[Chaos research, fractals, fuzzy logic. From stereotypes to reality--consequences for medicine]

Abstract

Both language and conventional mathematics aim to describe reality. Although language is more flexible, it is usually also inaccurate, while mathematics permits accurate presentations and clear prognoses. However, it is burdened by the fact that it is not everywhere applicable. Such chaotic structures as clouds, or lang-term weather forecasting, for example, cannot be expressed in terms of mathematics. Chaos researchers are attempting, in a non-linear world, to understand mathematically dynamic, apparently unordered systems. In this connection, the fractal dimension also appears--which can be employed in the area of diagnosis to define tumor contours. Fuzzy logic comes closer to reality by replacing the inflexible yes/no by a more or less option and by introducing linguistic nuances into machine-controlled processes. Chaos research and fuzzy logic teach us that there is no such thing as certainty of action or prognosis. In the world as it is, whoever claims to possess it is either naive or guilty of self-deception.