biology, Dragons, physics, thought experiment

Dragon Metabolism

As you might have noticed, I have a minor obsession with dragons. I blame Sean Connery. And, because I can never leave anything alone, I got to wondering about the practical details of a dragon’s life. I’ve already talked about breathing fire. I’m not so sure about flight, but hell, airplanes fly, so it might be possible.

But I’ll worry about dragon flight later. Right now, I’m worried about metabolism. Just how many Calories would a dragon need to stay alive? And is there any reasonable way it could get that many?

Well, there’s more than one type of dragon. There are dragons small enough to perch on your shoulder (way cooler than a parrot), and there are dragons the size of horses, and there are dragons the size of cathedrals (Smaug again), and there are, apparently, dragons in Tolkein’s universe that stand taller than the tallest mountains. Here’s a really well-done size reference, from the blog of writer N.R. Eccles-Smith:


The only downside is that there’s no numerical scale. There is, however, a human. And, if you know my thought experiments, you know that, no matter what age, sex, or race, human beings are always exactly 2 meters tall. Therefore, the dragons I’ll be considering range in size from 0.001 meters (a hypothetical milli-dragon), 1 meter (Spyro, number 3, purple in the image) to 40 meters (Smaug, number 11), and then beyond that to 1,000 meters, and then beyond to the absolutely ludicrous.

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A Toyota on Mars (Cars, Part 1)

I’ve said this before: I drive a 2007 Toyota Yaris. It’s a tiny economy car that looks like this:


(Image from

The 2007 Yaris has a standard Toyota 4-cylinder engine that can produce about 100 horsepower (74.570 kW) and 100 foot-pounds of torque (135.6 newton-metres). A little leprechaun told me that my particular Yaris can reach 110 mph (177 km/h) for short periods, although the leprechaun was shitting his pants the entire time.

A long time ago, [I computed how fast my Yaris could theoretically go]. But that was before I discovered Motor Trend’s awesome Roadkill YouTube series. Binge-watching that show led to a brief obsession with cars, engines, and drivetrains. There’s something very compelling about watching two men with the skills of veteran mechanics but maturity somewhere around the six-year-old level (they’re half a notch above me). And because of that brief obsession, I learned enough to re-do some of the calculations from my previous post, and say with more authority just how fast my Yaris can go.

Let’s start out with the boring case of an ordinary Yaris with an ordinary Yaris engine driving on an ordinary road in an ordinary Earth atmosphere. As I said, the Yaris can produce 100 HP and 100 ft-lbs of torque. But that’s not what reaches the wheels. What reaches the wheels depends on the drivetrain.

I spent an unholy amount of time trying to figure out just what was in a Yaris drivetrain. I saw some diagrams that made me whimper. But here’s the basics: the Yaris, like most front-wheel drive automatic-transmission cars, transmits power from the engine to the transaxle, which is a weird and complicated hybrid of transmission, differential, and axle. Being a four-speed, my transmission has the following four gear ratios: 1st = 2.847, 2nd = 1.552, 3rd = 1.000, 4th = 0.700. (If you don’t know: a gear ratio is [radius of the gear receiving the power] / [radius of the gear sending the power]. Gear ratio determines how fast the driven gear (that is, gear 2, the one being pushed around) turns relative to the drive gear. It also determines how much torque the driven gear can exert, for a given torque exerted by the drive gear. It sounds more complicated than it is. For simplicity’s sake: If a gear train has a gear ratio greater than 1, its output speed will be lower than its input speed, and its output torque will be higher than its input torque. For a gear ratio of 1, they remain unchanged. For a gear ratio less than one, its output speed will be higher than its input speed, but its output torque will be lower than its input torque.)

But as it turns out, there’s a scarily large number of gears in a modern drivetrain. And there’s other weird shit in there, too. On its way to the wheels, the engine’s power also has to pass through a torque converter. The torque converter transmits power from the engine to the transmission and also allows the transmission to change gears without physically disconnecting from the engine (which is how shifting works in a manual transmission). A torque converter is a bizarre-looking piece of machinery. It’s sort of an oil turbine with a clutch attached, and its operating principles confuse and frighten me. Here’s what it looks like:


(Image from

Because of principles I don’t understand (It has something to do with the design of that impeller in the middle), a torque converter also has what amounts to a gear ratio. In my engine, the ratio is 1.950.

But there’s one last complication: the differential. A differential (for people who don’t know, like my two-months-ago self) takes power from one input shaft and sends it to two output shafts. It’s a beautifully elegant device, and probably one of the coolest mechanical devices ever invented. You see, most cars send power to their wheels via a single driveshaft. Trouble is, there are two wheels. You could just set up a few simple gears to make the driveshaft turn the wheels directly, but there’s a problem with that: cars need to turn once in a while. If they don’t, they rapidly stop being cars and start being scrap metal. But when a car turns, the inside wheel is closer to the center of the turning circle than the outside one. Because of how circular motion works, that means the outside wheel has to spin faster than the inside one to move around the circle. Without a differential, they have to spin at the same speed, meaning turning is going to be hard and you’re going to wear out your tires and your gears in a hurry. A differential allows the inside wheel to slow down and the outside wheel to spin up, all while transmitting the same amount of power. It’s really cool. And it looks cool, too:


(Image from

(Am I the only one who finds metal gears really satisfying to look at?)

Anyway, differentials usually have a gear ratio different than 1.000. In the case of my Yaris, the ratio is 4.237.

So let’s say I’m in first gear. The engine produces 100 ft-lbs of torque. Passing through the torque converter converts that (so that’s why they call it that) into 195 ft-lbs, simultaneously reducing the rotation speed by a factor of 1.950. For reference, 195 ft-lbs of torque is what a bolt would feel if Clancy Brown was sitting on the end of a horizontal wrench 1 foot (30 cm) long. There’s an image for you. Passing through the transmissions first gear multiplies that torque by 2.847, for 555 ft-lbs of torque. (Equivalent to Clancy Brown, Keith David, and a small child all standing on the end of a foot-long wrench.) The differential multiplies the torque by 4.237 (and further reduces the rotation speed), for a final torque at the wheel-hubs of 2,352 ft-lbs (equivalent to hanging two of my car from the end of that one-foot wrench, or sitting Clancy Brown and Peter Dinklage at the end of a 10-foot wrench. This is a weird party…)

By this point, you’d be well within your rights to say “Why the hell are you babbling about gear ratios?” Believe it or not, there’s a reason. I need to know how much torque reaches the wheels to know how much drag force my car can resist when it’s in its highest gear (4th). That tells you, to much higher certainty, how fast my car can go.

In 4th gear, my car produces (100 * 1.950 * 0.700 * 4.237), or 578 ft-lbs of torque. I know from previous research that my car has a drag coefficient of about 0.29 and a cross-sectional area of 1.96 square meters. My wheels have a radius of 14 inches (36 cm), so, from the torque equation (which is beautifully simple), the force they exert on the road in 4th gear is: 495 pounds, or 2,204 Newtons. Now, unfortunately, I have to do some algebra with the drag-force equation:

2,204 Newtons = (1/2) * [density of air] * [speed]^2 * [drag coefficient] * [cross-sectional area]

Which gives my car’s maximum speed (at sea level on Earth) as 174 mph (281 km/h). As I made sure to point out in the previous post, my tires are only rated for 115 mph, so it would be unwise to test this.

I live in Charlotte, North Carolina, United States. Charlotte’s pretty close to sea level. What if I lived in Denver, Colorado, the famous mile-high city? The lower density of air at that altitude would allow me to reach 197 mph (317 km/h). Of course, the thinner air would also mean my engine would produce less power and less torque, but I’m ignoring those extra complications for the moment.

And what about on Mars? The atmosphere there is fifty times less dense than Earth’s (although it varies a lot). On Mars, I could break Mach 1 (well, I could break the speed equivalent to Mach 1 at sea level on Earth; sorry, people will yell at me if I don’t specify that). I could theoretically reach 1,393 mph (2,242 km/h). That’s almost Mach 2. I made sure to specify theoretically, because at that speed, I’m pretty sure my tires would fling themselves apart, the oil in my transmission and differential would flash-boil, and the gears would chew themselves into a very fine metal paste. And I would die.

Now, we’ve already established that a submarine car, while possible, isn’t terribly useful for most applications. But it’s Sublime Curiosity tradition now, so how fast could I drive on the seafloor? Well, if we provide compressed air for my engine, oxygen tanks for me, dive weights to keep the car from floating, reinforcement to keep the car from imploding, and paddle-wheel tires to let the car bite into the silty bottom, I could reach a whole 6.22 mph (10.01 km/h). On land, I can run faster than that, even as out-of-shape as I am. So I guess the submarine car is still dead.

But wait! What if I wasn’t cursed with this low-power (and pleasantly fuel-efficient) economy engine? How fast could I go then? For that, tune in to Part 2. That’s where the fun begins, and where I start slapping crazy shit like V12 Bugatti engines into my hatchback.


Death by Centrifuge

WARNING! Although it won’t contain any gory pictures, this post is going to contain some pretty gory details of what might happen to the human body under high acceleration. Children and people who don’t like reading about such things should probably skip this one. You have been warned.

In my last post, I talked a bit about gee forces. Gee forces are a handy way to measure acceleration. Right now, you and I and (almost) every other human are experiencing somewhere around 1 gee of head-to-foot acceleration due to the Earth’s gravity. Anyone who happens to be at the top of Mt. Everest is experiencing 0.999 gees. The overgrown amoebas at the bottom of the Challenger deep are experiencing 1.005 gees.

But human beings are exposed to greater gee forces than this all the time. For instance, the astronauts aboard Apollo 11 experienced up to 4 gees during launch. Here’s an awesome graph from NASA:

Fighter pilots have to put up with even higher gee forces when they make tight turns, thanks to the centrifugal acceleration required to turn in a circle at high speeds. From what I can gather, many pilots have to demonstrate they can handle 9 gees for 10 or 15 seconds without blacking out in order to qualify to fly planes like the F-16. Here’s an example of things not going right at 9 gees:

Yes, it’s the same video from the last post. I spent fifteen or twenty minutes searching YouTube for a better one, but I couldn’t find it. I did, however, discover this badass pilot in a gee-suit who handled 12 gees:

The reason we humans don’t tolerate gee forces very well is pretty simple: we have blood. Blood is a liquid. Like any liquid, its weight produces hydrostatic pressure. I’ll use myself as an example (for the record, I’m pretty sure I would die at 9 gees, but anybody who wants to let me in a centrifuge, I’d love to prove myself wrong). I’m 6 feet, 3 inches tall, or 191 centimeters, or 1.91 meters. Blood is almost the same density as water, so we can just run Pascal’s hydrostatic-pressure equation: (1 g/cc [density of blood]) * (9.80665 m/s^2 [acceleration due to gravity]) * (1.91 m [my height]). That comes out to a pressure of 187.3 millibars, or, to use the units we use for blood pressure in the United States, 140.5 millimeters of mercury.

It just so happens that I have one of those cheap drugstore blood-pressure cuffs handy. You wait right here. I’m gonna apply it to the fleshy part of my ankle and check my math.

It’s a good thing my heart isn’t in my ankle, because the blood pressure down there is 217/173. That’s the kind of blood pressure where, if you’ve got it throughout your body, the doctors get pale and start pumping you full of exciting chemicals. For the record, my resting blood pressure hovers around 120/70, rising to 140/80 if I drink too much coffee.

The blood pressure at the level of my heart, meanwhile, should be (according to Pascal’s formula) (1 g/cc) * (9.80665 m/s^2) * (0.42 m [the distance from the top of my head to my heart]). That’s 41.2 millibars or 30.9 mmHg. I’m not going to put the blood-pressure cuff on my head. To butcher that Meat Loaf song “I would do any-thing for science, but I won’t dooooo that.” I can get a good idea of the pressure at head level, though, by putting the cuff around my bicep and raising it to the same height as my head. Back in a second.

Okay. So, apparently, there are things I won’t do for science, but there aren’t many of them. Among the things I will do for science is attempting to tape my hand to the wall so my muscle contractions don’t interfere with the blood-pressure reading. That didn’t work out. But the approximate reading, because I was starting to fear for my sanity and wanted to stop, is 99/56. 56 mmHg, which is the between-heartbeats pressure, is higher than 41.2, but it’s in the same ballpark. The differences are probably due to stuff like measurement inaccuracies and the fact that blood vessels contract to keep the blood pressure from varying too much throughout the body.

Man. That was a hell of a digression. But this is what it was leading to: when I’m standing up (and I’ve had coffee), my heart and blood vessels can exert a total pressure of about 131 mmHg. Ordinarily, it’s pumping against a head-to-heart pressure gradient of 41.2 mmHg. But what if I was standing up and exposed to five gees?

In that case, my heart would be pumping against a gradient of 154.5 mmHg. That means it’s going to be really easy for the blood to flow from my brain to my heart, but very hard for the blood to flow from my heart to my brain. And it’s for that reason that the handsome young dude in the first video passed out: his heart (most certainly in better shape than mine…) couldn’t produce enough pressure to keep the blood in his head, in spite of that weird breathing and those leg-and-abdomen-straining maneuvers he was doing to keep the blood up there. People exposed to high head-to-foot gees see their visual field shrink, and eventually lose consciousness altogether. Pilots call that G-LOC, which I really hope is the name of a rapper. (It stands for gee-induced loss of consciousness, in case you were wondering).

You’ll notice that, in almost all spacecraft, whether in movies or in real life, the astronauts are lying on their backs, relative to the ground, when they get in the capsule. That’s because human beings tolerate front-to-back gees better than head-to-foot gees, and in a rocket launch or a capsule reentry, the gees will (hopefully) always be front-to-back. There is at least one documented case (the case of madman test pilot John Stapp) of a human being surviving 46.2 front-to-back gees for over a second. There are a few documented cases of race drivers surviving crashes with peak accelerations of 100 gees.

But you should know by now that I don’t play around. I don’t care what happens if you’re exposed to 46.2 gees for a second. I want to know what happens if you’re exposed to it for twenty-four hours. Because, at heart, I’ve always been a mad scientist.

There’s a reason we don’t know much about the effects of extremely high accelerations. Actually, there are two reasons. For one, deliberately exposing a volunteer to gee forces that might pulp their organs sounds an awful lot like an experiment the Nazis would have done, and no matter you course in life, it’s always good if you don’t do Nazi-type things. For another, building a large centrifuge that could get up to, say, a million gees, would be hard as all hell.

But since I’m playing mad scientist, let’s pretend I’ve got myself a giant death fortress, and inside that death fortress is a centrifuge with a place for a human occupant. The arm of the centrifuge is 100 meters long (as long as a football field, which applies no matter which sport “football” is to you). To produce 1,000,000 gees, I’d have to make that arm spin 50 times a second. It would produce an audible hum. It would be spinning as fast as a CD in a disk drive. Just to support the centrifugal force from a 350-kilogram cockpit, I’d need almost two thousand one-inch-diameter Kevlar ropes. Doable, but ridiculous. That’s the way I like it.

But what would actually happen to our poor volunteer? This is where that gore warning from the beginning comes in. (If it makes you feel better, you can pretend the volunteer is a death-row inmate whose worst fears are, in order, injections, electrocution, and toxic gas, therefore making the centrifuge less cruel and unusual.)

That’s hard to say. Unsurprisingly, there haven’t been many human or animal experiments over 10 gees. Probably because the kinds of people who like to see humans and lab animals crushed to a pulp are too busy murdering prostitutes to become scientists. But I’m determined to at least go through the thought experiment. And you know what, I’m starting to feel kinda weird talking about crushing another person to a pulp, so for this experiment, we’ll use my body measurements and pretend it’s me in the centrifuge. A sort of punishment, to keep me from getting too excited about doing horrible theoretical things to people.

The circumference of my head is 60 cm. If my head was circular, I could just divide that by pi to get my head’s diameter. For most people, that assumption doesn’t work. Luckily (for you, at least), my head is essentially a lumpy pink bowling ball with hair, so its diameter is about 60 cm / pi, or 19.1 cm.

Lying down under 1 gee, hydrostatic pressure means the blood vessels at the back of my head will be experiencing 14.050 mmHg more pressure than the ones at the front. From the fact that I don’t have brain hemorrhages every time I lie down, I know that my brain can handle at least that much.

But what about at 5 gees? I suspect I could probably handle that, although perhaps not indefinitely. The difference between the front of my head and the back of my head would be 70.250 mmHg. I might start to lose some of my vision as the blood struggled to reach my retinas, and I might start to see some very pretty colors as the back of my brain accumulated the excess, but I’d probably survive.

At 10 gees, I’m not so sure how long I could take it. That means a pressure differential of 140.500 mmHg, so at 10 gees, it would take most of my heart’s strength just to get blood to the front of my head and front of my brain. With all that additional pressure at the back of my brain, and without any muscles to resist it, I’m probably going to have to start worrying about brain hemorrhages at 10 gees.

As a matter of fact, the brain is probably going to be one of the first organs to go. Nature is pretty cool: she gave us brains, but brains are heavy. So she gave us cerebrospinal fluid, which is almost the same density as the brain, which, thanks to buyoancy, reduces the brain’s effective mass from 1,200 grams to about 22 grams. This is good because, as I mentioned, the brain doesn’t have muscles that it can squeeze to re-distribute its blood. So, if the brain’s effective weight were too high, it would do horrible things like sink to the bottom of the skull and start squeezing through the opening into the neck (this happens in people who have cerebrospinal fluid leaks; they experience horrifying headaches, dizziness, blurred vision, a metallic taste in the mouth, and problems with hearing and balance, because their leaking CSF is letting the brain sink downwards and compress the cranial nerves).

At 5 gees, my brain is going to feel like it weighs 108 grams. Not a lot, but perhaps enough to notice.

But what if I pulled a John Stapp, except without his common sense? That is: What if I exposed myself to 46.2 gees continuously.

Well, I would die. In many very unpleasant ways. For one thing, my brain would sink to the back of my head with an effective weight of 1002 grams. The buoyancy from my CSF wouldn’t matter anymore, and so my brain would start to squish against the back of my skull, giving me the mother of all concussions.

I probably wouldn’t notice, though. For one thing, the hydrostatic blood pressure at the back of my head would be 641.100 mmHg, which is three times the blood pressure that qualifies as a do-not-pass-Go-go-directly-to-the-ICU medical emergency. So all the blood vessels in the back of my brain would pop, while the ones at the front would collapse. Basically, only my brainstem would be getting oxygen, and even it would be feeling the strain from my suddenly-heavy cerebrum.

That’s okay, though. I’d be dead before I had time to worry about that. The average chest wall in a male human is somewhere around 4.5 cm thick. The average density of ribs, which make up most of the chest wall, is around 3.75 g/cc. I measured my chest at about 38 cm by 38 cm. So, lying down, at rest, my diaphragm and respiratory muscles have to work against a slab of chest with an equivalent mass of 24.4 kilograms. Accelerating at 46.2 gees means my chest would feel like it massed 1,100 kilograms more. That is, at 46.2 gees, my chest alone would make it feel like I had a metric ton sitting on my ribs. At 100 gees, I’d be feeling 2.4 metric tons.

But at 100 gees, that’d be the least of my problems. At accelerations that high, pretty much everything around or attached to or touching my body would become deadly. A U.S. nickel (weighing 5 grams and worth 0.05 dollars) would behave like it weighed half a kilogram. But I wouldn’t notice that. I’d be too busy being dead. My back, my thighs, and my buttocks would be a horrible bruise-colored purple from all the blood that rushed to the back of me and burst my blood vessels. My chest and face would be horrible and pale, and stretched almost beyond recognition. My skin might tear. My ribcage might collapse.

Let’s crank it up. Let’s crank it up by a whole order of magnitude, and expose me to 1,000 continuous gees. This is where things get very, very messy and very, very horrible. If you’re not absolutely sure you can handle gore that would make Eli Roth and Paul Verhoven pee in their pants, please stop reading now.

At 1,000 gees, my eyeballs would either burst, or pop through their sockets and into my brain cavity. That cavity would likely be distressingly empty, since the pressure would probably have ruptured my meninges and made all the spinal fluid leak out. The brain itself would be roadkill in the back of my skull. Even if my ribs didn’t snap, my lungs would collapse under their own weight. The liver, which is a pretty fatty organ, would likely rise towards the top of my body while heavier stuff like muscle sank to the bottom. Basically, my guts would be moving around all over the place. And, at 1,000 gees, my head would feel like it weighed 5,000 kilograms. That’s five times as much as my car. My head would squish like a skittle under a boot.

At 10,000 gees, I would flatten. The bones in the front of my ribcage would weigh 50 metric tons. A nickel would weigh as much as a child or a small adult. My bones would be too heavy for my muscles to support them, and would start…migrating towards the bottom of my body. At this point, my tissues would begin behaving more and more like fluids. This would be more than enough to make my blood cells sink to the bottom and the watery plasma rise to the top. 10,000 gees is the kind of acceleration usually only experienced by bullets and in laboratory centrifuges.

By 100,000 gees, I’d be a horrible fluid, layered like a parfait from hell: a slurry of bone at the bottom topped with a gelatinous layer of muscle proteins and mitochondria, then a layer of hemoglobin, then a layer of collagen, then a layer of water, then a layer of purified fat.

And finally, at 1,000,000 gees, even weirder stuff would start to happen. For one thing, a nickel would weigh as much as a car. But let’s focus on me, or rather, what’s left of me. At 1,000,000 gees, individual molecules start to separate by density. The bottom of the me-puddle would be much richer in things like hemoglobin, calcium carbonate, iodine-bearing thyroid hormones, and large, stable proteins. Meanwhile, the top would consist of human tallow. Below that would be an oily layer of what was once stored oils in fat cells. Below that would come a slurry of the lighter cell organelles like the endoplasmic reticula and the mitochondria. The heavier organelles like the nucleus would be closer to the bottom. That’s right: at 1,000,000 gees, the difference in density between a cell’s nucleus and cytoplasm is enough to make the nucleus sink to the bottom.

I think we’ve gotten horrible enough. So let’s stop the centrifuge, hose what’s left of me out of it, and go ahead and call up a psychiatrist.

But before we do that, I want to make note of something amazing. In 2010, some very creative Japanese scientists decided to try a bizarre experiment. They placed different bacteria in test tubes full of nutrient broth, and put those test tubes in an ultracentrifuge. The ultracentrifuge exposed the bacteria to accelerations of around 400,000 gees. Normally, that’s the kind of acceleration you’d use to separate the proteins from the membranes. It’d kill just about anything. But it didn’t kill the bacteria. As a matter of fact, many of the bacteria kept right on growing. They kept on growing at an acceleration that would kill even a well-protected human instantly. Sure, their cells got a little weird-shaped, but so would yours, if you were exposed to 400,000 gees.

The universe is awesome. And scary as hell.

Actually, I think I’ll let Sam Neill (as Dr. Weir in Event Horizon) sum this one up: “Hell is only a word. The reality is much, much worse.”


Cosmic Soup

I once heard someone (I think it was Neil deGrasse Tyson, but I might be wrong) describe the universe with a really cool analogy: it’s just like soup. You take onions and carrots and celery and mushrooms and rice and stick them in some water. Starting out, it’s not a soup. It’s a disgusting bunch of vegetables floating in some nasty cold water. But as it cooks, all the ingredients leach good stuff into the water and flavor each other, and eventually, you’ve got soup.

Which is a surprisingly good analogy for how our universe formed (at least, according to the best cosmological models we have as of January 2015 (I hate having to add that every time, but it’s true)). First, there was the big bang, which we know little about. The big bang cooled down and gave us a bunch of hydrogen, a little helium, and a tiny trace of lithium. Then it got too cold to make heavier atoms. Luckily, gravity kicked in. The hydrogen and helium (with some help from whatever the hell dark matter actually is) clumped together to form gas clouds. Those gas clouds collapsed to form stars. Those first stars were huge and bright and hot and died young. They died in massive supernovae, releasing heavy elements from their cores and creating new heavy elements on the spot from their high-energy radiation. Slowly, these heavier elements accumulated in the interstellar medium. Eventually, they started getting incorporated into the molecular clouds that went into forming new molecular clouds (I’m getting a horrible unwholesome image of a room full of people breathing each other’s flatulence; that’s why Neil deGrasse Tyson is on TV and I’m sitting here in my corner). These new molecular clouds could collapse to form not only stars, but also things like planets. And this went on and on until we reached today, which is (we think) about 14 billion years later. We’ve got chemistry all over the damn place. There’s chemistry in the sky and chemistry in the oceans and chemistry up to the tops of the highest mountains. My brain is full of chemistry (and from the sound of that sentence, my chemistry’s a little off again tonight…)

But what if it had happened differently? I mean, I’m pretty pleased with how our cosmic soup turned out (seeing as it allowed me to exist and all, which was nice of it), but you’ve got to admit that hydrogen, helium, and a tiny bit of lithium is pretty bland. It’s like that watery potato soup they give orphans in Christmas movies. Sure, it’ll keep you alive, but it’s not all that interesting. So what would happen if we started out with some different ingredients? What would we end up with then?

Let’s find out!

The Gumbo Universe: This universe starts out with a little of everything. Like I said, our universe started out with hydrogen, helium, lithium, and almost nothing else. And there’s a good physical reason for that: it cooled off so fast that there wasn’t time for anything more complicated than helium and lithium to form. It’s like flash-freezing: you don’t get any interesting crystals if you cool your water down too fast.

But in the Gumbo Universe, there are no such limitations. The universe starts out with all of the stable elements. The abundance of a given element is determined by its atomic number. Helium is ten times rarer than hydrogen. Lithium is ten times rarer than helium. And so on. The Gumbo Universe is 90% hydrogen, 9% helium, 0.9% lithium, 0.09% beryllium, 0.009% boron, 900 parts per million carbon, 90 parts per million nitrogen, 9 parts per million oxygen, 900 parts per billion fluorine, 90 parts per billion neon, and so on until uranium, element 92, which would make up only 90 atoms out of every 1, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000.

To my surprise, the Gumbo Universe’s hydrogen-to-helium ratio is pretty close to ours. But this universe has a massive overabundance of lithium, beryllium, and boron. These elements aren’t heavy by human standards (lithium floats in water, although not for very long, since it tends to catch fire and explode), but they might as well be lead boots as far as the cosmos is concerned. All these surplus heavy elements mean stars are going to form sooner, be denser, and probably start fusion sooner. Collisions with high-speed protons (i.e., the hot hydrogen atoms surrounding the metal-rich cores of these weird stars) will rapidly convert most of the lithium to helium (which also happens in our universe). The same thing will happen to the boron (interestingly, proton-boron fusion is being studied in our universe, since it doesn’t produce neutron radiation, which (because it’s evil) damages DNA and turns innocent substances radioactive). And when those beryllium atoms get hit by alpha particles (which are the same thing as hot helium nuclei, which, again, we’re going to have plenty of), they’ll turn into carbon and neutrons. The same thing happened in our universe, which is why, in element abundance graphs like the one in this paper, there’s a massive dip in abundance from lithium to beryllium to boron. Actually, physics ensures that, since the element composition of the Gumbo Universe starts out pretty similar to that of our universe, its ultimate composition is probably going to be similar, too.

Its structure, on the other hand, won’t be. At my estimate, I’d need at least four separate PhD’s and a supercomputer (which still I don’t have. Stupid thrift stores. Never have anything good.) to provide even a good guess what state the stuff in the Gumbo Universe would be like. I suspect the stars would be smaller, since their heavy-element cores would let them ignite fusion earlier, and their light would blow away what remained of their molecular clouds. These stars would probably be red dwarfs (or their exotic cousins), but probably wouldn’t be as long-lived as red dwarfs in our universe. As for galaxies, they’d probably still form (galaxy formation is driven mainly by the gravitation of matter and dark matter (whatever the hell it is)). As for whether they’d be larger or smaller than the galaxies in our universe, I can think up good arguments for both. I can see them being smaller because so many stars would form so quickly, which would blow away a lot of gas and slow star-formation rates, meaning lots of little galaxies a lot closer together. But then again, if the stars in the Gumbo Universe are red-dwarf-like, then their radiation pressure will be pretty weak, which might actually let galaxies grow larger than they do in our universe. I leave that as an exercise to the reader (which is the smart-ass way of saying “I can’t be bothered.”)

But what about the question that has plagued us (probably) since the dawn of thought: Could there be life forms in the Gumbo Universe? (Okay, I’m guessing Galileo didn’t ask himself that exact question, but you know what I mean. Although for some reason, I’m thinking Galileo would have really liked gumbo.) That’s really hard to answer. We know there’s life in our universe, but we don’t know how hard it is for life to form, how long it lasts once it forms, and whether it tends toward simplicity or complexity. But my guess is that the Gumbo Universe would be even more fertile than our own. It would have the elements needed to make life (hydrogen, carbon, oxygen, nitrogen, phosphorus, sulfur, et cetera) right from the start. And to boot, with its smaller stars, it would (probably) have fewer supernovae, which means larger portions of the galaxies would be habitable, since supernovae are probably very unhealthy for life as we know it.

The Julia Child Universe: Julia Child was famous for a lot of things. She was famous for her PBS cooking shows, for her attention-getting voice, for her love of cooking, and for being shockingly tall (6’2″ (188 cm), if IMDB is to be believed). I grew up watching her, but she was cooking on TV when my parents were children. She was famous for her show The French Chef, and one of her most famous recipes (and also the last meal she ate before she died, if Wikipedia is right) was her french onion soup. French onion soup is pretty much just finely-chopped onions simmered in beef stock.

And why on Earth, you may be asking, am I talking about TV chefs and onion soup? Because the French Onion Soup universe, like french onion soup itself, has very few ingredients. The French Onion Soup universe is made entirely of Uranium-238. You might be saying “That’s absolutely ridiculous.” And you’d be right. But I’ve never let that stop me before.

Well, to nobody’s surprise, the Julia Child Universe would be weird. We’d start out with a bunch of gaseous uranium plasma which would gradually cool and coalesce into little dust grains. Those dust grains would collapse. Since fusing two uranium nuclei requires an external energy input, there wouldn’t be any ordinary stars to begin with. There would, however, probably be medium-temperature white dwarfs and neutron stars, which would form straight from the interstellar medium, shortcutting all that hydrogen-burning nonsense stars in our universe have to go through. And, for the same reason all the planets in our solar system don’t get sucked into the sun and all the stars in our galaxy didn’t get sucked into the supermassive black hole at the center (the reason mostly being angular momentum), there would probably also be uranium planets.

Uranium-238 is pretty stable. It’s stable enough that, if you swallow it, your biggest problem isn’t that you just swallowed something radioactive; your biggest problem is that uranium is a toxic heavy metal. But it is radioactive, and when you’ve got enough of it in one place, that radioactivity adds up. U-238 is, for instance, one of the reasons Earth’s interior stays hot enough to be fluid.

But now we’re talking about planet-sized masses of U-238. If Earth were made entirely of uranium, it would have a radius of something like 4,000 kilometers, 60% of its actual radius. It would also produce 5e18 watts of heat from alpha decay (at least at the start of its life), which would be enough to make it glow cherry-red and probably melt.

Sadly, no planet is immortal, even when it’s made of solid uranium. U-238 decays (with a half life of 4.468 billion years) into Thorium-234, releasing an alpha particle (helium nucleus). Over time, the alpha particles will steal electrons from the uranium and thorium atoms, and all those uranium planets will develop helium atmospheres. But it doesn’t end there: Thorium-234 decays (by emitting an electron) with a half-life of 24 days into metastable Protactinium-234 (metastable meaning the nucleus is excited, and will therefore probably release a gamma ray). Regular Protactinium-234 decays by electron emission to Uranium-234, with a half life of 1.17 minutes. Uranium-234 is also an alpha emitter, meaning it decays into Thorium-230 and helium. Thorium-230 decays into helium and Radon-226, which has a half life of around one and a half thousand years. (And for those who are picky and obsessive like me, yes, there would be small quantities of other elements produced by things like spontaneous fission and cluster decay, but I’m keeping things simple.)

This is one weird planet we’ve got. By the time enough of it has decayed to give it an atmosphere as substantial as Earth’s, it’s still probably hot enough to glow. And that atmosphere is just about as toxic as you can imagine: it’s composed primarily of helium, so your voice would be all funny. The helium would also be scorching-hot, so your voice would get really funny. And it would be extremely dense and seriously radioactive, making it even worse than Venus’s atmosphere (which is the closest thing I can imagine to actual Hell).

But the decays would go on. Radon-226 is a noble gas. It decays into Radon-222 (again, by alpha decay), and then into Polonium-118 (not the kind of Polonium people use to poison Russian guys). As it decayed, there would be a fine snow of extremely radioactive isotopes, which would probably give the air an extremely faint blue glow. Most of those isotopes have half-lives measured in minutes or seconds (or microseconds), but you’d most likely end up with measurable quantities of Polonium-210 (that’s the kind you use to very suspiciously murder Russian guys), Lead-210, and Bismuth-210. But all roads that start at Uranium-238 eventually reach Lead-206 (sounds like a really terrible Johnny Cash parody). Lead-206 is stable, and makes up about a quarter of the lead atoms we find here on Earth (there are other stable isotopes). So, after around 4.4 trillion years, there would be less than one one thousandth of the original U-238 left. Pretty much everything else would be either lead or helium.

But that’s not the end. During its transformation to Lead-206, Uranium-238 has given birth to no less than 8 alpha particles, which will ultimately become helium atoms, So, after a long time, the mass of the Julia Child Universe would consist of 84.5% Lead-206 (by mass) and 15.5% Helium-4. 15.5% of one solar mass (in our universe, and when it’s made out of hydrogen) is enough stuff to make a proper star (albeit a small one). It’s harder to make a star out of helium, though, since helium atoms take more energy to fuse together. Stars weighing 15.5% of a solar mass generally can’t burn helium. That is, unless they have enormously dense, hot cores with crushing gravity. Which would most certainly be the case of some of our uranium white dwarfs and our neutron stars. So, for a brief while, stars would burn in our weird-ass sky. I say “a brief while” because, when you compress it to such high pressures and densities, helium tends to detonate more than burn. Our stars would last a few hours or a few days, burning purplish-white with fusion energy.

Helium fusion is a little complicated, which is why it takes stellar pressures to get it going. First, two helium nuclei fuse to form Beryllium-8. Then, another helium nucleus fuses with Beryllium-8 to form Carbon-12, which is the carbon on which our chemistry is based. But it gets better: it turns out that you can keep adding helium nuclei until you get all the way up to Iron-56 and Nickel-56, after which the fusion no longer releases energy. You’d end up with most of the ingredients for life as we know it, although they’d all be stuck on the surface of white dwarfs and neutron stars. Still, Frank Drake and Robert L. Forward made a passable case for life on a neutron star in Dragon’s Egg, so who knows? And white dwarfs tend to hold their heat for billions of years, so you might see very flat critters crawling around on miniature lead stars.

Surprisingly, even this weird universe would ultimately produce planets made of more familiar stuff. It turns out that collisions between neutron stars can produce elements like thorium and gold, and other elements which could fission into lighter elements. Neutron star collisions are pretty violent things, so some of this stuff would get flung out into space. Neutron stars have a death-grip on their matter, so I imagine it wouldn’t be nearly enough to form an actual proper hydrogen star, but it would probably be enough to form a planet.

Imagine it: a planet made of gold, iron, carbon, and uranium, with an atmosphere of helium and carbon dioxide, inhabited by radiation-hardened snails with lead shells. Sound implausible? How could it possibly be more implausible than the star-nosed mole?

The “Blinded by the Light” Universe: Can you tell my mom made me listen to too much classic rock when she was driving me to school? Until now, all our hypothetical universes have been made of matter: protons, neutrons, and electrons. But what if the mass of the universe was composed entirely of photons? That is, particles of light.

This one’s a lot trickier. In order for anything really interesting to happen, the universe has to expand in just the right way, and there has to be just the right number of photons. If the universe expands too fast (which can happen when there are too few photons) or too slow (if there are too many photons), it’ll end up as a diluted infrared soup (the former case) or a singularity (the latter). But if everything goes just right, and the universe expands and then comes to a halt while at least some of the photons have energies above 1022 kiloelectronvolts (meaning wavelengths shorter than 0.0012 nanometers), then interesting stuff can happen.

The universe is really weird. A gamma ray with an energy of 1022 kiloelectronvolts effectively has twice the mass of an electron. Thanks to quantum mechanics (the giver of headaches, by royal appointment), a gamma ray with an energy equal to or greater than 1022 keV can suddenly turn into an electron and a positron (its antiparticle). Normally, photons can’t interact with each other, since they have no charge. But if one photon should collide with another photon that’s momentarily popped apart into two charged particles, then they can interact. Sometimes, they can even bounce off of each other (see this Wikipedia article for a brief introduction).

But what exactly does that mean? Well, to be honest, I’m not sure. Photons are complicated. They have energy and angular momentum and all sorts of other stuff they didn’t teach in the English department. I don’t know whether life or intelligence of any kind could exist in this universe. But I imagine interesting structures could emerge, as long as there were enough high-energy gamma rays left over. I’m imagining a Feynman diagram big enough to wallpaper an airplane hangar, covered in a terrifying spiderweb of lines, photons bouncing off photons and transferring angular momentum back and forth. Let’s face it, that wouldn’t be any wilder than the universe we have: a soup of photons bouncing off of electrons, and electrons shuffling between atoms made of protons and neutrons.

The Universe is Made of Spiders: The Spider Universe has no explanation. It consists entirely of spiders which weave airtight tubular webs containing long-lived radio-isotopes. Plaques of mold feed on these isotopes. Fruit flies feed on the mold. Spiders feed on the fruit flies, and endlessly weave. Their air-filled tunnels are no thicker than your finger, and spread so thinly that each is separated from its nearest neighbor by the diameter of a star. But they’re all connected. Even though no single spider will ever travel from one node to the next in its lifetime, there is a steady traffic of genes to and fro. An endless parade of spiders, back and forth, back and forth in a network far more fragile and gossamer than the thinnest gold leaf.

In case you’re worried I just had a seizure there, I didn’t. I think. You see, according to recent physics, the universe as it exists today will collapse if its density is greater than one hydrogen atom per cubic centimeter. Locally, the density can be much higher (like, for example, on Earth). The same applies to mysterious networks of radioactive spiderwebs that appeared from nowhere at the beginning of time with no explanation. And when you consider that our current cosmological models pretty much all say “First there was the Big Bang, which for some reason created a bunch of energy and matter (but more matter than antimatter, for some reason). We don’t know why, but then everything else happened”, the spider thing doesn’t seem so far-fetched. Okay, maybe a little far-fetched, but isn’t it cool that we still have stuff to learn about the start of the universe?


All kinds of explosions.

As you’ve probably worked out by now, I’m a big fan of explosions. Since this ridiculous blog began, I’ve blown up rabbits (don’t worry–hypothetical rabbits), stellar-mass balls of gold, grains of neutronium, and I’ve nearly blown up the earth with an ultrarelativistic BB gun. As you’ve probably also figured out, I’m a big fan of bizarre thought experiments, thought experiments based on ideas boiled and distilled down to their absolute essentials. With that in mind, let’s blow some more shit up!

But before we can get started, we have to decide what an explosion is. For the purpose of this thought experiment, we’re going to use a one-meter-diameter sphere of space anchored to the surface of the Earth, just touching the ground. The explosions will consist of energy (in the form of photons of an appropriate wavelength) magically teleported into this sphere. (I still haven’t decided what symbol to use for the magic teleporter in my Feynman diagrams.) With that cleared up, let’s get blastin’.

The smallest possible explosion.

It’s pretty difficult to decide on the lower limit for the size of a one-meter-diameter explosion. First of all, that one-meter sphere is already full of all kinds of energy: solar photons, the kinetic energy of air molecules moving at high speeds, the rest-mass energy of those air molecules, et cetera. But even if the sphere were completely evacuated, quantum mechanics tells us that the lowest amount of energy that a volume of space can possess is greater than zero: its zero-point energy or vacuum energy.

To simplify things (and to keep me from having to learn the entirety of gauge field theory while writing a blog post), we’re going to say that the lowest-energy explosion we can create has the energy of the longest-wavelength (and therefore lowest-energy) photon we can fit in the sphere: 1 meter. That’s towards the high-frequency (short-wavelength) end of the radio spectrum. It’s not quite a microwave (those have wavelengths on the order of a centimeter), but it’s shorter than the photons used to transmit FM radio signals. Needless to say, it would impart a pretty much un-measurable quantity of energy to our sphere of air. A 1-meter photon carries 1.986×10e-25 joules of energy, the same energy as an oxygen molecule puttering along at a grandmotherly 6 miles per hour (10 kph).

The most efficient possible explosion.

But while we’re using our magic vacuum-fluctuation laser (lots of magic in this article…), we might as well see how big an explosion we can make with a single photon. We know the minimum is 1.986×10e-25 joules. But what’s the highest-energy photon we can stick in there? (Sounds like a plot to a horrible science porno…) I’m not a physicist, but I would guess that it’s a photon with a wavelength of 1 Planck length. Here’s my logic: the Planck length is the smallest length that makes sense according to our current laws of physics. To carry energy, an electromagnetic wave must change over time (or space, which work out to be part of the same thing). In order to take two different values, the wave’s crest and trough must be at least 1 Planck length apart. Of course, weird things happen on the Planck scale, so who knows if an electromagnetic field varying by a large quantity over 1 planck length would even make sense, or even behave like a photon, but you can say this with some certainty: a photon with a wavelength shorter than that doesn’t make a lot of sense.

A photon with a wavelength this short would be off-scale, as far as the electromagnetic spectrum goes. By definition, it would be a hard gamma ray, but that’s only because we humans don’t have access to the high-energy regions of the spectrum, so we say “Anything with a wavelength between A and B is an X-ray. Anything with a wavelength between B and zero is a gamma ray. Stupid gamma rays. Who needs ’em?”

This is a gross oversimplification, but photons tend to prefer to interact with objects that are roughly their same size. Visible photons interact with the electron clouds of  large molecules (like chlorophyll, which is good if you like oxygen). Infrared photons interact with large molecules directly, making them rotate or move. Radio-frequency photons interact only with big crowds of mobile electrons, like you find in plasma or radio antennas. In the other direction, ultraviolet photons interact with atoms and their bonds, either knocking outer electrons loose or breaking the bonds. X-ray photons interact with the tightly-bound electrons in lower energy states (I’m afraid to say “closer to the nucleus,” because that’s not quite right, and people smarter than me will make fun of me; but we’ll pretend that’s how it works to speed things along). Gamma-ray photons interact with the nucleus directly. They can push the nucleus into strange high-energy states or, if they’re the right wavelength, pelt protons and neutrons loose.

The physics of extremely short-wavelength gamma rays is much more complicated. That’s partly because, once a gamma ray passes an energy greater than 1022 keV (the kinds of energies you get when you heat something to several billion Kelvin) have enough mass-energy that they can spontaneously turn into matter: a 1023 keV gamma ray can briefly become an electron and a positron, which rapidly annihilate to re-form the gamma ray. The higher your photon’s energy gets, the more important these bizarre transformations become. Basically, once you get above 1022 keV, your photons start behaving less and less like light and more and more like matter.

Our Planck-length photon would (probably) be small enough to pass through all ordinary matter. It might pop a quark loose of a proton or a neutron, but I don’t really know. This photon would carry an energy far greater than 1022 keV. Indeed, its energy wouldn’t be measured in the peculiar particle-physics unit of the electronvolt, but rather in freakin’ megawatt-hours. This photon would add as much energy to our sphere as the explosion of three tons of TNT, which would form a cube large enough to contain our sphere with room to spare. From one…single…photon. Physics is scary.

Explosions, both conventional and nuclear (ain’t I posh?).

If you Google the phrase “largest conventional explosion,” you’ll probably dig up an article on Operation Sailor Hat, in which the U.S. Navy built a 500-ton Minecraft-style sphere of TNT:

It made a real mess of the decommissioned test ships anchored just offshore, and left a crater in Hawai’i that still exists to this day. It remains one of the largest intentional non-nuclear explosions humans have ever created. This isn’t relevant to our thought experiment, but I’m easily distracted by 500-ton piles of TNT.

In everyday life, a “conventional explosion” is one created by a chemical reaction of some kind. This ranges from the rapid burning of a lot of wheat dust in a grain silo to the bizarre high-tech cube-shaped molecule octanitrocubane. An explosion that gets most of its power from the fission of radioactive elements (or the fusion of light elements) is a nuclear explosion. Simple.

But you can think of it another way: the difference between conventional chemical explosions and nuclear explosions is a matter of temperature. Explosives like TNT produce gases with temperatures of thousands of degrees Kelvin. Nuclear explosions produce temperatures in the million to hundred million Kelvin range.

Since we’ve got a magic sphere of air we can pump energy into (how convenient!), let’s make one of each kind of explosion!

For the conventional explosion, we’ll heat the air to a temperature of 5,000 Kelvin (about as hot as the surface of the sun). Our sphere has a volume of 0.52 cubic meters, and air has a volumetric heat capacity of about 0.001 joules per cubic centimeter per Kelvin. Therefore, heating the air to 5,000 kelvin will require 2.6 million joules. We’re talking about a decent-sized bang here, equivalent to just over half a kilogram of TNT. Not exactly spectacular, but certainly not the kind of explosion you want to hold in your hand. (Actually, thinking about it, why would you want to hold any explosion in your hand? That was silly of me.)

For the nuclear explosion, we’ll heat our sphere to 10 million Kelvin, which is a compromise, since nuclear explosions are complicated beasties and their temperature varies very rapidly in the span of microseconds. I should point out that I’m still using a volumetric heat capacity of 0.001 joules per cubic centimeter per Kelvin, which is absurd. At these temperatures, we’re not just making molecules move faster–we’re breaking them apart. And blasting electrons off the individual atoms. Both of these things take energy, so heating the plasma to 10 million Kelvin will actually require more energy input than my idealized equation suggests. But I digress. We’re looking at an explosive energy of about 5.2 billion Joules, which is about one and a quarter tons of TNT. I’m disappointed. Even the smallest nuclear weapon ever made had a yield larger than that. (Incidentally, the smallest nuclear weapon ever made (by the U.S., at least) was the W54 warhead. This is what they used in the “Davy Crockett,” which was a nuclear warhead launched from a fucking bazooka. Think about that.)

But the real temperature of a young nuclear fireball (good name for a band) is probably higher than this. After the fission of the nuclear material is complete, there’s a brief period where the nuclear explosion is mostly made up of high-energy nuclear radiation (hard x-rays, gamma rays, and particles). Then, it gets absorbed by the evaporating bomb casing and the surrounding air and (mostly) turns into heat. It’s not unreasonable to assume that the temperature in a baby nuclear fireball (bad idea for a child’s doll) is closer to 100 million Kelvin, which works out to almost twelve and a half tons of TNT. Still not nuclear in the traditional sense, but certainly more than enough to bust up a whole city block.

Turning it up to 10.

I’m tired of messing around. I want a real boom. We’re sticking a full megaton into that sphere, and damn the consequences!

Well, with energy densities this high, you can’t really even pretend that the volumetric heat capacity equation applies. Even at 100 million Kelvin, we were getting into the region where atoms are stripped of most or all of their electrons, which is where matter stops behaving even remotely the way it does at ambient temperatures. Much hotter, and we’re going to start splitting the atoms themselves.

Instead, to describe the conditions in our magic sphere when 1 megaton is pumped into it, I’m going to make two assumptions: the energy is deposited over the course of 1 nanosecond, and the superheated sphere radiates like a thermodynamic blackbody, which is to say the same way red-hot steel does and stars (mostly) do.

An energy release of 1 megaton over 1 nanosecond gives us 4.184 trillion trillion watts of radiated power. The sphere will very briefly shine as bright as a small star, and will have a surface temperature of 69 million Kelvin. Then, ba-boom, say goodbye to your city. Next time you build a city, don’t go letting people like me build magic energy-spheres in the middle. I hope you’ve learned your lesson.

This thing goes to 11.

Sorry. Couldn’t help myself.

Let’s stick in 50 megatons now. That’s about the energy released by the Tsar Bomba, a Soviet hydrogen bomb that produced a mushroom cloud that rose above the top of the stratosphere. For comparison, really impressive explosions and big thunderstorms and volcanic eruptions and such are lucky if they can make it into the stratosphere at all, let alone breaking all the way through the damn thing.

I can do all the math here just like before: 210 trillion trillion watts, a temperature of 185 million Kelvin, yadda yadda yadda. The thing is, as I wrote in “A Piece of a Neutron Star“, up to a point, an explosion is an explosion. The energy of an explosion gets spread over a large volume fairly quickly, and ordinary fluid dynamics and thermodynamics take over. Ever notice how a conventional explosive produces a mushroom cloud that looks an awful lot like the mushroom from a nuclear explosion? That’s because both are powered by the same thing: a rising plume of hot air. While it’s true that in the nuclear explosion there’s a lot more air and it’s a hell of a lot hotter, it’s easy to see that the two are related. They’re part of the same spectrum. A nuclear explosion is like a conventional explosion, only it’s larger, and it produces a lot more radiant heat.

This thing goes to 111.

This scaling law (which real physicists have investigated in great detail) seems to hold for larger and larger energies. Small asteroid impacts create explosions that are very much like nuclear explosions (with some extra effects from high-velocity ejecta and from the entry trail and so on). Even impacts like Chicxulub (which may or may not have helped kill off the dinosaurs, but certainly ruined everybody’s day for several thousand years) produce a fairly ordinary shockwave, and then a fireball that reaches an enormous, but reasonable, size before cooling to ordinary temperatures. The excellent Impact Effects Calculator tells me that a Chicxulub-like impact would produce a visible fireball with a radius of about 66 kilometers. This would reach up through the stratosphere, and about halfway to the edge of space, so it would probably be flattened, with a blurry, undefined edge at the top, but it would still be very much like what it is: a 100 million megaton explosion.

But like all scaling laws, the explosion spectrum eventually gives out. Once you start imagining blasts with the same kinetic energy as, say, a 100-kilometer-wide stone asteroid, you’ve passed over a threshold. Beyond this threshold, the assumptions that let us imagine our earlier explosions break down. Assumptions like “Shockwaves and heat plumes travel through the atmosphere, but the atmosphere doesn’t go flying off or anything” and “The crust is firmly attached to the rest of the Earth.” (It’s nice that we live in a time when we can make assumptions like that. Not that we could live in a time when the crust wasn’t attached, but it’s nice to know we (probably) have that kind of stability). We move out of the realms of meteorology and geology and into the realms of astrophysics. When you talk about 100-kilometer asteroid impacts, you’re no longer talking about “an asteroid hitting the Earth.” You’re talking about “two celestial bodies colliding.” Things like organic life and atmospheres crumble (and burn and evaporate) before energies like this.

Which is a (very) roundabout way of saying that a 90-billion-megaton explosion isn’t really an explosion anymore. It’d blow the atmosphere off a pretty big portion of the planet, peel back the crust, and pave some or all of the Earth in magma. Larger explosions could put sizeable dents in the Earth, or blow off enough material to push it into a different orbit. Not that we care: we’ll all be dead. Again. Sorry. Planet-killing is a bad addiction to have.

Hey! Where’d my explosion go?

This transition from fluid dynamics to astrodynamics has an ultimate limit. You can only squeeze so much energy into a 1-meter-diameter sphere and have it come back out. For this, you have Albert Einstein and Karl Schwarzschild to thank.

Energy and mass are equivalent. Not only can one be converted into the other, but they also produce and react to gravity in the same way. Because of this, if you try to cram more than 3.029e43 Joules (7239 trillion trillion megatons) of energy into a sphere 1 meter across, you won’t get an explosion at all. Your energy, no matter what form it’s in, will vanish behind an event horizon. This is bad news for the Earth. Partly because this energy will weigh 56 times as much as the Earth (over a fifth the mass of Jupiter), and will therefore screw up its orbit and either freeze us or boil us. Of course, the slow and painful destruction of the entire human race, all of our infrastructure and achievements, everything you and I and everybody else cares about, and also all life on earth, is the least of our problems. Because now we’ve got a 1-meter black hole sitting in the middle of a public park somewhere (I moved it away from downtown, to be nice. Sorry.) The Earth will swirl into the hole like a sinkful of water down a drain. That’s not just me failing to be poetic, that’s about how it’ll be. The whole Earth wont’ fall into the hole in an instant, nor will it be instantly spaghettified. Remember that, until you get close to it, a black hole behaves like any other object of the same mass. So the bulk of the Earth will fall towards the hole (thereby putting the hole at the middle of the planet) and everything else will collapse around it. We will, briefly, have a planet cracked and hollowed like a broken Kinder egg. Then we will have a ball of incandescent gas around a tiny black hole. Then we will have an accretion disk whose molecules do not resemble the farmers, sailors, priests, road signs, eggs benedict, and fire ants they were once part of. This is the point at which the explosion stops being an explosion. This is the limit.

Hey, this thing goes to 10.999.

That’s no fun. Well, I tell a lie–black holes are great fun to play with. (From a large distance.) But we want explosions, not black holes! We can talk about black holes some other time (hint hint). What if we put a little less than 3.029e43 Joules into our magic sphere? If that happens, boy oh boy do we get some fireworks!

The first thing that’ll happen is that the spacetime around the sphere will go from the gentle curvature (gravity) produced by the Earth, Sun, and other celestial bodies to a violent light-bending time-warping curvature. This does not end well for us. (why would you think it would? You’re silly.) A single powerful pulse of gravity waves races out at the speed of light, turning the Earth to gravel in a few milliseconds. Right on its heels comes a wave of radiation with almost the power of a supernova (almost, as in, 0.3 times as energetic as a supernova. Serious shit.) The Earth does not have time to fall into the region of ridiculous energy density and turn it into a black hole. That’s because the Earth is busy turning into a pancake of purple-white plasma and racing outwards at high speed. If the pancake hits anything, the flash will destroy the solar system. (Which sounds like it should be a line from Spaceballs). If it doesn’t hit anything, the supernova will destroy the solar system.

The moral of today’s story is: Don’t trust a man who says he has a magic sphere. He might kill everything.

The other moral of today’s story is: If you study a little physics, you can take any thought experiment to its absolute logical limit. Which, as I’m discovering, is pretty damn fun.


Shaving too.

The hilarious and bizarre Mitch Hedberg once said “Every time I go and shave I assume there’s someone else on the planet shaving, so I say ‘I’m gonna go shave, too.'” Because I am an obsessive fool who can’t leave anything alone, I started wondering if you could actually reasonably say that. I mean, there are a lot of people in the world, and a lot of people who shave, so it’s entirely possible that there’s someone shaving every second of the day.

This is a perfect place for Fermi estimation, or, if you prefer, back-of-the-envelope calculation. It’s a great method for getting a quick idea of the scope of a problem.

There are about 7 billion people on Earth. In many cultures, only the men shave. Let’s assume that half of the people in the world are men. That gives us 3.5 billion potential shavers. But, except in rare cases, men don’t start shaving until their beards begin growing at puberty. Let’s say beard growth starts at age 15. A randomly-chosen person could be pretty much any age, let’s say from 0 to 70. Only that percentage of men between 15 and 70 shave, which comes out to 79%, or 2.756 billion.

It takes me about 15 minutes to shave. Let’s assume that all the men in the world shave every day at a random time of day (this ain’t a realistic asumption, lemme tell you, but it’ll help compensate for the fact that most of the men in the world are in a different timezone than me, and for other weird factors like that.) There are 96 15-minute blocks in a 24-hour day. The probability of a man picking a particular 15-minute block to shave is 0.01. Therefore, the probability of a man not picking a block to shave is 0.99. The probability of every shaving-age man not picking the block in which I’m shaving is 0.99^(2,756,000,000), or 2.045e-12029404. When you see a negative exponent that large, your number is, by any sensible definition, zero.

Mitch had it right. So, from now on, when I shave, I’ll say “I’m gonna shave, too.”


Exploding rabbits.

(Courtesy of Wikipedia.)

I have a thing against rabbits. I don’t like them. They fill me with contempt. There’s absolutely no reason for this. It’s an utterly irrational hatred. Because of this particular neurosis, during a conversation with a friend, I happened to say something about vaporizing a rabbit. That sent my loony swamp-bog brain spinning off on another of its tangents, and I started to wonder What would happen if you vaporized a rabbit?

For the sake of this thought experiment, I’m going to start off assuming that a rabbit weighs 1 kilogram. That’s within the mass range listed by Wikipedia, but Wikipedia can’t always be trusted. But by virtue of the fact that they exist, we know that rabbits weigh more than 0 kilograms, and by virtue of the fact that we don’t inhale rabbits and get horrible nibbling-rabbit pneumonia, we know that they probably weigh more than 0.000 000 000 000 001 kilograms (1 picogram, which is about the mass of a bacterium). And from this oft-referenced report from the BBC, of Ralph the Unthinkably Large Bunny (who I must admit is kinda cute), we know that rabbits can reach 7.7 kilograms. So 1 kilogram is not unreasonable.

Now that we’ve got that bit of pedantic obsessiveness out of the way, we can proceed.

Most organisms contain quite a lot of water. The density of a human being is similar to the density of water. (If you can float in a pond or a swimming pool, your density is less than that of water, meaning less than 1,000 kilograms per cubic meter. If you have to tread water, your density is higher than 1,000. For the record, I float.) So, for the sake of simplicity, let’s pretend that our 1-kilogram bunny is made entirely of water, like a really disappointing version of those chocolate Easter bunnies. Let’s also assume that it starts out at typical rabbit body temperatures: 100 Fahrenheit, 38 Centigrade, or 311 Kelvin. In order to vaporize this all-water rabbit, we have to add enough heat-energy to it to raise its temperature to the boiling point, which is 212 Fahrenheit, 100 Centigrade, or 373 Kelvin (Have you noticed that we have way too many fucking temperature units? It’s a pain.) That’s a difference of 62 Kelvin. To find out how much energy we need to boil this rabbit (and make some extremely watery rabbit stew), we need water’s specific heat capacity, which happens to be about 4.18 Joules per gram Kelvin.

Specific heat capacity is one of those nice units that just makes sense. Newton’s gravitational constant is measured in units of (Newtons * square meters) / (square kilograms). What the fuck is a square kilogram? Well, the constant is one of those universal constants that tells you, in a vague way, just how weak a force gravity is. Specific heat capacity, though, makes intuitive sense. Water has a specific heat capacity of 4.18 Joules per gram Kelvin (Not to be confused with Jules per Graham Kevin, who is the president of the Earth in the alternate reality where Canada became a totalitarian superpower). That means that, to increase the temperature of one gram of water by one Kelvin, you have to add 4.18 Joules of heat energy to it. The units tell you exactly what they mean, which is nifty.

Anyway, in order to heat our rabbit-shaped mass of water to boiling temperature, we need to add 259,200 Joules of heat energy. But notice that I said “to heat our rabbit-shaped mass to boiling temperature.” That’s not the same as actually making it boil. For that, we need to add extra energy. This extra energy won’t increase the temperature at all, but it will get the water over the hump and vaporize it. This extra energy is quantified by another constant: the specific heat (or enthalpy) of vaporization. For water, this is 2,260,000 Joules per kilogram. That means we need 2,260,000 more Joules to turn our rabbit-shaped water balloon into a rabbit-shaped cloud of steam. So, all told, we’re concentrating 2,500,000 Joules into a volume on the order of 1,000 cubic centimeters. 2,500,000 Joules is about the energy released in the explosion of half a kilogram of TNT, which seems to me (citation needed) like a decent fraction of a stick of dynamite.

Unfortunately, energy alone isn’t going to get us the explosion we’re looking for. Just because we have the equivalent of a stick of dynamite doesn’t mean we’re going to have the same explosion as a stick of dynamite. That energy is all bound up in the rabbit-shaped cloud of steam.

What will get us the explosion we’re looking for, however, is the fact that we’ve got a cloud of hot gas compressed to the density of water and eager to expand. From the ideal gas law (and assuming a rabbit volume of 1,000 cubic centimeters), the cloud will begin at a pressure of 1,699 atmospheres (172.19 megapascals). That’s about half the pressure generated by the burning gunpowder in a .357 magnum cartridge. Maybe not enough to kill you, but certainly enough to make your ears ring. And enough to make you stand in the meadow blinking while a fine mist of rain falls around a little crater in the grass, asking yourself what the hell just happened.

But you know what? Rabbits aren’t just made of water. They’re made of all sorts of weird shit like water, tubulin, hemoglobin, cadherin, vitamin D, collagen, phospholipids, and more rabbit-semen than anybody wants to think about. And from cooking (and from that one scene in The Lord of the Rings) we know that heating a rabbit up to boiling won’t destroy all of its chemical bonds.

I want to make sure this rabbit is gone. I mean gone. Vaporized. I want to rip its fucking molecules apart, so that there’s no trace of fucking rabbit left. I should probably talk to my therapist about this. But for now, I’ll finish what I started.

As it turns out, I can still reasonably assume that the whole 1-kilogram rabbit is made of water, because the hydrogen-oxygen bonds in water are some of the strongest you’ll find in ordinary materials (carbon-hydrogen bonds are stronger, but not by much; nitrogen-nitrogen bonds are much stronger, but there’s not a lot of gaseous nitrogen floating around in a rabbit’s tissues, so we don’t need to worry about it). We’re looking at 55.56 moles of rabbit (NOT 55.56 moles of rabbits; disgusting shit happens when you try to assemble a mole of small mammals). The bond-dissociation energy for the hydrogen-oxygen bond in water is a shade under 500,000 Joules per mole, and there are two such bonds in every water molecule, so the total energy will be about 1,000,000 joules per mole. That means that completely vaporizing a rabbit will require something like 55,500,000 Joules, which is (roughly) equivalent to the detonation of 10 kilograms of TNT. 10 kilograms of TNT works out to just over 6 liters, so imagine two three-liter soda bottles (or six big liter-size beer steins, or a 1-gallon jug and a half-gallon jug) filled to the brim with TNT. That’s more explosives than you find in some artillery shells. You know what that means?