Strange Loops, Formal Systems, and Aesthetic Computing

NAU EscherOriginally posted to Art Ed Forum


With all the talk about interdisciplinary connections in the arts, you may find it satisfying to know that some of them are coming back to meet us half-way. Take, for example, the recent interest taken in Aesthetic Computing in the fields of math and computer science. Apparently they’re catching on to the fact that the average person really can’t see the elegance inherent in the act of computation, but can see beauty in a fractal pattern laid out in front of them, and only have incredibly vague notions (if any at all) of how and if the two things are related. A similar theme is apparent in the book Gödel, Escher, Bach: an Eternal Golden Braid. Tesselations, fugues, Islamic tiling, mobius strips, Gödel’s Theorem, Strange Loops, and paradoxes of both logic and vision are all part of the same kind of thing, and art and mathematics aren’t as far separated as people often suppose – something which both Escher and many of the surrealists attempted to explore in their work to great effect, and which mathematicians in turn are trying to make more understandable to the public who don’t find such things readily intelligible.


I am of divided mind, however, regarding how this new interest could be used in the field of education. On the one hand, it’s all really fascinating stuff, and powerful enough to get many of the arts people interested in math, and visa-versa, as well as be a basis for the creation of beautifully integrated cross-curriculum projects, increasing understanding for all involved. On the other hand, if, say, the math, computer science, and design departments at a high school were to get together on an “aesthetic computing” project in the wrong way, then it could mean even more confusion and dislike. What the “wrong way” would be is, in my opinion, adopting anything – really anything at all – as a gimmick. Unfortunately, the more cross-curricular an undertaking becomes, and the more people are involved, the more opportunities seem to arise for gimmick-hood to flourish. On the one hand, it’s incredibly compelling to find out that the continuous staircase seen in Ascending and Descending by M C Escher is an instance of the same concept as Bach’s ever rising Canon (Canon Curcularis per Tonos from The Musical Offering), and is echoed in Gödel’s Theorem. Insights like that, when set forth clearly and interestingly (preferably with amusing acrostic dialogues based upon musical forms between Achilles and the Tortoise from Zeno’s famous proof of the impossibility of motion) off enough interest to get literature people (like me) to learn recursive computational definitions for no particular reason – and also brings much of the use of algebraic functions into the light. But there’s a great possibility that discretion would be used badly, and rather than using cool and interesting ideas or meanings as a springboard for getting into the real work of slogging through equations, playing fugues, or creating beautiful and mind-bending works of art, we would just dabble – pre-posterism, as Barzun would say.


Two outcomes, then, seem likely as a result of including Aesthetic Computation or brilliantly connected works, dependent on both presentation and reception. On the one hand, a student could look at the awesomeness of seemingly unconnected disciplines and be inspired to fill in the vast holes he saw in his present knowledge, whether that meant training his ear to subtle variations of pitch and tone so as the not only know, but hear all the amazing stuff going on; brush up his algebra so as to be able to read formal systems of thought based on algebraic functions, or practice drawing with precision so as to have the power to show impossible worlds and visual paradoxes to dazzle the eye. On the other hand, however, he could react by thinking that the greater knowledge of dazzling concepts and high ideas was sufficient, and the lower unnecessary, and grow impatient with laying foundations and scaffolding when the end result is so close and seems so tantalizing and so very unrelated to learning to shade or finding the value of x.


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