viz.

I don't often get terribly excited about geometry. But in the case of the above video I just can't help myself. My first impulse, after viewing the entire clip was to blame my sense of wonder on the soundtrack. By layering music from Inception Robert Mikhayelyan and Alex Gill are hitching their wagon onto an incredibly carefully manicured experience. Inception was sold as, and sold itself as, this evocative, mind-blowing experience. And whether or not the film actually accomplished that for any given viewer hardly matters in the face of a sale we could so easily read. Inception, both in and out of the film, sold its sense of wonder so blatantly that it's the sales pitch that sticks--slightly Pavlovian, we hear the music we prepare for befuddled amazement. 

Image credit: Bruce & Katharine Cornwell Journey to the center of a Triangle 

This geometry, though, moves past this simple explanation. The editors of this video have created another with the same music, and while fun enough it doesn't have near the same result (neither does, for example, something like Inception Cat). I don't think that we can pin everything on the effects of synchronicity either. There is a tangible pleasure in finding patterns and meaning in seemingly disparate events, and as exampled in things like The Dark Side of the Rainbow we work hard at experiencing these blended experiences as potent. Soundtracks, unplanned ones especially, invoke audience participation; they ask the viewer to create wonder for herself. It's easy with this video to line it up with different tracks, and I tested out several different pairings (Justice and Battles both work fairly well). What I found, though, is that I had been shifting the blame. It wasn't the audio, synchronous or otherwise, that produced the sense of wonder I experienced; it was clever pedagogy and the facts of the matter. 

Image credit: Bruce & Katharine Cornwell Journey to the center of a Triangle 

And while geometry as a general concept doesn't elicit much more than apathy from me nowadays (my ninth grade geometry class was an exercise in apathy and frustration) the specifics of it can be shocking. The underlying video, Journey to the center of a Triangle by Bruce & Katharine Cornwell, is more than just some visuals behind a soundtrack; it confounds our perception of reality. It shows that there are four distinct centers to any given triangle--the majority of which different than common sense would lead us to believe. As the video progresses through the different centers, performing each on different triangles, it deepens the world; it reveals an understanding of the world, perceptual truths about the world, that in the day-to-day are unthought. There is something deeply satisfying about the fundamental multiplicities espoused here. 

Image credit: Protious at en.wikipedia

More than simply presenting the facts of the matter, though, this video, true to its name, takes us on a journey. It begins by moving through the expected center of triangles. The centers are telegraphed to the viewer through the lines and circles it uses to find them. Throughout each method the viewer is able to see how, exactly the center is found, and the methodical pace gives him or her time to project a particular center ahead of any reveal. These projected expectations, though, are continually subverted, and it's that subversion that creates a lasting sense of wonder. While this could result in frustration there are so many triangles and examples that by the end of any given method we can catch up so that finally we project correctly and understand where and why a center appears. The video, in some ways, follows the example of Socrates and Meno's slave. The reader and slave both (well, in my experience) make the same common sense mistake while trying to find twice the area of a square. When Socrates then points out the error made and proper method we're both able to perform and understand the world in a new way.