Yard -> Yacht

What a consonant set of options to choose from today. I went with these two because we all know alliteration is the best literary device.

A yard is, by definition, exactly three feet. (That’s about a meter, more or less.) But “exactly three feet” is only helpful if you know how long a foot is, which historically wasn’t a given. So people would estimate a yard as the distance from their nose to their outstretched fingertips. (Of course, this meant different people had different “yards”, but generally they’d be close enough—unless you were buying from a giant. Then: Bonanza.) (Self-promotion time: If you’re really into units and measurements, I’ve scripted a number of videos about them.)

For me, one of the most interesting parts of all this is that, subjectively, stretching out an arm feels like pushing a hand away from our body—even though that’s not what happens. Our muscles can’t push on our bones; they can only pull on them. When you extend your arm, muscles in the back of your arm (your triceps) pull your forearm toward your elbow, swinging your hand away from your body as a result.

There’s a similar (for a very specific idea of “similar”) misconception that surrounds sails. People think they’re pushed by the wind (like bouncy castles), but that’s only true sometimes. If it were the only option, sailboats wouldn’t be able to go anywhere but downwind. To go upwind, though, sails act more like wings than anything else, propelling the ship below along more through lift than direct wind-on-sail impact. Sails are wings turned on their sides.

Skirting around the mechanics of lift for the second post in a row, this was just as true for the ships of the Spanish Armada as it is for today’s yachts.

At least, as long as those yachts have sails instead of motors. But motors are a story for another time, too.

Egg -> Ladybug

Ladybugs hatch from eggs. We’re done here.

What’s that? The header picture says to go from egg to ladybug, not vice versa? Well, that will take longer, and there will be dragons bridges.

Eggs are only fragile when squeezed the wrong way. If you squeeze top-to-bottom rather than side-to-side, eggs are shockingly strong. Your average chicken egg can withstand 100 pounds. Your average ostrich egg, 1000. (Although I live in Massachusetts, where there is no such thing as an average ostrich. There is only, “Oh my god is that an ostrich? How is it so big? Why’s it in the living room?”)

Incredulity over the existence of ostriches aside, let’s return to incredulity about the strength of eggs. Force on the top gets spread through the rest of the shell, just like in an arched bridge. But it’s more interesting than that cursory summary suggests. Eggs and bridges don’t merely spread forces. they transform tension into compression. Tension spreads a material apart while compression squeezes it together. Most materials, including eggshells and concrete, are stronger under compression than tension, because little cracks get shoved together instead of being opened wider.

Most, but not all. It’s fairly hard to tear a piece of paper by pulling two sides apart (tension) but fairly easy to crumple it by pushing the sides together (compression). That also makes paper easy to fold into airplanes. (I never got into the paper airplanes with flat ends, even though they always seemed to work better. I’m something of a purist.) Now, planes fly for a constellation of reasons that are a story for another time. Insects, on the other hand, fly for reasons that are (mostly) a story for right now. They push their wings down against the air, which, through Newton’s Third Law, pushes them back up. That’s far from the full picture, of course. Air’s viscosity and other aspects of fluid dynamics mean that insect flight is in truth as complex as anything else. But that’s the big-picture gist for all insects.

Including, of course, ladybugs. Now we’re done here.

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!