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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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 must 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 naïve 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.

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biology, Dragons, thought experiment

Even More Dragonfire

Because I like dragons and I can’t help myself. Don’t worry. This one won’t be nearly as long as my usual posts about dragons. If anything, it’s more to show the thought process that goes into my thought experiments.

Let’s dispense with the notion of dragonfire hotter than the surface of the sun, and with biologically-produced antimatter. Let’s pretend that dragons are made of fairly ordinary flesh. They breathe fire from their mouths (naturally), so they’re going to have to be careful not to burn their tongues off. Let’s assume they have funny saliva glands that mist their mucous membranes to stop them getting scalded off by direct contact with hot air and fire. There’s still thermal radiation to deal with.

According to NOAA (who usually talk about weather, but have, in this case, started talking about fire), exposure to thermal radiation at an intensity of 10 kilowatts per square meter will cause severe pain after 5 seconds and second-degree burns (nasty blisters) after 14 seconds. With that in mind, I want to find out how hot dragonfire can be before its thermal radiation is too much for a dragon’s mouth to handle.

Well, let’s assume a dragon’s mouth is a cylinder 1 meter long and 30 centimeters in diameter. Multiply the circumference of that cylinder by its length to get its surface area (minus the ends), and then multiply the area by 10 kilowatts per square meter to get the maximum radiant power that can reach the mucous membranes. The result: 9.425 kilowatts. Now, let’s model the jet of fire as a cylinder (again, without ends) 1 centimeter in diameter and 1 meter long. That cylinder can’t emit more than 9.425 kilowatts as radiant heat. Divide 9.425 kilowatts by the cylinder’s surface area. To stay below 9.425 kilowatts, the jet of flame can’t emit at an intensity higher than 300 kilowatts per square meter. Apply the Stefan-Boltzmann law in reverse to get an estimate of what temperature gas radiates at 300 kilowatts per square meter. That comes out to a disappointing 1,517 Kelvin, which is cooler than the average wood fire.

I’m not satisfied with that, so I’m going to cheat. Sort of. I’m going to assume that the dragon has a bone in its fire-spewing orifice that acts like a supersonic rocket nozzle, which allows it to emit a very narrow, fast-moving stream of burning gas. The upshot of this is that the jet becomes narrower than that of a pressure washer: 1 mm in diameter throughout its transit through the mouth. That’s a bit more encouraging: 2,697 Kelvin, about the temperature of a hydrogen-air flame (which means we can just use hydrogen as the fuel). It’s still nowhere as hot as I want it to be, but I don’t think Sir Knight is going to be walking away from this one.

We could, of course, push the temperature up by taking into account the fact that the dragon’s mouth isn’t a perfect blackbody, and reflects some of the radiation, but like I said, this isn’t a full post. I just wanted to show you guys how I flesh out an idea.

Stay safe out there. And don’t try to breathe fire.

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biology, Dragons, physics, thought experiment

Dragon Metabolism

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

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

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

dragon-size-full-chart

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

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