1104 Inversive Embodiment

Nylon (white), 3D print
(Selective Laser Sintering SLS),
piano wire (ø 0.8 mm, 26 x 16 x 22 cm

Inversive Embodiment uses a 4-dimensional translation of space to articulate the concept of soft malleable concepts of inverted space as a fully embodied architectural argument. The basis of this geometric translation is the mathematic theorem of inverse geometry, the study of a type of transformation of the Euclidean plane.  These transformations preserve angles and map generalized circles into generalized circles, where a generalized circle means either a circle or a line (a circle with infinite radius). Many difficult problems in geometry become much more tractable when an inversion is applied. Here the object explores this complexity in a culturally driven background of the data construct of the author’s own body, derived by a series of Magnetic Resonance Scan and the iconic monumental construct of St. Paul’s Cathedral. Similar to these tractable approaches in mathematics, the spatial complexities emerging by a translation of iconographic qualities within a cultural artificial construct, are explored, valued, and articulated in the work.

This artificial grown construct emerging from the construct equals the difficulties and opportunities in the inverse geometry where Zero, the origin, requires special consideration in the circle inversion mapping. The approach is to adjoin a point at infinity designated ∞ or 1/0 . In the complex number approach, where reciprocation is the apparent operation, this procedure leads to the Riemann sphere. It was subspaces and subgroups of this space and group of mappings that were applied to produce early models of hyperbolic geometry by Arthur Cayley, Felix Klein, and Henri Poincaré. Thus inversive geometry includes the ideas originated by Lobachevsky and Bolyai in their plane geometry. Furthermore, Felix Klein was so overcome by this facility of mappings to identify geometrical phenomena that he delivered a manifesto, the Erlangen program, in 1872. Since then many mathematicians reserve the term geometry for the group of mappings of some space characterized by a group invariant, a measure, like distance or angle. This complexity is replaced by the voxel driven data set that describes the author’s own human body. The reminiscent contextual elements bend away under a double-reflected space of the everted second dome of St Paul’s Cathedral. It is the last fragment of the triptych Embodiment series. It everts the author’s own unique corporeal data in an amalgamation with the sacrosanct structure of St Paul’s Cathedral. Magnetic Resonance Imagery is utilised to merge the grown with the artificial celestial construction. The final step is the melting and eversion – a turning inside-out of the embodiment.