Archive for the 'Cool Stuff' Category
Johanna Bobrow is by day a biologist at MIT, often by night a musician (both solo and in groups), sometimes in between an aerialist, and always my friend. When I first saw this video, I told her it was awesomer than the most awesome awesomeness ever. I firmly stand by that judgment.
It’s said that Pythagoras had a man put to death for blabbing in a public bar that the square root of two is irrational. Today I hope I can post this without fear of reprisals. I don’t know who first drew this beautiful proof, which works equally well in modern English and in ancient Greek:
If you want to compute the circumference of the observable universe to within, say, the width of a human hair, you’ll need to know about 35 digits of π, though this never seems to deter a certain sort of person from memorizing the first 100, 200 or 500 digits. But it turns out there’s no need to memorize anything at all! You can recover any number of digits you like from a simple little physics experiment that I just learned about, though it was invented over ten years ago by Professor Gregory Galperin of Eastern Illinois University. His lovely little paper is here.
To see how it works, start with two identical billiards lined up in front of a wall like so:
Now push Ball 2 toward Ball 1 and count the collisions: First Ball 2 collides with Ball 1 and pushes it toward the wall. (At this point Ball 2 has transferred all its momentum to Ball 1 and stops moving). Then Ball 1 collides with the wall and bounces back toward Ball 2. Then Ball 1 collides with Ball 2 and pushes it off to a far-away place. Three collisions. That tells you that π starts with a 3.
If you want more accuracy, make Ball 2 exactly 100 times as heavy as Ball 1. This time the sequence of events is a little more complicated, but it turns out there are exactly 31 collisons. That tells you that π starts with 3.1.
Or if you prefer, make Ball 2 exactly 10,000 times as heavy as Ball 1. You’ll get exactly 314 collisions. π starts with 3.14.
In The Big Questions, I wrote about an absolutely wonderful toy I had as a child. The Digi-Comp I was a completely mechanical computer; it ran on springs and rubber bands, and you built it yourself from a kit. You programmed it by placing little plastic cylinders (cut from drinking straws) on appropriate tabs, and you pushed a lever to run the program. The back of the computer was completely exposed, so you could watch the cylinders and straws and rubber bands push each other around — and see for yourself how those motions implemented the logic of your program and produced a result. As I wrote in The Big Questions, a child with a Digi-Comp I is a child with deep insight into what makes a computer work.
I am delighted that the Digi-Comp I is, after a 40 year hiatus, back on the market, though the modern version substitutes laminated binders board (i.e. high quality cardboard) for plastic. There is, I think, no better gift for a kid who likes computers, or likes logic, or likes knowing how things work.
Now an old friend (who shares my fond memories of this toy) writes to point me to yet another reincarnation of the DigiComp I — as a Lego project! Way cool.
I realize that my posting frequency has fallen off over the past few weeks, and I hope things will be back to normal pretty soon. Meanwhile, to hold you over, here is something amazing:
What you’re seeing there are two flat-screen TVs being carted around by robots, all of them (the robots and the TVs) being driven by staggeringly brilliant software. Read more here.
If you’re the sort of person who reads this blog, there’s a good chance you’re already familiar with John Conway‘s Game of Life. In case you’re not, here’s the executive summary:
Start with an infinite checkerboard. Color some squares black and others white. From here on, the game plays itself. Any white square with exactly two or three white neighbors stays white. All other white squares turn black. Any black square with exactly three white neighbors turns white. All other black cells stay black. Repeat.
The goal is to choose an initial coloring that yields interesting behavior, like a snail that crawls across the page.
But here’s the coolest one ever — the Game of Life plays the Game of Life:
Proof positive that I am not the world’s best dad:
Just to be clear, that is not me in the video; it is somebody who is clearly a much better father than I ever was! Original YouTube version is here.
This is a reminder that I’ll be teaching at this year’s Cato University, where I and a distinguished cast of faculty will lecture on the political, historic, philosophical and economic foundations of liberty. There will also be ample opportunity for informal conversations with the faculty and, even better, with the other students, who I have learned from past experience are always bright and lively and fun.
Come join us, July 29 through August 3, at Cato’s newly expanded headquarters in DC. The insights you’ll gain, and the friends you’ll meet, will last a lifetime.
Suppose you go around taking extremely close-up black-and-white pictures of randomly chosen natural and unnatural objects (rocks, trees, streams, buildings, etc.). What do they look like?
Well, each one looks like a patch of varying shades of gray, of course. But do some patches arise more than others? If each of your close-ups is, say, three pixels by three pixels, Which would you expect to see more of:
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:
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.
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.
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.
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.