I’m trying to write a conference paper manuscript for the AIAA GNC conference right now (why, oh, why isn’t it just an abstract, or even an extended abstract? a full manuscript at this point is going to be slathered with “TBD” and “preliminary” and “temporary” and promises for the future!), but I just discovered something that I had to write down for the benefit of other academic users of Microsoft Office since this has been bugging me since I got Office 2007:
I, personally, rebel against using TeX or its derivatives in my academic work. Yes, I can program in Matlab and Mathematica, and yes, I can create some pretty snazzy HTML/CSS web pages, so I’m not foreign to coding and markup languages, but really, I’m trying to concentrate on the science and engineering when I write a paper. I want to see what I will get. There is no reason at this point in the history of computers for me to have to use a command-line word processor that I have to compile. That sort of thing is for numerical scripts, not for documents.
Word 2007 took some great strides in the direction of making Office easier and better for technical purposes, with a WYSIWYG equation editor that you can control almost entirely from the keyboard using common operators and that automatically prettifies the equations as you write them. It’s way cool.
Word 2007 also has, from the beginning, included some automatic citation generating and outputting features. It’s almost like EndNote or BibTex and such, except that I don’t have to pay extra for them. However, it’s HUGE shortcoming was that it contained only 10 citation formats, and didn’t include some common technical formats. Right around the release of Office 2007, Microsoft blogs touting Word went on and on about how easy it would be for users to generate their own formats, since they used open XML files to create them. However, it turns out that those XML files are totally opaque to my understanding, and when I did try to change some things, I didn’t get what I expected. And it seemed like the rest of everybody agreed with me, because downloads for new citation formats did not immediately appear on the Internet.
I have finally, finally, finally found a web site with a small library of citation format files. It is here.
They unfortunately don’t have the AIAA format, which is what I use most often, but maybe they have something close. And, anyway, it adds to my options for the future. 🙂
First: great movie, literally awesome visuals, stunning effects, good acting and execution, fun alien creatures, who cares if it’s a retelling of Pocahontas.
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 requiremotion 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!
This story has one purpose: to build on this entry to demonstrate how a space battle might actually play out. It has the thinnest of plots and the flattest of characters. My goal was to be as “hard” in the science as possible, at least conceptually–not that I can’t perform the necessary orbit calculations (see, e.g., this) but to show that a writer need only know some basic concepts, and could then use them for dramatic effect.
Anyway, I hope it’s entertaining.
(A hearty “thank you!” to the readers over at Gizmodo, some of whose comments on this article helped shape bits of this story.)
I had a discussion recently with friends about the various depictions of space combat in science fiction movies, TV shows, and books. We have the fighter-plane engagements of Star Wars, the subdued, two-dimensional naval combat in Star Trek, the Newtonian planes of Battlestar Galactica, the staggeringly furious energy exchanges of the combat wasps in Peter Hamilton’s books, and the use of antimatter rocket engines themselves as weapons in other sci-fi. But suppose we get out there, go terraform Mars, and the Martian colonists actually revolt. Or suppose we encounter hostile aliens. How would space combat actually go?
First, let me point out something that Ender’s Game got right and something it got wrong. What it got right is the essentially three-dimensional nature of space combat, and how that would be fundamentally different from land, sea, and air combat. In principle, yes, your enemy could come at you from any direction at all. In practice, though, the Buggers are going to do no such thing. At least, not until someone invents an FTL drive, and we can actually pop our battle fleets into existence anywhere near our enemies. The marauding space fleets are going to be governed by orbit dynamics – not just of their own ships in orbit around planets and suns, but those planets’ orbits. For the same reason that we have Space Shuttle launch delays, we’ll be able to tell exactly what trajectories our enemies could take between planets: the launch window. At any given point in time, there are only so many routes from here to Mars that will leave our imperialist forces enough fuel and energy to put down the colonists’ revolt. So, it would actually make sense to build space defense platforms in certain orbits, to point high-power radar-reflection surveillance satellites at certain empty reaches of space, or even to mine parts of the void. It also means that strategy is not as hopeless when we finally get to the Bugger homeworld: the enemy ships will be concentrated into certain orbits, leaving some avenues of attack guarded and some open. (Of course, once our ships maneuver towards those unguarded orbits, they will be easily observed – and potentially countered.)
What are a long car trip and hosting boring virtual office hours good for? Thinking about how our science and society would be different if the Earth had rings. Science fiction writers, take note.
As I was writing that earlier post, my officemates and I got into a discussion about some of the implications to (at least Western) science and philosophy of such a ring system. One of them suggested that the rings, which would be mostly aligned with the Earth’s equator but would precess with the Moon, would be quite obviously separate from both the purported “celestial spheres” and the Earth, so maybe the ancient Greeks could have dispensed with that destructive Platonic notion much earlier in the history of Western science.
I got thinking and realized that, in addition to their own dynamics, the rings would have a few other obvious effects on the science of those cultures at high enough latitudes to get a good view of the ring system, without seeing them edge-on.
First, the shadows of the Earth and Moon would be visible on the rings. These shadows would be shaped like portions of circles, and would vary in size and shape with time of day, month, and year. From observations of these shadows, easily possible with the naked eye, the Greeks, Egyptians, and Chinese ought to have been able to show without any doubt that the Earth and Moon are spherical. They may have been able to deduce the position of the Earth’s spin axis and axial tilt by comparing the shape of the rings and the shadows on them to the time to year. (These experiments could be quite simple: make a stiff, lightweight circle or hoop, hold it at arm’s length at night, move the circle in and out and tilt it back and forth until its edges line up with the shadow on the ring. Add a little simple geometry, and BAM: I would have just found the axial tilt of the Earth.) They should also have provided some kind of estimate of the distance to the Moon, as observers could compare the size of the Moon with the size of its shadow. And comparing the Earth’s shadow on the rings to the positions of the background stars would have given the ancients an incredibly accurate nighttime clock.
Second, and perhaps most importantly of all, the rings would vary radially in opacity. This would make them beautiful to behold, yes, but it would also give naked-eye astronomers an absolute scale for photometry. Annuli of the rings would block out the light from some stars, but not others. The thicker rings would block more stars than thinner rings, giving a gradation of occultation scales. By comparing which rings block out which stars, observers would have been able to make statements about the relative brightness of the stars with a degree of precision unknown until Christian Huygens arrived on the scene – even surpassing the precision of that experiment. Still more exciting, if the ring was able to occult the Sun, that same method could have been used to measure the light output of the Sun. Now, coupled with the insight that the Sun is a star and a crude estimate of the Earth-Sun distance, an observer should have been able to deduce from naked-eye observations approximate distances to the stars.
I’ll say that again: If the Earth had rings, the ancient Greeks, Chinese, and Egyptians might have had a sense of the scale of the Cosmos. The Romans and Indians might have known what a parsec is.
Furthermore, this photometry could have been used on the visible planets as well as stars. That would have told the ancient astronomers that Mercury, Venus, Mars, Jupiter, and Saturn were a lot closer to the Earth than the stars. In fact, if the ancient photometers tracked the brightness (and, therefore, distance from the Earth) of each planet over time, they would have noticed something interesting: the planets move in circles about a point that is not located within the body of the Earth, but is rather in the Sun. The heliocentric model for the Solar System would have been adopted in ancient times.
Now, knowing that the planets go around the Sun, and the stars are all rather a long way away from the Sun and from each other, ancient astronomers might have realized that other stars could have planets just like the Sun does. Think about what that idea might have done to Western philosophy and religion in their formative years: other Earths? In the sky?! Going around other Suns?
Here’s a possibility I’m not sure about: if the ring was thick enough, it’s possible that it might dim the Sun enough that an observer could safely look at our star with their naked eyes. If so, then sunspots might have been visible to the ancient civilizations. In that case, they might have known that the Sun is not a perfect glowing sphere, and that it rotates. They might have known about the 11-year solar cycle.
And then, imagine what could have happened once Galileo stormed onto the scene with his telescope. When he looked at Saturn, he would have known exactly what he was looking at. “Ears” indeed! By watching Saturn’s rings wax and wane with each Saturnian year, he would have identified the orientation of Saturn’s ringplane to the ecliptic. Knowing that Saturn has rings would have told scientists that Earth’s features are not unique to our own planet.
Early telescopes might have been powerful enough to identify some of the larger rocky chunks making up the Terrestrial rings. Observing their orbits at different radii within the ring could have lent a lot more data to scientists like Kepler and Newton, who were trying to figure out what forces kept the planets in orbit. Armed with data on the orbits of ring particles and Kepler’s Laws, early scientists might have been able to get a pretty good estimate for the mass of the Earth and fix the Earth-Sun and Earth-Moon distances pretty accurately.
I’m thinking that, given how great a dynamical laboratory the Saturnian ring system is, rings around the Earth would have allowed the progress of science to advance much more rapidly, as the rings would provide a precise tool for measurements of position, time, and distance of celestial bodies. If the laws governing those bodies had been puzzled out, say, before Christianity dominated Europe, imagine what society would have resulted….
I’m home for Thanksgiving, and at my mom’s suggestion, I just listened to storyteller Jay O’Callahan perform part of his work about NASA, “Forged in the Stars,” on the “Living on Earth” program for NPR. If you’re at all interested in space exploration, NASA, or just hearing a good story, it is well worth listening to this performance, which you can do by clicking the download link on this web page.
NPR will air the full performance of “Forged in the Stars” during the last week of December. O’Callahan has performed the piece at JPL and JSC, and received standing ovations for it. Here’s to him for doing a little bit to capture the public interest once again.
One of the most majestic and awe-inspiring structures in the Solar System is the Saturnian ring system. My sister sent me this video, which imagines what that same ring system would look like around the Earth – and what it would look like in our sky when viewed from the surface. The result is pretty wonderful to imagine:
However, sciency guy that I am, my very first thought on seeing this video translocate the Saturnian rings around the planet Earth was, “Hey! The Cassini Division’s still there!”
The significance of that gap between Saturn’s A and B rings is that it’s one of the most clear markers of the interaction between Saturn’s moons and the rings. All of the various gaps and spaces between the rings come from orbital resonances between the rings particles and various moons. If, for example, a ring particle orbits twice around Saturn for every orbit of the moon Mimas, then Mimas will pump energy into the orbiting particle and it will move into a higher-energy orbit with a larger semimajor axis – thus clearing a space in the rings (for the 2:1 Mimas resonance, the Huygens Gap).
That made me wonder just what a Terrestrial ring system would look like. We have only one moon, but it’s incredibly massive compared to the Earth. In fact, the Earth/Moon system has the largest moon-to-planet size ratio, by any measure, in the Solar System. (Sorry, Pluto/Charon!) Our single moon compared to Saturn’s dozens means that our ring system would be much more orderly, with many fewer and much more regularly spaced gaps. However, the huge size of the Moon means that the weaker resonances would have a stronger effect. The Saturnian rings show evidence of weak resonances all the way out to the double digits – like, say, 9:14 resonances – so I’d argue that weaker-still resonances would still be visible in the Earth-Moon system.
So, I wrote a little Matlab script. Clearly, this was more important today than getting my work done.
As in that video, I placed the outer limit of my hypothetical Terrestrial ring system at the Roche Limit, ~2.86 Earth radii from the center of the orbit. This is the innermost limit at which a fluid satellite could hold itself together, by its own self-gravity, against being ripped apart by tidal forces fromt he Earth. Outside this limit, the rings could start to aggregate together into moonlets. I bounded the inside of the ring at 1.59 Earth radii on the inside, coinciding with the definition of the outer limit of the exosphere. Even in low Earth orbit, atmospheric drag would eventually cause ring particles to fall into the deeper atmosphere, so I felt this would be a good value to pick to ensure that the ring would have a long enough lifetime to persist for millions or billions of years.
I started my script with a ring opacity of 100% at all radii and put a fuzzy boundary on the ring system at either end. Then I had Matlab calculate the orbital radii of every ring-Moon resonance from 1:1 to 100:100 using Kepler’s Third Law. For each resonant semimajor axis that fell between the Roche limit and drag limit, I subtracted a narrow Gaussian from the ring opacity as a function of radius. Since my big 100×100 matrix of resonances had some repeats (like 3:4 and 6:8), several of these Gaussian functions would add together and decrease the ring opacity further, crudely estimating the effect of stronger resonances. Finally, I lowered the albedo and tweaked the color of the rings from what they are at Saturn, to make them look more like they’re made of rock rather than ice, which sublimes away in space at our distance from the Sun. This is what I got:
The Earth's hypothetical rings
Earth's Rings in a more Moon-like color
The rings in this image go around the Earth’s equator, inclined 22 degrees with respect to the field of view because of the Earth’s obliquity. Sadly, my Matlab graphics cannot handle casting the shadow of the rings onto the Earth, and I had to Photoshop in the shadow of Earth on the rings for effect. Still, pretty cool looking. Here’s the punchline: the ring system viewed from directly above the ring plane, with a white background so you can easily see the pattern:
From directly above the ring plane and backlit
You can see that the lunar resonances don’t start to have a major effect until about halfway through the ring system. This pattern, and the coloration, are mainly what that video was missing.
Of course, I don’t have the complete story, either. Again, our Moon is huge and that will do even more to the rings’ shape. The Moon’s orbit is inclined 5 degrees to the Earth’s equator, so the tidal torques from the Moon should make the rings precess around the Earth with a one-month period. (That precession would lag the Moon, so we wouldn’t always see the rings piercing the Moon in our night sky.) In addition, I suspect that the lunar tides would twist the rings a bit, pulling them into a spoked configuration like Cassini has seen at Saturn.
It’s definitely fun to think about how these rings would look from vantage points on the Earth. Actually, since my ring system starts well above low Earth orbit, I have to wonder what they would look like to spacewalking astronauts…
More importantly, why does a recent Gallup poll, as reported by Newsweek, say that 58% of Republicans believe that Palin is qualified for the job of being President, but 65% of them would vote for her. For those of you who know that probabilities must add up to 100% and possess the skill of subtraction, this means that at least 7% of Republicans think that Palin is unqualified to be President but would still vote for her. Gallup.com does not report the actual intersection between these sets, so keep in mind that 7% is a lower bound on that figure.
Um, hi, Republicans? Just FYI, no cause for alarm, but… There is something wrong with your brains.
