26 Chaos
How is it possible to have a theory of chaos? Surely chaos happens in the absence of
theory? The story goes back to 1812. While Napoleon was advancing on Moscow, his
compatriot the Marquis Pierre-Simon de Laplace published an essay on the deterministic
universe: if at one particular instant, the positions and velocities of all objects in the
universe were known, and the forces acting on them, then these quantities could be
calculated exactly for all future times. The universe and all objects in it would be
completely determined. Chaos theory shows us that the world is more intricate that
that.
In the real world we cannot know all the positions, velocities and forces
exactly, but the corollary to Laplace’s belief was that if we knew approximate
values at one instant, the universe would not be much different anyway. This was
reasonable, for surely sprinters who started a tenth of a second after the gun had
fired would break the tape only a tenth of a second off their usual time. The
belief was that small discrepancies in initial conditions meant small discrepancies
in outcomes. Chaos theory exploded this idea.
The butterfly effect
The butterfly effect shows how initial conditions slightly different from the
given ones, can produce an actual result very different from the predictions. If
fine weather is predicted for a day in Europe, but a butterfly flaps its wings in
South America then this could actually presage storms on the other side of the
world – because the flapping of the wings changes the air pressure very slightly
causing a weather pattern completely different from the one originally forecast.
We can illustrate the idea with a simple mechanical experiment. If you drop a
ball-bearing through the opening in the top of a pinboard box it will progress
downwards, being deflected one way or the other by the different pins it
encounters on route until it reaches a finishing slot at the bottom. You might
then attempt to let another identical ball-bearing go from the very same position
with exactly the same velocity. If you could do this exactly then the Marquis de
Laplace would be correct and the path followed by the ball would be exactly the
same. If the first ball dropped into the third slot from the right, then so would