Category: Mathematics

Fun with Wikipedia Networks

Kyle 1 Comment

So the mouse-over text of today’s xkcd (“Wikipedia trivia: if you take any article, click on the first link in the article text not in parentheses or italics, and then repeat, you will eventually end up at ‘Philosophy.'”) has inspired a little playful procrastination. I’d love to put together one of those fun xkcd-style info graphics (the ones with results of interesting little Internet experiments, e.g. “Numbers,” “Regrets,” “Dangers,” etc.) with the results of some collective poking around. Data so far (from myself, Katy “Southside” Huff, Matt Waldron, and Eric “Wolfman” Howell):

“xkcd”: 19 clicks
“Kadevu”: 21 clicks
“Walker Percy”: 27 clicks
“Kevin Bacon”: 13 clicks
“Wisconsin Badgers”: 27 clicks

Also, can someone who knows more about graph theory than I do give us some vocabulary to flesh out the kinds of data we can gather (or wish we could gather)? For instance, Matt Waldron asks via Twitter “I wonder what the longest non-loop answer is (i.e. was the furthest ‘point’ from Philosophy)?” His point about loops (graph theory: “cycles”) is an interesting one. Has anyone found a cycle yet? I thought I had one in the Percy chain, but it turns out there are separate articles for “Meaning (philosophy of language)” and “Meaning (linguistic).” (This is one of those moments where I wish I were a better programmer and could just start writing code to explore all these questions. I’d also need to not be on the clock with someone else’s money, which may actually be all that is stopping me.)

Anyway, if you’re looking for a few minutes off from whatever you doing (I myself am determined to finish my Walker Percy paper for the upcoming Christian Scholars Conference), please consider checking out a few articles’ paths to “Philosophy” and report back!

News Wire: (Mostly) Underwater Edition

Kyle

Three of the four science stories that caught my eye this morning take place under water:

“Case study: Making waves with new power generation technology” (Financial Times)
“What’s Making That Awful Racket? Surprisingly, It May Be Fish” (New York Times)
“Growing Pains for a Deep-See Home Built of Subway Cars” (New York Times)

Not content with those choices? The last story involves the Monty Hall problem applied to psychology experiment:

“And Behind Door No. 1, a Fatal Flaw” (New York Times)

The answer to the MHP is pretty neat, a great example of the kind of reasoning you can do when you’re willing to consider the counterintuitive.

(Full disclosure: the MHP, along with the Birthday problem and the Shake of the Day problem, have all been covered by what we might as well call the Society for Spontaneously Arguing About Math in Taverns. I originally got it wrong.)

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.

“The Proof” That I’m a Nerd

Kyle 1 Comment

Well, once again, one of my Saturday posts is just going to be me telling you about whatever Julie Rehmeyer’s written in the Science News “Math Trek” feature this week. This time around, it’s Sophie Germain. She’s a really interesting figure in the history of math (and especially the history of gender bias in STEM fields), so I encourage you to check out the story for that very good reason on its own merits.

That said, I felt particularly compelled to point this article out because one of the interviewees is a bit hard on Legendre, Germain’s supposed mentor. I spent the entire frustrating day Friday solving a neutron transport problem using a method that Legendre is in small part responsible for, albeit very indirectly (the P-N method expands the angular neutron flux in Legendre polynomials), so I couldn’t pass up the opportunity stick it to him in my pathetically insignificant way. (I wonder what portion of all blog content has that general M.O.? You gotta assume it’s a pretty decent chunk.)

Anyway, if you check out that article, you’ll see that it involves Germain’s efforts to tackle Fermat’s last theorem. And I can’t mention Fermat’s last theorem without pointing you toward my favorite episode of Nova: “The Proof.” Seriously, if you want to find out (or be reminded) that math can be full of drama and intrigue and heartache, please check it out.

Here’s a little taste. I admit that it doesn’t make thrilling reading, but I swear these guys are captivating when they tell the story. I don’t know who any of them are (well, except Wiles, and only because he proved the theorem), but it’s fascinating to watch people with such a depth of passion talk about their trade. Honestly, sometimes it’s even funny. You’ve gotta picture this as a series of talking heads interviews being cut in and out of:

JOHN COATES: The name of the lectures that he announced was simply “Elliptic Curves and Modular Forms.” There was no mention of Fermat’s last theorem.

KEN RIBET: Well, I was at this conference on L functions and elliptic curves, and it was kind of a standard conference and all of the people were there. Didn’t seem to be anything out of the ordinary, until people started telling me that they’d been hearing weird rumors about Andrew Wiles’s proposed series of lectures. I started talking to people and I got more and more precise information. I have no idea how it was spread.

PETER SARNAK: Not from me. Not from me.

JOHN CONWAY: Whenever any piece of mathematical news had been in the air, Peter would say, “Oh, that’s nothing. Wait until you hear the big news. There’s something big going to break.”

PETER SARNAK: Maybe some hints, yeah.

ANDREW WILES: People would ask me, leading up to my lectures, what exactly I was going to say. And I said, “Well, come to my lecture and see.”

KEN RIBET: It’s a very charged atmosphere. A lot of the major figures of arithmetical, algebraic geometry were there. Richard Taylor and John Coates. Barry Mazur.

BARRY MAZUR: Well, I’d never seen a lecture series in mathematics like that before. What was unique about those lectures were the glorious ideas, how many new ideas were presented, and the constancy of its dramatic build-up. It was suspenseful until the end.

This Algorithm Kills Fascists

Kyle

There’s a great art-meets-science article in this week’s Science News (it turns out their “Math Trek” feature is usually killer). Julie Rehmeyer does a nice bit of science writing here, giving just the right amount of detail about how Howarth and Short’s algorithms were used to restore the only known live recording of the great Woodie Guthrie. There’s even a short audio sample.