Troll in the Heater

My life as an engineer has recently been busy, occasionally frustrating (I’m talking to you, Mathematica), but I can say that it’s never boring. Even so, I've been thinking that certain aspects of the classes I’m taking could use a little more fun.

First up, mass and energy balances. Say you have a heater that increases the temperature of a water stream from 50°C to 75°C. 125 kg of water enters the heater, but 117 kg of water exits. A mass balance (or basic math) tells you that 8 kg of water is missing. Well, at this point you could speculate that there’s a leak in the heater or that water is building up in the system. Or you could decide that neither of those explanations is that plausible and conclude that there must be a troll in the heater drinking the missing water.

Moving on to linear algebra: we learned how computers use 4x4 matrices to perform transformations on coordinates to make them look 3D from a viewer’s perspective. Our example was a falling building (“don’t worry; the building’s only three units high and you’re standing five units away”). Apparently, when viewed on a 2D screen, this building:

should look like this as it falls:

I know, you’re waiting for my first video game to come out, aren't you?

Then in physical chemistry, we’re dealing a lot with operators that do things to functions. For example, we have an operator that takes the derivative of a function and one that multiplies a function by x. So that we know they’re operators, they wear hats like this: . But those are boring hats. I like these better:

There are some special operators called Hermitian operators. They don’t like people and live alone in huts in the middle of nowhere. [Not really. They’re named after the French mathematician Hermite.]

Finally, if a band called Schrodinger’s Cats put out an album called Wanted Dead and Alive, wouldn't you want to listen to it too?