xkcd

What’s the world’s center of population?

The center of population for a region is, roughly, the center of mass of the inhabitants. The Census bureau defines the center of population of the US (currently in Missouri) as

the point at which an imaginary, flat, weightless, and rigid map of the United States would balance perfectly if weights of identical value were placed on it so that each weight represented the location of one person on the date of the census.

This definition breaks down for populations on curved surfaces. For the earth as a whole, the center of mass obviously falls deep inside the planet.

This problem is easy to fix. I figure a better definition would be the point at which the sum of straight-line surface distances to each person is minimized. This is equivalent to the standard definition for a flat region, but it has the advantage that you can use it to define the center of population for a sphere.

I’ve never seen anyone who’s calculated the earth’s center of population so defined, but it doesn’t seem like it would be hard. Does anyone have the answer?

Bonus: find the center of population for other groups. What is the center of population of native English speakers? internet users? … bloggers?

Edit: I was standing the shower just now when I realized that the generalization I was using had to be wrong. I got it from this page on Wolfram Mathworld,

The centroid of point masses also gives the location at which a school should be built in order to minimize the distance travelled by children from cities, located at the positions of the masses, and with equal to the number of students from city (Steinhaus 1999, pp. 113-116).

and did try to check out the citation while writing, but it was to a book and I was much too lazy for that. However, I think the Wolfram paraphrasing is wrong — it’s not the distances that are minimized; it must be some other quantity. You can see that this is wrong for center-of-mass of two people at A and one person at B. It’s probably sums of squares that are minimized (as suggested in a comment, and which works for the three-person example) but I don’t see an obvious proof of this.

I was cleaning my room when I found this list in a pile of papers:

It’s my handwriting from the last couple years, and it looks faintly familiar, but for the life of me I have no idea what it means or why I wrote it.

… can anyone help figure this one out?

A number of people have asked me about building the robot sketched in yesterday’s strip. You’re definitely welcome to, and I’d love to see the results.

There are a couple engineering details that might trip you up. Rotating the webcam is one of them — I don’t make this explicit, but the idea in the blueprint was that there would be a servo inside the robot rotating the retaining magnets, which could be powered off the main battery. In practice, it might be better to put the servo on the outside and power it off the webcam battery — or, if you can find one cheap, simply use an omnidirectional camera.

The reason this is necessary is that I don’t think the internal robot, which is holding the webcam, will spin easily on hard surfaces. This is also the reason the robot uses Mechanum wheels instead of a simpler and cheaper design with a powered wheel on each side and castors or bearings on the front and back. If anyone has any ideas for making the robot spin more easily, I’d love to see them. Or perhaps you can try building the simpler design and see how quickly and reliably it can turn. If it works, it eliminates about half the cost of the project.

If anyone sends in any interesting material on this, I’ll be happy to put it up on a wiki somewhere so other people can tweak the design and develop a how-to. As far as I know, no one has built a robot quite like the one in the comic, so it’d be a great project.

Possible additional feature: cover the robot with little flaps or ridges, add some tweaks to protect the camera, and it becomes amphibious.

Edit: I’ve covered a few additional questions, including why the camera isn’t inside the ball, in this comment.

Quick, name a few recent popular movies where the two top-billed stars are female.

Here’s a miscellaneous survey I just did, tallied by gender of top billed/second billed star:

There were about 110 movies with a male lead and 5 with a female lead. Of the second-billed females, nearly all are written as love interests of the first-billed man. There were over sixty movies in the sample with two male stars top-billed. The only movies with two top-billed female roles, on the other hand, were The Devil Wears Prada and Scary Movie 4.

My cousin has been working on tallying (by hand!) all movies with two top-billed female stars. She reports that there are staggeringly few of them, and the roles fall mainly in two genres: mother-daughter bonding movies and horror films.  Hollywood is not creating female heroes.

Suppose we had a generic Michael Bay/Jerry Bruckheimer movie with some evil organization (say, a shadow government headed by Dick Cheney or whatever) bent on destroying something (say, the internet). Who would you rather see battling their way through the system to stop them — another basic Bruce Willis/Denzel Washington/Vin Diesel character? Or River Tam, Sarah Connor, Lola from Run Lola Run, or Beatrix Kiddo? Not only could the film industry suck less in the examples it sets, we could have some awesome movies.

Notes: If anyone wants to expand my list into a more comprehensive and authoritative survey, I’d love to see the results. I did my tally by hand, using The Numbers for the basic lists and stars, plus IMDb and Wikipedia to get a consensus on billing order.

Happy pi day, everyone!

My skateboard was broken for the past five or six months, and rather than get it repaired, I traded it in for a new, more powerful model. For a cost of about $120, I now have a board that can go zero to 20 mph in four seconds. This is a pretty alarming speed and has finally gotten me to buy a helmet, but it also means I’m one step closer to becoming a Kourier. I just need to talk to Neal Stephenson about some engineering issues with those radial-spoke wheels …

For anyone interested in buying a board, I recommend going to eBay and looking for a cheap used one to try the idea out. My first board, a vaguely toy-like e-skateboard ($31 on eBay in 2004) had an 80-watt motor (still surprisingly powerful — it managed to tow four people at one point). I bought a few other cheap used ones, and then, having decided these things were indeed awesome, I decided to spend some more money on a proper board for getting around the city. I got a 250-watt Exkate Raptor 3.0 for $320, which I talked about in an earlier post.

This new board, a Pro Module 600, is also made by Exkate (now Altered Electric Skateboards):

The old 250-watt board was still not quite powerful enough to climb Somerville hills without complaint (I’m at the upper end of the 170-lb weight limit), but this new one has a 600-watt motor, which handles them no problem.

According to Science, 600 watts is about 80% of a horsepower.

This suggests that if you found a smallish horse (say, 75% the strength of a standard one), and started a tug-of-war using this new board, you could actually win.

This is of course dependent on friction and when the board can actually supply maximum power and so on. But let’s pretend it would work.

Edit: Taylor of Exkate posted with some technical info, and I answered some other questions in the comments. He mentions that if you want to order a board, call him (949.951.9500) and mention xkcd for free shipping (which can be significant). Disclaimer: They aren’t paying/giving me anything, they didn’t ask me to write this, etc. If you’re interested but don’t want to spend a lot yet, I recommend trawling eBay for a cheap board to try the idea out.

I posted a while back about a ball pit I’d installed in my room. Everything in that post was true, but the pictures were a little misleading.

Looking at that, you don’t necessarily realize how cramped those people are. I framed the pictures to make it look larger than it actually was (THAT’S WHAT SHE SAID). In fact, the ball pit was only about the size of a large bathtub or small jacuzzi. In the pictures on the site, it was barely deep enough to be buried in, and when we shrunk the area to make it deeper, it was barely big enough for two people.

When people came in and saw it, they were always startled at how small it was (also what she said). There was no room for hide and seek, and barely even space for surreptitious ball-pit groping. This was a terrible state of affairs. It was nice to sit in, but really, why bother having a ball pit if we were gonna do such a half-assed job of it?

Well, as of this week, the situation has been rectified.

We all chipped in and quintupled the volume of the ball pit. It’s now set up opposite a hacked-together server-projector system (yes, that means Guitar Hero in the ball pit — that’s a controller you see on the left). It’s lined with blankets and foam padding, and is oh so comfortable. We’ve had two people fall asleep in it already.

For sanitary reasons, we of course have a few rules:

It’s still only half the size of the recently-constructed Last.fm ballpit. But it’s finally big enough to really hide in, stretch out, and grab someone’s ass without them being sure who did it.

On the other hand, it has the slightly unnerving effect that we now have no idea how many people are in the apartment at any given time.

For science, the next experiment will be “what do cats think of ball pits?”

A big thanks to khmer for putting together the piano arrangement in today’s comic.

Thanks also to the readers who tried playing it. I hope you didn’t realize what it was until too late.

Holy crap. This strip’s been up for 800 seconds and it’s already the most controversial thing I’ve ever written, beating out comics about cunnilingus, the Obama endorsement, and my making 4chan tiny on the map of the internet. It turns out everyone and their mother has a fruit opinion, and every one of those opinions is now in my inbox.

Just remember to keep some perspective. If you think watermelon is delicious, and I think it’s only so-so, the important thing is that we each find something we like. Who’s to say whose taste is right?

I am. You are wrong; watermelon is overrated.

Also, I have never liked cantaloupe. It brings down otherwise tasty fruit salads. There, I said it.

Solar sails suck.

In a 2002 paper, Laser Elevator: Momentum Transfer Using an Optical Resonator (available at your local school/library, possibly electronically — J. of Spacecraft and Rockets 2002), Thomas R. Meyer et. al. talk about a neat way to get a lot more speed out of light reflection than with a regular solar sail. The basic physics are pretty simple, and it’s a fun subject to think about.

When a photon hits a solar sail, it gives the sail momentum. If the photon has momentum P and bounces off a stationary sail, it looks like this:

Think of where the energy is in this system. Before it hits, the photon has energy E. After it bounces, the photon still has roughly energy E. But the sail’s moving, so where did it get its kinetic energy? (Remember, energy — unlike momentum — has no direction.)

The answer lies in the word “roughly”. The photon loses a tiny fraction of its energy to Doppler shifting when it’s reflected, but only a tiny fraction. It is this tiny fraction that goes into pushing the sail. This is a phenomenally small amount of energy — far less than a percent of what the photon has. That is, not much of the photon’s energy is being used for motion here.

This is why solar sails are so slow. It’s not that light doesn’t have that much energy, it’s that it has so little momentum. If you set a squirrel on a solar sail and shone a laser on the underside, do you know how much power would be required to lift the squirrel? About 1.21 gigawatts.

This is awful. If we were lifting the squirrel with a motor, railgun, or electric catapult, with 1.21 gigawatts we could send it screaming upward at ridiculous speeds.

This is where Meyer and friends come in. They’ve point out a novel way to extract momentum from the photon: bounce it back and forth between the sail and a large mirror (on a planet or moon, perhaps).

With each bounce, the photon loses a little more energy and adds another 2P to the sail’s momentum. The photon can keep this up for thousands of bounces — in their paper, Meyer et. al. found that with reasonable assumptions about available materials and a lot of precision, you could extract 1,000 times the momentum from a photon before diffraction and Dopper shifts killed you. This means you only need 1/1,000th the energy to levitate the squirrel — a mere megawatt.

This isn’t too practical for interstellar travel. It requires something to push off from, and probably couldn’t get you up to the necessary speeds. It may, they suggest, be useful for getting stuff to Pluto and back, since (somewhat like a space elevator) it lets you generate the power any old way you want (a ground nuclear station, solar, etc). But more importantly, it’s kind of neat — it helped me realize some things about photon momentum that I hadn’t quite gotten before. It’s like Feynman says, physics is like sex — it may give practical results, but that’s not why we do it.

Now we’ll let things get sillier. I spent a while trying to brainstorm how to use this with a solar sail (that is, using the sun). I imagined mirrors catching the sun’s light and letting it resonate with a sail.

But you really need lasers for this — regular light spreads out too fast. Maybe a set of lasing cavities orbiting the sun …

Supplemented by a Dyson sphere …

And since by this point we’ll probably have found aliens …

Why settle for interstellar communication when you can have interstellar war? And we could modulate the beam to carry a message — in this case, “FUCK YOU GUYS!”

Space has been a little disappointing for the last few decades. Since the moon, everything has turned out kind of barren. Every SETI-related result of the past 30 years has been disheartening — “there was once water on Mars” doesn’t really do it for me. There are two big exceptions. One is Jupiter and Saturn’s moons, which are still cool and could do with more checking out.

The other is the search for other solar systems. Starting in 1995, we’ve been finding craploads of planets around every star we look at. The better we build our telescopes, the more planets we see. It seems more and more likely that a lot of stars have solar systems like ours. And if Mars could’ve had water, and we have water, water probably isn’t uncommon. Things are looking up for life in the universe, even if they’re looking down for our neighborhood.

I think we haven’t made contact with aliens by radio yet because we’re looking in a very limited set of places, not because they’re not there. I think it’s more likely that ET is using tight-beam lasers to communicate between star systems; it’s silly to expect them to dump powerful uncompressed signals toward us on the few frequencies we’re searching at the times we happen to look toward them. I think it’s very likely that there’s a lot of life out there; we’ve barely started searching.

In the next decade or so, we’re gonna get a lot better at seeing other solar systems. We’ll be getting new planet-finding telescopes built — there’s immediate-future stuff like Kepler, and there’s also the possibility of giant optical arrays in orbit or on the moon that can directly image earth-like planets around other stars. The data will start pouring in soon, and space will be exciting once more.

All that said, most applications of the Drake Equation are pretty shoddy. You can’t extrapolate from one damn data point no matter how much you want to. But this isn’t really Dr. Drake’s fault. He’s doing the best he can.

Edit: Regarding today’s comic: Dr. Drake’s first name is Frank, not Francis. He is an astrophysicist, not a 16th-century British Vice-Admiral. Thank you to the several readers who wrote in to correct me — I had always thought Francis Drake was just one long-lived and supremely-accomplished person.