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"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at any given moment knew all of the forces that animate nature and the mutual positions of the beings that compose it, if this intellect were vast enough to submit the data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom; for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes."

-Marquis Pierre Simon de Laplace
1749-1827 French Mathematician & astronomer
In 1946, soon after the ENIAC became operational, von Neumann began to advocate the application of computers to weather prediction.  As a committed opponent of Communism and a key member of the WWII-era national security establishment, von Neumann hoped that weather modelling might lead to weather control, which might be used as a weapon of war. Soviet harvests, for example, might be ruined by a US-induced drought. On this basis, von Neumann sold weather research to military funding agencies
Edward Lorenz – US mathematician, weather forecaster for US Army Air corps during WWII. Made mathematical models of weather systems, noticed ‘unpredicatable behaviour. wrote a set of equations for convection to explain weather pattern. He made the equations as simple as possible, but left in non-linear terms.
Certain non-linear systems that show apparently random motion show a strange form of order when plotted in a suitable phase space - the motion never repeats itself, but is confined to a fixed region of space - a strange attractor
This was formulated to describe how a population varied from one generation to the next. eg xt could be the population of frogs in a pond (described as a fraction between 0 and 1), k is the average number of offspring produced by each adult, and (1-xt) is the feed-back term due to overcrowding.
What happens as k changes?
Mitchell J. Feigenbaum (1944-)
1964 MIT
Early 1970’s Los Alamos work on turbulent flow.
Assumptions for approximate solution:
One of the three bodies has negligible mass and therefore doesn't affect the other two. The two large bodies move about a common centre in circles rather than more general ellipses
The three bodies move in a single plane