Click to edit Master text styles
"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
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.
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-)
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