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:



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:


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:



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:



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.

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…