Matematic

The internet had lots of great and terrible uses of math and mathematical visualizations in September 2016! This is our opportunity to applaud the winners and be confused by the blunders. Here are a few of my favorites:

1. The Gold Star goes too...
Henry Segerman for his amazing 3D mobius transformation henry_segerman_terdragon_smallartwork. In particular, I want to call out his Stereographic projections. A Stereographic projection is a mapping (that is, a function) that projects a sphere onto a plane. In the case of Segerman's art, you can shine a light from above to make the projection appear.

screen-shot-2016-10-04-at-5-49-03-am

Stereographic projections have a strong and beautiful connection to moebius transformations. Moebius (or Möbius, like the Moebius band!) transformations have a key part to play in understanding complex analysis. In particular, they encompass a particular type of mappings (functions) that map the complex plane back onto itself. Stereographic projections have the power to make something really complicated appear relatively simple. To really understand why stereographic projections are so meaningful, I recommend the "Moebius Transformations Revealed" by University of Minnesota professor, John Rogness. I promise that there are almost no equations and you'll probably learn something:

Do you need one of these in your life?

2. Terrible Use of "Mathiness"
My least favorite mathematical graphic from September has to be the Bloomberg BusinessWeek's visualization on income. Income is a really important topic. And the idea that "everybody thinks they're middle class" is an important piece of the puzzle to understanding why income inequality is growing over time.  However, I strongly disagree with the way they presented the material.

First, let's take a moment to wonder at the title: "Everybody thinks they're middle class." The visualization gives only 5 individual's opinions, and yet we presume to call this a representation of "everyone"? In high school I learned that three points make a line... but hopefully we all realize that a 5 person sample out of more than 300 million Americans does not a statistical sample make! And since, with a sample size of 5, it's not providing scientific insights, then I'm left to believe that it's goal has to be emotional insights to the nontechnical audience... which is also does poorly.

How well does it communicate with a nontechnical audience member? The article is basically one big visualization with a little bit of text:

bloomberg_middle_class This is a visualization showing the annual income of Americans. Annual income is on the x-axis against the percentage of the population who have that income level on the y-axis. How to read it? Well, one can learn that approximately 10% of the population makes $30k and about 4% of the population make $100.  Basically, this visualization is like a histogram with a million little rectangles... drawn as a continuous line. However, it obfuscates what percentage of the total population are above and below each data point.

Our society has been very focused on the top 1%. So, when I look at this graphic, I want to understand where in this visualization the top 1% is. I'm also curious about other things, like: what is the mean income of this study? It's really hard to tell when you look at the Bloomberg graphic. What I really want is something more like a Pareto chart or a cumulative distribution curve:

Here we get the histogram AND information about the cumulative values. So I can visually see when I've reached 50%, 80%, or 98% of my population sample by reading the right y-axis. Ultimately I think the Bloomberg visualization falls short of providing insights to anyone in both content and visualization. Better luck next time, Bloomberg!

3. Math Graphic of the Month
I'm guessing that if you are reading this website, you probably believe in math and science. Thus, I think you will also appreciate that science (and math!) do not have political agendas. Simply put, mathematics is a tool to learn about and communicate the facts of the world. In our social climate, I think it's important to remember that there is a division between science and state. They have different goals and different aims. And math, if math had opinions and emotions (which is doesn't!)... anyways, if it did, Math couldn't care less about which way you vote. In short, I think this is a beautiful reminder:

You can buy yours here.

Did you have a favorite experience with math on the internet in September? Share it in the comments below! Until next time, have a mathy October!