engineering, math, physics, thought experiment

The Treachery of Plumb-Lines

I’m pretty sure that’s my most pretentious article title to date, but really, the only pretentious thing about it is that it’s a Rene Magritte reference, because if you read it literally, that’s exactly what this article is about.

Imagine two skyscrapers. Both start from ordinary concrete foundations 100 meters by 100 meters, and each will be 1,000 meters high, when finished. We’ll call the first skyscraper Ruler, and the second skyscraper Plumb, for reasons I’ll explain.

Ruler is built exactly according to architectural specifications. Every corner is measured with a high-grade engineer’s square and built at precisely 90 degrees. Importantly, Ruler is constructed so that every floor is precisely 10 meters above the previous one, and every floor is 100 meters by 100 meters. This is done, of course, using a ruler. Because it’s kept so straight and square at every stage, Ruler is a very straight, square building.

Plumb, on the other hand, is kept straight and square using one of the oldest tricks in the architect’s book: the plumb-bob. True story: plumb-bobs are called that because, back in the day, they were almost always made of lead, and the Latin for lead is plumbus (or something like that; I took Latin in high school, but the teacher got deathly ill like two weeks in, so I never learned much). A well-made and well-applied plumb-bob is an excellent way to make sure something is absolutely vertical.

The builders of Plumb do use a ruler, but only to mark off the 10-meter intervals for the floors. They mark them off at the corners of the building, and they make sure the floors are perfectly horizontal using either a modified plumb-bob or a spirit level (which is largely the same instrument).

One might assume that Plumb and Ruler would turn out to be the exact same building. But anybody who’s read this blog knows that that’s the kind of sentence I use to set up a twist. Because Plumb was kept straight using plumb-bobs, and because plumb-bobs point towards the center of the Earth, and because the 100-meter difference between the east and west (or north and south walls) gives the bobs an angle difference of 0.009 degrees, Plumb is actually 11 millimeters wider at the top than at the bottom. Probably not enough to matter in architectural terms, but the difference is there.

Not only that, but Plumb’s floors aren’t flat, either, at least not geometrically flat. The Earth is a sphere, and because Plumb’s architects made its floors level with a spirit level or a plumb-bob, those floors aren’t geometrically flat: they follow the spherical gravitational equi-potential contours. Over a distance of 100 meters, the midpoint of a line across the Earth’s surface sits 0.2 millimeters above where it would were the line perfectly, geometrically straight. This difference decreases by the time you reach the 100th floor (the top floor) because the sphere in question is larger and therefore less strongly curved. But the difference only decreases by around a micron, which is going to get swamped out by even really small bumps in the concrete.

“Okay,” you might say, “so if you blindly trust a plumb-bob, your building will end up a centimeter out-of-true. What does that matter?” Well, first of all, if you came here looking for that kind of practicality, then this blog is just gonna drive you insane. Second, it doesn’t matter so much for ordinary buildings. But let’s say you’re building a 2,737-meter-long bridge (by total coincidence, the length of the Golden Gate Bridge). If you build with geometric flatness in mind, your middle pier is going to have to be 14.7 centimeters shorter than the ones at the ends. That’s almost the length of my foot, and I’ve got big feet. It’s not a big enough difference that you couldn’t, say, fill it in with concrete or something, but it’d certainly be enough that you’d have to adjust where your bolt-holes were drilled.

What’s the moral of this story? It’s an old moral that probably seems fairly ridiculous, but is nonetheless true: we live on the surface of a sphere. And, when it comes down to it, that’s just kinda fun to think about.

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biology, science, silly, thought experiment

Life at 1:1000 Scale, Part 1

You can’t see it, but out in the real world, I look like a Scottish pub brawler. I’ve got the reddish beard and the roundish Scots-Irish face and the broad shoulders and the heavy build I inherited from my Scotch and Irish ancestors (the hairy arms come from my Italian ancestors).

What I’m saying is that I’m a bulky guy. I stand 6 feet, 3 inches tall. That’s 190.5 centimeters, or 1,905 millimeters. Keep that figure in mind.

When I was a kid, the motif of someone getting shrunk down to minuscule size was popular. It was the focus of a couple of books I read. There was that one episode of The Magic Schoolbus which was pretty much just The Fantastic Voyage in cartoon form. There was the insufferable cartoon of my late childhood, George Shrinks.

As a kid, I was very easily bored. When I got bored waiting in line for the bathroom, for instance, I would imagine what it would actually be like to be incredibly tiny. I imagined myself nestled among a forest of weird looping trees: the fibers in the weird multicolored-but-still-gray synthetic carpet my school had. I imagined what it would be like to stand right beneath my own shoe, shrunk down so small I could see atoms. I realized that the shoe would look nothing like a shoe. It would just be this vast plain of differently-colored spheres (that was how I envisioned atoms back then, because that’s how they looked in our science books).

Now, once again, I find myself wanting to re-do a childhood thought experiment. What if I were shrunk down to 1/1000th of my actual size? I’d be 1.905 millimeters tall (1,905 microns): about the size of those really tiny black ants with the big antennae that find their way into absolutely everything. About the size of a peppercorn.

Speaking of peppercorns, let’s start this bizarre odyssey in the kitchen. I measured the height of my kitchen counter as exactly three feet. But because I’m a thousand times smaller, the counter is a thousand times higher. In other words: two-thirds the height of the intimidating Mount Thor:

mount_thor

(Source.)

I remember this counter as being a lot smoother than it actually is. I mean, it always had that fine-textured grainy pattern, but now, those textural bumps, too small to measure when I was full-sized, are proper divots and hillocks.

I don’t care how small I am, though: I intend to have my coffee. Anybody who knows me personally will not be surprised by this. It’s going to be a bit trickier now, since the cup is effectively a mile away from the sugar and the jar of coffee crystals, but you’d better believe I’m determined when it comes to coffee.

Though, to be honest, I am a little worried about my safety during that crossing. There’s a lot more wildlife on this counter than I remember. There’s a sparse scattering of ordinary bacteria, but I don’t mind them: they’re no bigger than ants even at this scale, so I don’t have to confront their waxy, translucent grossness. There is what appears to be a piece of waxy brown drainage pipe lying in my path, though. It’s a nasty-looking thing with creepy lizard-skin scales up and down it. I think it’s one of my hairs.

I’m more concerned about the platter-sized waxy slab lying on the counter next to the hair. There are two reasons for this: First, I’m pretty sure the slab is a flake of sloughed human skin. Second, and most important, that slab is being gnawed on by a chihahua-sized, foot-long monstrosity:

8f87b071ca15a175804fa780020feade

I know it’s just a dust mite, but let me tell you, when you see those mandibles up close, and those mandibles are suddenly large enough to snip off a toe, they suddenly get a lot more intimidating. This one seems friendly enough, though. I petted it. I think I’m gonna call it Liam.

My odyssey to the coffee cup continues. It’s a mile away, at my current scale, but I know from experience I can walk that far in 20 minutes. But the coffee cup is sitting on a dishcloth, drying after I last rinsed it out, and that dishcloth is the unexpected hurdle that shows up in all the good adventure books.

The rumpled plateau that confronts me is 10 meters high (32 feet, as tall as a small house or a tree), and its surface looks like this:

cover-12-3_1

(Source.)

Those creepy frayed cables are woven from what looks like translucent silicone tubing. Each cable is about as wide as an adult man. If I’d known I was going to be exposed to this kind of weird-textured information overload, I never would’ve shrunk myself down. But I need my coffee, and I will have my coffee, so I’m pressing forward.

But, you know, now that I’m standing right next to the coffee cup, I’m starting to think I might have been a little over-ambitious. Because my coffee cup is a gigantic ceramic monolith. It’s just about a hundred meters high (333 feet): as tall as a football field (either kind) is long–as big as a 19-story office building. I know insects my size can lift some ridiculous fraction of their body weight, but I think this might be a bit beyond me.

All’s not lost, though! After another twenty-minute trek, I arrive back at the sugar bowl and the jar of coffee. Bit of a snag, though. It seems some idiot let a grain of sugar fall onto the counter (that grain is now the size of a nightstand, and is actually kinda pretty: like a huge crystal of brownish rock salt), which has attracted a small horde of HORRIFYING MONSTERS:

pharoh-ant4-x532-new

(Source.)

That is a pharaoh ant. Or, as we here in the Dirty South call them, “Oh goddammit! Not again!” In my ordinary life, I knew these as the tiny ants that managed to slip into containers I thought tightly closed, and which were just about impossible to get rid of, because it seemed like a small colony could thrive on a micron-thin skid of ketchup I’d missed when last Windexing the counter.

Trouble is that, now, they’re as long as I am tall, and they’re about half my height at the shoulder. And they’ve got mandibles that could clip right through my wrist…

Okay, once again, I shouldn’t have panicked. Turns out they’re actually not that hostile. Plus, if you climb on one’s back and tug at its antennae for steering, you can ride it like a horrifying (and very prickly-against-the-buttock-region) pony!

I’m naming my new steed Cactus, because those little hairs on her back are, at this scale, icepick-sized thorns of death. I’m glad Cactus is just a worker, because if she was a male or a queen, I’m pretty sure she would have tried to mate with me, and frankly, I don’t like my chances of coming out of that intact and sane. Workers, though, are sterile, and Cactus seems a lot more interested in cleaning herself than mounting me, for which my gratitude is boundless.

I’ve ridden her to my coffee spoon, because I’m thinking I can make myself a nice bowl of coffee in the spoon’s bowl.

I’ve clearly miscalculated, and quite horribly, too: the bowl of this spoon is the size of an Olympic swimming pool: 50 meters (160 feet) from end to end. Plus, now that I’m seeing it from this close, I’m realizing that I haven’t been doing a very good job of cleaning off my coffee spoon between uses. It’s crusted with a patchy skin of gunk, and that gunk is absolutely infested with little poppy-seed-sized spheres and sausages and furry sausages, all of which are squirming and writing a little too much like maggots for my taste. I’m pretty sure they’re just bacteria, but I’m not going to knowingly go out and touch germs. Especially not when they’re just about the right size to hitch a ride on my clothes and covertly crawl into an orifice when I’m sleeping.

You know what? If I can’t have my coffee, I think this whole adventure was probably a mistake. I think I’m going to return to my ordinary body. Conveniently (in more ways than one), I’ve left my real body comatose and staring mindlessly at the cabinets above the counter. He’s a big beast: a mile high, from my perspective. An actual man-mountain. I’ll spare you the details of climbing him, because he wears shorts and I spent far too long climbing through tree-trunk-sized leg hairs with creepy-crawly skin microflora dangerously close to my face.

Now, though, I’m back in my brain and back at my normal size. And now that my weird little dissociative fugue is over, I can tell you guys to look out for part two, when I’ll tell you all the reasons there’s no way to actually shrink yourself down like that and live to tell about it.

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physics, science, silly, thought experiment

The Overkill Oven

As I was lying in bed last night, I started wondering: “What if I had an oven that could heat its contents up to nuclear-fusion temperatures?” This is why I have trouble sleeping: my brain is very badly-wired. But still, that’s a perfect question for this blog. But as I was preparing to write the article, I got to thinking: Why limit myself to nuclear-fusion temperatures? Nuclear fusion only requires a few billion Kelvin. There are processes (particle-accelerator impacts and cosmic-ray collisions) that reach a trillion trillion kelvin!

Overkill Oven 450 Kelvin

Here’s my new oven. You’ll notice it has quite a few temperature knobs. That’s because, if I tried to fit 10^24 Kelvin all on one knob, that knob would have to be the size of a galaxy before the 100-Kelvin interval marks were far enough apart to see with the naked eye. The cool thing about the decimal number system, though, is that I only (“only”) need 24 knobs, each only marked with 10 intervals, to set temperatures hot enough to melt protons.

This new oven has a couple of interesting features. The first is the patented ceramic bowl-schist lining. Bowl-schist is an exotic metamorphic rock I imported from a parallel universe. Its heat conductivity is so low you could put a block of it next to a supernova and it’d be just fine. The second important feature is the power supply. Naturally, I can’t plug a fancy oven like this into a standard 240-Volt U.S. oven socket. Instead, the cable passes through a very narrow wormhole into the Handwavium Universe, which is stuck mid-big-bang, and therefore is absolutely flooded with energy. With all that set up, let’s cook! To celebrate my new oven, I think I’ll make a big beef roast, with some potatoes, peas, carrots, onions, and herbs and spices.

0.001 Kelvin

The trouble with the Oven of Doom is that the controls are a little difficult to get used to. But hey, I play Dwarf Fortress, so I’m no stranger to shockingly opaque controls. Still, starting out, I accidentally set the oven almost to zero Kelvin. I didn’t realize this until I saw the fur of oxygen and nitrogen ice growing all over my roast. Luckily, the Death Oven is also completely hermetically sealed during operation, to prevent operator death, so I didn’t freeze out all the air in the house. And defrosting was easy.

450 Kelvin

Overkill Oven 450 Kelvin

After that initial hiccup, my roast is coming along nicely. I’m making a brisket roast, so I should probably cook it long and low and slow, so it gets nice and tender. I just hope I don’t run out of patience before

1,000 Kelvin

Overkill Oven 1000 Kelvin

Well that could have gone better. In my defense, this oven has a lot of knobs, and if there’s anything resembling a knob or switch, I am compelled to fiddle with it. The roast was on fire for a few minutes, but once most of the fat burned off, it settled down. Now I’m left with an oven full of glowing orange soot and carbonized meat and vegetables. I can probably find some creature willing to eat it…

5,000 Kelvin

Overkill Oven 5000 Kelvin

The trouble with having a fancy high-power oven is that it’s really tempting to turn it up unnecessarily high in the hopes of getting your food finished as quick as possible. I think there might be something to all this “slow food” stuff I keep hearing about. Trying to cook my roast at 5,000 Kelvin has reduced it to a cloud of white-hot soot with a pale yellow vapor of sodium, potassium, and iron simmering over it. Still, at least I can be sure it’s safe for the people who insist on having their beef well-done.

10,000 Kelvin

Overkill Oven 10000 Kelvin

You know, I should probably close the shutter over that porthole… It’s getting awfully bright in there. I’m pretty sure the roast hasn’t escaped, but truth be told, when I look in there, all I see is this screaming blue-white fog of ionized carbon. On the plus side, if I hurry up and buy a second roast, I can cook it with the light from the first one.

100,000 Kelvin

Overkill Oven 1e5 K.png

I think I’m starting to understand now why the oven’s window is more of a peephole. It’s only three inches across, but already I shouldn’t be able to stand in front of it without my legs evaporating. Actually, I shouldn’t be able to have the peephole open without my house exploding in a horrendous fireball. The oven’s emitting more power from radiant heat alone than the Three Gorges Dam. But I can hold my hand in front of the porthole, no problem. I think I’m starting to see why the department store I bought it from was called BS & Sons…

5,000,000 Kelvin

Overkill Oven 5e6 K.png

I don’t think I have the right to keep calling this thing a roast, do I? It’s really just a soup of highly-ionized carbon, oxygen, iron (from the myoglobin in the meat, and from what used to be my nice new roasting pan), nitrogen, sulfur, and trace metals. On the plus side, I’ve got my own pet solar flare now!

10,000,000 Kelvin

It’s not all bad news, though. The oven is now self-powering. All those hydrogen atoms that used to be part of things like fats, proteins and starches have long since evaporated into a searing plasma. Now, though, they’re colliding fast enough that they’re starting to fuse. Not only am I getting extra energy from this, but I’m making homemade helium, too! Cooking’s fun!

100,000,000 Kelvin

Well, I’ve gone and overdone it again. I burned up all the helium I just made! Now it’s gone and fused to make more carbon vapor. I should probably call somebody about this. Frankly, at this point, I’m afraid to turn the oven off. I mean, since the thermal conductivity is pretty much zero, it’s never going to cool down. And if I open the door, I’m going to release as much energy as detonating 30 tons of TNT. I think I’ll just wall off the kitchen and pretend none of this ever happened…

500,000,000 Kelvin

I am now essentially cooking my roast with a continuous nuclear explosion. Also, I’m pretty sure that, even if I managed to cool it down, not even a physicist with a mass-spectrometer would be able to identify what the roast used to be. That’s partly because, of course, it’s been thoroughly vaporized. But also, the carbon nuclei have started fusing to form weird stuff like neon. If you find an organism that likes to eat neon, send it my way. I’ve got a roast for it.

1,500,000,000 Kelvin

My oven now contains as much energy as a half-kiloton nuclear explosion. The oxygen nuclei are fusing to form things like phosphorus, magnesium, and silicon. If the peephole wasn’t made of pure handwavium crystal, it would be emitting more power (briefly) than the Sun.

3,000,000,000 Kelvin

The good news is that I got my roasting pan back, and then some! All the light atoms have pretty much fused into heavier elements, which have fused to form Nickel-56. If I opened the door, I would be violently vaporized, but after the fallout cooled, the Nickel-56 would decay into Cobalt-56 and then Iron-56, and I’d be able to re-cast my roasting pan!

12,000,000,000 Kelvin

All that brilliant blue-white death-light that filled the oven is finally starting to fade. The bad news is that that’s only fading because the thermal radiation is so intense that it’s actually spontaneously turning into matter and antimatter, forming electron-positron pairs. The other bad news is that I’ve lost my roasting pan again: the energy of the particles in the oven has exceeded the binding energy per nucleon of iron, which is the tightest-bound atomic nucleus. In other words, my stupid iron atoms are starting to melt and shed protons and neutrons. Oh well. Maybe I’ll make some really exotic elements and get them named after me. And if IUPAC won’t name them after me, I’ll threaten to open my death-oven, which has long since become a weapon of mass destruction.

5,900,000,000,000 Kelvin

By now, the iron nuclei should have melted. All I need to do is heat them a little more to get that nice gooey brown crust. Except, I just checked, and I’m pretty sure the protons and neutrons are also melting. It’s just a very thin soup of quarks and un-named nonsense particles in there. Just like the Standard Model, amirite? Sorry. I shouldn’t be joking about particle physicists. Actually, speaking of particle physicists, could somebody call one of them? Because I’ve got three kilograms of pure quark-gluon plasma that they’ll probably want to study. You know, if they’re obscenely brave and not concerned about the 1.9 megatons of thermal energy packed into my oven. To be fair, if the door was gonna fail, I’m pretty sure it would have done it by now.

I’m really glad I spent the extra money on the Handwavium Universe power connector. In the 15 minutes it took me to obliterate my roast and put the entire Earth in jeopardy, the oven was drawing 8,830 terawatts. I’ll have to check the electrical panel, but I’m pretty sure 37 billion amps is above the rating of the breaker for the kitchen. Now all I need to do is call BS & Sons customer service and see if there’s a way to dump what’s left of my roast back into the Handwavium Universe. I don’t think I’ll be hurting anything: the HU is way hotter than my oven can get. Actually, the HU is so hot that the laws of physics themselves are above their melting point.

Standard
biology, math, science, short, statistics, thought experiment

Short: Immortality Math

There are people out there who are quite seriously trying to make human beings immortal. It sounds like something from a bad 1970s pulp comic, but it’s true. Of course, when serious people say “immortal,” they’re not talking Highlander. They’re talking biological immortality, sometimes called by fancy names like “negligible senescence”: the elimination of death by aging. Whether we can (or should) ever achieve biological immortality is a question I’ll leave to people smarter than me, but either way, biological immortality doesn’t mean full immortality. It just means that you can no longer die from, say, a heart attack or cancer or just generally wearing out. You can still quite easily die from things like falls, car accidents, or having Clancy Brown chop your head off with a sword.

There are a number of organisms out there which are either believed or known to be biologically immortal, or at the very least, nearly so. These include interesting but relatively simple organisms like hydras and jellyfish, but also more complex organisms like the bristlecone pine (many living specimens of which are confirmed to be over 1,000 years old, and one of which is over 5,000 years old), and the lobster. (Technically, though, the lobster isn’t really immortal, since they most molt to heal, and each molt takes more energy than the last, until the molts grow so energy-intensive they exhaust the lobster to death.) For the record, the oldest animal for which the age is well-established was a quahog clam named Ming Hafrun, who died at 507 years old when some Icelandic researchers plucked it out of the water.

If a human was made biologically immortal, how long could they expect to live before getting hit by a bus or falling down the stairs (or getting stabbed in the neck by Christopher Lambert)? That’s actually not too hard to estimate. According to the CDC (see Table 18), there were 62.6 injury-related deaths per 100,000 Americans, in 2014. With a bit of naive math (I’m not adjusting for things like age, which probably inflates that statistic a fair bit, since older people are at a higher risk of falls and similar) that means the probability of death by accident is 0.000626 per year, or roughly 0.06%. Knowing that, it’s almost trivial to compute the probability of surviving X years:

probability of surviving X years = (1 – 0.00626)^X

This formula is based on one of my favorite tricks in probability: to compute the probability of surviving, you do the obvious and convert that to the probability of not-dying. And you can take it one step further. At what age would 90% of a biologically-immortal group still be alive? All you have to do is solve this equation for N:

0.9 = (1- 0.00626)^N

which is no trouble for Wolfram Alpha a math genius like me: a biological immortal would have a 90% chance of surviving 168 years. Here are a few more figures:

  • A 75% probability of living up to 459 years.
  • A 50% probability of living up to 1,107 years.
  • A 25% probability of living up to 2,214 years.
  • A 10% probability of living up to 3,677 years.
  • A 5% probability of living up to 4,784 years.
  • A 1% probability of living up to 7,354 years.
  • A one-in-a-thousand chance of living 11,031 years.
  • A one-in-a-million chance of living 22,062 years.

For reference, the probability of a member of a population surviving (in the US, in 2012, including death by biological causes) doesn’t drop below 75% until around age 70. To put it in slightly annoying media jargon: if we’re biologically immortal, then 459 is the new 70.

Standard
silly, thought experiment

Short: Zeno from Coast to Coast

There’s an old joke. A mathematician and an engineer die in a car crash and go up to Heaven. They meet Saint Peter up there, and he leads them to a mile-long hallway with a big pearly door with a gold handle at the other end. Saint Peter says “Both of you have done good things and evil things in your lives. To test if you’re inherently good-natured and worthy of getting into Heaven, I’m going to put you through a challenge. Whenever I sound my trumpet, you’re allowed to walk half the remaining distance to the door. If you get to the door, you can open it and go to Heaven. But if you move more than I tell you to, or try to cheat, you’ll go to Hell.”

The two guys confer for a second. The mathematician says “It’s a trick. We’re going to Hell anyway: no matter how many times you divide the distance in half, it’ll never be zero. We’ll never actually reach the door.”

They don’t get a chance to say anything else: Saint Peter sounds his trumpet. Both guys walk half a mile, to the middle of the hallway. The mathematician is getting antsy. Saint Peter sounds his trumpet again, and they walk a quarter-mile. He sounds it again: they walk an eighth of a mile. Again: 330 feet. Again: 165 feet. By now, the mathematician’s shaking and sweating and turning beet-red. The engineer starts to say something to him, but the mathematician screams and starts running back the way he came. He doesn’t get ten paces before a hole opens beneath him and he falls into a pit of fire and brimstone.

After Saint Peter’s sounded his trumpet ten times, the engineer’s only a foot or so from the door. He turns back and looks at Peter and says “Is it all right if I reach out and turn the handle?” Saint Peter says “Of course.” The engineer opens the door. On the other side is Heaven, full of angels on clouds and such. Saint Peter says “Well, you opened the door. Go ahead and walk through.” The engineer walks through Saint Peter goes with him and says “One warning, though: all our rulers are warped, our T-squares are crooked, and our compasses are made out of rubber.” The engineer thinks for a second and says “I see. Look, is it still possible for me to go to Hell? Have they got an opening?”

That joke is one of the many warped forms of Zeno’s Paradox. It should be impossible to reach any destination, since first you have to cover half the distance, and then you have to cover a quarter of the distance, and then an eighth, and so on, and you never actually arrive. Well, I’m going to take that literally. I’m going to imagine traveling from the west coast of the United States (specifically, from The Riptide bar and honky-tonk on Taraval and 47th, in San Francisco, California) to the east coast (specifically, to the parking lot of the Holiday Inn in Wrightsville Beach, North Carolina). That’s a distance of 4,014 kilometers. I’m going to imagine covering that distance in the same fashion as in that joke: covering half the remaining distance each time. I’m going to move once every ten seconds.

1/2

I travel 2,007 kilometers in 10 seconds. I’m traveling at about 201 kilometers per second, meaning I carve a ram-heated plasma trail through the air, setting a swath of the United States on fire as I travel. If I were human (which I’m clearly not, if I’m doing this kinda shit), I’d be pulped by the acceleration required to follow the curvature of the Earth at these speeds. I stop not too far from Dodge City, Kansas. Good thing I already have to move again, because I’m pretty sure there’s an angry mob gathering.

1/2 + 1/4 = 3/4

I travel 1,003.5 kilometers in 10 seconds. I’m still setting fire to every object I pass, blinding bystanders, and knocking down trees and buildings with my shockwave. I’ve broken every window in Wichita, Kansas and Springfield, Missouri. I pause, momentarily, in the westernmost tip of Kentucky. If I were human, I’d still have been pulped by the acceleration.

1/2 + 1/4 + 1/8 = 7/8

I travel just under 502 kilometers in 10 seconds. I’m moving as fast as some of the fastest shooting stars, but at ground level. I’m wrecking everything I pass in a way the Chelyabinsk meteorite could only aspire to. My shockwave and fireball cause burns, injuries, and structural damage in Knoxville and Nashville. I scream over the Blue Ridge Mountains and stop just short of Asheville, North Carolina, which I’ve been to, and which is a nice town.

1/2 + 1/4 + 1/8 + 1/16 = 5/16

I travel 251 kilometers this jump. The centripetal acceleration required to follow the curve of the Earth is an almost-survivable 10 gees. I’m still meteoric, though, blasting through Asheville, narrowly missing Gastonia, and ruining the lives of everyone in south Charlotte. I stop not far past Charlotte. I didn’t plan it this way, but I’ve visited my hometown on my accidental rampage.

31/32

I travel 125 kilometers. Still fast enough to cause a hell of a shockwave and probably a bit of a plasma trail, but now I’m only going as fast as a high-velocity railgun projectile. To stick to the Earth, I have to accelerate downwards at 2.5 gees, which is very much survivable, especially for only ten seconds. I stop not far north of Lumberton, North Carolina, which I’ve never visited, but I’ve heard is another nice little town. We’ve got a lot of those in North Carolina, actually. It’s kinda cool.

63/64

I travel roughly 63 kilometers in 10 seconds. I’m moving at the speed of a very ambitious bullet. My centripetal acceleration is just over half a gee. I stop in a track of farmland with not much around me.

127/128

This jump covers 31 kilometers at the speed of a sniper-rifle bullet. My acceleration is 0.15 gees, which is the kind of acceleration people experience in cars on a regular basis. I’m not far outside the city limits of Wilmington, NC, in the woods between a church and a water treatment plant (according to Google Earth.)

255/256

I’m still moving like a bullet, covering 15.7 kilometers in 10 seconds. I stop over a river in Wilmington’s northern outskirts, near a drawbridge and what looks like an oil-tank complex.

511/512

I travel 7,839 meters in 10 seconds, which brings me down to the muzzle velocity of an ordinary handgun. I come to a stop on the roof of a Home Depot in Wilmington.

1023/1024

This jump is 3,920 meters at around Mach 1. I’m still probably bursting eardrums wherever I pass, but those newly-deaf people should count themselves lucky: there’s a lot of people burned to ash on the West Coast.

2047/2048

1,960 meters at the speed of an ordinary airplane. I stop in a marsh on the bank of the estuary that separates Wrightsville Beach from Wilmington. People are no longer being injured by my passage, but they’re probably pretty horrified to see a human being moving this fast. Plus, it’s been over a minute and 45 seconds since my accidental rampage began. That’s probably fast enough for people to post pictures of my path of destruction on Twitter.

4095/4096

I only travel 979.911 meters this time at an almost-sensible 219 mph (352 km/h). I manage to cross the estuary, although I’m still in the damn marsh, not yet to Wrightsville Beach. I stop near what, on Google Maps (on November 27th, 2016, anyway) looks like a horrifying half-mile long translucent river-worm:

Weird Thing in Wrightsville.png

Some may say it’s just a boat wake. I say they’re just blinding themselves to the truth that Big Google Data Brother Government Conspiracy (LLC) is trying to hide from the people. That’s what you’re supposed to say when you find weird shit in Google Earth, right?

8191/8192

I’m still going way over the posted speed limit as I cover the next 489.956 meters. Still stuck in this damned marsh, too.

16383/16384

A 244.978-meter jump at a sensible 54 mph (88 km/h). I’m starting to feel a little like the mathematician in the joke: all of a sudden, things are moving painfully slow.At least I’m out of the stupid marsh, and passing through a fairly pleasant-looking seaside housing development.

32767/32768

122.489 meters covered at a very pleasant 27 mph (44 kph). I’m almost within the ordinary residential speed limit! I’m only a block from the Holiday Inn, so tantalizingly close. I must persevere! I wanna be the engineer in the joke, not the mathematician! Hell sounds terrible!

65535/65536

A nice neat number. 2^16. 10000000000000000, in binary. I travel 61.244 meters. Less than the length of any sort of football field. I’m moving at 6.1 meters per second. A decent sprinter could manage that. Usain Bolt could most certainly manage that.

131071/131072

30.522 meters this time. I’m jogging across the parking lot, almost a literal stone’s throw from the Atlantic.

262143/262144

15.311 meters covered this jump, and 15.311 left to go. I can look into the windows of the Holiday Inn, and see all the employees on their phones reading about the carnage in California.

524287/524288

7.656 meters. A man passing me in the Holiday Inn parking lot wonders why I’m walking so damn slow.

1048575/1048576

3.828 meters. I’m walking at less than 1 mile per hour, which feels really weird when I do it in real life. I’m starting to regret many decisions. Plus, people are starting to get suspicious of me.

2097151/2097152

1.914 meters left to go. If I fell flat on my face (which is starting to seem like a good idea…), my head would push the front door open.

1 – 2^(-22)

Less than a meter to go. As I stand almost within arm’s reach of the hotel’s front door, people are giving me looks usually reserved for those who start talking about lizard people at bus stops.

1 – 2^(-23)

Half a meter. Finally–finally–I can reach out and push the door open. And thus, my bizarre trip comes to an end. I’ve covered 4,013,716.5 meters in about 3 minutes and 45 seconds. I’ve killed many, many people and injured countless others. There will be an investigation. Even though this isn’t exactly the sort of thing the FBI is used to, they’ll probably do their damndest to figure out just who or what set the west coast on fire, smashed millions of windows, and made a sonic boom over North Carolina. There’s probably enough security camera evidence to find me. Until then, I’ll just catch some sun on Wrightsville Beach.

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physics, Space, thought experiment

Hypothetical Nightmares | Black Holes, Part 3

Imagine taking all the mass in the Milky Way (estimated to be around a trillion solar masses) and collapsing it into a black hole. The result wouldn’t be an ordinary black hole. Not even to astrophysicists, for whom all sorts of weird shit is ordinary.

The largest black hole candidate is the black hole at the center of the quasar S5 0014+813, estimated at 40 billion solar masses. In other words, almost a hundred times smaller than our hypothetical hole. As I said last time, as far as astronomical objects go, black holes are a fairly comfortable size. Even the largest don’t get much bigger than a really large star. Here, though, is how big our trillion-sun black hole would be, if we replaced the sun with it:

Galaxy Mass Black Hole.png

(Rendered in Universe Sandbox 2.)

The thing circled in orange is the black hole. When I started tinkering with the simulation, I was kinda hoping there’d be one or two dwarf planets outside the event horizon, so their orbits could at least offer a sense of scale. No such luck: the hole has a Schwarzschild radius of 0.312 light-years, which reaches well into the Oort cloud. That is, the galaxy-mass black hole’s event horizon alone would extend beyond the heliopause, and would therefore reach right into interstellar space. Proxima Centauri, around 4.2 light-years from Earth, is circled in white.

The immediate neighborhood around a black hole like this would be rough. We’re talking “feral children eating the corpse of a murder victim while two garbagemen fight to the death with hatchets over who gets to empty the cans on this street” kind of rough. That kinda neighborhood. No object closer than half a light-year would actually be able to orbit the hole: it would either have to fall into the hole or fly off to infinity.

That is, of course, if the hole isn’t spinning. As I said last time, you can orbit closer to a spinning hole. But I’m going to make a leap here and say that our galaxy-mass black hole isn’t likely to be spinning very fast. Some rough calculations suggest that, if it were rotating at half the maximum speed,the rotational kinetic energy alone would have several billion times the mass of the sun. I’m going to assume there’s not enough angular momentum in the galaxy to spin a hole up that much. I could be wrong. Let me know in the comments.

Spin or no spin, it’s gonna be a rough ride anywhere near the hole. Atoms orbiting at the innermost stable orbit (the photon sphere) are moving very close to the speed of light, and therefore, to them, the ambient starlight and cosmic microwave background ahead of them is blue-shifted and aberrated into a horrifying violet death-laser, while the universe behind is red-shifted into an icy-cold nothingness.

But, as we saw last time, once you get outside a large hole’s accretion disk, things settle down a lot. When it comes to gravity and tides, ultra-massive black holes like these are gentle giants. You could hover just outside the event horizon by accelerating upwards at 1.5 gees, which a healthy human could probably tolerate indefinitely, and which is very much achievable with ordinary rocket engines. The tides are no problem, even right up against the horizon. They’re measured in quadrillionths of a meter per second per meter.

Of course, if you’re hovering that close to a trillion-solar-mass black hole, you’re still going to die horribly. Let’s say your fuel depot is orbiting a light-year from the hole’s center, and they’re dropping you rocket fuel in the form of frozen blocks of hydrogen and oxygen. By the time they reach you, those blocks are traveling at a large fraction of the speed of light, and will therefore turn into horrifying thermonuclear bombs if you try to catch them.

But, assuming its accretion disk isn’t too big and angry, a hole this size could support a pretty pleasant galaxy. The supermassive black hole suspected to lie at the center of the Milky Way makes up at about 4.3 parts per million of the Milky Way’s mass. If the ratio were the same for our ultra-massive hole, then it could host around 200 quadrillion solar masses’ worth of stars, or, in more fun units, 80,000 Milky Ways. Actually, it might not be a galaxy at all: it might be a very tightly-packed supercluster of galaxies, all orbiting a gigantic black hole. A pretty little microcosm of the universe at large. Kinda. All enclosed within something like one or two million light-years. A weird region of space where intergalactic travel might be feasible with fairly ordinary antimatter rockets.

You’ll notice that I’ve skipped an important question: Are there any trillion-solar-mass black holes in the universe? Well, none that we know of. But unlike some of the other experiments to come in this article, black holes this size aren’t outside the realm of possibility.

I frequently reference a morbid little cosmology paper titled A Dying Universe. If you’re as warped as I am, you’ll probably enjoy it. It’s a good read, extrapolating, based on current physics, what the universe will be like up to 10^100 years in the future (which they call cosmological decade 100). If you couldn’t guess by the title, the news isn’t good. A hundred trillion years from now (Cosmological Decade 14), so much of the star-forming stuff in galaxies will either be trapped as stellar corpses or will have evaporated into intergalactic space that new stars will stop forming. The galaxies will go dark, and the only stars that shine will be those formed by collisions between high-mass brown dwarfs. By CD 30 (a million trillion trillion years from now), gravitational encounters between stars in the galaxy will have given all the stars either enough of a forward kick to escape altogether, or enough of a backward kick that they fall into a tight orbit around the central black hole. Eventually, gravitational radiation will draw them inexorably into the black hole. By CD 30, the local supercluster of galaxies will consist of a few hundred thousand black holes of around ten billion solar masses, along with a bunch of escaping rogue stars. By this time, the only source of light will be very occasional supernovae resulting from the collisions of things like neutron stars and white dwarfs. Eventually, the local supercluster will probably do what the galaxy did: the lower-mass black holes will get kicked out by the slingshot effect, and the higher-mass ones will coalesce into a super-hole that might grow as large as a few trillion solar masses. Shame that everything in the universe is pretty much dead, so no cool super-galaxies can form. But the long and the short of it is that such a hole isn’t outside the realm of possibility, although you and I will never see one.

The Opposite Extreme

But what about really tiny black holes? In the first post in this series, I talked about falling into a black hole with the mass of the Moon. But what about even smaller holes?

Hobo Sullivan is a Little Black Pinhole

Yeah, I feel like that sometimes. I mass about 131 kilograms (unfortunately; I’m working on that). If, by some bizarre accident (I’m guessing the intervention of one of those smart-ass genies who twist your wishes around and ruin your shit), I was turned into a black hole, I’d be a pinprick in space far, far smaller than a proton. And then, within a tenth of a nanosecond, I would evaporate by Hawking radiation (if it exists; we’re still not 100% sure). When a black hole is this small, Hawking radiation is nasty shit. It would have a temperature of a hundred million trillion degrees, and I’d go off like four Tsar Bombas, releasing over 200 megatons of high-energy radiation. Not enough to destroy the Earth, but enough to ruin the year for the inhabitants of a medium-sized country.

There’s no point in trying to work out things like surface tides or surface gravity: I’d be gone so fast that, in the time between my becoming a black hole and my evaporation, a beam of light would have traveled a foot or two. Everything around me is as good as stationary for my brief lifetime.

A Burial Fit for a Pharaoh. Well, for a weird pharaoh.

Things change dramatically once black holes get a little bigger. A hole with the mass of the Great Pyramid of Giza (around 6 billion kilograms) would take half a million years to evaporate. It would still be screaming-hot: we’re talking trillions of Kelvin, which is hot enough that nearby matter will vaporize, turn to plasma, the protons and neutrons will evaporate out of nuclei, and then the protons and neutrons themselves will melt into a quark-gluon soup. But, assuming the black hole is held in place exactly where the pyramid once stood, we won’t see that. We’ll only see a ball of plasma and incandescent air the size of a university campus or a big football stadium, throbbing and booming and setting fire to everything for a hundred kilometers in every direction. The Hawking radiation wouldn’t inject quite enough energy to boil the planet, but it would probably be enough (combined with things like the fact that it’s setting most of Egypt on fire) to spoil the climate in the long run.

This isn’t an issue if the black hole is where black holes belong: the vacuum of space. Out there, the hole won’t gobble up Earth matter and keep growing until it destroys us. Instead, it’ll keep radiating brighter and brighter until it dies in a fantastic explosion, much like the me-mass black hole did.

Can’t you just buy a space heater like a normal person?

It’s starting to get cold here in North Carolina. Much as I love the cold, I’ve been forced to turn my heater on. But, you know, electric heating is kinda inefficient, and this house isn’t all that well insulated. I wonder if I could heat the house using Hawking radiation instead…

Technically, yes. Technically in the sense of “Yeah, technically the equations say yes.” Technically in the same way that you could technically eat 98,000 bacon double cheeseburgers at birth and then go on a 75-year fast, because technically, that averages out to 2,000 Calories per day. What I mean is that while the numbers say you can, isolated equations never take into account all the other factors that make this a really terrible idea.

A black hole with the mass of a very large asteroiod (like Ceres, Vesta, or Pallas) would produce Hawking radiation at a temperature of 500 Kelvin, which is probably too hot to cook with, but cool enough not to glow red-hot. That seems like a sensible heat source. Except for the fact that, as soon as you let it go, it’s going to fall through the floor, gobble up everything within a building-sized channel, and convert that everything into superheated plasma by frictional effects as it falls into the hole. And except for the fact that if you’re in the same neighborhood as the hole, you’ll simultaneously be pulled into it at great speed by its gravity, and pulled apart into a bloody mass of fettuccine by tidal forces. And except for the fact that, as the black hole orbits inside the Earth, it’s going to open up a kilometer-wide tunnel around it and superheat the rock, which will cause all sorts of cataclysmic seismic activity, and ultimately, the Earth will either collapse into the hole, or be blasted apart by the luminosity of the forming accretion disk, or some combination thereof.

Back to the Original Extreme

But there’s one more frontier we haven’t explored. (I was watching Star Trek yesterday.) That is: the biggest black hole we can reasonably (well, semi-reasonably) imagine existing. That’s a black hole with a mass of around 1 x 10^52 kilograms: a black hole with the mass of the observable universe. Minus the mass of the Earth and the Sun, which make less of a dent in that number than stealing a penny makes a dent in Warren Buffett’s bank account.

The hole has a Schwarzschild radius of about 1.6 billion light-years, which is a good fraction of the radius of the observable universe. Not that the observable universe matters much anymore: all the stuff that was out there is stuck in a black hole now.

For the Earth and Sun, though, things don’t change very much (assuming you set them at a modest distance from the hole). After all, even light needs over 10 billion years to circumnavigate a hole this size. Sure, the Earth and Sun will be orbiting the hole, rather than the former orbiting the latter, but since we’re dealing with gravitational accelerations less than 3 nanometers per second per second, and tides you probably couldn’t physically measure (4e-34 m/s/m at the horizon, and less further out, which falls into the realm of the Planck scale), life on Earth would probably proceed more or less as normal. The hole can’t inflict any accretion-disk horror on the Sun and Earth: there’s nothing left to accrete. Here on Earth, we’d just be floating for all eternity, living our lives, but with a very black night sky. If we ever bothered to invent radio astronomy, we’d probably realize there was a gigantic something in the sky, since plasma from the Sun would escape and fall into a stream orbiting around the hole, but we’d never see it. What a weird world that would be…

Then again, if the world’s not weird by the end of one of my articles, then I’m really not doing my job…

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physics, thought experiment

Spin to Win | Black Holes, Part 2

In the previous part of this series, I tried to analyze what it would be like to fly an Apollo Command Module into black holes of various sizes. This time, though, I’m going to restrict myself to a single 1-million-solar-mass black hole. The difference is that, this time, I’m going to let the black hole spin (at 98% of the maximum possible spin, which is pretty average for a fast-spinning hole). But I’m getting ahead of myself. Before I go on, here’s my vehicle:

Apollo 11.jpg

(From the website of the Smithsonian Air and Space Museum)

That’s the actual command module Michael Collins, Buzz Aldrin, and Neil Armstrong took to the Moon (minus the Plexiglas shroud, of course). It would fit in even a medium-sized living room. This time, the crew will consist of me, Jürgen Prochnow (Das Boot Jürgen, naturally. Captain’s hat and all), and Charlize Theron. I was gonna take David Bowie and Abe Lincoln along again, but frankly, I’ve put Bowie through enough, and Lincoln was just so damn grim all the time.

Anyway, back to the subject at hand: the scary monster that is a rapidly-spinning black hole. All the black holes I discussed in the last part were Schwarzschild black holes, meaning they had no spin or electric charge. This black hole, though, is a Kerr black hole: it spins. The spin means this trip is a whole new ballgame. We’re still going to die horribly, of course, but hey, at least it’ll be interesting.

The first difference is that you can get closer to the event horizon of a spinning black hole. For a non-spinning black hole, there are no stable circular orbits closer than one and a half times the radius of the event horizon (the Schwarzschild radius), because in order to be in a circular orbit any closer, you’d have to travel faster than light. For spinning ones, there’s a lozenge-shaped region outside the event horizon called the ergosphere (My first-born daughter will be Ergosphere Sullivan). Objects near a rotating hole (or any rotating mass, to a lesser extent) are dragged along with the hole’s rotation. But inside the ergosphere, though, they’re being dragged along so fast that, no matter what, they can’t stand still. Inside the ergosphere, you have to rotate with the hole, because traveling anti-spinward would require going faster than the speed of light.

Here’s roughly what a free-fall trajectory into our Kerr black hole would look like (looking down at the hole’s north pole):

098-kerr-black-hole-infall

The ergosphere is the gray part. The event horizon is the black part.

Jürgen and Charlize are suspicious of me, but I gave them my word that we’re just orbiting the black hole. To make some observations. For science, and all that. When they’re not looking, I’m gonna hit the retro-rocket and plunge us to our deaths. I feel like there’s a flaw in my reasoning, but I don’t have time for such things.

Even orbits don’t work the way they normally do, near a spinning hole. Orbits around ordinary objects are very close to simple ellipses or circles. But, sitting in our command module, here’s what our orbit looks like (starting from parameters that should have given us a nice elliptical orbit):

Kerr BH Stable Orbit.png

This is because, when we orbit closer to the hole, we get a kick from the spin that twists our orbit around.

From nearby, a non-rotating black hole looks like its name: a black circle of nothingness, surrounded by a distorted background of stars and galaxies. From our orbit around the spinning million-solar-mass hole, though, the picture is much different:

Orbiting a Kerr Black Hole.jpg

(Picture and simulation by Alain Riazuelo.)

In that picture, the hole’s equator rotates from left to right. The reason the horizon is D-shaped is that photons coming from that direction were able to get a lot closer to the horizon, since they were moving in the direction of the rotation. On the opposite side, the horizon is bigger because those photons were going upstream, so to speak, and many of them were pulled to a halt by the spin and then either pulled into the hole, flung away, or pulled into a spinward orbit. Black holes are bullies. Spinning ones say “If you get too close, I’m going to eat you. And if you’re standing within a few arm’s lengths, you have to spin around me, or else I’ll eat you.”

(Incidentally, if you read about the movie’s background, the black hole in Interstellar was spinning at something like 99.999999% of the maximum rate. Its horizon would have been D-shaped like the picture above, from up close. From a distance, it would have looked…well, it would have looked like it did in the movie. They got it right, because they hired Kip motherfucking Thorne, Mr. Black Hole himself, to help write their ray-tracing code.

Speaking of Interstellar, the fact that you can get so much closer to a spinning black hole than a non-spinning one (providing you’re orbiting spinward) means you can get much deeper into its time-dilating gravity well. That means, as long as the tides aren’t strong enough to kill you, you can experience much bigger timewarps. The only way to get the same timewarp from a non-rotating black hole is to apply horrendously large forces to hover just outside the horizon. It’s much more practical to do in the vicinity of a spinning hole. Well, I mean, it’s no less practical than putting a Command Module in orbit around a black hole.

According to the equations from this Physics Stack Exchange discussion, as Jürgen, Charlize, and I zip around the hole close to the innermost stable orbit, time is flowing upwards of four times slower than it is for observers far away. I’m gonna keep us in orbit for a week, to lull my crewmates into complacency, so I’ll have the element of surprise when I try to kill us all. Well, we think it’s a week. Everyone outside thinks we’re orbit for a month and change

Then, without warning, I flip us around, turn on the engines, and take us into the hole. Jürgen fixes me with those steely blue eyes and that pants-shittingly intimidating face he was doing all through Das Boot. Charlize spends fifteen seconds trying to reason with me, then realizes I’m beyond all help and starts beating the shit out of me. Did you see Fury Road? She can punch. Neither of them can do anything to stop me, though: we’re already seconds from death.

But because this is a big black hole, the tides are gentle, at least outside the horizon. They’re stronger than the tides the Moon exerts on the Earth (which are measured in hundreds of nanometers per second per second), but they’re not what’s going to tear us to pieces.

What’s going to tear us to pieces is frame-dragging. Let’s go back to the metaphor of the whirlpool. The water moves much faster close to the center than it does far away. Because your boat is a physical object with a non-zero size, when you get really close, the water on one side of your boat is moving significantly faster than the water on the other side, because the near side is significantly closer than the far side. This blog hasn’t had any horrible pictures recently. Here’s one to explain the frame-dragging we experience:

Horrible Frame Dragging.png

In this picture, the capsule orbits bottom-to-top, and the hole rotates clockwise (this is the opposite of the view in the orbit plots; in this picture, we’re looking at the hole from the bottom, looking at its south pole; the reason has nothing to do with the fact that I screwed up and drew my horrible picture backwards).

Space closer to the hole is moving faster than space farther from the hole. The gradient transfers some of the hole’s angular momentum to the capsule, which is bad news, because that means the capsule starts spinning. It spins in the opposite direction of the hole (counter-clockwise, in the Horrible Picture (TM)).

I say the spin is bad news because, from the research for “Death by Centrifuge“, I know that things get really messy and horrible if you’re in a vehicle that rotates too fast.

Here’s a fun fact: Neil Armstrong came perilously close to death on his first spaceflight. During Gemini 8, while Armstrong and crewmate Dave Scott were practicing station-keeping and docking maneuvers with an uncrewed Agena target vehicle, the linked spacecraft started spinning. Unbeknownst to them, one of the Gemini capsule’s thrusters was stuck wide-open. Thinking it was the Agena causing the problem, they undocked. That’s when the shit really hit the fan, though I think Armstrong probably described it more gracefully. A video is worth a thousand words: here’s what it looked like when they undocked. Before long, the capsule was tumbling at 60 revolutions per minute (1 per second), wobbling around all three axes.

Did you ever spin in a circle when you were a kid? I did. Did you ever try it again as an adult, just to see what it was like? I did. I spent the next fifteen minutes lying in the grass (because I couldn’t tell which way was down) wondering if I should just go ahead and puke. Human beings don’t handle rotation well. According to this literature survey (thanks to Nyrath of Project Rho for helping direct me to it; it was hell to try and find a proper paper otherwise), average people do okay spinning at 1.7 RPM. At 2.2 RPM, susceptible people will probably start puking everywhere. At 5.44 RPM, ordinary tasks become stressful, because, thanks to the Coriolis effect (that troublemaking bastard), things like limbs, bodies, and inner-ear fluid don’t move normally, which plays hell with coordination. Also, it makes you puke. At 10 RPM, even the tough subjects in the study were seriously distressed.

Armstrong and Scott were spinning six times faster. When you spin, your brain loses the ability to compensate for movements of the eyes: you lose the ability to stabilize the image on your retinas, and the world wobbles and jumps. That’s bad news, especially if, for instance, you’re stuck inside a metal can which is spinning way too fast, and the only way you can stop it spinning way too fast (so that you don’t die) is by focusing your eyes on buttons and moving your Coriolis-afflicted hands to press them. Armstrong was an especially tough, calm dude, and he managed it, even though both men were starting to have serious vision problems. He did what any good troubleshooter would do: he switched the thrusters off and then on again (more or less). That saved the mission.

Now, I don’t know how fast the black hole will spin us, because the math is very complicated. But considering it’s a black hole we’re dealing with, probably pretty fast. Like I said, nothing about black holes is subtle. At 10 RPM, I throw up. My vomit describes a curved Coriolis-arc through the cabin and splatters on the wall. Jürgen doesn’t throw up until 20 RPM (after all, he’s a seafaring submarine captain). Charlize doesn’t throw up until 25,because she’s a badass.

At 60 RPM, I’m already screaming my head off, hyperventilating, and desperately regretting my decision to plunge us into a black hole. I try to hit buttons (pretty much at random), but I can’t get my fingers to go where I want them, and I press all the wrong ones. Jürgen is trying to calm me down and telling me he wants proper damage reports, but in my panic, I’ve forgotten all my German. Charlize has written both of us off and is trying to re-orient us and thrust away from the horizon, but it’s already too late.

At 60 RPM, the centrifugal acceleration on the periphery of the CM is already over 7 gees. There’s probably a bit of metal creaking, but nothing too serious. Because the crew couches are only a foot or so from the center of mass, we only experience an acceleration of 1.2 gees. For the moment, our main problem is that we’re punching and/or throwing up on each other.

At 120 RPM, the command module is starting to complain. Its extremities experience 28 gees. Panels slam shut. A cable pops loose and causes a short that trips the circuit breakers and kills our power. Even in our couches, we’re feeling almost 5 gees. I’m making a face like this:

gloc-face-735x413.jpg

(Source.)

At 200 RPM, the heat shield, experiencing 77 gees of centrifugal acceleration, cracks and flies off. It’s possible that the kick it gets from leaving our sorry asses behind, combined with the kick from being in the hole’s ergosphere (sounds dirty) is enough to slingshot the fragments to safety. Kind of a moot point, though, since I only care about the human parts, and all of those have blacked out at 13 gees.

Somewhere between 200 RPM and 500 RPM, the hull finally tears open. The bottom dome is flung off, letting important things like our air, our barf bags, and possibly our crew couches, fly out. Not that it matters: at 83 gees, we’ve all got ruptured aortas, brain hemorrhages, and we’re all in cardiac arrest.

At 1000 RPM (16.7 revolutions per second), the command module is flung decisively apart. Thanks to conservation of angular momentum, all the pieces are spinning pretty fast, too. Jürgen, Charlize, and I, are very dead, and in the goriest of possible ways: pulped by centrifugal force, and then shredded as we were spun apart.

The fragments closer to the horizon appear to accelerate ahead of us. The parts farther away fall behind. Most of the fragments fall into the hole. Spaghettification takes a while: once again, a more massive hole has weaker tides near the horizon.

As for what happens as we fall into the really nasty part of the hole (because it was sunshine and jellybeans before…), physics isn’t sure. The simplest models predict a ring-shaped singularity, rather than a point-shaped one. Some models predict that the ring singularity might act as an actual usable wormhole to another universe. But it’s also possible that effects I don’t pretend to understand (which have to do with weird inner horizons only rotating holes have) blue-shift the infalling light, creating a radiation bath that burns our atoms into subatomic ash. Either way, we’re not going to be visiting any worlds untold.

Once again, I’ve killed myself and two much cooler people. At least I only did it once this time. In the next and final part, I’m going to spend a little more time playing around with far less realistic black holes. (WARNING! Don’t actually play with black holes. If you have to ask why, then you skipped to the end of both articles.)

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