# Long-distance teleportation is hard, you guys.

I was not expecting this to be this hard.

The question is: Given only teleportation and no other superpowers, can you reliably travel transcontinental distances without instantly dying?

The reason it’s hard is that the point you start from and the point you end at are not stationary relative to each other. The Earth is rotating on its axis. It’s also revolving around the sun and whirling around the galaxy and for all I know it’s disco dancing through the cosmic microwave background, but the rest of those aren’t relevant.

Here’s why the earth’s rotation is a problem, helpfully explained in comic form:

Little did Calvin know that if he ever invented teleportation his life would depend on this very thing.

The point toward the middle of the record is a point toward one of the poles, closer to the axis of rotation. The point on the edge is a point on the equator, away from the axis. They’re moving at different speeds. Say you’re in San Antonio, and you teleport to Mexico City. Well, Mexico City is moving seventy-eight miles per hour faster than San Antonio. The nearest wall rushes you at 80mph from the west, and I don’t like your chances. And that’s two cities that are pretty close together.

But that’s with cities that are basically on the same line north to south. If they’re not, then it’s both more complicated and way more dangerous. Places at different latitudes are moving at different speeds, but places at different longitudes are moving different directions.

Suppose this diagram represents the earth, with us looking down on it from above the North Pole. (This is in fact exactly what it represents.) The earth rotates counterclockwise around its axis, which is helpfully labeled A. There’s nothing at point C; don’t bother going there. It’s spinning counterclockwise: If you’re at point D then your current movement is directly left.

Your speed is based on your latitude: at the equator it’s about 1080 miles per hour, where I am in Los Angeles it’s about 895, at the North or South Pole it’s zero. So if you’re at point D, you’re moving to the left very fast. If you then teleport to point B, you’re still moving to the left very fast. You smash into the earth instantly and die.

The obvious solution is to teleport to the point precisely ninety degrees east of you. For instance, from B to D on that diagram (Just pretend they’re ninety degrees apart.) Then the direction you’re currently traveling in is straight up. You go up, eventually gravity turns you around, and you come back down into the middle of the Atlantic. Bring a parachute and a life raft. Or, if you’re Indiana Jones, just a life raft.

This doesn’t work. Partly because the very fast speeds in question are in fact faster than the speed of sound. You’re not surviving that. More importantly, even if you do use that trick, it just cancels out the momentum you already had. It doesn’t get you moving in the direction Point D already is. Stopping only helps if you’re aiming for one of the poles; you need to match the speed and direction of your destination.

OK, next obvious solution (spoiler: this one doesn’t work either). You can try to get to the point 180 degrees across from you like this: Teleport 90º east, as before. You fly up. When gravity remembers to pull you back, you start falling. Note that, if you started at the bottom of the circle, you are now on the far right, and “falling” means falling left. At some point before you hit the ground, teleport straight up and keep falling. You speed up, gaining 22 miles per hour each second. (I’m starting to regret not using metric for this post.) Eventually you’re moving at the right speed. Since you’re already going in the right direction, you can now safely teleport to your destination. (This can get you to one of two points: The farthest point on Earth from where you started, or the point that corresponds to that one but on the other side of the equator.)

Except that it doesn’t work. It doesn’t work because of one of the most annoying things in the history of physics, air resistance. Human terminal velocity is around 120 mph, and you can’t get much faster than that while falling through air on earth. Depending on where you want to go, you might need to be moving several times that.

So you do it from higher up, outside Earth’s atmosphere. On the bright side, there’s no air. It won’t interfere with your attempts to speed up. On the less bright side, there’s no air. If you know enough to not hold your breath, you’ll survive with no permanent damage for up to ten uncomfortable seconds. But by fifteen you’ll lose consciousness, presumably lose your ability to teleport, and then die. So let’s keep it under ten seconds of vacuum exposure.

Unfortunately, this can’t work. Earth’s gravity can give you 22 miles per hour extra speed for each second you spend in freefall, but you only have ten seconds. Say you’re falling at 120 miles per hour the regular way, then get another 220 from doing that insanely dangerous thing for ten seconds. That’s still not fast enough. If you’re aiming for somewhere equatorial, you need to be able to reach 1080 mph.

The problem here is that Earth’s gravity can’t accelerate you enough. (And no, you don’t get to bring rockets with you.) So, it’s time for another obvious solution: Teleport to Jupiter! This involves some major headaches, because it turns out that your departure and destination cities are not actually in the same orbit as Jupiter. So now we actually do have to think about position relative to the sun as well as position relative to Earth’s axis.

The plan is the same as before: Teleport to a specific point above Jupiter. Spend up to ten seconds letting its gravity pull you toward the planet. This will never take more than ten seconds thanks to Jupiter’s gravity; exactly how long it takes depends on how close to Earth’s equator your destination is. Pick the point above the planet in such a way that the line from where you are toward Jupiter is the vector that will, in a few seconds, make your velocity match the velocity of your destination. Once you’re going at the right speed in the right direction, teleport to where you want to go. You’re travelling at insane speeds, your destination is travelling at insane speeds, and if you did the math right then you’ll match up perfectly.

We can’t always do this. Earth and Jupiter are moving at up to 100,000 mph relative to each other depending on the time of year, and it would really suck if you forgot about that and burned up in its atmosphere. In order to avoid complicated math, let’s say you only do it when Earth and Jupiter are moving along parallel lines. This happens about twenty-two times every twelve years.

With the two planets moving in the same direction, or in directly opposite directions, you just have to pick the time of day when that direction is the vector you want. (Or, once again, the exact opposite direction.) Then you teleport directly in front of or directly behind Jupiter, get the velocity to match your target city, and there you go. Because “teleport interplanetary distances instantaneously and use a gas giant’s gravity to change your velocity at 10g for a few seconds in hard vacuum before teleporting back to the planet you started from” is totally a reasonable thing.

# The Galactic Empire is bad at numbers

The evil lord Darth Vader, obsessed with finding young Skywalker, has dispatched thousands of remote probes into the far reaches of space….

This isn’t just unlikely to work, it’s so unlikely to work that it’s not even worth considering. Have you ever tried to find one person out of one hundred quadrillion? If so, did you even think about searching by brute force? “Nope, that’s not him. Next?” Those droids simply aren’t capable of finding Luke just from being on the same planet. Darth Vader could probably do it, thanks to magic, but those droids can’t.

Hoth has a surface area of about 160 million square kilometers, all of which is ice. That’s more space to search than the land area of Earth. The droid is probably smart enough to aim for the equator, since if people are on that planet they’re more likely to be where it’s only mind-bogglingly cold. Even so, it’ll have to search through an awful lot of nothing to find the Rebels. From what we see, it’s not equipped to travel across the world, and it didn’t know where the Rebel base was until after it landed. This isn’t Phineas and Ferb, so naturally, the movie-makers handwaved the problem by having the droid land within visual range of the very person it was looking for. Starting off with a coincidence of that magnitude is not a good sign. But that’s not even the biggest problem.

A galaxy has an awful lot of planets. According to here, there are probably billions of habitable planets in our galaxy. (And he shows that using simple math that even Star Wars writers could understand.) According to Wookiepedia, that galaxy has an awful lot of planets, of which about a billion are inhabited. That means that the odds of a probe droid even hitting the right planet are a literal one-in-a-billion shot.

But it’s even worse than that! They aimed probe droids at the uninhabited planets, too. We know that because Hoth was, as far as they knew, uninhabited. So they had to find one guy out of not one planet, not two planets, but one hundred and eighty billion planets. Obviously they got really lucky when the droid landed on a random point on the planet and just happened to be within visual range of the very person they were looking for, but that’s not even the biggest problem. The much bigger problem is that even if the droids could instantaneously search any planet they landed on, they’d have to get there first.

We could give the Empire the benefit of the doubt. After all, they’re a civilization capable of blowing the Olympian gods out of the water. Maybe they used enough droids to have a chance? Well, let’s check the numbers. Episode V takes place three years after the Battle of Yavin, so Vader has been looking for Skywalker for no more than three years. To land a droid on every planet, they’d need sixty billion droids per year. Maybe they can do that? I have no idea what the Empire’s manufacturing capabilities are like. Let’s find out.

A probe droid is 1.6 meters long, so one hundred and eighty billion of them in one place would cover 1.6^2*180*10^9=461 billion square meters. We’re talking enough area to cover Austria. Five times.

Put another way, if that number of probe droids were all flying in formation, it would take up a volume of 1.6^3*180^9=737 billion cubic meters. If they were arranged in a sphere for some reason, that sphere would be about 5.6 kilometers in diameter. That’s a lot of droid. Remember the asteroid Apophis? The one that had an unusually high chance of hitting Earth and got way more publicity than it deserved? It was .32 km across, about a fifth the diameter of this mass of probe droids. The Empire would have to have built this many in under three years. Can they do that?

Absolutely. Remember, these people rank high on the Kardashev scale. The second Death Star was 900 kilometers across. Four years after the destruction of the first, it was some significant fraction of the way completed. So in terms of sheer amount of mass manufactured, enough probe droids to send one to every planet in three years would not be a problem.

But they didn’t do that! They only sent thousands, not hundreds of billions. So their odds are back down to a couple chances in a million. If they have, say, 20,000 probe droids, then it’s one in nine million. It’s more likely than winning the lottery, but less likely than being dealt a royal flush in poker. They could have made enough droids to have an actual chance, but they didn’t. Clearly the problem is that Darth Vader isn’t obsessive enough. But he’ll get lucky anyway, because when movie makers get lazy, coincidences happen.

Never tell me the odds! —Darth Vader

# Why C-3PO is Secretly the Main Character of Star Wars

A long time ago (in internet time, not galactic time), someone challenged me to write this post. Past-me gave it up as impossible, so I’m doing it instead.

The first clue is in the fact that C-3PO keeps turning up around important people. This isn’t much of a clue; after all, diplomats and politicians are the ones who use protocol droids the most and it makes sense that the same droid would be passed around among those people. But it is important to note. It means that C-3PO knows more about what’s going on in the galaxy than nearly anyone else.

He is, after all, one of only four characters to appear in every movie. Nobody saw all the events depicted, and barely anyone was in a position to even find out about all of them. But it’s a safe bet that C-3PO is one of them. Talking to the people who just happened to be the witnesses to the plot of Star Wars is literally his job as a communicator, and nobody bothers to hold their tongue around the protocol droid. It’s like how nobody notices the mailman, except more so. But don’t just take my word for it; have an example. When Anakin and Padme were secretly married, who saw it? Nobody, not even C-3PO, said or implied it was unusual for him and R2-D2 to know highly volatile secrets.

The movie makers thought of this. They didn’t want to leave someone  around from the prequels who could tell Luke and the rest everything. So they inserted a line, “have the protocol droid memory-wiped.” We have no reason to think the order wasn’t carried out. But what’s missing is, they didn’t do the same to R2-D2. Maybe because he’s not shaped like a human so it doesn’t occur to them that he might know things. And who does C-3PO talk to more than anyone else? Clearly this is not an effective memory wipe.

Speaking of R2-D2, his continued presence is sort of surprising. Diplomats and senators might be likely to employ a protocol droid, but what possible use could they have for an astromech? It’d be like if a real-world dignitary hired a personal assistant and a full-time mechanic. Nevertheless, R2-D2 is always around wherever C-3PO is. The most likely explanation is that C-3PO is able to convince his employers to go slightly out of their way to use that particular droid. That’s not hugely significant, but it does require him to have more influence than he appeared to use in the movies (i.e., none).

So by the start of the original trilogy, the droids know what happened in the prequels. This is our first clue that there is definitely some plot going on. They could have simply told Luke or the Rebels about Darth Vader’s backstory. They could have at least informed Luke that they’ve seen the name Skywalker before. But they didn’t. They never once even say the word “Jedi” or let slip that they fought in the Clone Wars. This means that they are consciously, actively trying to keep a low profile even from the Rebels, even while they try to make sure they win. This also explains why C-3PO uses the voice he does. He has an artificial voice box; he could sound like James Earl Jones if he wanted to. He picks the least intimidating, most ignorable voice possible. Nobody notices the mailman, and they definitely don’t pay attention to a protocol droid.

And most importantly of all, C-3PO knew what would happen on Endor. There was no obvious reason for him to go there, but he never once asked “why am I going along.” A shiny and definitely not camouflaged protocol droid in the middle of a secret military operation? Something’s up. C-3PO as he was portraying himself to the Rebels would have liked nothing more than to not go to Endor, and it’s not like anyone would insist on it or even suggest it.

But when they got there, they found that someone had trained the Ewoks into a fighting force capable of interfering with stormtroopers. You didn’t think hunter-gatherers could do that on their own, did you? That’d take someone like a Clone War veteran or two. It couldn’t have been a member of the Alliance; they didn’t even know the Ewoks existed. But they have somehow set up an effective resistance. Some of the traps the Ewoks used were useful only against AT-STs, meaning they were built and invented recently. (The thing with all the logs rolling down the mountainside could knock over anything big, but the two tree trunks swinging down simultaneously would be useless against a predator or anything else capable of looking sideways.)

And what’s the first reaction of the Ewoks when they see C-3PO? They recognize him. What’s the alternative, that they start worshipping anything shiny? They must have seen plenty of Imperial machinery, but didn’t have that reaction then. And they didn’t react much to seeing R2-D2, which is also why we know it’s 3PO behind this particular plot and not R2. Well, that and the fact that R2-D2 doesn’t speak the language.

Also worth noting is that C-3PO tells Luke that it’s “against his programming to impersonate a deity.” This is an obvious lie. Luke had other things on his mind at the time, but the viewer has the time to notice that a droid’s programming is not analogous to ethics. If it were against 3PO’s programming, it wouldn’t be that he considered it wrong or unpleasant; it’d be impossible. He would no more be able to impersonate a deity than my calculator can tell me 2+3=6.

Finally, there is one detail hiding in plain sight throughout all of the original trilogy. Every time 3PO introduces himself, he calls himself “C-3PO, human cyborg relations.” As a droid built in a nine-year-old’s garage, he can only really be said to have one relation: Anakin Skywalker. And at the time of the original trilogy, Anakin Skywalker is indeed a human cyborg. C-3PO knew Darth Vader was Anakin Skywalker before George Lucas did. And now you can’t unsee it.

So obviously C-3PO is up to something involving both lying to the Rebels and saving their bacon. What is it? I wish I knew. One thing’s for certain, though. There’s a lot more to this droid than you see.