You will see a lot of guys hooah-ing and a lot of wreckage.

I’m not going to do a general review of “Battle: LA,” nor a general critique of the science. (I will leave the latter up to Ryan, and I’m sure if he does such a critique it will be a fantastic read.) I will say that I liked how the aliens basically use guns and jets/rockets instead of inexplicable hover-things and energy blasters, and I liked that the reason the aliens are unstoppable at first is not because of their tech but because our soldiers don’t understand how to fight them. (Of course, the usual video-game rules of technology apply: three bazillion M-16 rounds fired into an alien aren’t enough to kill it; but do one quick alien autopsy in the field and suddenly all our guns work with full effectiveness!)

It’s the premise of the movie I want to poke at. The whole reason the aliens are attacking Earth is to claim our resources. Sound familiar? In a brief glimpse of a TV news program, Professor Greybeard explains (scientists, get your cringes ready!):

The aliens must be attacking us for our resources. Specifically, our water. 70% of Earth’s surface is covered with water, and the chemical composition of our water is unique in the solar system: it is in liquid form.

(I paraphrased from what I could recall.)

This is both factually inaccurate and a ridiculous premise for an alien invasion, for three reasons:

1. The Earth’s water has exactly the same chemical composition as water anywhere else in the Solar System: two hydrogens stuck to an oxygen. And, in fact, water is one of the most common molecules in the Solar System – nay, universe!
2. The Earth is not the only place in the Solar System where liquid water exists: scientists are about as sure as scientists can be that there is liquid water under the crusts of Europa and Enceladus, and possibly Ganymede and Titan as well.
3. Water (liquid or ice) is available in many places throughout the Solar System, and as it turns out, the water on Earth’s surface is one of the hardest places to get at it, if your starting point is space.

Now, I will have to explain #3 a bit. My point relates to the depth of the Earth’s gravity well: in the words of xkcd, the reason “why it took a huge rocket to get to the Moon but only a small one to get back.” If aliens wanted to take our resources, presumably they want to do so because they need those resources for something. And since this alien civilization apparently makes a living moving from planet to planet (or star system to star system), they are going to have to move these resources or their products off of the planets they were harvested from. That means, for every kilogram of water the aliens pump out of Earth’s oceans, they need to produce spacecraft, rockets, and fuel to get the water up into space again. Think of how big the Space Shuttle is, and how much fuel we load it full of, just to get school-bus-sized Space Station modules into orbit. Contrast that with the tiny Lunar Module ascent rocket from the Apollo days.

Clearly, there must be a better way to get water off of planets. So, without further ado, the Quantum Rocketry Guide for Successful Star System Invasion and Resource Extraction for Nomadic Species:

———————————————————

Step One

When to implement: as your invasion force approaches the heliopause

Tools required: telescopes, spectrometers

Survey the target system. Identify (if any) the home world of all radio-capable species. Identify all (if any) interplanetary spacecraft and immediately dispatch combat drones to shadow, assess, and possibly destroy them. Important note: if there are more than a several dozen such spacecraft, be prepared to complete only the first two to three steps in this guide, as further exploitation may result in retaliatory attacks.

Separate the remaining target bodies in the stellar system into three categories:

1. Resource-rich small bodies. This class includes comets with large mass fractions of water ice and asteroids or moonlets with useful metal or mineral compositions.
2. Resource-rich mid-sized bodies. This class includes moons and small planets with metal- and mineral-rich crusts.
3. Resource-rich planets. This class includes Earth-sized or larger planets and gas giants which contain useful minerals and gases. The cut-off between class 2 and class 3 will depend on the surface escape velocities of the bodies and the capabilities of your species’ ascent engines.

Disregard the home planet(s) of any technological civilizations located. Keep those planets under surveillance, and be prepared to deploy additional combat drones. (Your combat drones use radio, which lets you control them over interplanetary distances, right? And you have some diversified vehicles with independent AI intelligence or actual crews, right? Remember, you don’t want to keep all your klat’thra eggs in the same xikot!)

Step Two

When to implement: as your invasion force nears the first class 1 targets, in the stellar system’s Oort Cloud, Kuiper Belt, or orbiting outer gas giants.

Tools required: cutting tools, robotic manipulators, small thrusters, and foundry ships

Begin direct, in-space processing of class 1 bodies. Use heat to cut comets up into manageable-size ice fragments and then spray-coat them with epoxy to prevent sublimation of any of the precious resource. Attach small thrusters to these fragments to propel them off of their parent comets and towards your cargo and refinery vessels. Use other cutting and manipulator tools to break metal asteroids down into useful chunks, and harvest stony asteroids for useful minerals. Attach small thrusters to these chunks, as well.

Begin processing of resources with foundry ships to produce additional foundries, combat drones, or scout ships as necessary.

As a contingency, attach larger engines to some of the unusable asteroids. If necessary, these can be used to bombard pesky indigenous species – or at least give them something to worry about – from a safe interplanetary distance. As complete extraction of resources from a star system may take up to several centuries, depending on your species’ level of robotics and self-manufacturing capability as well as your long-term goals and objectives, such bombardment may be periodically necessary to ensure the uninterrupted operation and safety of your equipment.

Step Three

When to implement: when your invasion force reaches class 2 targets, most likely a rocky outer planet (if any) or the moons of an outer system giant planet (if any).

Tools required: descent engines, accelerators, mining equipment, planetary rovers, robotic manipulators, and foundry ships

Establish mining outposts on all icy or rocky class 2 targets and commence strip-mining the target bodies. On layered bodies like Europa, mine the ice (as a mineral) uniformly across the planet so that the thermal gradient freezes liquid water further down, preventing any of the water from boiling off into space and freeing your operation from having to build lots of tanks to hold liquid materials. On bodies with resource-rich atmospheres or surface liquids, such as Titan, your facilities will require the equipment to condense and package usable gases and liquids.

Construct linear accelerators, rail guns, or light gas guns on the surface. Use these facilities to catapult packages of mined resources into orbit around the target body, where they can be conveniently processed by refinery ships or stored in cargo vessels.

Step Four

When to implement: when your invasion force reaches class 3 targets, such as Mars-like inner planets.

Tools required: descent engines, ascent engines with in-situ fuel-production capability, surface factory components, mining equipment, planetary rovers, robotic manipulators, and foundry ships

Class 3 targets are those resource-rich bodies that are too large for catapult launches to reach orbit. These targets will require many ascents to deliver their resources, and will only present a net gain for your operation if you utilize fewer of your current in-space assets than the resources your equipment can deliver to orbit. Thus, mining and planetary ascent equipment should be manufactured in-situ, leaving your operation’s in-space assets free to process class 1 and 2 targets.

Begin by landing surface factories, exploratory rovers, and mining devices that can manufacture duplicates of themselves along with planetary ascent vehicles. On gas giants, a similar methodology can be applied but with buoyant balloon-based facilities. With a modest initial drop from orbit, your operation will soon see orbital delivery of ascent vehicles filled with metals, minerals, gases, and liquids mined from the planet below. From orbit, your craft can direct the resource packages to refinery or cargo ships.

Naturally, the operation will not be able to extract 100% of a target planet’s resources, as some resources will be tied up in the construction of mining apparatus, ascent vehicles, and fuel. Yield may be below 20-30% depending on the capabilities of your civilization. For that reason, this guide strongly suggests that the home planets of any technological civilizations be ignored unless the resources available on those planets are sufficiently desirable to justify the possibility of facing armed resistance and the military expenditures that such resistance will necessitate. In such cases, this guide recommends utilizing targeted asteroid impacts to limit the military-industrial base of such civilizations before commencing any extraction operation.

Step Five

When to implement: upon reaching the desired level of resource extraction

Tools required: N/A

Congratulations! If you have reached Step Five, you have successfully completed a star system invasion and resource extraction. This guide now recommends using your species’ foundry ships to deconstruct all recoverable vehicles and equipment from your completed operation. You may now proceed to the next target star system, and with vastly expanded resource capabilities!

A note: Advanced resource-gathering possibilities exist if your species possesses the technologies to extract plasmas from, enclose a Dyson sphere around, or otherwise manipulate the target system’s central star. See supplement.

———————————————————

And now, I shall return to a more, um, human perspective. If some aliens tried to pull this one us, we would see – through our telescopes – robot refineries chewing up all the asteroids and comets in our Solar System; ice blocks being cut from Europa, Ganymede, Callisto, Enceladus, Titan, Rhea, Triton, Pluto, and other icy moons; and Mars and Mercury being strip-mined for metals. There’s very little about Earth’s resources that makes our planet really unique, and so the aliens wouldn’t bother with us. They wouldn’t need to. (Unless, of course, our governments got it together enough to recognize that our long-term future would be at stake and launched a crash military space program. Then the aliens would bother with us.) There would be very little that we could do, with our current capabilities; and when the aliens finish we would just see them leave.

I can, however, think of two reasons that might make the Earth worth invading to any species using the guidelines above. One is that the Earth is unique among all the bodies in the Solar System, so far as we know, in that it has plate tectonics. This constant churning and recycling of our crustal material might, conceivably, produce some kind of mineral resources that are only available on the Earth. That said, those resources would have to be pretty darned precious to get the aliens to try and launch an extraction campaign on the Earth – but if they went ahead with the operation, a bombardment from space would be the first order of business. I’m sorry to say it, but unless our near-Earth object detection gets way better, then not only will Earth be at risk from killer asteroids, but we simply won’t know what hit us in the unlikely event of alien invasion.

The second reason is more interesting: perhaps it is the Earth’s habitability (as defined by a species like us) that makes it desirable. Perhaps the aliens aren’t looking for resources – because they can have all the resources they want on worlds like asteroids and moons that are far easier to access – but maybe terraforming (extraterraforming?) presents some insurmountable barriers such that it is more efficient to seek out habitable planets in other star system and then fight for them. Incidentally, this is the premise behind the really excellent Old Man’s War books by John Scalzi. This scenario also might make the aliens less likely to pound us with rocks from orbit.

The guidelines for stellar system invasion I wrote above are based on two premises: first, a large technological disparity between the invasion force and the indigenous civilizations;  second, the goal of maximum resource extraction for minimal input effort. These premises lead me directly to an alien-invasion doctrine of quick victory by overwhelming force. However, since a lot of the challenge of moving things through space involves trying to reduce the mass of the things that are moving, it would make a lot of economic sense for the invasion force to build its vehicles and weapons on-site rather than carry them along everywhere. This is the flaw in the alien invasion plan: any non-trivial space defense force would represent a significant military investment by the marauders before they can begin extracting any benefit from the target system. Clearly, in order to defend the future of mankind against alien attacks, we must begin work on the Earth Defense Force as soon as feasible!

Blizzard isn’t alone in this, of course. For all its repetitive gameplay, Assassin’s Creed tried to be as much like playing inside a movie as it could (it’s only a matter of time until someone takes a similar engine to make the Bourne Identity video game, and that will be awesome). The Star Wars universe became an interactive movie with The Force Unleashed, especially on the Wii, which let players wave their hands through the air to control the Force (at least, in a rudimentary way). But besides the gameplay elements, The Force Unleashed is a great example for having production values right up there with movies – that game had some of the best concept art I’ve ever seen, the story was clearly thought out and compelling, and the acting was very well done. Speaking of acting, video games were once the realm of C-list voiceovers, but now we now have the likes of Martin Sheen voicing characters in Mass Effect 2 – which had a tremendous cinematic trailer, enough to make me wish for an XBox.

I really like this trend. It makes video games into – gasp – a reputable medium for storytelling. I don’t think this format will ever replace books or movies, but it can certainly come up right beside them as a way to tell an interesting tale, describe compelling characters, teach us something about human interactions, and make the audience think.

Oh – what prompted this sudden post, you ask? Easy:

Not only is this an insanely high-production-value cinematic trailer, but it is clearly investing the StarCraft II story with a great deal of emotional content. Yeah, sure, it’s emotional content I’ve seen in movies/books/TV before – what is important to my point here is that the last time we saw this stuff, in the original StarCraft, it was from a standard RTS top-down perspective with voiceovers on little moving head-and-shoulders portraits of Kerrigan and Raynor. Now we see it as if it’s got a film director behind it. And now all the gamers get immersed in not only the plot but the characters’ experiences and sensations. Exciting stuff for storytellers!

While I worried that you had caught Disneysequelitis with Toy Story 2, you even showed me that you could make a great sequel.

The Incredibles and Wall-E very quickly became some of my favorite movies. They’re both visually stunning with engrossing plotlines and characters that make me smile.

But this time, Pixar…this time I think you’re going to hit me too close to home!

“Avatar” changed my mind a little, in that many more of the scenes looked so damn cool in 3D. But the more I thought about it, the more I became convinced that while the 3D experience was pretty neat, if I go see “Avatar” any more it will be in 2D, because it really didn’t add that much to the movie. The forest creatures and sweeping panoramas will look just as good projected in 2D. The only aspects of that movie that would miss out are the holographic computer displays, and those aren’t really that important.

In fact, I think that Hollywood ought to just abandon this 3D movie kick. It’s not that I get a headache or think that cool things can’t possibly be done in 3D. It’s that even when filmmakers do the cool things, it adds so little to a movie that I’m definitely not inclined to shell out for a 50% surcharge on a ticket. Here’s why…

Here’s a terrible schematic cartoon of a person looking at an object located a distance x from their nose:

Geometry of a horrible disembodied cartoon face

When this person looks straight at the object, their eyes angle inwards from a direct line forward by ?. (I only drew one eye, because the situation is the same for the other.) Suppose that the object moves away from the person, on a direct line drawn from their nose, by a distance ?x. This reduces the angle ? by ??, as you can see in the picture. That angle, from each eye, is what your brain figures out distances from using your binocular vision. From this situation, I can write down the following two equations.

Then, with a little rearrangement of Eq (2) and plugging in Eq (1), I get this funky expression:

Here’s what this equation says: given the half-width of a person’s face r, the distance to the object x, and the minimum angular deflection of the eyeball the person can distinguish ??, the object must move a certain minimum distance away from their nose before they can distinguish that it moved. I expressed that distance as a fraction of the original distance x. For example, let’s say that r is 3 cm and ?? is 1° – meaning that this person’s brain cannot really tell if their eye moves by an angle of less than 1°. Then, if the object is x = 1 m away from their nose, ?x/x is about 1.4. This means that the person cannot tell if the object moves away from them, as long as it doesn’t move any more than 1.4 times away from them than its original distance. Alternatively, this means that the person can’t really tell the difference between an object 1 m away from them and one 1.4 m away.

Let’s keep r = 3 cm, and plot ?x/x for a couple sample values of ??.

Apparently, the better angular resolution your eye and brain have, the less a distant object has to move in order for you to tell that it’s moving. (For two eyes, you’re really figuring out the difference between the angle of each eye to gauge distance, but this is probably an okay approximation.) I have to admit that I don’t actually know what the average value of ?? is for a human, but I imagine that a fraction of a degree isn’t too far off.

Here’s the punchline of my plot. Even if you can distinguish a tenth of a degree of angular difference between the directions your eyes point, if an object is 15 meters away from you, with stereo vision along you won’t really be able to tell that a second object is farther away unless it’s seven times farther away. And the ?x/x curves asymptote at a finite value of x. (You might have been able to tell that as soon as you saw the presence of tangent in Eq. (3), but I like gleaning information from plots. What can I say, I’m an experimentalist! Ooh, I should do an experiment to figure out my ??!) This means that no matter how good your eyes are, there is some distance beyond which you can’t tell how far away things are. This really shouldn’t be that surprising – ever been to the Grand Canyon, scouted from the top of a mountain, or looked out of an airplane? What’s even more important is that this distance is not that far away from you. Even if you have really good binocular vision, this distance is probably less than about ten meters!

The truth is that our binocular vision is really not that effective at long range. It’s for close-in tasks that require manual dexterity. Try this experiment: close one eye – or, if you feel piratey, put on an eyepatch. Now try and see specifically what tasks you find difficult, choosing tasks at a range of distances from you. Can you tie your shoe? Make a sandwich? Thread a needle? How about lobbing a ball of paper into a wastebasket? Tossing a dart? Making a free throw? You will probably find that you fumble over your fingers when doing things close to your face, but when you’re looking farther away, your performance isn’t impacted that much.

For those tasks that require far-field attention, our brains don’t use binocular vision to figure out how far away objects are. Instead, we use a combination of other techniques: our brains interpret which objects in our field of view are in or out of focus, compare how much objects appear to move in perspective as we shift our point of view, or compare distant objects to the scale of objects that we know the size of.

What does all this boil down to for 3D movies? Well, unless all the action takes place within a few feet of your nose, a movie can look 3D just by using camera motion and focus. That will correlate completely with our everyday experience.

Small depth of field when everything is far away

The other problem with using stereo vision to make a 3D movie is that most movie action does not take place in scenes with large enough depth of field for the effect to really be apparent to us. “Depth of field” means, roughly, what’s the range of distances away from the viewer that the objects in the scene cover? That is, what’s the difference between the distance to the farthest object and the distance to the nearest object? In a panoramic landscape shot, all objects are far away. In an interior shot, all objects are close in. For a stereo vision 3D effect to be really noticeable to humans, you need distant objects and close objects – hence all the “ohmigosh that thing just popped out of the screen at me!” gimmicks that 3D movies try to pull – which is not usually a situation movie scenes present unless they were specifically arranged that way. Or, you have to hunt around in the scene specifically to find objects that are really close and really far away.

Small depth of field with all near objects

What made “Avatar” different was that they did manage to arrange many scenes with a large depth of field, without obvious gimmickry, in the process of showing off Pandora.

A wide range of depths for full depth of field

Even in “Avatar,” the 3D wasn’t always used to great effect. It looked best on the holographic consoles – because the hologram is in the near field and the human characters are clustered around it in the far field – and the flying-over-landscapes shots – because the flying vehicle or animal is in the near field and the landscape sweeps around us. But in the first shot of the movie, we see an extreme close-up of Jake Sully’s eye, viewed over the bridge of his nose, in 3D. The focus is on his eye. So we have a giant out-of-focus nose popping out of the screen. The focus alone is enough for our brains to determine the three-dimensional structure of the face! And if you try to focus on the fuzzy nose, you get conflicting inputs. (That’s why some people get motion-sick in 3D movies. Motion sickness comes when your senses disagree with each other or with your brain.)

The panoramic scenes in “Avatar” were spectacular, but many scenes were interior shots of the human base or deep within the forest. In these situations, the low depth of field issue arises. When I saw the movie, I so impressed with the vibrant colors and exobiology in the forest that I barely noticed any 3D effects. (Okay, the close-up of the da-Vinci-flying-machine-chameleon was awesome.) Many human-base-interior shots were from the perspective of Sully’s video blog, so again, pretty small depth of field with Sully’s face in the foreground and the back wall of a trailer in the not-too-distant background, with the middle ground cluttered up by all kinds of scientific equipment. But those shots had computer graphics popping right out of the screen, looking very cool and futuristic and 3D in front of the image they were recording. (I even noticed that the images on computer screens angled away from the viewer looked 3D.) In several of Jake’s monologue scenes, I found myself paying much more attention to the little 3D objects than to what he was saying. Maybe this would have mattered more if his monologues had been better written, I guess.

And then, of course, there’s the pretty weird effect you get when an obviously three-dimensional foreground object is not all the way on screen. Like, say we get a torso shot of Sigourney Weaver as a Cat in a Stanford Shirt Playing Basketball. Her upper body and head are three-dimensional, show up nicely in front of the distant base buildings and trees, and then suddenly she disappears into flatness below her stomach. Or say we get a swooping, attacking Scorpion helicopter coming in from stage right – all of a sudden, half a chopper pops into view.

“Avatar” definitely scored points from me for most effective use of 3D scenes to date. But I’m worried that the standard it sets will be for big blockbusters that lean on artificial three-dimensionality more than anything else. As I said above, getting three-dimensional perception from stereoscopic vision alone is really too much to expect of our eyes. And when I do get it, it’s likely that my attention will be on the 3D effects rather than the story. I think that’s one of the major reasons why I barely noticed that “Up” was in 3D, except for a few scenes – I wasn’t looking for it, and because of my depth-of-field arguments above, I tend not to notice the 3D in 3D movies unless I am specifically looking for it. So, I think I will stretch my money a bit more in the future.

What I absolutely did not expect when I finally got to see James Cameron’s ‘Avatar’ yesterday afternoon was to see my own research appear in the movie. Granted, it doesn’t take a front-row seat and it doesn’t play any major plot roles. As I was driving home with my girlfriend (a fellow aerospace engineer), we got into a discussion about how this was a reasonably hard sci-fi movie. None of the technologies seem particularly farfetched: ducted-fan helicopters exist on Earth at a low technology readiness level (TRL), as do exoskeleton power suits. 3D glassy computer displays aren’t a stretch, nor are hovering VTOL aircraft on a low-gravity world. The flight to Alpha Centauri takes 6 years, meaning some reasonable sort of sublight propulsion. The ship Sully arrives on even has rotating segments, big radiators, and solar collectors. The avatars themselves don’t even seem too crazy, since we keep hearing about advanced prostheses that can be controlled by a user’s thoughts. (I’ll reserve judgment on mixing alien and human DNA until we have real alien DNA on hand.) Nor does a planetwide neural interface – though I have to wonder what selective pressures would cause such a thing to evolve – given that we have bacterial, fungal, and other life forms on Earth that can split and recombine, blurring the distinction between organisms.

But surely, I thought, those floating mountains are ridiculous. Visually stunning, yes, and great for those 3D flying scenes. But physically ludicrous.

Pandora's Hallelujah mountains

We are led to believe, in the movie, that these mountains float against the force of (albeit reduced) gravity because there is an exceptionally strong magnetic field generated on Pandora. Cameron even gives us direct evidence of that field: you know how iron filings align themselves with a magnetic field, like that of a bar magnet?

Iron filings aligning themselves with magnetic field lines

Well, the magnetic field on Pandora is so strong that geologic formations align themselves with the magnetic field. The field is so outrageously strong that whatever iron content is in Pandoran minerals – most likely not 100%, even if those rocks are pure hematite or magnetite or something like that – is sufficient to make rocks suspend themselves against gravity in the shape of the magnetic field lines:

A field that bends rock to its will!

I know for experience that this might not necessarily be impossible, for a sufficiently strong magnetic field. After all, in my lab is a whopping-big NdFeB rare-Earth magnet about the size of a margarine tub, and even when it’s contained within its sarcophagal wooden box, I can get six-inch steel bolts to suspend themselves, against gravity, at a 45° angle in its field. So, for a sufficiently strong magnetic field, this flux-line rock formation is not at all out of the question, believe it or not!

How about the mountains themselves? Couldn’t the magnetic field strong enough to make these “flux arches” also levitate mountain-sized chunks of rock?

Well, I thought, surely not if it is solely the repulsion of like magnetic poles that is responsible. After all, Earnshaw’s theorem says that the familiar field sources that drop off with distance, like gravity, electrostatic attraction, and magnetostatic attraction, cannot be arranged in a passively stable configuration. If you don’t believe me, then I set for you a challenge: get some ordinary bar magnets, and lay them out on a table. Try to arrange them in such a way that they are within a few centimeters of each other, but the attraction of opposite poles and repulsion of similar poles cancel out so that the entire arrangement sits on the table without moving. (For safety’s sake, do not do this with the rare-earth magnets I mentioned above, because when you fail at the challenge, the magnets will jump towards each other with substantial force. Rare-earth magnets are brittle and will shatter if that happens, sending neodymium shrapnel flying around – if they didn’t pinch your fingers when they impacted.) You will find that no matter how hard you try, no matter how many friends you get to hold the magnets in position and simultaneously release them, no matter how you angle them and tweak them, you won’t ever be able to prevent at least one of the magnets from attracting or repelling some other magnet. The whole arrangement will either fly apart or collapse together. You might think that in 3D you’d be able to come up with some super-clever configuration that is stable, but, in fact, if you move beyond the two dimensions (and three degrees of freedom) of the table top the situation gets far worse, because all the bar magnets try to align themselves with one another in 3D. So, a combination of purely magnetic and gravitational forces cannot result in a stable configuration of those mountains.

“But, ha!” you say. “You must be wrong! You said that a combination of gravitational field sources can’t be in a stable arrangement, and clearly, the planets of our solar system have been stably orbiting each other for four billion years! And I’ve even seen those Levitron tops – magnetic tops that stably levitate against gravity, just like those mountains!“

The Levitron: just two magnets, one inside a spinning top

The key difference between a Levitron or an orbit and the bar magnets on a table top are that they are dynamically stable. They require motion to preserve stability. Stop the planets from orbiting, and they will fall into each other and the Sun. Stop the Levitron from spinning, and it flops over – aligning itself with the magnet in the base – and drops to the ground. So, for Pandora’s mountains to levitate like that, they must be spinning or moving in some way. It might be the case that, if they were at Pandora’s equator, the repulsive magnetic force actually “cancels out” the low gravity of the moon enough that the mountains are actually in circular orbits about Pandora’s equator. But that situation is dynamically tricky, requiring exquisite balances of forces – and I would estimate from the different sizes of floating mountains that they have different magnetic mineral contents, so the balance between gravity and magnetism would be different for each mountain and each would have a different orbit. Doesn’t work.

So what’s the answer? Well, it’s all in those little gray crystals the imperialist human colonists of RDA are after. Unobtainium.

An unobtainium crystal, unobtrusively levitating. Wait, what?

Above is a picture of an unobtainium crystal from the movie. It’s levitating above some crazy sci-fi antigravity contraption, that holds it stably up in the air where people can poke at it, spin it, pluck it out of midair and play with it before putting it back in exactly the same spot again. Now, wait a minute – where have I seen this behavior before? Oh, right. My research lab.

A rare-earth magnet levitating over a high-temperature superconductor

That is a picture I took of a NdFeB magnet, stably levitating over the high-temperature superconductor yttrium barium copper oxide, or YBCO. (For scale, the magnet is 3/4″ across.) You can do everything with that magnet that they do with the sample of unobtainium in ‘Avatar.’ Leave it alone, and it happily floats in midair. Poke it, and it rocks a little before going back to its equilibrium position. Give it a twirl, and it’ll spin over the YBCO – and if the magnet isn’t cylindrically symmetric, it’ll eventually stop spinning and settle down again. Pull it away from the YBCO, and you can put it back later and watch it float in exactly the same midair spot as when it started. You can even pin different sizes and shapes of magnets – all stable against gravity. This whole setup would work perfectly if the magnet was on the table and the YBCO was doing all the floating, too. It’s all because the magnet induces currents in the YBCO that are not opposed by any resistance – “supercurrents” – which generate their own magnetic fields that then interact with the magnet.

“Wait,” you ask, “that magnet is just a magnet. The supercurrents make magnetic fields. I thought you said that magnetic field sources couldn’t be arranged in a stable configuration! It’s Earnshaw’s Theorem again.”

That would be an astute question. The answer is that, in this case, the superconductor doesn’t have a fixed magnetic field. As the magnet moves around – let’s say it starts to fall from its equilibrium position, because gravity is pulling on it – then its motion causes the supercurrents in the YBCO to move around. The new distribution of supercurrents gets superimposed on top of the previous distribution of supercurrents, with the net result that the magnetic field from the YBCO tends to push back on the magnet, keeping it in its original position. It’s as if the field lines of the magnet get stuck, or trapped, in the volume of the superconductor. The effect is called “magnetic flux pinning” for that very reason, and it happens with Type II, or “high-temperature” superconductors. (If you know about Meissner repulsion, flux pinning is related but not the same.) So, that blue-glowing antigravity generator in the RDA command center, with the levitating sample of unobtainium, is very likely just a magnet. And the Hallelujah Mountains are just a scaled-up version of the magnet and YBCO in my lab.

But, you probably noticed from that photo, the YBCO has to be below liquid nitrogen temperature in order to superconduct and exhibit flux pinning. Clearly, Pandora is not at cryogenic temperatures, which pretty much pegs “unobtainium” as a room-temperature superconductor – a type of material that is highly sought-after in research labs today, and would indeed be extremely valuable. That means that the Hallelujah Mountains on Pandora likely consist of large deposits of unobtainium, which are flux-pinned to the stupendously powerful magnetic field lines coming from that field sources on the planet. This explains the value of unobtainium, how the mountains levitate the way they do, and why the floating mountains are so close to the flux arch structures.

There’s another interesting link between ‘Avatar’ and flux pinning. Remember how I said that the effect of flux pinning is as if a magnet’s field lines get stuck within the superconductor? Well, if you had a good electricity and magnetism course, that notion might sit uncomfortably with you, because you were probably taught that “field lines” or “flux lines” are not physically real, but are a good visualization tool for magnetic fields, which exist everywhere around a magnet and not just in neat little looping lines. Well, you’d be right, but things tend to get kind of weird inside superconductors. Magnetic fields are quantized just like everything else, and it is these magnetic flux quanta that get “stuck” inside the YBCO. In fact, they actually get trapped on impurities within the YBCO’s crystal structure. You might think that these quanta of magnetic flux would be called “fluxons,” but because they correspond pretty well to magnetic field lines, papers on superconductivity and flux pinning tend to throw around several names for them – like “flux lines,” “field lines,” and “flux vortices.” That last name likely comes from the fact that, in the superconductor, each of the magnetic field lines induces a little loop of electric current that races in a circle around the flux line, like a little vortex. The sum total of all these little currents adds up to the distribution of supercurrents that gives us flux pinning.

In ‘Avatar,’ every time they fly near the flux-arch structure, they talk about a “flux vortex.” It sounds like your classic sci-fi trope of combining sciency-sounding words. (“Invert the phase capacitors!”) But, hmm…maybe, just maybe, that’s not mere technobulshytt after all!

I’m pretty convinced that all this isn’t accidental. The filmmakers had every intention of unobtainium being a room-temperature supercondcutor and the floating mountains being flux-pinned to the field source within the planet. Because I know that this is not the first article on the web about it! But the fact that it’s my own research in this movie: now that is cool! (For the uninitiated, I’m working on using flux pinning to assemble and reconfigure modular spacecraft. More info on my web site and my research group web site. You can also check out Youtube videos of me demonstrating flux pinning and our microgravity experiments with flux-pinned spacecraft mockups from last summer.)

Of course, ‘Avatar’ doesn’t get it all right. And they shouldn’t be expected to. I know from my research that flux pinning is a very short-range effect; getting those mountains to levitate would require a (probably literally) mind-bogglingly powerful magnetic field. Not something I’d expect to see from a planetary dynamo. Nor would a dipolar magnetic field within Pandora explain the flux arches: those are clearly centered on a magnetic field source at the surface of the world. And if the field source is powerful enough to get the rocks to bend around and follow field lines – all the aircraft, armor suits, guns, mobile lab trailers, and equipment carried by the human scientists and soldiers probably has more than enough ferromagnetic metal content to be ripped towards the field source. And that doesn’t even account for this happening:

Oh, well. But, speaking as someone who hopes that our future space program will involve spacecraft build out of components that “levitate” near each other without touching, but still acting as if they are mechanically connected, I would sure love to see some room-temperature superconductors and floating mountains!

First, I am impressed with how much the show’s creators, writers, and artists have paid attention to the probable operation of a near-future space program. Of course, the show makes the usual sci-fi physics gaffes. “Defying Gravity” goes to unusual lengths to rationalize shooting a space series in terrestrial gravity (“centrifuge” is a fine explanation for me, “magnetic nanospray” and “electrostatic nanofibers,” eh…not so much – novel attempt, though), there are silly numerical issues like pressurizing a spacesuit to 5 atm (never mind the entirely ridiculous  idea of a human-rated “Venus suit”), and this show, like almost every other sci-fi, doesn’t come close to getting the physics of tethers right. However, I’ve just come from a summer at NASA Johnson Space Center, and I am incredibly impressed with this show’s depiction of mission control, the MCC/spacecraft communications, space jargon, uniforms and suits, the art of the spacecraft interior, potentially realizable space technology, and the fact that they do depict zero gravity with much greater frequency than most other sci-fi. From my (albeit limited, but still quite extensive compared to the general public) exposure to the astronaut office at JSC, it seems to me that this show’s depiction of the Astronaut Office and the experience of being an astronaut is about as spot-on as it could be.

Second is the point that this series was apparently, according to Wikipedia, pitched to the networks as “Grey’s Anatomy in space.” I couldn’t care less about the soap-opera-y who’s-sleeping-with-who dynamics of a show like that, but there’s plenty more going on that make “Defying Gravity’s” characters fun to watch. In contrast to shows like “Star Trek: (pick your favorite)” – which highlights some aspect of human nature or morality by having our intrepid characters encounter a planet peopled by a species that embodies a single, streotypical trait – and “Battlestar Galactica” – which explores the interactions between its characters against the backdrop of larger questions about what it means to be free, human, just, etc. – “Defying Gravity” is a show almost purely about the interactions between the characters and how their past experiences impact those relationships. Certainly, Trek and BSG include those elements, but “Defying Gravity” removes most of the external influences on the characters. (Not all, of course, because external stressors are great for getting characters to look at themselves or their companions.) Now, using a long-duration spaceflight with astronauts cooped up in close quarters, millions of miles from assistance, communication, or rescue to set up a character study is absolutely nothing new to science fiction in general (see, e.g., Poul Anderson’s Starfarers and Tau Zero, many of Ben Bova’s novels, and the beginning of Kim Stanley Robinson’s Mars saga) – but it is new to mainstream movie and television sci-fi. Fortunately, these are pretty interesting characters, they seem like three-dimensional people, and the show so far has been about how they each come to terms with their own past at the beginning of their six-year voyage. I definitely like seeing the space program as the setup for such drama. Which brings me to…

Last, and certainly not least, this show is extremely pro-space. (Just listen to Maddox Donner’s voiceover monologue at the close of the pilot episode!) I love what it says about viewing audiences: the mainstream media is comfortable with, and thinks the public is comfortable with, a relationship drama set on a spacecraft against a background of mostly-real physics and operations. It helps to make astronauts feel not just like heros, but like real people. As if – gasp – we could grow up wanting to be an astronaut and hold on to that dream even if we don’t picture ourselves as the perfectly polished John Glenn or Neil Armstrong type. We can be good at things, bad at things, have our own flaws, and still go become astronauts, mission controllers, and engineers. That is a message that I really, really want to get out into the public. If we can get the more adult audiences likely to watch “Defying Gravity” thinking that it’s okay to keep dreaming to be an astronaut, then we’ll raise a generation of kids who are willing to hold on to that dream and become the scientists, engineers, and space explorers of the future. Augustine Commission, NASA management, and politicians, please take note!

The two-second, non-spoiler plot outline is that Rockwell plays Sam Bell, a blue-collar astronaut who works in a one-man mining outpost on the far side of the moon with no live communications to anyone. He’s about to end his three-year contract when, after an accident, he goes out onto the surface and finds a man who happens to look and act exactly like Sam Bell. Now they have to figure out what’s going on.

The movie is a tour de force for Rockwell’s acting, since he spends most of the time playing against himself. The obvious effects aside, he handles the dialog naturally enough that I really forgot that he had to play the two separately – he was really acting with himself. It’s also incredible that he was able to bring out the subtle differences between the Sam Bell who has been in the outpost for three years and the newcomer Sam Bell. There were some physical differences between the two characters, but sometimes it was hard to tell which was which based on visual impression alone. Yet it was always easy to tell one from the other as they interacted. Rockwell really put a lot of ordinary-guy-ness into the character, and put a lot of thought into the effects of isolation and delayed communication. They way his characters handle the mystery they’ve been thrown into is simulatneously heartbreaking and triumphant.

Now I have to talk a bit about the science fiction in this movie. This is sci-fi in its purest form: science and fiction, with a strong grounding in both solid scientific concepts and in dramatic and chracter development. The science is, in fact, not too far removed from our own – perhaps fifty years off – and it looks like everything grew out of the space program as we know it today. The movie goes to show just how well adhering to real science instead of going for cheesy effects, laser sounds in space, and ridiculous robots can move the drama along. Sam Bell eats freeze-dried, reconstituted astronaut food. He has to wear a familiar white spacesuit. His lunar outpost is all form-built white surfaces, but he still uses sticky notes. He has to exercise to keep his muscle tone. And all these things contribute to the frustrations he experiences in his lonely three-year stay.

However, there is only one bit of science that is absolutely necessary to move the plot along – the explanation for Sam’s duplicate. I got the feeling that this sort of story could have happened in many different places or times, and the science fiction is only a vehicle to move the plot along and let us watch these characters deal with their situation. I definitely appreciated that – it’s about time sci-fi broke out of the rut it’s been in, where it’s all about action-adventure and CG explosions.

(Just FYI: Yeah, they really could have done a better job making 1/6 gee gravity apparent. Yeah, there are some sounds in space – but at least they’re muted, BSG-style. And yeah, the rover design is kind of poor for the Moon. But those are about the only scientific gripes I can put down, and look how tiny and insignificant they are!)

This is also a very smart movie. The film shows you enough information to show you what’s going on, and by the end, I understood all that had happened. But it doesn’t tell you straight up what’s happening. There are no scenes where a character explains to another character what just happened or why they are in the situation they are. Instead, we see Sam figuring things out, and we figure things out along with him. It felt like a very participatory movie to me, and I enjoyed that aspect of it a great deal.

This is a wonderful sci-fi movie. It’s definitely an homage to some of the classics, most obviously the spaceship scenes in 2001 (you know, the best part of that movie), and an homage to the days of the classic Heinlein-style sci-fi that followed on the heels of real space exploration; it brings back the feel of when people followed both space movies and space news. And I’m all for that.

For what it’s worth, I hope this movie gets a much bigger exposure in national release. I will also secretly hope for an Oscar nod for Sam Rockwell, because I think the critics have long overlooked SF as a genre in which great acting and writing can happen.