Chin -> Penguin

Chins are funny. Every human has one; no human knows why.

No other primate (extinct or extant) has a chin. Everyone else’s mouth curves inward at the bottom, making chins a curiously and uniquely human trait. There are a few popular ideas for why chins evolved, but none of them holds water. Or food. None of them holds whatever’s in your mouth like your trusty chin does. The proposals that say chins served an evolutionary purpose (whether mechanical or sexual) don’t hold up to scrutiny, while what seems like the best idea (that chins were simply exposed as our ancestors’ faces shrunk) is difficult to prove. It’s a chin-undrum. (That’s conundrum, but chin.)

All I know, really, is that when I’m outside in a blizzard, I need to keep my chin covered because of our old friend the square-cube law. Chins have a lot of surface area, so they lose heat quickly, but they only get warmed at the same rate as the rest of the body (which has less surface area compared to its volume than a chin does). Combine those and it means that chins, ears, fingers, toes, and noses lose heat faster than it’s supplied.

Emperor Penguins have learned the square-cube law, too; it’s why they huddle by the thousands through the Antarctic winter instead of letting every individual fend for themselves. Each member of the huddle has some of their body exposed to the wind and some exposed to other (warm) penguins. Less heat escapes to the wind than it would if everyone were alone. This shielding works so well, in fact, that the penguins at the center of the huddle can get too warm! They move away from the middle to cool off.

When they move to the edge, those on the edge get to shuffle their way toward the middle. They get to warm up and stay alive after bearing the brunt of the cold, the same way members of a household might rotate shoveling duty when it’s really cold outside so that no one gets frostbitten.

At least, that’s the hope—in both cases.

Blueprint -> Drip

This is one where any pair would have been fun to dive into. But I’ve been programming a lot recently, so blueprint it is.

Blueprints are plans, originally for buildings but now metaphorically for just about anything. Real architectural blueprints, though, are always at a certain scale—dimensions are 1/10 the length they’ll be in the final building, say. And that scale is critical. the strength of a material goes up with its cross-sectional area (the square of its length) while weight increases with volume (the cube of length). This critical relationship between squares and cubes is known, sensibly enough, as the square-cube law. It means materials get heavier faster than they get stronger. A building built 15 times larger than a 1/10-scale blueprint will collapse like a house of toothpicks.

This isn’t just about engineering, either. An elephant is not simply a large mouse. The square-cube law means that an elephant shrunk to inches long would have absurdly thick legs, while a mouse inflated to 20 feet long couldn’t stand. (In another consequence of the same law, the giant mouse would explode while the tiny elephant froze.) (Also, it helps us know how big dinosaurs were.) In a computer, of course, you can make materials and legs any strength, regardless of size. But too-small supports will look weird: You can’t have giant simulated animals walking on string-bean legs. Even giraffe legs are thicker than you might imagine.

Chaos is another tricky thing to do in a computer. Chaotic systems turn tiny changes at one moment into enormous divergences later on, and computers have to make small approximations all the time—whether that’s something like rounding 1/3 to 0.3 or breaking time into discrete moments. But on the other hand, the advent of fast computers was one reason chaos was discovered when and how it was: Chaotic systems are often much easier to study in a computer than experimentally, since experiments always have little uncertainties. This is why fluid dynamics is dominated by simulations.

I could say more about chaos and I’m sure I will eventually, but suffice to say for now that one of the early chaotic systems studied both experimentally and computationally, was, of course, a dripping faucet.

Also, I’m going to shamelessly plug the physics simulations and visualizations I’ve been building. Check them out!