A loop of square cross-section, when placed on one side of the beam, has got four edges and four surfaces (front / back / inside / outside). Yet when 'folded' diagonally across one edge of the beam, the 'resulting' loop, in a Moebius strip-like manner, has only got one edge and two surfaces (one surface covering / 'connecting' 'back' and 'front', and one surface covering / 'connecting' 'inside' and 'outside' of the loop) - despite locally still being of square cross-section and still having the same surface area as the loop placed on one side of the beam.

 

 

 

 

 

 

 

 

 

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Two different situations of 'a' loop, yet a transformation of 'the same loop' in the mind. What has been lost in the 'transformation'?  What stays the same? 

 

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The Euler characteristic (V-E+F=) - a topological invariant and intrinsic property- reveals that the two loops are essentially different:

Euler characteristic of the loop on one side of the beam:  0 -4 +4 = 0

(Not only the circle, cylinder and torus share this same Euler characteristic of zero, but, more surprisingly, also the Moebius strip and the Klein bottle.)

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Euler characteristic of the loop 'folded' across one edge of the beam:  0 -1 +2 = 1

(An interval (a line with two end points), as well as a disk, a real projective plane (a one-sided surface which cannot be embedded in standard three-dimensional space without intersecting itself; its construction based on the Moebius strip) and tetrahemihexahedron share the Euler characteristic of 1.)

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It is not possible to continuously deform the loop with Euler characteristic of 0 into a loop with Euler characteristic of 1. 'The loop' physically manifests a quality / the grammar of the space which it is embedded in. Information is uncovered through the application of this abstract tool. A thought implies / uncovers 'layers' of information - 'belonging' to neither exclusively the mind nor exclusively to the wood.  'The same loop' is tested in a wide range of contexts and situations - almost like on optical device.

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(I did not start out with knowledge of topology, but uncovered some of its fundamental principles through carving itself. Carving led me to explore topology and consequently I began to examine my work in hindsight through topological terms. What is the nature of this process? The discovery of a small number of shapes and principles have appeared as a complete whole that can -seemingly infinitely- be analysed from countless angles. Like striking the same bell with different 'hammers' resulting in different sounds. Each new work is thus not an addition or progress, but rather an inversion, endlessly 'looking in' on itself, continuously using the same form to measure that which it is confronted with and in this process also revealing something about this form itself. 'Art' and 'sculpture' were an entry point in the beginning, yet -through the discovery of the loop- I have entered a completely unknown realm which neither belongs to science nor any other field I know. 'Art' and 'sculpture' are not redundant, but continue to work as reference frames / one aspect of the prism that is 'the work'.)

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The Shape Of Information follows the contour of one segment of the invertible cube by Paul Schatz. The same contour is examined in Parallel Diagonals, The Same Thing, Spirit Level, Spatial Tear and Zero Intrinsic Curvature. Together they outline the knowable information / (about) that which is not knowable in a cubic volume of wood. 

The cubic volume is re-applied/ re-examined as an idea / principle as much as the idea of the loop itself.

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