Two lessons from fractals and chaos
Larry S. Liebovitch, Daniela Scheurle · Complexity · 2000
We used to think that a good measurement is characterized by its mean and variance and that a good theory is characterized by its ability to predict the values measured in an experiment. The properties of nonlinear systems called fractals and chaos have now taught us that this isn't necessarily true. Data from fractal systems extend over many scales and so cannot be characterized by a single characteristic average number. Data from chaotic systems do not repeat the same time series of values, even if they are started very close to the same initial conditions. This means that a valid mathematical model will not be able to predict the values of the time series.