Fractal Models

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Models must be realistic not precise!

It is sickening to see how people in the CAE industry keep on insisting on building larger, more complex and, at the same time (wow!) more accurate models. Nature is not precise! Isn’t Computer Aided Engineering supposed to help engineers imitate reality? This is what Benoit Mandelbrot says: “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line”. While the past decades have marked and established the spectacular success of the finite element science in engineering, we still have a long way to go.

Fractals, chaos, the principles of uncertainty and of quantum mechanics eventually manifest themselves in the macro-scale to the engineer in the form of tolerances and scatter. Revisiting Mandelbrot’s sentence in a more engineering-oriented perspective, one may say that materials are not homogenous, boundary conditions are not ideal, geometry is not perfect and loads are subjected to unexpected fluctuations. Uncertainty in other words. Uncertainty originates from the very heart of physics and is deeply rooted in the nature of matter and therefore, not surprisingly, it accounts for a huge chunk of the phenomena we observe. So how can we speak of accuracy in an uncertain world? Models must be realistic not precise.

Another point CAE practitioners miss is the Principle of Incompatibility: High complexity is incompatible with high precision. The more something is complex, the less precise can our statements about it be. A few examples: the global economy, our society, climate, traffic in a large city, the human body, etc., etc.

The more something is complex, the more it can surprise you. See what Aristotle had to say in his book on ethics: “An educated mind is distinguished by the fact that it is content with that degree of accuracy which the nature of things permits, and by the fact that it does not seek exactness where only approximation is possible”. Models must be realistic not precise. Fractals can help us.

Jules Ruis.


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