297
Here, turbulence forms at the tip of a
vortex left in the wake of an aircraft’s
wing. Study of the critical point beyond
which a system creates turbulence was
key to the development of chaos theory.See also: Isaac Newton 62–69 ■ Benoît Mandelbrot 316
FUNDAMENTAL BUILDING BLOCKS
calculated. However, the behavior
of many processes, such as waves
crashing on a beach, smoke rising
from a candle, or weather patterns,
is chaotic and unpredictable. Chaos
theory seeks to explain such
unpredictable phenomena.
Three-body problem
The first strides toward chaos
theory were taken in the 1880s,
when French mathematician Henri
Poincaré worked on the “three-body
problem.” Poincaré showed that for
a planet with a satellite orbiting a
star—an Earth-Moon-Sun system—
there is no solution for a stable
orbit. Not only was the gravitational
interaction between bodies far too
complex to calculate, Poincaré
found that tiny differences in initial
conditions resulted in large and
unpredictable changes. However,
his work was largely forgotten.
A surprise discovery
Few further developments occurred
in the field until the 1960s, when
scientists began to use new,
powerful computers to predict the
weather. Surely, they reasoned,
given enough data on the state of
the atmosphere at a given time
and enough computational power
to crunch the data, it should be
possible to know how weather
systems evolve. Working on
the assumption that ever-larger
computers would increase the
range of predictions, Edward
Lorenz, an American meteorologist
at the Massachusetts Institute
of Technology (MIT), tested
simulations involving just three
simple equations. He ran the
simulation several times, each time
inputting the same initial state and
expecting to see the same results.
Lorenz was astounded when the
computer returned hugely different
outcomes each time. Checking his
figures again, he found that the
program had rounded up the
numbers from six decimal places
to three. This tiny alteration to the
initial state had a major impact
on the end result. This sensitive
dependence on initial conditions
was named the “butterfly effect”—
the idea that a small change in a
system, as trivial as a teaspoonful
of air molecules moved by a
butterfly flapping its wings in
Brazil, can be amplified over time
to create unpredictable outcomes,
such as a tornado in Texas.
Edward Lorenz defined the
limits of predictability, explaining
that the impossibility of knowing
what will happen is actually
written into the rules that govern a
chaotic system. Not only weather,
but many real-world systems are
chaotic—traffic systems, stock
market fluctuations, the flow of
fluids and gases, the growth of
galaxies—and they have all been
modeled using chaos theory. ■Edward Lorenz
Born in West Hartford,
Connecticut, in 1917, Edward
Norton Lorenz received his
MSc in mathematics from
Harvard in 1940. During
World War II he served as a
meteorologist, forecasting
the weather for the US Army
Air Corps. After the war,
he studied meteorology at
Massachusetts Institute
of Technology (MIT).
Lorenz’s discovery of
sensitive dependency on
initial conditions (SDIC) was
accidental—and one of the
great “eureka” moments in
science. Running simple
computer simulations of
weather systems he found
that his model was churning
out wildly different outcomes,
despite being supplied with
almost identical starting
conditions. His seminal 1963
paper showed that perfect
weather prediction was a pipe
dream. Lorenz remained
physically and academically
active all his life, contributing
academic papers, and hiking
and skiing until shortly before
his death in 2008.Key work1963 Deterministic
Nonperiodic Flow