Category: Online Dating

Music To My Ears, and Eyes

Kyle

I’m telling you, Julie Rehmeyer is fast becoming one of my favorite science writers. Her Science News Math Trek piece this week follows up on a paper by music theorist Dmitri Tymoczko that represents musical chords in hyperdimensional geometries. Even cooler than Rehmeyer’s very accessible written description of the work, though, are the accompanying videos (1 2). It turns out that Tymoczko’s techniques explain some of what goes on harmonically in Chopin’s E-minor prelude, and the videos capture the effect beautifully.

Still, I was initially skeptical about Tymoczko’s ideas in the last graph:

What’s particularly amazing, Tymoczko says, is that the mathematics needed to describe these spaces wasn’t even developed in Chopin’s time. Nevertheless, he says, “it is unquestionable that he had some cognitive representation of the space. So there was this period of history where the only way Chopin could express this abstract knowledge was through music. His knowledge of four-dimensional geometry was most efficiently expressed through piano pieces.”

I’m not sure I share Tymoczko’s certainty that Chopin knew anything about what we would call four-dimensional geometry, abstractly or otherwise. But the more I watch these videos, the less I doubt that he “had some cognitive representation” of some idea that Tymoczko’s merely learning another way of exploring. I doubt he’ll be able to fully grasp whatever that idea is any more meaningfully than Chopin could, but it’s hard to fault either for trying, and in the meantime we all get to bask in the beauty.

Sorry to get all heavy on you. I think today’s Daily Office reading sort of puts you in the mindset to want to ponder these things: “For now we see in a mirror, dimly, but then we will see face to face. Now I know only in part; then I will know fully, even as I have been fully known.”

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I’ve been warned by a psychologist friend about the strength of the science in some of these fMRI studies, but I nonetheless thought this piece was also interesting. Douglas Adams would be pumped about the music & math/science vibes in this week’s Science News coverage.

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Congrats to the Badgers for clinching sole possession of the Big Ten Championship today at Northwestern. Speaking of Northwestern, I stumbled across this post from a Northwestern student giving online dating a go. Good writer, interesting stuff.

Go With The (Nework) Flow, Part I

Kyle

Some preliminaries:

(1) I couldn’t resist posting a link to this New York Times piece about eHarmony, et al. The “Algorithms of Love” in the headline alone made it worth it. (By the way, I love it when copy editors choose to force “EHarmony” and the like when these ridiculously capitalized words come up at the beginning of a sentence. It’s like a little “screw you and your trademark” from the folks for whom sloppy capitalization is almost an affront. Speaking of which, sorry for the up-style headlines on this blog. I abhor up style, but I somehow backed myself into this corner and am not about to back down now.)

(2) My friend Rachel just let me know that you can hear David Foster Wallace reading “The View from Mrs. Thompson’s” from Consider the Lobster on “KCET Podcast: Hammer Conversations” (Episode 16), which is available on iTunes. I listened to it this evening, and it’s terrific. Copy snobs will love the little explanation about his use of em dashes, but anyone will almost certainly be moved by the story. Plus Wallace’s reading voice matches his “authorial voice” really well, in my opinion.

OK, on to the main event. I mentioned a couple posts ago that I hope to use this space as a sort of whiteboard for trying out ideas, and I’m expecting to need such a space in the coming weeks. I’m getting ready to start working on the algorithms for matching material offers and requests in GENIUS and as such am learning about solving network flows problems. Wanna learn a little bit about them with me? If so, read on.

We’ll start with the basic first lesson, which I sat through just the other day. The gist of flow networks is that you’ve got a collection of nodes with material traveling between them along directed connections called arcs. Nodes are either sources (supply nodes that create material), sinks (demand nodes that consume material), or transshipment nodes that simply send a material along.

What we try to solve for in these problems is an optimal flow vector, which is just a fancy name for a long list that says how much of the material flows along each arc. The vector is optimal in the sense that it represents the flow for which the problem constraints are met in the cheapest way possible (there’s a cost associated with moving a unit of material along each arc). The problem constraints are flow bounds (upper and lower limits on how much flow must move along an arc) and conservation of flow, which says that the outflow minus the inflow at each node must equal either zero (for transshipment nodes) or the supply or demand of the node (for sources and sinks, respectively). The second set of constraints are also called divergence equations.

Brief mathematical note for those who are interested: network flow problems are special cases of linear programs, albeit much easier to solve ones (via the network simplex method, rather than general linear programming’s modifier-less simplex method). There are also, apparently, special algorithms for solving various special-case problems that can be posed as network flow problems, including Euler’s famous Konigsberg Bridge Problem.

What does all this have to do with the nuclear fuel cycle? Stay tuned as I try to figure that out.