Werewolves in Alabama - A Mathematical Reflection on Kid Rock's Single

"All Summer Long," a single from Kid Rock, samples not one but two iconic rock/pop hits: "Werewolves in London" and "Sweet Home Alabama. "Mathematically, it's a savvy move, and not just from the perspective of putting one's eggs in multiple baskets.

Mathematicians like to think about recipes as points or solids in multi-dimensional spaces. That is, the parameters for the perfect muffin or bubble gum pop hit can be visualized not as a collation of numbers, but a place. In the case of muffins, we can draw a set of axes and let one axis represent the amount of flour, another the amount of sugar, a third the amount of butter. If there are more than three ingredients, then our space becomes a hyperspace and we simply keep adding axes: salt, bananas, nuts, peanut butter, cranberries. The fact that we can't visualize such a hyperspace doesn't mean we can't imagine it. Once we have this space, we can start mapping out special regions within it: there is a hypersurface that passes through all possible recipes (of the ingredients we're considering) with a certain amount of sodium per hundred calories. All of the higher-sodium recipes lie on one side of that hypersurface; all that have lower sodium fall on the other side. There is a hypersurface enclosing all muffins that cost less than $0.60 to produce at current market rates (imagine watching this multidimensional blob pulsate and mutate with fluctuation market prices); another surface contains all muffins that consumers rated eight out of ten or higher overall. Importantly, these criteria may produce two or more unconnected blobs: for example blueberries, but it may not be possible to gradually decrease the one ingredient while increasing the other and always obtain a delicious muffin. (Moving along a trajectory that varies the amount of third ingredient, say grape jelly, may bridge the two blobs.)

Which brings us back to Mr. Rock and his summer hit. Like muffins, songs have recipes, albeit with different attributes and ingredients than muffins.

Song length is an attribute: number of verses, overall structure (verse/chorus/verse/chorus? with or without a bridge? an instrumental solo?), how many singers, how many of each instrument are all additional attributes that are easily quantifiable and can be visualized as axes. Other attributes are harder to turn into quantifiable questions of degree: what genre is the song? what is the overall mood? (Music and lyrics might have two different mods, contributing to the effectiveness of the song.) We can quantify these qualities, albeit somewhat subjectively, by choosing an appropriate number of sufficiently distinct songs and comparing our song to them: on a scale of one to one hundred, how closely does our song resemble/evoke Tupac's 'I Get Around'? Black Sabbath's 'Iron Man'? Carly Simon's 'You're So Vain'? After an appropriate number axes have been chosen, one can start plotting points, each one representing a pop hit. One may choose a different color of point to distinguish between the mediocre and the spectacular hits: equivalently one may add an axis for number of singles sold or weeks on the Top 40. After doing all this, one can start looking for patterns in the terrain: maybe all of the superhits are clustered over here and the duds tend to be down there. Maybe there's an axis where all the hits lie between two values, or a collection of axes where in the hits tend to lie on a particular line or hypersurface. With only a few axes, one can always argue that an apparent correlation is coincidence, that the actually hit-making quality is along an axis or axes not yet captured. But as more and more axes are added, one can be more and more confident that one's analysis are valid.

I'd like to think that some datahead working for Infanspetroco performed such an analysis, identified a correlation in holographic attributes between two classic hits, further identified a 'sweet spots' a certain distances between them, and created the Kid Rock single. Almost certainly the process was applied much more informally or not at all. But the mathematical and analytical sophistication is there, and I believe it's only a matter of time before we wan, if we choose, use mathematics to create work of artistic and popular merit.