Tuesday, November 22, 2011

Just because there's a "=" in it doesn't mean it's an equation

Note: One of the reasons for writing this post was to test CodeCogs Online LaTeX Equation Editor as a way of posting LaTeX on Blogger. As you'll see, it actually works (it's not the first thing I've tried, believe me).

A popular science magazine Wired recently featured an interesting blog post briefly introducing 9 Equations True Geeks Should (at Least Pretend to) Know. Of course, the list starts off with Euler's identity


which is often described as "the most beautiful formula ever". Then there's also Boltzmann's entropy formula (engraved on his tombstone):


where k is supposed to be Boltzmann's constant and W is "the number of microstates corresponding to a given macrostate," whatever that means.

Which brings me to my to my next point: After reading the post, you won't really be able to pretend to know those nine equations. The more complicated ones don't even come with explanations of what their terms are (not like it's even plausible to give those explanations in a blog post). For example, if you're not a physicist, stare for a bit at Schroedinger's wave equation and then tell me how you'd go about "pretending to know it":


Piece of cake, right? There's, like, a partial derivative in there, and a second-order one as well. And apparently it has something to do with waves. What, did you ask me what that m term stands for? Well, it's physics, right, so it's probably mass... Or something. Anyway, like I said it's about waves.

Number eight on the list of nine is particularly puzzling. All it says is


where R-nought denotes the average number of people an individual infected with a pathogen will go on to infect. If that R-nought thing is less then one, the disease will die out; if it's greater than one, it will spread.

My problem with equation number eight is that it's not an equation. (If what you're thinking at this moment is something along the lines of "Well duh, of course it's not an equation, it's an inequality," please stop reading this now and just go away. I don't care that it's not literally an equation. If they threw in Bell's inequality there, I wouldn't have a problem with it.) The thing is that the remaining eight equations are something qualitatively different than this one. It's more or less the difference between equality and assignment in computer programming. The other equations (or inequalities) are logical statements; the "=" sign in them is a predicate which can be either true or false. "R-nought is greater than one" is not a logical statement; it's an assignment of a range of values to a parameter. What's funny is that the whole statement "If R-nought is greater than one then the disease will spread" actually is (kind of) an equation.

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