TY - JOUR T1 - Die Gleichnissprache der Mathematik A1 - Kowol, Gerhard JA - Elem. d. Naturw. JF - Elemente der Naturwissenschaft PY - 1999 VL - 70 SP - 33 EP - 38 DO - 10.18756/edn.70.33 SN - p-ISSN 0422-9630 LA - de N2 -

Betrachtet man auch nur ein wenig die Forschung in den Naturwissenschaften der letzten Jahre und Jahrzehnte, so ist eine Tendenz zum extremsten mikroskopischen Bereich unübersehbar. So suchen beispielsweise die Physiker nach immer noch kleineren Teilchen, die letztlich die materielle Welt aufbauen und deren Eigenschaften erklären sollen. Die Biowissenschaften und die Medizin wiederum sind auf der Jagd nach den Genen, die sämtliches Leben steuern und für dessen vielfältige Ausprägungen verantwortlich sein sollen. Durchgängig scheint es zum Ideal geworden zu sein, kleinste Bausteine - die durchwegs nicht—sinnlicher Natur sind - aufzufinden und daraus das Gegebene vollständig zu erklären. [...]

 

N1 -

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.
 

AB -

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.
 

ST - Die Gleichnissprache der Mathematik UR - https://dx.doi.org/10.18756/edn.70.33 Y2 - 2024-12-08 04:36:33 ER -