Delicate, Fractal, Dynamic

Chaos and fractals: Laplace’s demon is wrong!

«The geometry of nature has a fractal face.»

Benoît B. Mandelbrot (1924–2010)

Laplace’s demon was named after his intellectual father, French mathematician and physicist Pierre Simon Laplace (1749-1827). He took the view that if one knew all laws of nature and all initial conditions, it would be possible to calculate every past and future state of the universe. For Laplace’s demon, the world is a thoroughly calculable clockwork.

In contrast, American mathematician and meteorologist Edward Lorenz (1917-2008) – one of the fathers of modern chaos theory – referred to what he called the butterfly effect: a single flap of a butterfly’s wings may lead to a sudden change in the general weather situation. This means: the smallest causes may sometimes have big effects. This is a property that is typical of chaotic systems. Numerous phenomena determined by the laws of nature – such as the weather – can therefore inherently be calculated only to a very limited extent. Laplace’s demon is wrong! He overlooked that the initial conditions of a system can never be measured exactly.

Questions of complexity during a development over time, of calculability and predictability are a matter for chaos theory. The analysis of complex patterns is a matter for fractal geometry.


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