Thursday, October 1, 2015


I was traveling for most of August and September but now that I'm back in my office, I've gotten caught up on most of the blogs I follow. A few weeks back Alex Tabarrok had a cute mathy post on the Frechet probability bounds with the warning "super wonky!" in the title. My reaction was first "duh" and then "wait, this actually has a name?" (This probably goes a long way to explaining my teaching evaluations :)

I love Alex's explanation and love that he posted it; I in no way mean that it's too trivial to be interesting. But it's such a perfect example of something that looks scary if you write it down in formal notation and give it a high-falutin name, and it scares people off who don't read math all the time so that you have to put "super wonky!" warnings on things, but if you think about a simple example for a few seconds it's incredibly simple. Much simpler than the concepts involved in most of Alex's non-wonky posts.

Anytime I teach anything involving math (and I try not to teach anything that doesn't involve math, math is too fun!) I spend a significant amount of time trying to convince students that math is not actually scary and that they definitely shouldn't memorize equations for everything. If you understand that a linear relationship is just something that starts at a particular spot and then follows a particular slope, you don't need to memorize the equation for a line, or the point-point formula, or the point-slope formula, and I loathe that the ubiquitous approach presents those three separate equations that students then copy down and memorize.

Here's an example of the Frechet probability bounds. If 80% of people are Caucasian and 70% are Christian, there has to be some overlap. In fact, at least 50% of people have to be both Caucasian and Christian. On the other hand, there might be more overlap; it could be that 70% of people are Caucasian Christians, 10% are other Caucasians, and the other 20% are Buddhist Asians. Take a second to picture the possibilities and those numbers will be obvious to you; if you get stuck, see Alex's post for a nice way to diagram it.

That's it. One tiny concept (your groups of people have to overlap somehow to fit within the population you have) with some fancy notation and a fancy name that scares people off.

I should add, I'm not actually opposed to fancy names, in fact I love jargon of all kinds when used to improve precision and economy of language rather than to obfuscate or sound smart. When I went to mathcamp in high school and learned the name for the "pigeonhole principle" I also thought it was hilarious that this warranted a name - all it says is that if you have more pigeons than holes, some pigeons are gonna have to share holes (in fact this is the fundamental concept at work in the Frechet bounds as well) . But it's actually great that it has this name because it can be applied in creative ways in much more complicated proofs that don't immediately seem to have anything to do with counting holes, and all you have to do is say "by the pigeonhole principle" for the experienced reader to quickly deduce what are the pigeons and what are the holes and how their relative number is relevant, without you having to spell it out.


JohnRaymond said...

"economy of language" I like it!

Vera L. te Velde said...

yeah ever since you told me that's a thing in linguistics (not the same as how I'm using the word, though, I don't think?) I've wanted to learn more about it. someday...