Wow, I have been slacking in the posts department -- but I swear it's because I've been busy doing productive things, and not slacking in other departments, too! (OK, maybe a liiiiitttle bit of slacking, but Netflix has so many movies and TV shows to choose from!) But since today is a SNOOOOOW DAAAAAY(!), it seems like a good time to start getting caught up! I've actually got a handful of things to post about, but they are all reasonably distinct enough to warrant separate posts, so for that reason (and not at all in the interest of slightly inflating my post-count), I'll do it that way.
First up...
The Joint Math Meetings, 2014: The Joint Math Meetings were held in Baltimore this winter! I'd never been (they were always in the middle of UMCP's January qualifying exams, which seems like a bit of an oversight on UMCP's part, hint-hint ;-) ), so since I'm done with all that this year, and the meetings were right in my neighborhood, I was excited to go! And rightly so -- they were awesome. There are sessions -- not just talks, but entire sessions -- dedicated to the intersection of math and pretty much every other discipline you could imagine. I went to some great talks and sessions ranging from the esoterically theoretical, to the athletically statistical, the biometrically applicable, and thoughts on teaching in and out of the classroom. But, this being predominantly an art blog, I'll focus on one of my favorites: The Intersection of Math and the Arts. There were the usual suspects: the golden ratio in the arts, various topological/geometrical concepts translated directly to patterns and design (think M.C. Escher). There was even a collection of various knitted forms, including tori, Möbius strips, and Klein bottles, among other crazy things. And while I just happen to have those links handy, there was plenty of other cool work at the Juried Mathematical Fiber Arts Exhibit. But I digress (slightly). There were two talks, in particular, that really stuck with me:
It Came from the Fourth Dimension!: Visualizing Higher Dimensions through the Art of Comic Books, by Daniel Look: Anyone ever read Flatland? It's OK if you haven't (confession: I haven't either :-/ ). But I know the gist (at least enough to satisfy the needs of this post): imagine a bunch of polygons, points, lines, and whatever other 2-or-smaller-D beings you like, all living in an infinitely long/wide piece of paper with infinitesimally small thickness. And this 2D world is all they have the capacity to know. What would it look like to them if they encountered a 3D object passing through their world? Say, if you stuck your finger through their infinite-piece-of-paper? All they know is their 2D world -- they can't "look up," and see your finger coming. All they see is a point that suddenly appears, that slowly grows in to a line, and maybe shrinks back down to a point and disappears as you pull your finger out. That's all you can see from inside this 2D world!
Now imagine the analogue for a 4D creature entering our 3D world. Would it look like a point that just suddenly appeared, and grew into a face, or a hand, or a blob, right before your eyes, and then shrank down and disappeared just as quickly? What about having the ability to come and go as it pleased from a locked, sealed room -- much like how in the 2D world, you could stick your finger through the page outside of a circle, then take your finger out, and put it back in through the circle, all without ever breaking or even touching the circle itself? Well, this talk gave a look at how two different comic book artists decided to interpret and express this mathematical concept, using storylines with an "It Came From the Fourth Dimension!"-style villain to explore!
Movie Magic: The Mathematics Behind Hollywood's Visual Effects, by Eitan Grinspun: This was a great talk, all about some of the technical aspects of animating movies like Frozen, Brave, and Tangled, and even the CGI effects in movies like The Hobbit. How do they get the hair to bounce, and flow, and stick out all funny when they need it to? How do they get the smoke to look so realistic? Comforting for a campfire? Menacing in an explosion? What about snow falling, piling, and otherwise being flung around? Well, it turns out that there is some pretty extensive math and physics going on under the hood to model all this stuff!
Need to figure out how to get a dress to flow and whip around while the princess is dancing? How about the dress and the slip, doing so in concert? And without the slip doing something crazy like "slipping" (seewhatididthere?) through the dress here and there, all willy-nilly? You've probably seen some similar mistakes in video games, where some object concealed by another just happens to flicker into existence at times and places it shouldn't. Anyway, the slip is the inner layer, the dress is the outer layer, and it needs to stay that way even during the most spirited of dancing (I mean, these are family-friendly movies, after all, right?!)! Well, it turns out that there's a nice technical concept at work there, too, called collision detection, that models how the slip and dress might interact in motion!
And, while I'm certainly no expert, it turns out that all sorts of famous equations model our physical world, from simple motion to incredibly complicated fluid dynamics. And since physics and math go hand in hand, and math and computation do, too, it's only natural to bring computers onto the scene to crunch these numbers and simulate the physical world. And this kind of physical, mathematical, and computational modeling is pervasive in animating a fictional universe, and absolutely essential to bringing to life all the fabulous, realistic, and lovable characters and stories you see on the silver screen!
Recap: Whew! That was a long one! Like I said, there were a ton of great talks, and I'm sorry I couldn't talk about them all -- but as the title of this post says, I'm a busy boy! I hope you enjoyed the two talks I did write about as much as I enjoyed listening to them.
Stay tuned! More posts to follow, including my latest academic endeavors, and my very first professional photo shoot!
