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The edge / boundary of the moebius band with three half twists, when split lengthways, releases the trefoil knot. This knot is 'folded' into the paradigm of my work for observation. To avoid arbitrariness the line is thought of as behaving like a knotted flexible chain that is hanging and thus shaped by gravity. The resulting shape has a propellor-like twist. The way the lines wrap around each other reveals that this knot is shaped like two offset halves of the Aleph shape. Trefoil Knot 1  serves as an entry point into my continued investigation of knots and knotted surfaces.

 

 

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There is no difference between the line itself in Trefoil Knot and the rounded line / loop in Aleph, for example. Intrinsically it does not carry any information that would signify difference, but as a result of its positioning and direction in space and in relation to itself, information 'comes in', as if existing 'outside' or 'on top of' the lines. How can something that in itself remains completely invariant in the various 'sculptures' (the continuous loop out of a rounded line) be the carrier or producer of difference? 

 

Where is the information which we call 'knot' located ? Is the information equally distributed on / in the line? (How can 'local information' affect the shape 'globally'? How can one deduce the global shape from purely local information ?) The information 'knot' seems to be embedded in the line not only as a result of how it sits in space but how it sits in space in relation to itself. The way the line sits in space 'adds' information to the unchanging line? Do extrinsic and intrinsic information remain separate? Or: how exactly do they 'connect' ? Is the orientation in space actually 'part of' the nature of these lines or does it 'belong' to the observer / to logic?

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(The uniform and continuous moebius band with three half twists containing the trefoil knot seems to have something essential in common with the single straight line 'containing' a diagonal ... in both the line itself seems independent from the shape on the whole, yet detrmined by it a once. A straight line is diagonal and twist producing only in relation to the surrounding space or in relation to other lines - and when controlled by gravity - and logic. It is 'diagonal' in itself only when enlarged through logic and as seen as a body with 'front', 'back' and 'sides'.  see: Parallel Diagonals)