One of the upper-level undergraduate math courses I’ve taught regularly over the years is abstract algebra (my school offers it in even falls, so it’s part of my load this semester). In the class, we look closely at the some of the basic properties encountered pretty early on in mathematics (associativity, inverses, and the like) and investigate other sets/structures called groups that have those properties. One tool we use to examine groups with only a few elements is called a Cayley table, which summarizes how elements are combined. (An aside: I’ve used cayleytable as a moniker to comment in various online fora over the years).
We always discuss in my class that there are only two different group structures with set size four–that is, there are only two distinct ways to fill out a Cayley table for sets with four elements. One of these is called the Klein four-group. You can imagine my ears perked up a decade or more ago when I learned at a math conference about a men’s a cappella group called The Klein Four. Turned out they were five (?) math grad students at Northwestern University, and they wrote and performed math-themed songs. Their best-known work, such as it is, is the love song “Finite Simple Group (of Order Two);” the lyrics bring smiles to faces of mathematicians everywhere, trust me. I plan to show the video to my class next week.
All of this is lengthy introduction to where I really want to go today. When I first watched “Finite Simple Group (of Order Two)” on YouTube back in 2006 or whenever, one of the recommended videos in the sidebar was Klein Four’s take on “Twelve Days of Christmas.” When I clicked on it, I discovered a version like no other I’d ever heard, with snippets of other holiday tunes thrown in, including “Deck the Halls,” “Santa Claus is Coming to Town,” and “I Have a Little Dreidel.” In the lower right corner at the beginning and end of the vid, there’s arrangement credit to Straight No Chaser; at the time that meant nothing to me. Within in a few years, though, SNC’s even more amazing version, the song that launched their recording career, came across my screen. It gets plenty of play on radio stations at this time of year now.
“The Twelve Days of Christmas” was their first encore at the show last Thursday, and they mixed things up a little bit with it–they were having Hanukkah in Africa this time.
The Music of My Life 