Recent challenges of the mechanistic world picture seem only to have strengthened the position of mathematics. So it continues to guarantee perfect predictability, the dream of physicalism. During recent decades, however, computer simulations have shown mathematicians that even simple sets of equations may have, not an exact, but a whole range of solutions. With some of their examples we demonstrate the unpredictable behavior of simple systems. As a result, the dream is over. On the other hand, mathematicians also discovered that (...) previously 'chaotic' phenomena could be represented by relatively simple formules. This leads to a dramatic increase in the explanatory power of mathematics. This change of the scientific scenery will have a profound methodological impact on the relationship between the natural and the other sciences. (shrink)
Zusammenfassung Negative gegenseitige Befruchtung mag als seltsamer Titel erscheinen. Gegenseitige Befruchtung scheint per definitionem etwas Positives zu sein. Aber diese Untersuchung will die Aufmerksamkeit auf die Tatsache richten, daÃ in einer groÃen Anzahl von FÃ¤llen die gegenseitige Befruchtung einige negative Effekte auslÃ¶st; einige von ihnen mÃ¶gen sogar katastrophal sein.
Summary A pattern can be found in the history of semiconductor electronics, which largely appears to coincide with that of scientific revolutions as described by Thomas Kuhn1. However, the history of semiconductor electronics has some characteristics which suggest that Kuhn's model requires correction in important respects.