in the vertigo of translations
by Dario Srbic
At the first site, the five platonic solids depicted in the photograph (Fig. 1) 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 (a cube) 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. [1] 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, then the path of translations does not form a perfect self-identifying circle, but a figure of a spiral or vertigo emerges where the start of the cycle is not coincidental with the last beginning or even a previous end. The stochastic movement with the varying circumference of the circle unfolds into vertigo that may fold unto itself and, in doing so, form a shape with the geometrical qualities of Klein's bottle. It does not have an inside or outside nor up or down but is a continuous surface with only one side.
It is difficult to evoke a notion of translation without dragging along the Platonic discourse of original and copy, a deterministic hierarchy established with the primacy of the ideal model over its imperfect material actualisations in reality, mirroring the inferiority of a translation with respect to the original. This neat, mathematically well-behaved metaphysical relationship can similarly turn vertiginous through a non-deterministic movement that gets magnified to a scale where previously negligible differences begin to matter, bringing messiness, dizziness, and instability into the picture or, in this case, a photograph.
Fig. 1: Platonic Solids. 3D print in plastic, 2022.
In a metaphysical framework, the translation is a product of the difference between two identities – the set of words used in the original work (A) and the group of words corresponding to the meaning in the initial set (B) – where the translation function f defines connections and mappings between the two sets. Ideally, f would be bijective, where each x from A would map to exactly one y from B, forming a perfect one-to-one correspondence between the members of the sets, allowing for the lossless, repeatable, and reversible translations between the two sets. It would also be stable, meaning that the translation function would yield the same results as the process unfolds in time. This would be the case if "aufheben" would translate to and only to "sublate", for example.
If two members of A map to one member of B, the translation loses its injective properties, which demands that no member of B can be mapped to more than one member of A. The translation is still a function with an embedded loss since the differentiation of two members of A collapses to one member of B. Translating, sublating, preserving, and cancelling to "aufheben" collapses all the possibilities in English to one in German. In the case that one member of A can be mapped to two members of B, translation ceases to be a function, but a mere relation, in which the meaning of A is necessarily altered since one of the possibilities from B must be assigned to A with all other possibilities being lost in the work of translation. To translate "aufheben", one needs to choose depending on context abandoning all other options (unless one translates Hegel).
In conclusion to his book "Shadows of the Mind", Roger Penrose distinguishes between three worlds: mathematical emerging from mental, physical emerging from mathematical, and mental arising from physical.[2] If relations between the worlds were bijective (one-to-one mapping for each element in the corresponding sets), neither the direction of the movement nor the number of cycles in the movement would matter at all. The move would reproduce the same circle ending exactly where the previous translation started and with the latest translation ending in the perfect reproduction of the original.
Since the mappings are not bijective, each translation yields a different work, not only representing a previous translation but generating a new expression, a product of a previous translation with an applied transformation. The start, the direction of the movement, and the number of cycles transversed deliver different results, not repeatable in its entirety, even if all mentioned parameters stay the same. Each start (even from precisely the same point) produces a different translation or a different copy, no matter how close the initial conditions of the translation process are. In the case of the platonic shapes above, 3D print emerges as a material, physical expression from a perfect mathematical model. They are translated from the mathematical into the physical world with all its by-products, such as elephant feet, curling of layers and angles, filament snap, and gaps in the wall, to name a few.[3]
This translation consists of several inter-translations needed to transform the original model into a 3D print. Smooth NURBS expressed as parametrised mathematical functions are translated into a stereolithography model containing a series of linked triangles to describe surface geometry.[4] In the next step, the stereolithography model is imported into a slicer, software that performs two translations. First, it translates free standing model into a printable model by generating support structures according to the physical constraints of the 3D printing process and the printer itself. Second, it translates those layers into G-code, a computer numerical-control programming language consisting of simple commands that determine the parameters of translation: the movement of the print head, the temperature and the amount of the material extruded.[5] In the last step, those commands are sent to a 3D printing machine, which translates them through its firmware into the physical movements of the head, heating and extrusion of the material used to create a 3D print. The perfect lines of the mathematical model are expressed as a movement of a head depositing material horizontally or a group of layers stacked on top of each other vertically (Fig. 2). Described in this way, the process still strives to preserve resemblance to the original model and the possibility of its recognition, that sets aside the imperfections of the material expression.
Fig. 2: Hexahedron and Icosahedron. 3D print in plastic, 2022.
The loss and the inadequacy of translation relate closely to Plato's discourse on the model and the copies. In Deleuze's reading of Plato, there are two kinds of copies: copies-icons, "always well-founded" that are faithful since they are based on the resemblance to the original model, and simulacra-phantasms, "always engulfed in dissimilarity".[6] Resemblance situates itself as a criterion of difference with "the superior identity of the Idea which founds the good pretension of the copies, as it bases it on an internal or derived resemblance".[7] Consequently, a copy of a copy without an original, a simulacrum -- the nested relation of translation -- will necessarily produce copies which are further away from the original, with each iteration deteriorating the relationship to the original. Without bijective property, the translation relation cannot be inverted and hence cannot recreate an originating model entirely from a copy.
A photograph of a hexahedron (Fig. 3), yet another translation responsible for the visible curvature at the top of the cube, reveals an indispensable element of the translation from a 3D model to a 3D print: a support structure. Hidden inside the model, it holds the sides of the hexahedron together and supports the top of it. Without this structure, the walls could significantly deform, and the top side would slump down inside the cube since the melted and extruded plastic could not cool fast enough and strive towards the bottom side, thanks to the physical conditions dictated by gravity. The support structure is not a mere by-product of translation, but its constitutive element, without which the cube could not be 3D printed at all. 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 translation, melted with and inseparable from the outlines of the sculpture representing a hexahedron.
Fig. 3: Hexahedron. 3D print in plastic, 2022.
The move away from a rigid, deterministic view of translation as the preservation of the original is portrayed in Walter Benjamin's text "The Translator's Task", where the translation does not constitute the finding of corresponding words, thus forming a lesser copy of the original. Still, it is a new expression of the text (or a model, an image or dataset), a transformative act that reveals the untranslatability (the perfect one-to-one mapping) of the original work.[8] With each new translation, a new meaning, interpretation, and expression is produced, which uncovers something new that was hidden in the previous translations and the original itself.
In this sense, translation is not a generic operation of mapping one language to another, decoupled from the original and simply applied to it, but a unique relationship forming from the original and the translation and informing them both. According to Benjamin, translation is properly essential to some works.[9] Perhaps the best example of such work is W.G Sebald's Austerlitz.[10] While the original is written in somewhat antiqued German, Anthea Bell's translation generates an odd, fresh rhythm to the novel. At the time of the writing, Sebald was completely fluent in English and could have translated, if not even written, the work itself in English. And yet he understood that the work needed a translation not by himself but by Anthea Bell, to reach the unfolding of its expression. By writing it in German, Sebald already anticipated translation as part of the work. Translated work is not a better copy of the original, an inverse of what translation in Platonic terms means, but a break from a hierarchical order, a product of the encounter (translation) between the German and English expressions, or as Hannah Scheithauer suggests:
Bell suggests that Sebald saw failures in translation as the expression of a more fundamental break within language itself. A sense of deep-seated untranslatability, which is not limited to a text's movement between languages but relates to all forms of linguistic expression – paradoxically – emerges at the very core of what Austerlitz seeks to express.[11]
The anticipation of translation is a constituent part of 3D modelling when the final product is intended to be printed. An artist or designer pre-emptively avoids certain design elements known to be unprintable or incorporates them in excess to examine how the translation will fail. It is not an inversal of the copy and its twisting back to insult or threaten the original, but the reversal of the metaphysical process of hierarchisation and categorisation into an emergent process consisting of translation as an encounter from which both the work as a model and the work as a copy emerge.
While Deleuze did not spare any chance to insult or threaten metaphysics, he defines the reversal of Platonism not as a primacy of a copy over the original but as an entirely different configuration, similar to Benjamin's understanding of the translator's task in which forms are not eternal but is constantly in a state of becoming, not being pre-existing models but emerging from the interaction between the virtual and the actual:
For there is a vast difference between destroying in order to conserve and perpetuate the established order of representations, models, and copies, and destroying the models and copies in order to institute the chaos which creates, making the simulacra function and raising a phantasm - the most innocent of all destructions, the destruction of Platonism.[12]
Within this framework, 3D print can be seen as a form of simulacrum, not a mere replica of the original, but a blurring or dithering between reality and its representation, reversing the direction of translation, and varying the circumference of its movement. Its vertiginous repetition, produced by stochastic nesting of translation, a simulacrum - not a copy without the original, but the copy with the original - emerges from the process of translation.
Fig. 4: Tetrahedron, Dodecahedron, and Octahedron. 3D print in plastic, 2022.
This vertiginous movement was meticulously described in a science-fiction short story, "Pay for the Printer", by Philip K. Dick, which simultaneously critiques the rise of mass production and predicts the rise of 3D printing technology. Biltong, a benign alien species, can replicate objects and thus supply the humans who lost the ability to produce them. At first, Biltongs can produce perfect copies, but with time, the original objects deteriorate, as well as with ageing Biltongs with their ability to create exact replicas. If the original is lost, then a copy is used for replication, degrading the result even further. Copied buildings start to collapse while a copy of newspapers becomes unreadable, a jumble of meaningless words: "A vague blur of broken type, watery ink that still hadn't dried, faint, streaked and uneven."[13]
On the one hand, the description of the copy of the newspaper can be seen as a bad copy or a bad translation. Just as in the photograph of a tetrahedron, dodecahedron, and octahedron (Fig. 4), lines of deposited plastic reveal an edge that is not a straight line as deviations from the smooth NURBS of a mathematical model. On the other hand, the degraded, unreadable copy of a newspaper is the shift from discursive into figural, where the materiality of the print becomes palpable. The lines in the print are not anymore, an imperfect representation of the smooth line but an expression of the vertiginous movement of the printer head from the bottom of the tetrahedron to its apex, defining the rhythm of the process when a hand glides across it, reminiscent of the rhythm present in Bell's translation of Sebald's work.
Fig. 5: Octahedron. 3D print in plastic, 2022.
In the last figure (Fig. 5), an octahedron rests in the middle of the picture, as its usually represented in drawings and digital renderings, laying on one of its faces, unable to float on one of its apices as it usually does in the geometrical drawing, hiding five of its polygons, less recognisable, if at all, as an octahedron. Through the careful placement of light that hits it from the sides, a fragile, ghostly figure emerges in the middle of the picture, otherwise invisible if the angle of light hitting the object was to change. It is a shadow of the internal supporting structure that holds the octahedron together, all to gladly dismissed in the Platonic framework of resemblance and recognition, tolerated as a necessary by-product of imperfect translations, and dismissed (aufgehoben) as soon as the octahedron is identified.
At the same time this shadow constitutes a marker of translation, a central element in the reconfigured framework of difference, a generative encounter of the original and translated work, of a model and the copy, outside of the static, hierarchal order. None of the apices rages above the others as a primary, apart from the one below the shadow of translation (difference), with the other two peaks resting on a visibly curved connecting line, neither the original nor copy being a lesser version of the other, but both equally valid expressions of reality. In this constellation the idea of a static and authentic expression takes a back seat while the importance of the multiple, dynamic, and transformative nature of expression emerges in the figure of translation.
To end with a slightly different beginning, the question Jacques Derrida poses in the first sentence of the introduction to Philippe Lacue-Labarthe's Typography regarding the impossibility of translation of the term without taking into account the role and the place in the whole of Lacue-Labarthe's work can be paraphrased from: "How are they going to translate désister?" into: how are they going to translate a shadow?[14]
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Footnotes
[1] Aufheben is German word that Hegel choses to name a centre concept of his metaphysical movement and which translates in English to sublation. But it also translates into elevating, preserving and cancelling, mirroring this movement in which the one sides erases the other while it preserves and elevates itself into sublation. For the contemporary critique of Hegelian metaphysics of sublation see Johnny Golding (2021), "The Courage to Matter," in Sometimes Hard, Usually Soft. The Future of Knowledge Systems, ed. Martin Reinhart and Mattia Paganelli (Berlin, Boston: De Gruyter).
[2] Roger Penrose (2005), Shadows of the Mind: A Search for the Missing Science of Consciousness (London: Vintage), 412-417.
[3] Sean Aranda (2022), 3D Printing Failures: How to Diagnose and Repair All Desktop 3d Printing Issues, (Independent Publishing).
[4] NURBS are non-uniform rational B-Splines or mathematical representations of 3D geometry. See Arturo Tedeschi (1884), AAD Algorithms-Aided Design. Parametric Strategies Using Grasshopper (Brienza: Le Penseur Publisher), 121-122.
[5] For the definition and commands of G-Code see Diego García Cueva and Gianluca Pugliese (2020), Advanced 3D Printing with Grasshopper (Independently published), 31-38.
[6] Gilles Deleuze (1990), The Logic of Sense, ed. Constantin V Boundas, trans. Mark Lester and Charles Stivale (New York: Columbia University Press), 256.
[7] Ibid., 257.
[8] Steven Rendall (1997), "The Translator’s Task, Walter Benjamin (Translation)", TTR 10, no. 2: 151-165.
https://doi.org/10.7202/037302ar .
[9] Ibid. 153.
[10] W.G. Sebald (2001), Austerlitz, trans. Anthea Bell (London: Penguin Books).
[11] Hannah Scheithauer (2023), "Translation and its Failures: W.G. Sebald’s ‘Austerlitz’ and Anthea Bell at UNIQ,"
e-mail message to author, January 20, 2023.
[12] Gilles Deleuze (2004), Difference and Repetition, trans. Paul Patton (London: Continuum), 266.
[13] Philip K. Dick (2017), "Pay for the Printer," in Second Variety and Other Classic Stories (New York: Kensington), 242.
[14] Philippe Lacoue-Labarthe (1998), Typography : Mimesis, Philosophy, Politics, ed. Christopher Fynsk (Stanford: Stanford University Press), 1.