The most fun you can have on the Internet is to find a beautiful, succinct argument with a conclusion so unexpected it seems like magic. For today’s fun, I am indebted to Michael Lugo, at God Plays Dice.
Lugo’s original post is so good it seems almost superflous to paraphrase it, but I can’t resist the temptation.
Drill a tunnel through the earth, from anywhere to anywhere — New York to Maine, or New York to Australia, or wherever else you like. Like so:
Now drop the object of your choice (Lugo suggests a burrito, but you might prefer a gravity-driven train) into the tunnel entrance and wait till it comes out the other side. It’s a standard calculus problem to calculate how long you’ll have to wait: The answer is 42 minutes, regardless of the length of the tunnel. I’m sure I once found it surprising that the tunnel length doesn’t matter, but I’ve known it long enough that I now take it in stride. So that’s not how Lugo surprised me.
The surprise is that if you change the size of the earth (while maintaining its density), the answer is still 42 minutes. Whether the earth is the size of a pea or the size of the solar system, it’s a 42 minute trip from one end of the tunnel to the other. (We’re — quite reasonably — ignoring the effects of relativity here. For an earth that was half the size of the universe, we’d have to make some corrections.)
Why so? You could, of course, discover this through a direct calculation. But Lugo provides a much slicker argument, namely:
Continue reading ‘Tunnel Vision’
Today I want to tell you about the single most counterintuitive-but-true thing I’ve ever heard.
Suppose you’re observing something that changes over time — say the Dow Jones average, or the temperature in Barrow, Alaska, or the number of people who have been shot by terrorists so far this year. Suppose you have absolutely no prior information about how this thing behaves — in particular, you might have no way of knowing whether it changes continuously (like the temperature) or whether it’s subject to sudden changes (like the number of terrorist victims). You have no formula for it; you don’t even know whether there is a formula. It could be absolutely anything.
Continue reading ‘The Most Counterintuitive Theorem EVER’
If you haven’t seen this, you should see it. You don’t need to know or care much about baseball to be delighted. It’s the bottom of the eighth, tie score, bases loaded.
Click here to comment or read others’ comments.
Two Russian girls arrive in DC as part of a travel exchange program for which they’ve paid about $3000. The program promises them jobs on arrival but fails to deliver. Instead, they are instructed to travel to New York City to do “hostess work” in a place called the Lux Lounge. Their American friend, currently in Wyoming, pleads with them not to go, but after some initial hesitation they board a Greyhound bus to New York, insisting that everything is fine.
Where can the panicked friend turn? To the Internet, of course. He posts a plea for help. Commenters jump into action, contacting police and social service agencies, pooling information to figure out what bus the girls are likely to be on, and arranging to have them escorted to a police station. A couple of hundred comments later, the girls are safe and sound. One commenter adds:
This is the best use of the Internet that I, personally, have ever seen. I’m so proud to be a member of this community.
Indeed.
Click here to comment or read others’ comments.
Like everyone else I know, I am of course a longtime fan of the webcomic XKCD. But somehow it took me until last week to become aware of the frequently brilliant competitor Luke Surl, of which the above is a delectable example. What else out there am I missing?
Hat tip to Harry Brighouse of Crooked Timber.
Click here to comment or read others’ comments.
Between The Folds is a striking documentary about the art and science of origami. I’ve watched an advance copy, provided by the producers, and it’s really quite mesmerizing. Roughly half the program is devoted to artists like Satoshi Kamiya, who folded this extraordinary dragon, according to the rules of origami, from a single piece of paper with no cuts. In the second half, we meet mathematicians and scientists like Robert Lang,
pictured here in front of the folding lens he designed for the Hubbell Space Telescope—folded, it fits inside a small rocket ship for delivery to its destination in space, where it unfolds automatically—and Erik Demaine, the paperfolding enthusiast and Macarthur “genius” award winner who is applying origami to the design of synthetic proteins that fold reliably into the proper configurations.
“Between the Folds” has its national television debut tomorrow night (Tuesday, December 8 on PBS; check your local listings for the time). Or check here for additional showings.
