Usefulness of Mathematical Symbols in a Fight


Garbage math

I really liked xkcd’s take on numerical analysis and error propagation:


A good mathematical explanation of this comic can be found here:

Error Types


A brief explanation can be found at

Large number formats

A great explanation of the comic can be found at

Fun with dimensional analysis


How to picture an exponent

While I’m easily amused by math humor, I rarely actually laugh out loud after reading a comic strip. That said, I laughed heartily after reading this one.


Differentiation and Integration

As I tell my calculus students, differentiation is a science. There are rules to follow, but if you follow them carefully, you can compute the derivative of anything. This leads to one of my favorite classroom activities. However, integration is as much art as science; for example, see my series on different techniques for computing

\displaystyle \int_0^{2\pi} \frac{dx}{\cos^2 x + 2 a \sin x \cos x + (a^2 + b^2) \sin^2 x}

The contrast between differentiation and integration was more vividly illustrated in a recent xkcd webcomic:


Significant Digits and Useless Digits

A pet peeve of mine is measuring things to far too many decimal places. For example, notice that the thickness of these trash bags is 0.0009 inches (0.9 mil) but is 22.8 microns in metric. There are two mistakes:

  • While the conversion factor is correct, there’s no way that the thickness is known within only 0.1 microns, or 100 nanometers. That’s significantly that a typical cell nucleus.
  • Less importantly, if they rounded correctly, it should be 22.9 microns, not 22.8.

My favorite example that I’ve personally witnessed — that I wish I had a picture of — is measuring student’s perceptions of a professor’s teaching effectiveness is 13 decimal places.

This webcomic from xkcd illustrates the point both cleverly and perfectly.


How To Annoy a Statistician


An Interview with Randall Munroe interviewed Randall Munroe, the author of the wildly popular xkcd webcomic. I recommend the whole interview, but I thought that the follow few paragraphs were exceptionally insightful.

One thing that bothers me is large numbers presented without context. We’re always seeing things like, “This canal project will require 1.15 million tons of concrete.” It’s presented as if it should mean something to us, as if numbers are inherently informative. So we feel like if we don’t understand it, it’s our fault.

But I have only a vague idea of what one ton of concrete looks like. I have no idea what to think of a million tons. Is that a lot? It’s clearly supposed to sound like a lot, because it has the word “million” in it. But on the other hand, “The Adventures of Pluto Nash” made $7 million at the box office, and it was one of the biggest flops in movie history.

It can be more useful to look for context. Is concrete a surprisingly large share of the project’s budget? Is the project going to consume more concrete than the rest of the state combined? Will this project use up a large share of the world’s concrete? Or is this just easy, space-filling trivia? A good rule of thumb might be, “If I added a zero to this number, would the sentence containing it mean something different to me?” If the answer is “no,” maybe the number has no business being in the sentence in the first place.