorenz perfectly encapsulated this unknowability in the title of a talk that he gave to the American Association for the Advancement of Science in 1972. The question it asks has since lodged itself in the public's consciousness: “Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?” But the influence of chaos theory extends far beyond meteorology, and much deeper: it challenges the entire deterministic world view, as was confidently expressed, for instance, by the mathematician and philosopher Pierre-Simon Laplace, who stated at the beginning of the nineteenth century that the entire future could be determined by constructing and solving the equations governing all components of the Universe.

Although the existence of chaos had been recognized before Lorenz — notably in the 1890s by Henri Poincaré, in his study of the motions of three or more gravitating celestial bodies — it was Lorenz's meteorological demonstration and analysis that established the universal applicability of the concept, and earned him the title 'the father of chaos'. But it took a decade for chaos theory to percolate through to the general scientific community. When it finally did, it launched a revolution, rapidly extending its sway into many fields of physics, chemistry, biology and engineering — and, in doing so, becoming part of the popular lexicon.

Lorenz received many honours and prizes in recognition of his work, among them the Crafoord Prize — established by the Royal Swedish Academy of Sciences to recognize work in fields not covered by the Nobel prizes — in 1983, and the Kyoto Prize in 1991. The citation for that prize lauded “his boldest scientific achievement in discovering 'deterministic chaos', a principle that has profoundly influenced a wide range of basic sciences and brought about one of the most dramatic changes in mankind's view of nature since Sir Isaac Newton”.