Chaos in the Laboratory
The butterf ly effect was actually discovered in conjunction with continu-
ous processes. The development of the transistor made reasonably priced
computers available in the late 1950s and early 1960s. Formerly, comput-
ers had been hugely expensive arrays of power-hungry vacuum tubes, but
by the early 1960s, all universities and many businesses had purchased
computers. Business, of course, was using the computers to speed up the
computations and store the data needed for commerce, but the universi-
ties were using computers to explore computationally intensive problems
that were previously inaccessible.
Dr. Edward Lorenz, a professor at MIT, began his career as a mathemati-
cian, but later turned his attention to the problem of describing and fore-
casting the weather. The variables involved are governed by differential
equations and systems of differential equations,^6 which describe how the
rates at which variables change are related to their current values. These
equations, though quite complicated, are associated with continuous
processes.
Solving differential equations is an important part of science and engi-
neering, because these are the equations that ref lect the behavior of
physical processes. However, rarely can one obtain exact solutions to dif-
ferential equations. As a result, the industry standard approach is to use
numerical methods that generate approximate solutions, and numerical
methods are most effectively implemented by computers.
One day in 1961, Lorenz programmed a system of differential equations
into a computer that probably computed at less that one-tenth of 1 percent
of the speed of whatever happens to be sitting on your desk at the moment.
As a result, when the time came for lunch, Lorenz recorded the output,
turned off the computer, and grabbed a bite. When he returned, he decided
to backtrack a little, and did not use the most recent output of the computer,
but the output it had generated some iterations previously. He expected the
output from the second run to duplicate the output of the previous run (af-
ter all, they were running the same iterations), but was surprised to see that
after a while, the two sets of outputs differed substantially.
Suspecting that there was either a bug in the program (this happened
frequently) or a hardware malfunction (this happened more frequently in
1961 than it does today), he checked both possibilities assiduously—only
to find that neither was the case. Then he realized that in reinitializing
the computer for the second run, he had rounded off the computer output
to the nearest tenth; if the computer said that the temperature was 62.3217
degrees, he had rounded it off to 62.3 degrees. In those days, one had to
The Disor ga nized Universe 179