Good: Escher and Blog … an Infernal Golden Opportunity, or: Welcome to the Wonderful World of High Technology

The blog post is titled “3D Print the Impossible! Turning Escher Drawings into Read 3D Models“. As the first paragraphs states, “The researchers […] have used their own Objet 3D printer to re-create the impossible Escher Drawings as real, tangible 3D models.” The video is fascinating, and I’ve always been fascinated by Escher … it was a preexisting love of Escher and Bach that drove me to “Gödel, Escher, Bach”, on to Gödel, and on to the world of Hofstadter in general. Life is full of strange loops.

Here I’m just interested in the blog post and how it leads me to thoughts of aesthetics, paradox, and metaphysics. This is more rhapsody than argument, with loops back to time spent abroad, museums and art, and plenty of videos from YouTube.

I. Commentary

Back to the claims of the blog title and description of the project … I suppose it depends on what you mean by ‘real’ and ‘model’. Objects — here ‘3D’ would be redundant as 3D-ness is a trait all ‘objects’ have (not the same as ‘thing’ and not the same as ‘concrete’ vs ‘abstract’, ‘real’ vs ‘imaginary’, etc.; shadows are real and concrete but not 3D) — have been created. The ‘hook’ is that a 3D printer was used, but while that might speak to some level of innovation or technical accomplishment, it’s mainly a mechanical advancement (it would make such objects relatively quick, easy, or inexpensive to make now that a pattern has been designed); the same objects could be made ‘by hand’ with different costs, materials, and degrees of precision. But back again to ‘real’ and ‘model’; by virtue of being an object, these things are real. Real is at best an intensifier here and lends no real (ahem!) substance, so we can reduce this to printing 3D vs. 2D models; something has been printed … is it a model?

A model models something; it represents or stands in for in some regard. A scale model has proportional superficial traits. Models are frequently not made of the same material as that which they model. A model may be made after the fact (such as railroad models, model cars and planes, and so on), may precede the ‘real’ item as a suggestion or proof of concept, or may be a ‘prototype’ of sorts. Models are often not meant as static objects but as things that model behavior, that can be used or tested, can stand in in some regard for that which they model. Models are often changing; ‘fidelity’ is a trait models should have, but fidelity such models is often instrumental: a model is ‘good’ insofar as its behavior represents or predicts the behavior of that which it represents. Thus: weather models, models of the early universe, economic models. Models operate by a certain degree of analogy of relationships: the parts of the model do not have to relate directly to the parts of that being modeled (depending on the type and purpose of the model), but parts must relate to each other appropriately in model and modeled.

Do these 3D objects model? Escher’s drawings do not model or represent ‘actual’ or ‘real’ objects in the world, not even possible objects in the world. It’s not just Escher’s drawings are 2D, but that they are only 2D. The printed objects represent the items from Escher’s drawings, but can only be said to model them with great difficulty. To skip to the point that should have been made in the first paragraph: these printed objects are just 3D optical illusions.

II. Illusions

Two main museums stand across from each other at Heroes’ Square (Hősök tere) in Budapest, the Museum of Fine Arts on the left and the Palace/Hall of Art on the right. The former contains some nice instances of late 19th-century decadence (e.g. Franz von Stuck), some El Greco, some Goya …; the latter houses rotating collections, frequently of more contemporary works. During one visit over a decade ago I had the pleasure of encountering several 3D optical illusions.

During my first stay in Hungary a roommate and I took a day trip to Pécs, which houses the Op-art centric Victor Vasarely museum; here the works align more with 2D optical illusions, with color interaction, with the figure-ground relationship. Some were purely flat, static objects that insinuated motion; others were paintings that suggested depth, but only when you did not stare too long and hard at them. Sculptures were static but appeared to confound perspective and depth, they shifted the convex and concave through light and shadow but were actually flat.

Back to Budapest.

One particular work on a far wall caught my attention. From a distance it was flat an unmoving, uninteresting. At a distance of a meter or two it leapt out at me and followed my eye as I moved left and right; it was a bit like a 3D movie but in ‘real life’ … this painting was attacking me! Changing as I changed, moving as I moved. And once I got even closer I could see that what appeared flat actually had depth.

The illusion was broken.

This particular illusion was an inversion, as we’re most used to ‘faking’ depth or three-dimensional objects with two dimensions, or in one two-dimensional drawing suggesting first one representation and then another (hag or beautiful girl? faces or vase? face or fruits and vegetables … gestalt part-whole relationships and so on); here three were pretending to be two and catching the observer in the crossfire.

But only at the sweet spot, in a Goldilocksian not too far, not too close matter of perspective.

These printed Escher objects are just classy 3D illusions whose magic is shattered when perspective shifts. They are fragile, regardless of what material from which they are made.

III. The Aesthetic

Kant suggests in the 3rd Critique that part of our interaction with objects we judge beautiful, to which we ascribe the predicate ‘beautiful’, though it is subjective, not objective, is a manner of interaction, a capturing and keeping of attention. This may be metaphorical; I like to imagine it as physical and physiological. The beautiful keeps us in a tension; it does not repel us or send us away, but it also does not draw us too near to the point of desire, wanting to have, possess, consume. Chocolate and the erotic pull us in, consuming us as we consume them. The merely ugly sends us away, and the mundane does not keep our attention. The beautiful captures our eye or ear — or other sense? — and we engage in a back and forth with it.

The sublime a-la-Kant works within a similar framework, but more extreme; it repulses and then attracts. It repulses us through our senses, as it is overwhelming in quality or quantity, but intellectually, through our reason and the power of that faculty we are drawn back in. Whereas in the beautiful the senses and understanding come to an understanding, a balance or harmony of sorts, with the sublime the understanding is defeated, the powers of perception dominate but are overloaded, and reason comes to the rescue, proving itself potent where mere understanding lacked.

And then there is the disgusting, which Kant barely mentions but which decades earlier in his “Laokoon” Lessing addressed. Treating it as an extreme form of ugliness and addressing metaphorical taste to the sense of taste — disgust, that which is displeasing to the taste, vs. the eyes or ears, etc. –, Lessing observed that in contrast to certain forms of ugliness and media of representation, the painter (or sculptor) could not avail himself of the disgusting as an object of representation. A regularly ugly person could be painted beautifully (just as a beautiful object from nature could be painted either beautifully or in an ugly, insufficient manner) and ugliness could be treated beautifully in poetry, but the disgusting? The sensory traits alone dominate in it, and there is little or no gap between object and representation; there is no beautiful portrayal of the disgusting. Any fitting or successful painting of the disgusting will become disgusting itself.

What about Escher?

Without doing a great deal of thought or analysis, my instinct would be to align many of Escher’s works more closely with our reactions to the beautiful, not that his works are beautiful, only that the manner in which we respond coincides better. There is a feeling of attention-grabbing (and maintaining); we do not just glance and look away, but our gaze is captured, intrigued. The “what” of the presentation — the epistemological level, that of knowledge — cannot dominate, partially because of the visual-spatial paradoxes presented; there is nothing “to know”, and instead we’re intrigued by the “how”, how it was done and how it works. There is a tension between parts and whole, with the whole being presented to us in an unstable way, the parts, though, being quite detailed and concrete. That having been said, aspects align with the disgusting and the sublime. In the disgusting the sensory detail overwhelms and category boundaries are disregarded. In the sublime the magnitude or potency of the perceptual realm dominates allowing no synthesis in a meaningful concept by way of using just the understanding; instead reason intrudes and suggests a unifying ‘idea’. Here, though, we do not have the repulsion of the disgusting, and we do not need to jump to ideas (aesthetic, bordering on moral) as in the sublime; instead what Escher aligns with more closely is the grotesque, or at least certain kinds of the grotesque.

In making these ‘objects’ ‘real’ I encounter a level of disappointment, perhaps mainly intellectual. They are reduced to matters of easy illusion, an illusion easily dispelled. Unlike Escher’s drawings, they are not aesthetic objects.

IV. What-If …

Let us assume for the moment that ‘objective’ and ‘subjective’ are both relatively well defined and meaningful. Roughly speaking ‘objective’ will refer to traits that inhere in an object; ‘subjective’ to traits or judgments provided by a subject (frequently but not always ascribed to an object).

A modest proposal might be, in this thought experiment, that the ‘reality’ of an object — not merely its existence, its physicality, but its reality in a sense aligned with the Hegelian “the real is the rational; the rational is the real” — is concordance of the subjective and the objective. But going further, or at least shifting my goalposts a bit, perhaps objectivity is more a matter of stability rather than locus of traits. This shift not to subtly to matters of substance and accident, essence and existence.

Returning to the concrete …

… what’s interesting about these Escher objects and illusions in general is not their truth value — and in that regard, yes, they are aesthetic rather than theoretical objects in a Kantian sense –, but how they work in terms of perception and perspective. Escher’s drawings are static and flat; they are ‘impossible’ or ‘paradoxical’, but not exactly illusions. They do not deceive, they do present something unreal as real any more than a painting of a unicorn is an illusion. No particular angle or distance, etc., changes their nature (as their nature is only that which is on the paper, not how we abstract them or try to actually embed them in 3-space); but the 3D models of them are illusions that do change based on how we stand relative to them. Escher’s drawings exist permanently and stably in 2-space; the models exist with fragility in 3-space. By turning the the cube or triangle or the Belvedere we see the curves and bends that make the 3D-ness of the construction possible. On the one hand their paradox is reduced to mere illusion, and on the other what existed in suspension collapses.

What paradoxes threaten is to be real, not mere illusions. Paradoxes that reduce to logical tricks or to faulty reasoning, to illusion or to falsehood, are safe parlor games. Paradoxes that reduce to the kind of assumptions we make or axioms we hold to be true reveal something about how we reason; they are formalist in a sense and reveal how we conventionally construct meaning and reality. More dangerous is the paradox that cannot be tamed, cannot be dismissed; it’s not exactly irrational in the sense of counter-rational; instead it suggests something not so much faulty but rather limited about the nature of our abilities to reason. In a sense, then, they are sublime objects; they confound our understanding even though our senses can take them in, but through their pure sensuality to which no concept applies — their impossibility, their paradox — they suggest ideas about reason, reasoning, and the nature of the world. They provide a sense of wonder and in so doing transcend the merely mundane, if only aesthetically.

But where was I coming from and going to in this section before becoming sidetracked with or by the issue of paradox? Objectivity … reality … a thought experiment. A significant developmental milestone is recognition of continuity, object permanence; when the doll disappears behind he sofa, does the child think the doll is behind the sofa, or that the doll has winked out of existence? This is partly temporal, partly spatial. It’s partly phenomenology and psychology, and partly metaphysics. Relatedly we have the matter of recognizing an object as ‘the same’ object regardless of perspective — distance, angle, other aspects –, and the more stable an object, the more ‘real’ and more ‘objective’ in some sense?

And so when I observe these illusions I get the opposite of object permanence and object stability; instead, changes in perspective change the object, destabilize it, wink it out of existence. *POOF*; what I thought was a cube, even an ‘impossible’ one — a concept, a logical construct –, parts and a whole that made some level of sense even though the relationships connecting parts together and into a whole did not, dissolves into mundane parts and comprehensible relationships that fail to make an interesting object. This is not just the perspective shift of the hag-beauty, the face-vase, but a quantitative-qualitative shift between something that only made sense as being greater than the sum of its parts to something that could only be described as the sum of its parts.

V. Links and Thoughts

Object Permanence

Op Art

Optical Illusions


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