Blow Up Maps

We are learning about blowup maps in Algebraic Geometry. They take a perfectly nice plane into a copy of itself except at one point. At that point you get a whole line thrown in, with points corresponding to the different lines in the original plane that went through your point. So now your previously nice plane wraps around this line. This is supposed to be useful. I guess it is in the same way that a nifty piece of new software is cool. You know, the one that replaces the perfectly good version you were using for the sake of some bells and whistles that you don't even want and don't have time to learn to use because you are busy figuring out how to do the basic stuff that you used to be able to do but now can't figure out because all the buttons moved and once you do get the bells and whistles down they'll come out with a new version and then you'll have to start all over. Yeah, that's math class. Once I get blowups down they'll hit me from behind with some other insane construction.