Monday, March 12, 2012

Art and Elsewheres

Hiroshi Sugimoto, Surface of Revolution with Constant Negative Curvature, 2008

I’m interested in abstraction as a real issue for creative collaborations between art and science. As I wrote in my last post, science habitually turns to orders of abstraction and mind-bendingly variable magnitudes of scale when it turns to mathematics; but ‘abstraction’ also has a very specific meaning for art, and especially modern painting. So what happens when you put these two kinds of abstraction — mathematical and aesthetic — together?

Mathematics: A Beautiful Elsewhere was an exhibition at the Fondation Cartier pour l’art contemporain, Paris late last year that put leading mathematicians and artists into contact with a open collaborative brief. The curator quotes the mathematician Alexandre Grothendieck to describe the exhibition’s aim as offering visitors “a sudden change of scenery.” The show was unusual enough to elicit some thoughtful response, not least a long interview with David Lynch, who contributed a film. "If you think of cosmology, you picture colourful nebulae; with neurology, intricate brain scans," notes the New Scientist. "But what does mathematics look like?" The answer is, implicitly, abstraction. The Nature review was a bit more curmudgeonly, accusing both the artists and the mathematicians of insufficient or obtuse communication. Other pieces in the show included included a live video feed from the CMS and ATLAS experiments at the Large Hadron Collider in CERN, Geneva: a groundbreaking-everyday kind of experiment which this reviewer — an astronomer — describes as "the mathematical word made flesh." For another commentator, the dominant theme was mystery: 
Mystery is perpetuated not only within the pieces and puzzles themselves, many of which are initially impenetrable to the mathematically untrained. It also lies more fundamentally within the very essence of the subject under examination. The message runs clear throughout: mathematics is in itself a mystery, the truth of which may never be attained. 
Sea Waves (wave equation) image from the film Mathematical Paradises, 2011.


Talking with Shaun recently about fractals and the questions they raise — are they art? are they science?  Does the mathematical basis and quality of endlessness make this an 'aesthetic' or a 'natural' object? — reminded me of the persistent problem of vocabulary for the desire to talk across these particular disciplinary lines. In a book titled What is Philosophy?, a collaboration between a philosopher and a practicing psychoanalyst, Giles Deleuze and Felix Guattari express the problem in this way:
When philosophy compares itself to science it sometimes puts forward a simplistic image of the latter, which makes scientists laugh. … Paul Klee’s vision was certainly more sound when he said that mathematics and physics, in addressing themselves to the functional, take not the completed form but formation itself as their object. … If philosophy has a fundamental need for the science that is contemporary with it, this is because science constantly intersects with the possibility of concepts and because concepts necessarily involve allusions to science that are neither examples nor applications, nor even reflections.
(Deleuze and Guattari, What is Philosophy? 154-5, 162)
Ulam’s Spiral, in The Room of the Four Mysteries, part of a film by Beatriz Milhazes.

It strikes me that Mathematics: A Beautiful Elsewhere is an attempt in the right direction at a real space of collaboration — the kind of thing that Deleuze and Guattari would call taking "not the completed form but formation itself as [its] object." This is for a couple of reasons. One, the sheer range of works and collaborations in the show. Each is a sincere attempt to bridge the gap through multiple types of visual languages, and in a range of different media, and no individual piece can claim to individually crack the problem. This variety is an important part of making the viewer aware of the potential heterogeneity of the art/science matrix. By comparison, the CERN residency picked only a single artist following a wide call for proposals, which is a relatively pre-determined approach that is more likely to fall into the trap of fixating on artistic personality.

Second, Michel Cassé — an astrophysicist and a co-curator of the Mathematics show — put a range of experienced specialists together, gave them an open brief, but required the outcome to take the form of an art exhibition. This is a useful constraint for a topic so predisposed to wander into the literally ineffable. And so, for all the occasional accusations of impenetrability by the critics, this is an approach to disciplinary collaboration that I hope we see more of in contemporary art: process-oriented, carefully conceptualized collaborations that are not just flashy "allusions to science" but that prioritize the actual objects, methods, and incipient discourses that might fail, may communicate only partly, but begin to construct the common vocabulary.

Live video feeds from experiments at the Large Hadron Collider in CERN, Geneva


  1. An Ulam spiral is my desktop background at the lab. Sometimes I just sit and stare at it.

    1. For some reason I think I already knew that. You must have written about it on facebook or twitter at some point.

      I'm not a number theorist, but I did take some number theory-ish courses when an undergraduate in Auckland. One of the things that really struck me then was how, out of such a small number of fundamental axioms and then just the simple application logical reasoning, so much structure can develop. This alone is worthy of wonder, but sometimes the forms, and behaviour, and rules of the emergent structures are really beautiful.

      I think the Ulam spiral is quite a nice, elegant and simple example of this. Prime numbers are so easily defined and yet understanding the full set of prime numbers is still revealing surprises in the 21st century. The emergent patterns in the (20th century) Ulam spiral hint at some deep and profound *thing* lurking to be discovered. I can see why so many number theorists end up going nuts searching for that *thing*.

      Fractals, though, show this even more. The patterns in the video Michelle linked to in her post were not designed by an imaginative human. None of the images seen in the fractal in that video were designed. There is of course some freedom in how to render the image but the structures just come from a very concise algorithm. What is also amazing is that only small alterations to the algorithm itself can produce final images that look completely unrelated.

    2. Bermondsci can you say a bit more about why the Ulam spiral is so fascinating, or what you get out of staring at it? Talking with Shaun about fractals, part of what was fascinating for me was hearing his description, from a specialist background, of something that I'd otherwise have understood pretty differently as a game background.

  2. And if you happen to be in Paris, head on over to one of the Cartier Foundation's Nights of Uncertainty, "a series of encounters open to all—novices, seekers, initiates—designed to continue the experience of the 'sudden change of scenery' offered by the Mathematics exhibition."

  3. I wish I could have made it to this actually (and in the future I might put the effort in to go to something like this - if it's in Europe), but as a second best option, I've finally found time to read all the reviews of it that you linked to. I have to admit to relating to the Nature review quite a bit, which wasn't entirely curmudgeon - it did have positive points. But, relating to the negative parts of the review... specifically, it criticised the mystery parts of the exhibit (which, actually, some of the other reviewers particularly liked).

    The specific exhibits that Nature criticised the most were the ones that had things like a bunch of scholarly textbooks and a few quotes, or had a live-feed of the LHC and a bunch of Feynman diagrams. And, many of the exhibits that had equations describing mathematics flash on a screen, or on a wall, but completely unexplained. I don't see how that helps anything, if you're going to show the equation you need to explain what it is, otherwise it is just like showing hieroglyphics. What's the point? The beauty of the equation certainly isn't in its visual aesthetic when you write it down, so I don't see the point in showing it at all, really.

    I suspect the reason they did show it is a misguided attempt to make things mysterious and impressive. But this sort of exhibit should be trying to undo that stigma, not promote it. Making it seem otherworldly and mysterious just promotes the idea that this stuff isn't understandable, especially when you flash equations on a screen. It is no different to flashing a foreign language on a screen. If you don't speak the language, it's just a bunch of symbols.

    As with Nature though, I did like the idea of the exhibit that had a few mathematicians speaking in front of a camera about exactly what they found beautiful in maths. That is a step in the right direction.

    I've just been reading your other post that discussed taking abstract science and somehow making it more concrete, bringing it into the collective imagination. I really liked that idea. The brilliance of the moon landings is that people look at those pictures and they understand exactly what they're seeing. Sure it is a pretty picture, but that's not what is striking, nor what caused them to enter the collective imagination.

    I do, however, agree that this is an important step to be taking (as well as the CERN residency programme). If not for anything else except that it helps that people are doing the wrong thing, because then we can realise what is the wrong thing. If I'd been put in their position I might have done something very similar and only realised it was the wrong thing afterwards, with hindsight.

    Similarly, with this blog, I'm already learning a lot about the real problems any sort of public description of science must face.

    And if I sound overly critical of people's attempts to somehow do this concretisation and bring science into the collective imagination it isn't because I think I can do better, it is hard, and at least these guys are also trying... but most of those exhibits seemed to be just pretty pictures using maths as a theme, not something that actually deposits something of what makes the maths itself beautiful on to the imagination of the viewer.

    1. The Ulam spiral kind of works in that respect because what it is is so easily explained. If all they showed was the image and said "oh, look what the crazy maths has made, isn't that crazy and impossible to understand?" like they did with the Feynman diagrams, etc. it wouldn't work, but if they explain how it is made and then show it, that works.

      Like with the equations, the thing about a Feynman diagram that generates awe is not the diagram itself The diagram is just notation, a method to remind ourselves what numbers go where in a calculation. Instead, it is what the diagram represents that is worthy of awe. You may as well make something up and claim its mathematics if you're going to show unexplained equations and Feynman diagrams.

      The thing the exhibits were actually exhibiting was the disconnect between mathematics and the public imagination. That itself does have some awe to it, the idea that one collection of people have learned something that so few other people have learned is a bit mind-blowing and is my hunch as to the non-Nature reviewers liked the exhibit - it certainly wouldn't have been boring to see. But that awe isn't nearly as awesome as the actual things those mathematicians have learned.