In the Vertigo of Translations

Five white 3D-printed platonic solids arranged on a grey surface against a black ground — *Platonic Solids* — 3D print in plastic, 2022. Courtesy of the artist

Year: 2022
Medium: 3D prints in plastic; photographs
Solids: Five — tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron
Translations: NURBS → stereolithography → slicer → G-code → firmware → deposited plastic
Text: “In the Vertigo of Translations”, in radical ⇌ matter Journal #One, 2023

At first sight the five platonic solids seem, if not perfect, then at least like a faithful translation from the smooth definitions of the mathematical world into the dirty materiality of the physical world. A 3D print of a hexahedron is recognisable as such without measuring the length of its sides or the angle between them. And what seems to be a translation from one world to the other is comprised of several hidden translations, each of them aiming to sublate (aufheben) the previous translation while preserving (aufheben) it and cancelling (aufheben) it at the same time. Such is the game of Hegelian metaphysics and its circular motion. Identifying a hexahedron and a dodecahedron through recognition erases all differences generated in the translation process.

If the circular, deterministic movement is replaced by a stochastic one, the path of translations does not form a perfect self-identifying circle. A spiral emerges — a vertigo — in which the start of the cycle does not coincide with the last beginning or even a previous end, and which may fold onto itself to form a shape with the geometrical qualities of Klein’s bottle: no inside or outside, no up or down, a continuous surface with only one side.

A 3D-printed cube in the foreground with an icosahedron behind it, both showing horizontal layer lines and seams — *Hexahedron and Icosahedron* — 3D print in plastic, 2022. The perfect line of the model, expressed as stacked layers. Courtesy of the artist

A Grasshopper node graph: one number slider fanning out into five parallel chains of plane, radius and platonic-solid components — Grasshopper® definitions of the platonic solids, 2022 — one slider, five parallel chains. Courtesy of the artist

Each translation yields a different work, not merely representing the previous translation but generating a new expression. The start, the direction of the movement and the number of cycles traversed deliver different results, not repeatable in their entirety even when every parameter stays the same. Smooth NURBS, expressed as parametrised mathematical functions, are translated into a stereolithography model of linked triangles; the slicer translates a free-standing model into a printable one by generating support structures, then translates those layers into G-code; the firmware translates G-code into the movement of a head, a temperature, an amount of material extruded. What arrives at the end carries the by-products of every step — elephant feet, curling of layers and angles, filament snap, gaps in the wall.

The support structure is the case that decides the argument. Hidden inside the model, it holds the sides of the hexahedron together and carries its top; without it the walls would deform and the top would slump into the cube, the extruded plastic unable to cool fast enough against gravity. In the metaphysical framework it is a necessary evil, to be avoided and hidden. In the framework of constitutive difference it is an essential expression of the translation, melted into and inseparable from the outlines of the object — and the photograph is yet another translation, responsible for the visible curvature at the top of the cube. On the edges of the tetrahedron, the dodecahedron and the octahedron, the same logic shows as lines of deposited plastic that refuse to resolve into a straight line.

A printed cube lit from the side, a diamond lattice showing faintly through its wall and the top edge visibly curved — *Hexahedron* — 3D print in plastic, 2022. The internal support structure, showing through the wall. Courtesy of the artist

Close view of a tetrahedron apex against a dark ground, with an octahedron and a dodecahedron edge behind it, layer lines along every edge — *Tetrahedron, Dodecahedron and Octahedron* — 3D print in plastic, 2022. Courtesy of the artist

Benjamin’s translator does not find corresponding words to make a lesser copy; the translation is a new expression that reveals the untranslatability of the original. Sebald wrote Austerlitz in German while fluent enough in English to have written it there, and understood that the work needed Anthea Bell rather than himself — translation anticipated as part of the work. Read that way, the 3D print is a simulacrum in Deleuze’s sense: not the primacy of a copy over an original, but a different configuration entirely — not a copy without the original, but the copy with the original.

In the last figure an octahedron rests on one of its faces, unable to float on an apex as it does in a geometrical drawing, hiding five of its polygons, barely recognisable as an octahedron at all. Light placed carefully from the sides raises a fragile, ghostly figure in the middle of the picture, invisible at any other angle: the shadow of the internal structure that holds the solid together — tolerated as a by-product of imperfect translation, and dismissed (aufgehoben) the moment the octahedron is identified. Derrida opens his introduction to Lacoue-Labarthe’s Typography by asking how they are going to translate désister. The question here is the paraphrase: how are they going to translate a shadow?

An octahedron resting on one face, lit from the sides, a faint V-shaped shadow of its internal structure rising through the wall — *Octahedron* — 3D print in plastic, 2022. The shadow of translation. Courtesy of the artist