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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astronomy, image, pixel art, science, short, Space, Uncategorized

Pixel Solar System

pixel-solar-system-grid

(Click for full view.)

(Don’t worry. I’ve got one more bit of pixel art on the back burner, and after that, I’ll give it a break for a while.)

This is our solar system. Each pixel represents one astronomical unit, which is the average distance between Earth and Sun: 1 AU, 150 million kilometers, 93.0 million miles, 8 light-minutes and 19 light-seconds, 35,661 United States diameters, 389 times the Earth-Moon distance, or a 326-year road trip, if you drive 12 hours a day every day at roughly highway speed. Each row is 1000 pixels (1000 AU) across, and the slices are stacked so they fit in a reasonably-shaped image.

At the top-left of the image is a yellow dot representing the Sun. Mercury and Venus aren’t visible in this image. The next major body is the blue dot representing the Earth. Next comes a red dot representing Mars. Then Jupiter (peachy orange), Saturn (a salmon-pink color, which is two pixels wide because the difference between Saturn’s closest and furthest distance from the Sun is just about 1 AU), Uranus (cyan, elongated for the same reason), Neptune (deep-blue), Pluto (brick-red, extending slightly within the orbit of Neptune and extending significantly farther out), Sedna (a slightly unpleasant brownish), the Voyager 2 probe (yellow, inside the stripe for Sedna), Planet Nine (purple, if it exists; the orbits are quite approximate and overlap a fair bit with Sedna’s orbit). Then comes the Oort Cloud (light-blue), which extends ridiculously far and may be where some of our comets come from. After a large gap comes Proxima Centauri, the nearest (known) star, in orange. Alpha Centauri (the nearest star system known to host a planet) comes surprisingly far down, in yellow. All told, the image covers just over 5 light-years.

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geology, image, science

Pixel Earth 2

1 Radian Wedge Pixel Art.png

A slightly more comprehensive version of the previous post. Once again, each pixel is 1 kilometer deep. The pixels at sea level (the thin green line near the top) are 1 kilometer wide, corresponding to a total width of 6,371 kilometers at sea level or an angular width of 1 radian, or 57 degrees. There’s an increasing horizontal distortion as you go towards the inner core (orange), which becomes infinite at the very bottom row.

In this picture, you’ll find Krubera Cave, the Burj Khalifa, the Kola Superdeep Borehole, a typical thunderstorm, Mt. Everest, a typical volcano, a subduction zone, an airliner at cruising altitude, and the International Space Station. Try and find them: it’s like a badly-drawn Where’s Waldo!

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geology, image, physics, science, short

Pixel Earth 1

I present you: a scale model of the Earth’s surface, from an altitude of 400 kilometers down to a depth of 300 kilometers. At this scale, every pixel is 1 km by 1 km.crust-1-px-eq-1-km-numbered-large

 

Legend:

  1. The International Space Station at perigee.
  2. The aurora borealis.
  3. The greatest altitude at which human beings have died: cosmonoauts Georgy Dobrovolsky, Vladislav Volkov, and Viktor Patsayev died just before the reentry of Soyuz 11, when the explosive decoupling of the descent module opened an oxygen seal in the cockpit.
  4. The highest altitude reached by the Air Force’s X-15, which still holds the speed record for a crewed aircraft, and which was among the first crewed vehicles to cross into space.
  5. The official edge of space: the Kármán line, at around 100 kilometers’ altitude. Above this line, you have to move faster than orbital velocity for wings to provide usable lift, so you might as well just orbit.
  6. The streak denotes the range of altitudes at which meteors glow.
  7. The streak denotes the altitudes at which the 2013 Chelyabinsk meteorite glowed. The starburst denotes the approximate altitude at which it exploded.
  8. The altitude at which the Space Shuttle Columbia stopped sending telemetry and began its final breakup.
  9. On a less sad note: the altitude from which Felix Baumgartner began his famous skydive.
  10. The top of the troposphere (where weather happens); the beginning of the stratosphere; the top of thunderstorms in middle and tropical1 latitudes.
  11. 10,000 meters: the altitude at which passenger airplanes cruise.
  12. The summit of Mt. Everest.
  13. The Challenger Deep (over 10,000 meters deep).
  14. The deepest active mining operation: 4,000 meters, at the Mpomeng gold mine in South Africa.
  15. The deepest human beings have ever drilled: 12 kilometers at the Kola Superdeep Borehole, in Russia.
  16. The deepest confirmed location in a natural cave: 2 km, in Krubera Cave, in Abkhazia, Georgia (the Eastern European Georgia, not the American one.) The cave very likely goes deeper.
  17. Volcanic magma chambers. Contrary to popular belief, most of the mantle is a plastic solid (like very, very stiff Silly Putty), rather than molten. Magma is the exception. The magma chamber that feeds Hawai’i’s volcanoes is on the shallow end of the spectrum. The magma chamber underneath the Yellowstone Caldera (which provides heat for Yellowstone’s famous geysers) sits at around 25 to 35 kilometers deep. We have actual rough maps of it. It’s awesome.
  18. The Mohorovičić discontinuity (or Moho; no, not the KSP one): the official boundary between crust and mantle. It can be as shallow as 5 kilometers deep (beneath the seafloor) and 90 kilometers deep (under mountains); it averages 35 kilometers deep.
  19. Very deep magma chambers.
  20. The end of the asthenosphere, a region of rock made weak and squishy (relatively speaking) by the enormous temperature and pressure. This starts beneath the solid crust (the lithosphere). Its boundary isn’t well-defined.
  21. A hot plume in the upper mantle. Droplets (well, droplet-sized compared to the whole Earth) of lower-melting-point material rise through the mantle to fill magma chambers.

(I should point out that I’m not a geologist. If I’ve made a mistake, please let me know. You won’t hurt my feelings. I’d rather admit I’m wrong than put out a misleading graphic.)

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Uncategorized

Give me a Trillion of Everything!

I think one trillion is my favorite number. The word “trillion” just has a nice sound to it. It could be the name for a classy British stripper. But it’s also a good number for bridging the gap between “numbers human beings can kinda get their heads around” and “numbers that make human beings’ eyes glaze over.” One trillion certainly isn’t as intuitive as three, or one thousand, but it’s more intuitive than something like 10^80. So today (in a slight nod to an earlier post), I want to see what it’s like to have a trillion of various things just lying around.

Gold atoms. Who wouldn’t want a trillion gold atoms? If you just stack them in a cube, that cube will have edges 10,000 atoms long. That works out to a cube 2.72 microns on an edge. Okay, so a trillion atoms of gold isn’t as impressive as I thought. I don’t think it’ll ever catch on as a currency, seeing as if you handled it too roughly, it’d slip between the cells of your finger and disappear into your bloodstream.

But actually, gold atoms don’t stack in a neat cubic lattice. They, like many other metal atoms, arrange themselves in a face-centered cubic lattice, which is also the most efficient way to stack oranges or cannonballs (hands up everybody who can’t help but think of Kurt Vonnegut). So a real trillion-atom gold bar (still measuring 10,000 atoms along every edge) would actually be 2.72 microns long, 2.36 microns wide, and 2.22 microns thick. My entire investment could be eaten by a particularly zealous amoeba.

Bacteria. E. coli is a useful bacterium. For one thing, it’s easy to grow in the lab, which lets scientists observe bacteria without the hassle of giving them weird shit like quaternary ammonium salts or whatever those other stubborn bacteria like. For another, their dimensions are conveniently close to nice, round numbers: the average E. coli bacillus is about 1 micron in diameter and 2 microns long. So what if you had a trillion of them? Well, let’s stack them in a 10,000 x 10,000 x 10,000 cube again. This bacterial block would be one centimeter wide, one centimeter high, and two centimeters long. It would be a slimy, milky mass the color of bad mozarella. You could eat it on a cracker. (Sorry.)

Human cells. I don’t like human cells, because they’re all lumpy and irregular and hard to measure. Lucky for me, there’s a kind of tissue called simple cuboidal epithelium, found in the ovaries, the thyroid glands, and, as pictured below, the little pee-secreting tubules of the kidney:

(Source.)

In addition to being nicely-shaped, keeping our bodies from filling with urine (that’s how kidneys work, right?), and having a cool name (“Cuboidal” is a great word. Even better than “furan.”), they’re also pretty regular in size: about 10 microns on an edge. And being cubes, I don’t have to bother with all that hexagonal-close-packing math. I can just multiply 10 microns by 10,000. One trillion human cells would form a gelatinous cube (no, not that kind) ten centimeters on an edge. It would be a horrible meaty cube weighing around a kilogram. You could eat the whole thing if you were really hungry (it’d weigh the same as a 35-oz porterhouse). I don’t recommend that, though: I tried some cooked kidney once, and I couldn’t quite get over the fact that, with every bite, I got the stench of one of those public urinals that hardly ever gets flushed.

Eugh. Let’s move on to something less horrible.

(Left picture source. Right picture source.)

I might have been lying about that. These are Dust mites, which I never realized bear a very suspicious resemblance to the headcrabs from Half-Life 2. I honestly think the one on the right is cute, but then again, I’ve probably got so many holes in my brain a squirrel could use it to store nuts for the winter. I had to include both of these pictures because the one on the right is a classic well-proportioned dust mite (lovely eyeless arachnids that they are). But the one on the left is posing with a motor and gearbox whose gears are the size of blood cells. How could I not include that?

But back to the matter at hand: I want a trillion dust mites. (Leave them at the corner of 7th and Walthrop and we’ll release your mother unharmed.) An average dust mite measures around 300 microns wide, 300 microns tall, and 400 microns long. My trillion-mite brick measures 2 meters by 2 meters by 4 meters. In other words, I’ve now got a heap of creepy-crawlies big enough to fill a medium-sized closet. I’d be concerned about them giving me allergies, but imagining a cube of mites larger than me has made me pee my pants, which is a more immediate concern.

Peas. (I was tempted to use a horrible pun as a segue, but the thought made me throw up in my mouth.) I really like peas. My parents never had to tell me to finish my peas. I ate the little buggers right up. Plus, they’re another conveniently uniform object we can use to demonstrate just how massive a trillion is. According to this USDA pea-grading document (the existence of which pleases me), a green pea averages 8 millimeters in diameter. Since peas are irregular and don’t stack as neatly as gold atoms, I’m going to come up with the volume of my trillion-pea cube a different way. We’ll assume they’re roughly hexagonally-close-packed, which means that only 74% of the volume will be occupied by peas. The rest will be air. We end up with about 362,300 cubic meters of peas. They would form a cube big enough to span the width of a football field (either kind), and most of the length: 71 meters on an edge. The peas would weigh 180,000 metric tons, apparently half as much as the Empire State Building. Here’s the kind of vehicle you’d need to transport that much stuff:

(Source.)

I’m now imagining an alternate reality in which the Persian Gulf is a global center of pea production. In which the economic fate of the world is determined by the price of a barrel of green peas. In which pea tankers with armed guards criss-cross the Pacific. It wouldn’t be any weirder than this reality.

 People. There are not a trillion human beings on Earth. According to most of the estimates I’ve ever read, the Earth can’t support a trillion people. But that doesn’t mean we couldn’t make a trillion clones and plop them down. Let’s be all sociological and assume that every human being belongs to a family of five, and that one hectare (10,000 square meters) is enough space for their house and enough crops to keep them alive. (One hectare is about the area of the grassy center of a standard athletic track, or the area of a rugby field, or the area of a square that could enclose the base of the Statue of Liberty.) So we have 200 billion families, each requiring 10,000 square meters.

People can live in the ocean, right? And you can grow a pretty good selection of crops in Antarctica, right? Because it turns out that a trillion humans requiring a fifth of a hectare each would require thirteen times the Earth’s land area (arable or not). They’d require ten times the Earth’s surface area. Probably not going to happen, although I really, really like the image of farmers in wetsuits paddling around their kelp fields with rakes.

But if it was just a trillion-person crowd (doomed to starvation), what would that look like? We’ll assume they’re all pretty friendly, and so they only require a square one and a half meters on a side. Whether they assembled in a square, a circle, or some other roughly-symmetric shape, the crowd would be about 1500 kilometers across. That’s a quarter of the size of the United States, China, or the Roman Empire at its peak (thanks, Wolfram Alpha).

Now, a human being breathes something like 11,000 liters of air in a day. That means our crowd is going to be breathing the volume of Lake Superior daily. An average resting adult requires something like 210 milliliters of oxygen per minute. Taken together, they’d require sixteen Amazon Rivers’ worth of oxygen flow. Much to my surprise, they probably wouldn’t suffocate. If we assume each person has access to the air in their square from sea level to the “death zone” (an altitude of about 8,000 meters, where the oxygen concentration is low enough to become acutely lethal), they’d all be able to breathe for about 20 years. Plenty of time for photosynthesis to replace the oxygen. And plenty of time for that crowd to become very, very smelly. And hungry. And violent. We probably shouldn’t have made a trillion clones. I blame you for giving me the idea.

And now, we’ve hit another limit. We’re already talking about continent-scale collections of objects, and like I said, human beings aren’t all that good at understanding things on really large scales. So I’ll stop at our trillion-person Woodstock before I start imagining the stink of two trillion unwashed feet.

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Uncategorized

Charlotte vs. The Comet 2: This Time, I Got It Right

A few weeks ago, I posted a scale comparison between comet 67P/Churyumov-Gerasimenko and the city of Charlotte, North Carolina, the city I live in. It was wildly, offensively inaccurate: somehow, I shrank the comet by a factor of five. Well, now that the ESA has finally released their shape model for the comet, I can just import the model into Blender, convert it into a .dae file, scale it until it’s (approximately) the right size, and stick it in Google Earth to get an idea of the comet’s scale.

67 P vs. Charlotte NC

The larger lobe is 4,100 meters long, and the whole comet dwarfs Charlotte. In fact, it looks like Charlotte is being menaced by a legless puppy. There’s an image for you…

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Uncategorized

Fun With Logarithms 3: Orders of Magnitude

I started hearing the term “Orders of magnitude” long before I knew what it meant. It’s actually a simple and extremely handy convention. 10 is one order of magnitude larger than 1. 100 is one order of magnitude larger than 10. 0.000001 is six orders of magnitude smaller than 1. Simple.

The best thing about orders of magnitude is that they allow you to get an intuitive grasp on large numbers, which are just about as unintuitive as it gets, and with hardly any math or research necessary. Here’s an example.

I’m 1.9 meters tall (6’3″, if you insist). A peppercorn has a diameter of about 2 millimeters. A millimeter is 1,000 microns. Ordinary bacteria have dimensions of around 1 micron. Therefore, a peppercorn is about 1,000 times larger than a bacterium.

A peppercorn is pretty small, but if you look at it closely, you can still make out details: peppercorns have weird little wrinkles and chips and dust on their surfaces. A peppercorn is an easy object to comprehend. To comprehend the size of a bacterium, go the other direction: imagine an object 1,000 times larger than a peppercorn. That comes out to about 2,000 millimeters, or 2 meters. That means I am to a peppercorn as a peppercorn is to a bacterium. Or, if you want to use me as your basis, a bacterium sitting on a peppercorn is like me standing on the summit of a 1,900-meter mountain. That’s close to the same as me standing on top of El Capitan:

(Source and licensing.)

(I’m not actually in this photo, but I like to pretend I’m tied to one of the trees up there, being tickle-tortured by Angelina Jolie as Maleficent. Hey, it’s my fantasy. I can do whatever I want.)

Anyway.  Bacteria are pretty small. But they’re not as small as viruses, which have dimensions measured in tens or hundreds of nanometers. Twenty nanometers is about eight orders of magnitude smaller than me, so a virus standing next to me is like me standing next to Jupiter.

That’s a lot less intuitive. I know mathematically how big Jupiter is, but it doesn’t make any sense to my gut, and it’s important to take the gut into consideration if you really want to get a feeling for anything. Luckily, you can chain orders of magnitude end-to-end.

A 20-nanometer virus particle is 100 times smaller than a 2-micron bacterium. Therefore, if El Capitan represents me, and I represent a bacterium (which is a weird thought), the virus will be 1.9 centimeters across, or about the size of a wine grape. A virus compared to a person is like a grape on the summit of a mountain. That’s stretching the powers of intuition, but it’s still comprehensible.

Let’s have more fun! A football field (American football or the football that most of the world calls football but Americans call soccer, the proper name of which people really like to argue about for some reason) is about 100 meters from end to end. I stood on many such fields in gym class as a child, so I have a pretty good intuitive grasp of their size. 100 meters is a large distance, but not so large you can’t wrap your head around it, so it’s useful for making even harder order-of-magnitude comparisons.

Most atoms are around 200 picometers across. 1 nanometer is 1,000 picometers, so 100 picometers (ignoring the factor of two, which you’re allowed to do in order-of-magnitude math) is ten orders of magnitude, or ten billion times, smaller than a meter.

A human hair is about 100 microns in diameter, and is another good basis for comparison, since 100 microns is about as small as something can get and still be visible to the average naked eye. 100 microns is 4 orders of magnitude smaller than 1 meter. 100 picometers is 10 orders of magnitude smaller than 1 meter. Therefore, 6 orders of magnitude (or a factor of 1 million) separate the diameter of an atom and the diameter of a hair. It just so happens that a 100-meter football field is 6 orders of magnitude larger than a 100-micron-diameter hair. So an atom in a strand of hair would be in the same proportion as the diameter of that hair compared to the length of a football field.

This same kind of sloppy-but-useful math can be applied to understand astronomical distances, too, up to a point. The Earth has a diameter of about 12,000 kilometers (closer to 12,700, actually, but we’re not being that precise). 12,000 kilometers is 10 million times larger than 1.2 meters. The earth, therefore, is about 10 million times larger than me. Something ten million times smaller than me would be 1.9 microns across, which is the size of a bacterium. Therefore, the bacteria sitting on my skin feel just as small as me standing on the Earth. Which is weird and almost poetic. Almost.

But my understanding of 1.9 microns is abstract. (How many times have I said “intuitive” and “abstract” so far? You have my permission to begin a drinking game. Intuitive abstract intuitive abstract intuitive abstract intuitive abstract. Enjoy your evening and try to vomit into the toilet. Intuitive. Abstract.) Let’s use a football field as our basis instead. I am 7 orders of magnitude smaller than the Earth. In order to be 7 orders of magnitude smaller than a football field, an object would have to be 7 – 2 = 5 orders of magnitude smaller than a meter, or 10 microns. Still too small.

El Capitan is about 1,000 meters tall (it’s actually over 2,000, but that’s within the same order of magnitude). That’s 3 orders of magnitude larger than a meter. To be 7 orders of magnitude smaller than El Capitan, an object would have to be 4 orders of magnitude smaller than a meter, or 100 microns, which is the diameter of a hair or a speck of dust. So we are all specks of dust sitting on the mountaintop that is the Earth. (Feel free to punch me for that sentence, if you happen to meet me in the street. Seriously. I’d punch myself right now, except I keep flinching out of the way.)

You can also use this kind of tricky math to build toy models of astronomical systems in your head. For instance: what would the Earth and Moon look like, locked in their orbits, if you saw them from a distance?

Well, the Earth is about 10,000 kilometers across. The moon is about 3,000 kilometers across, or one-third of an Earth diameter. Imagine a really big grape sitting next to a smallish grape, and you’ll have about the right proportions. A coin and the bottom of a drinking glass are also in similar proportions.

The Moon’s semimajor axis is about 300,000 kilometers, so it’s usually separated from the Earth by 30 Earth diameters or 100 Moon diameters. Here’s an experiment you can try at home: set a cup on the floor and line up 98 coins next to it (Not 100, because one and a half coins will be inside the cup and half a coin will be inside the coin representing the moon). Actually, I hate it when people say “Here’s an experiment you can try at home.” I’m gonna be nice and do it for you, although admittedly I’m going to have to switch up and use a coin to represent the Earth, because otherwise, the system would be larger than my floor. But I cheated and did the math and got the proportions right.

EarthMoon

Consider that penny. That’s here. That’s home. That’s… No. Sorry. I can’t be sarcastic about Carl Sagan’s Pale Blue Dot speech. Just go watch it. Watch it twice. No smart-assery here: it’s one of the best speeches I’ve heard in my life.

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