Relating Fight Club to Groundhog's Day through Calculus

Groundhog's Day is about Phil Conners, a man who relives the same day over and over, for years, until he gets it right. At the beginning of the film we see the core of who he really is; an egocentric person. However, as time passes he develops into an empathetic, caring individual.

Fight Club on the other hand is about Jack, a man who is trying to find himself by breaking out of his surroundings.  Tyler Durden, Jack's alter ego, pushes Jack to do things he wouldn't normally do. Durden also pushes other people to what they believe to be the brink of their own destruction to make them see what in life is important to them. How are these two seemingly opposite movies related? Through math, the universal language. 

In calculus we are taught how to find the volume of a shape through integration. There are two methods, the washer method and the shell method. I will be talking about the shell method. As defined the shell method is a method of computing the volume of a solid of revolution by integrating over the volumes of infinitesimal shell-shaped sections bounded by cylinders with the same axis of revolution as the solid.   

 How to relate these two concepts is that the solid volume is a metaphor for what you want your life to be. the infinitesimal shell shaped sections are small pieces of your life that are shaped and formed and ultimately add to the final volume. The dt part of the formula could be days, as in the span of a lifetime, one day could be considered an infinitesimal piece.  We just keep going around and around each day until we get it right.  Now, there are different functions your life can take. There are doctor functions, generated by going to med school. There are teacher functions, generated by going to college and getting an education degree, and so on and so forth. But, what happens when you don't have a function, like Jack? He's looking for who he is, but he doesn't know.  In the Just Let Go scene, Tyler asks Jack and the two men in the back of the car, what they want to do before they die. One in the back answers, "to build a house." The other answers, " to paint a self portrait." Jack on the other hand answers that he doesn't know. In this case, it would seem that the function would merely be a constant. When you integrate a constant all that comes out is that constant multiplied by distance from the origin and time. It's the same thing, day in and day out until you reach the outer limit (death) and just comes out as a cylinder. 

Phil shapes his life in a similar way. He initially is a constant, egocentric individual. But eventually, with all these infinitesimal changes to his life, he generates a function for becoming an empathetic human being. 

While the initial shapes representative of Jack and Phil's lives are similar ( probably a solid cylinder)  the solid volumes that comes out are completely different. They used the same general means of getting to these new solid shapes. That is, adding an finite number of layers to get the final outcome.