Fermi Estimation with Liquid Mercury Splash Fights

The semester is over (sorry, quarter system folks, but you can get your revenge in August and September), and you just want to put your feet up and surf the Internet. Of course, there are lots of ways you might accidentally learn something while you do that. One of them is reading the xkcd “what if?” blog by Randall Munroe. Of course, xkcd is a favorite comic for a lot of math nerd types. “What if?” takes the more data-driven side of the xkcd comic and runs with it, figuring out answers, or at least reasonable guesses, to bizarre questions Munroe’s readers ask.

My favorite “what if?” so far is about extreme boating. “What would it be like to navigate a rowboat through a lake of mercury? What about bromine? Liquid gallium? Liquid tungsten? Liquid nitrogen? Liquid helium?” I learned that liquid mercury may be the least dangerous of all the options (but still, you should not get into a splash fight on a liquid mercury lake), that aluminum absorbs gallium (to the detriment of the structural integrity of any aluminum boats on gallium lakes), and that tungsten has such a high melting point that it’s hard to study in liquid form because it would melt any container we put it in. For some reason, I find that hilarious.

Everybody jumping on Rhode Island. Image: Randall Munroe.

Everybody jumping on Rhode Island. Image: Randall Munroe.

Or another gem: what happens if everyone on earth stands in Rhode Island and jumps at exactly the same time? Munroe does not stop with the physics, he goes on to the aftermath, the nightmarish logistics of having 7 billion people together in Rhode Island.

“Any two people who meet are unlikely to have a language in common, and almost nobody knows the area. The state becomes a patchwork chaos of coalescing and collapsing social hierarchies. Violence is common. Everybody is hungry and thirsty. Grocery stores are emptied. Fresh water is hard to come by and there’s no efficient system for distributing it.
Within weeks, Rhode Island is a graveyard of billions.”

There’s how fast we could drain the ocean, whether soda cans would be effective for carbon sequestration, and exactly how many world economies Au Bon Pain would need to pay a $2,000,000,000,000,000,000,000,000,000,000,000,000 lawsuit it’s facing. (Answer: a lot.)

“What if?” is not exactly mathematical, although it does have a lot of numbers in it. But I see it as a great way to play with Fermi estimation problems, which often show up in physics and engineering. Munroe’s answers are more thoroughly researched than a “real” Fermi problem, but the big idea of making carefully chosen, well-thought-out simplifying assumptions is there. Along with a lot of interesting chemistry and physics trivia. I could see these problems as part of a general education math or physics class. Students could look at the questions, figure out their own strategies for solving them, and compare their solutions to Munroe’s.

Whether or not you want to use the posts deliberately to induce learning, they’re always entertaining. (They might even help you get a friend to like math!) If browsing through the blog archive is not enough for you, there’s a book coming in September.

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