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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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13 thoughts on “Give me a Trillion of Everything!

  1. A trillion stars perhaps? – If stuck together in form of a cube (let’s forget gravitational pull and enormous radiation pressure that the whole ‘construction’ would have caused), one of it’s edges would have length of 13,926,840,000 kilometers (I use our Sun as the average star) so we could obtain a cube of roughly 93,1 AU X 93,1 AU x 93,1 AU, so it would fit nicely inside current heliopause. Imagine that! Even better if the project was done by one of the ‘long scale’ countries…
    And great blog!

    • I actually want to write another post at some point talking about the scale of the solar system. For this post, I decided to stop when I got to large-but-manageable collections. Trouble is, in the past, when I’ve tried to scale up from human-scale to solar-system-scale, the comparison gets sort of lost and abstracted. That might be more my fault than the fault of human understanding, though.

  2. These are fascinating size comparisons, and they do a great job of illustrating perspective. I will probably use more than one of these when I have to lecture about atoms.

  3. Thanks, I did enjoy reading this! And it inspired me to pick up a calculator and do some tinkering of my own.
    So on a completely different scale, a trillion seconds ago, the Earth was in the Palaeozoic era, and dinosaurs were millenniums in the future! Phew.

    • I’d like to write more posts about a “temporal” sense of scale. But time, being more nebulous than physical size, is a little harder.

      Incidentally, you might enjoy “The Five Ages of the Universe,” which hypothesizes about the future of the universe using a really neat logarithmic time scale.

  4. Thanks for these fun facts 🙂 Today i heard my yoga teacher say we had 72 trillion cells in our body, and i really felt like she pulled that out of her… kundalini chakra. I might just reblog!

    • I don’t know whether my ideas come from anywhere more sanitary, but I do subject them to some sort of fact-checking.

      Your teacher’s statement is the wonderful kind of statement you can check with a quick back-of-the-envelope calculation. Human tissue cells average around 10 microns across (see this page, for starters). An average-sized human being could fit snugly into a cuboid 1.75 meters by 0.3 meters by 0.1 meters (although you might have to rearrange some appendages slightly). Divide each of those dimensions by 10 microns to get the number of cells along each edge, then multiply the numbers back together to get an approximation of the number of cells in the human body. I came up with 53 trillion, but you’ve got to take into account that there’s going to be some empty space, especially around the legs. We’ll say 25% of the cuboid will be empty space, which gives us closer to 40 trillion. So your yoga teacher wasn’t that far off, but I’d like to see whether or not she did the math. 🙂

      Incidentally, some proper scientists have estimated that there are about 37.2 trillion cells in the body. The fact that I got that close is entirely dumb luck.

  5. Pingback: Approaching Infinity | Sublime Curiosity

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