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!

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[…] 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 […]

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