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Walking along a sonic Möbius strip


Hegel bemerkte irgendwo, daß alle großen weltgeschichtlichen Tatsachen und Personen sich sozusagen zweimal ereignen. Er hat vergessen, hinzuzufügen: das eine Mal als Tragödie, das andere Mal als Farce. [Marx]

If one imagines to be a two-dimensional person walking on the surface of the Möbius strip, there is something to observe. Since there is no top-down view through a third dimension that would immediately reveal the entire structure of the strip, it is necessary to walk along the surface of the strip to find out that one is on such a strip. If an object such as a clock face is left at rotation 0 and the 2 dimensional being walks along the tangential field for a rotation of 2π, the being will encounter the clock face again, but now this clock face is mirrored. But this rotation of the mirroring is something that the 2-dimensional being cannot do by itself, because it would require to pick up the clockface, rotate it, and then put it back, which is only possible in the third dimenson, so it is obvious that one must be on a Möbius strip.

A Möbius strip can be the spot where Marx’s dialectic meets Nietzsche’s eternal return. Since a Möbius strip has only one side, this allows to travel endlessly over the whole strip without the necessity to change sides, it can therefore be seen as a representative of an eternal return which blurs the boundaries of beginning and ending. Music often uses repetition as a fundamental element, which goes down to the microstructure of noise vs. sound. A composition therefore relies on such repetitive patterns, but pure repetition is an act of science, not of art (for the sake of argument, it is necessary to add a phenomenological perspective on repetition). The Möbius strip allows us to encounter the same space, but the second time the encounter will have changed while still being the same spot.


Möbius strip

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