Die Gleichnissprache der Mathematik

Elemente der Naturwissenschaft 70, 1999, P. 33-38 | DOI: 10.18756/edn.70.33


In modern science the opinion predominates that the sensible reality can be explained by means of smallest components (elementary particles, genes). Goethe’s view is quite opposite. He says that the simple and imperfect elements can only be understood by looking at the composed and perfect objects. But the stupendous results of modern science make it difficult to argue in his direction. An analogous problem can be found within mathematics, if one looks at the axiomatics of Euclidean geometry. Up to the end of the last century, the basic elements always have been points, lines and planes, but in modern times these have been reduced to points alone. Since the mathematical theory itself does not differ in any way, it seems that the second view is preferable according to the minimum principle. But if one takes a superior point of view, which in this case means to pass over to projective geometry, it becomes clear that this opinion is wrong.

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