Hey Kids! “Math Doesn’t Suck.” That’s what we learned in tonight’s episode.
First, Sheldon takes us on a visit in his mind to Flatland. Flatland is a small book written over 100 years ago about a people living in a world with only two space dimensions. Its inhabitants call their two directions North/South and East/West. They are unconcerned with our own three-dimensional world that includes a third direction; Up/Down. Its a book that nearly every one of my physics friends, as well as those in math, engineering and computer science read as a teenager. Except me…Flatland was the Moby Dick to my Zelig.
So the episode shamed me into finally reading Flatland. I figured that by now it wouldn’t have anything new about dimensionality I hadn’t picked up somewhere else. But I was wrong. Something I had never considered is that being from a world that is one dimension larger allows you to peer inside everything in a world one dimension smaller. For example, here is a picture of a Flatlander’s house:
Since the Flatlanders (not to be confused with The Flatlanders) have no concept of covering the “top” and “bottom” of their houses, we can see right inside their rooms and even their cabinets. More abstractly put, we can see the inside of circles, which they cannot. Similarly a four-dimensional being could see right inside one of our spheres. Four-dimensional people could see right inside every part of our bodies, organs and even cells as if they were all laid out on paper.
But one page in Flatland really blew me away. Gravity cannot point “down” for them because they have no concept of down. It points South in Flatland. It is never explained, but this could be achieved by tilting Flatland relative to the Earth. Flatland would be tilted in a dimension they cannot even comprehend. Also gravity is much stronger in some regions of Flatland than others. So it seems that Flatland is not so flat at all…it must not only be tilted, but curved space like so:
The increased “steepness” on one end means gravity has a stronger effect there. Because Flatlanders have no idea of Up/Down, they have no concept of “steepness” either. Therefore they have no explanation for the variation of gravity in their land. In the language of modern mathematics we can say that Flatland is a two dimensional world, but it is “embedded” in a three dimensional one. It would be decades after this book was published that Albert Einstein described the possibility of gravity in our own world being related to curvature of space. Like many science fiction writers, Flatland’s author, Edwin Abbot, was a step ahead of the physicists.
Little books like this can give a pre-teenager or teenager a taste for mathematics that lasts a lifetime. Which brings us the the second bit of mathematics in the episode:
I am sure the viewers noticed a bit of mathematics “stunt casting”. At a university mixer, Raj meets Abby who is played by Danica McKellar. Yes, she is the McKellar of the Chayes-McKellar-Winn Theorem (“Percolation and Gibbs States Multiplicity for Ferromagnetic Ashkin-Teller Models on Z²”). She wrote this paper while still an undergraduate math major (at my university, U.C.LA.) Basically her theorem tells you how magnets must behave if you put them in a particular configuration.
Danica McKellar proceeded to write a wonderful set of books for pre-teen and teenage girls about mathematics, Math Doesn’t Suck followed by Kiss my Math about algebra and pre-calculus respectively. A third book is on the way.
I bought them to take a look, and will be sending to my niece. These are terrific books with real-world examples that connect directly to mathematics curricula. They are fun and quirky. But make no mistake…The content is serious math. For example, she explains prime factorization, in terms of a middle-school crush. She gives little tricks to conquer the dreaded “word problems”. She warns against common mistakes: 33 is not 9. She includes testimonials from her friends, women who used math to succeed, such as a petroleum engineer and the finance director of a style magazine. Other times she just gives friendly advice about growing up such as explaining why young women should not try to dumb themselves down to be popular. The first book leads up to and includes algebra. The second gives the reader all she needs for pre-calculus. Somehow it still all looks fun. I will see if my niece agrees.
The examples are intended to resonate with young women. I was having dinner with two female friends last month who remembered math from middle school. They pointed out to me that many of the examples in middle-school math books use examples like football, that would more likely interest boys than girls. No one would accuse Danica McKellar of doing that in these books.
As we saw from Sheldon’s childhood love of Flatland, a small book can make a big impact on the life of a pre-teen future mathematician, physicist or engineer. So consider picking up Danica McKellar’s books for the tweenager you know. Even if you don’t know any young women, you can click here and Danica McKellar will send books to the library or school of your choice and send you an autograph.