When Healing Becomes Educating, Vol. 2 - Waldorf Research Institute

sequence of steps, and finally also the geometric forms used in
technology. Natural objects, on the other hand, are neither linear
in form (they are essentially fractal, the term will be discussed
later) nor is it usually possible to define their function in terms
of causal chains; instead, we have multidimensional causal
complexes. K. Lorenz has coined the apt term “action complex.” 3
The origins of chaos theory go back to the last century, when the French
mathematician Henri Poincar took a critical look at Newton’s celestial
mechanics and above all the work of Laplace. Pierre Simon de Laplace
(1749–1824) stood for absolute determininism, postulating that someone
who had full knowledge of the location and velocity of all particles of matter
that existed in the universe at a particular time would be all-knowing, both
historian and prophet, able to quantify past and future with equal accuracy.
Poincar showed that a quantitative model, however precise the figures used,
would never permit us to forecast the future, as even minor deviations may
result in decisive changes at a future date. It is now generally accepted that
there is no way of foreseeing the future of our planetary system, as it is
impossible to quantify its masses and movements completely. Rudolf Steiner
spoke of this in the astronomy course he gave in January 1921, saying the
reason was that the orbital periods of the planets were incommensurable. 4
Irrational numbers cannot be given in simple fractions, or with a limited
number of figures after the decimal point, and accurate calculation is
therefore impossible.
In the mid-1960s, the meteorologist Edward Lorenz, working on quite
a different problem, came across the same situation. He had been working
on weather forecasting, feeding all kinds of important initial data into
his computer. It took the computer quite a long time to do the necessary
calculations and on one occasion Lorenz had to go and do something else,
which meant he had to stop the process. To save valuable time, he made
a print-out of the intermediate results, so that he might continue from
that point on his return. Having done so he was surprised to find that
the computer prediction was completely different from those produced in
earlier simulations using the same initial conditions. At first he thought the
computer had developed a fault, but in the end he saw what had happened.
The intermediate results had been printed out to three decimal places, yet
the computer had actually been working with six. Lorenz had accepted
that there would be an error of the magnitude of a few thousands when
he input the intermediate results, but this had led to a complete change in
developments. His discovery was called the law of sensitive dependence on
initial conditions or the “butterfly effect”: Even a minor element such as the
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